Melt flow as a factor of glass melting

1Laboratory of Inorganic MaterialsJoint workplace of the University of Chemistry and Technology Prague

and the Institute of Rock Structure and Mechanics of the ASCRV Holešovičkách 41, 182 09 Prague, Czech Republic

2Glass Service, a.s.Rokytnice 60, 755 01 Vsetín, Czech Republic

17th Conference on Electric Melting of Glass, Prague, September 2019

Lubomír Němec1

Marcela Jebavá1

Petra Cincibusová1

Pavel Budík2

batch-to-glass

conversion

sand dissolution

bubble removal

Outline

○ Three aspects of continual glass melting. Can a melting space work as a

chemical reactor?

o Character of the melt flow and quantity ui (2-nd region)

○ Energetic model and its predictions (2-nd region)

○ Principal results of homogenization (2-nd region)

○ The structure and fundamental factors (1-st region)

○ Overall characters o flows and results (1-st with 2-nd region)

○ Problems, hesitations and expectations

1-st region 2-nd region

image of a simple

melting space

Three aspects of continual glass melting

Three aspects characterize a glass melting chemical reactor:

1. Kinetics of phenomena described by kinetic equations ( ሶ𝑟, 𝜏𝑟𝑒𝑓).

2. Phenomena ordering described by their serial and parallel courses,

controlling phenomenon.

3. Road of the process – spatial map of phenomena. We need a quantity

describing the road of the process:

Rate of 𝜏𝐻𝑟𝑒𝑓to 𝜏𝐺 - space utilization – quantity expressing the road of the

process (glass flow quality):

Kinetics and road (space utilization) are expressed separately and can be this

way examined.

batch-to-glass

conversion

(sand) dissolution

bubble removal

First region - kinetics Second region - kinetics and road

Mass element needs kinetic time (𝜏𝐻𝑟𝑒𝑓) and residence time (𝜏𝐺) to realize

process. (𝜏𝐺 ≫ 𝜏𝐻𝑟𝑒𝑓).

𝑢𝐻=𝜏𝐻𝑟𝑒𝑓

𝜏𝐺; 𝑢𝐻 ∈ 0; 1 ; ሶ𝑀 =

𝜌𝑉

𝜏𝐻𝑟𝑒𝑓𝑢𝐻; 𝐻𝑀

𝐿 =ሶ𝐻𝐿𝜏𝐻𝑟𝑒𝑓

𝜌𝑉

1

𝑢𝐻

2-nd region: Character of the melt flow and quantity uH

uH is calculated by the parallel mathematical modelling of melt flow

and melting phenomena.

piston flow: 𝑢𝐷 = 𝑢𝐹 = 1

isothermal uniform flow: 𝑢𝐷 = 0.445, 𝑢𝐹 = 0.667

transversal circulations: 𝑢𝐷, 𝑢𝐹 = 0.5 − 0.8

longitudinal circulations: 𝑢𝐷, 𝑢𝐹 = 0.05 − 0.2

(the space is divided into input and free level regions):

How does uH reflect the character of the melt flow?

And how does uH relate to fundamental quantities determining the

character of melt flow? (Energetic model).

𝑢𝐷= 1 −𝑚𝐺 1 −𝑚𝐷 ; 𝑢𝐹= 1 −𝑚𝑣𝑖𝑟𝑡ℎ0

ℎ𝑣𝑖𝑟𝑡

1/3

2-nd region: Energetic model and its predictions,

uH dependence on input quantities Energetic model provides a macroscopic view on the character of melt flow

and facilitates predictions of the beneficial melt flow.

Model defines the characteristic velocities of longitudinal and transversal

circulations as a function of flow rate and energy variables.

𝑣𝑙𝑐 = −𝐶1 1 − 𝑘1 𝐻𝑀𝑇 ሶ𝑀 + ሶ𝐻𝐿 − 1 − 𝜉 ሶ𝐻𝐿

𝑣𝑡𝑐 = 𝐶3 1 − 𝑘1 ሶ𝑀𝐻𝑀𝑇 + ሶ𝐻𝐿 + 1 − 𝜉 ሶ𝐻𝑠𝑖𝑑𝑒

𝐿

𝑣𝑙𝑐 increases 𝑚𝐺, 𝑚𝑣𝑖𝑟𝑡, 𝑢𝐻 = 𝑢𝐻𝑏𝑎𝑙 − 𝐾 𝑣𝑙𝑐at 𝑣𝑙𝑐=0, balanced state, unif. flow, 𝑢𝐻 = 𝑢𝐻𝑏𝑎𝑙(max)

𝑣𝑡𝑐 is efficient when 𝑣𝑡𝑐/𝑣𝑙𝑐> 4 and spiral flow sets up,

generally, 𝑢𝐻 grows with 𝑣𝑡𝑐

Suppression of longitudinal circulations is the principal step to

achieve high space utilization; k1 is the most significant quantity.

vlc, vtc

1-st 2-ndvlc: flow tension between

1-st and 2-nd region

0

5

10

15

0 0.5 1

M, M

ba

l, M

crit[kgs

-1]

k1

Mbal…

ሶ𝑀𝑏𝑎𝑙 =ሶ𝐻𝐿 𝑘1 − 𝜉

𝐻𝑀𝑇 1 − 𝑘1

2-nd region: Energetic model and its predictions, the diagram

of melt flows and position of ሶ𝑴𝒄𝒓𝒊𝒕

ሶ𝑀𝑏𝑎𝑙 =ሶ𝐻𝐿 𝑘1 − 𝜉

𝐻𝑀𝑇 1 − 𝑘1

u: Left side: 𝑘1 ↑ , ሶ𝐻𝐿 ↑, 𝐻𝑀𝑇 ↓, 𝜉 ↓, ;

Spiral flow: 𝑣𝑡𝑐/𝑣𝑙𝑐 > 4

Arrang. of energ. barriers:

𝑢𝐻 𝑙𝑜𝑛𝑔. > 𝑢𝐻 𝑡𝑟𝑎𝑛𝑠.Long. barriers do not

support vlc

Balanced energ. state (𝑣𝑙𝑐 = 0):

Right side: opposite tendencies: 𝑘1 ↓

When the values of ሶ𝑀𝑐𝑟𝑖𝑡

and ሶ𝑀𝑏𝑎𝑙 curve mutually

approach, uH and ሶ𝑀𝑐𝑟𝑖𝑡

grow in the following step

↑

0

2

4

6

8

10

12

14

0 0.2 0.4 0.6 0.8 1

M, M

bal, M

crit[kgs

-1]

k1

Mbal [kg/s]

𝜉 →

ሶ𝐻𝐿←→𝐻𝑀𝑇

ሶ𝑀𝑐𝑟𝑖𝑡

If the relevant quantity grows:ሶ𝑀𝑏𝑎𝑙

↑↓↗

Two heating arrangenets longitudinal and transversal barrier, 𝑇𝑖𝑛=1320°C, 𝑇𝑎𝑣𝑒=1420°C

Inflow of primary cold melt containing sand particles, bubbles, best heating arrangement

The melting performance at uniform-like flow increased several times (uH→0.5), the values

of the critical melting performance > 25 t/(m3day).

𝑘1=0.8

𝑘1=0.9

𝑘1=0.6

2-nd region: Principal results of homogenization

Fig. Trajectory of critical bubble which defines critical melting

performance ሶ𝑀𝑐𝑟𝑖𝑡

Hrbek L. et al. JNCS (2017), (2018).

0

1

2

3

4

5

6

7

8

0.4 0.5 0.6 0.7 0.8 0.9 1

M, M

cri

t,Mb

al[k

g/s

]

k1 [fraction of energy in the input part]

Longitudinal barriers do not support

longitudinal circulations

Mcrit1320 oC

[kgs]

Mcrit1320 oC,

transversal

[kgs]

Mbal1320 oC

[kgs]

6.75x2x1m

1-st region: The structure and fundamental goal The intended first conversion region is attached to the referred homogenization

module (T-shape was prefered).This is now the input space for heating and conv.

The horizontal feeding of batch from both sidewalls was selected.

The volumes of regions were considered approximately equivalent, the capacities

of both regions were assumed comparable under given conditions.

The power supply to the 1-st region was planned to cover the maximum assumed

homogenization performance (positioned close to ሶ𝑀𝑏𝑎𝑙 𝑘1 curve).

The efficient absorption of heat by the batch was supported by the use of vertical

electrodes and burners.

The goal: to achieve the balanced state in the complete space under conditions

when both regions attain their achievable melting capacity (batch conversion –

melt homogenization)

0.265

0.27

0.275

0.28

0.285

0.29

0.295

0.3

0.305

0.6 0.7 0.8 0.9 1

MS

ba

tch

[kg

m-2

s-1]

k1

Dependence of MSbatch [kgm-2s-1] on

k1 , small T-furnace

transversal section

k1 as factor affecting both space utilization and batch conversion by the melt flow character

1st and 2nd region: Character o flows and results

1. 𝑘1 is smallሶ𝑀 should be small

2. 𝑘1 > 0.7ሶ𝑀 grows

3. 𝑘1 → 𝑘1 ሶ𝑀𝑏𝑎𝑙

4. 𝑘1 > 𝑘1 ሶ𝑀𝑏𝑎𝑙

Energy under batch from both 1st and 2nd region, long. circul.

𝑇1 < 𝑇2

Smaller part of energy under batch from 2nd region, verticalcirc. in 1-st region

𝑇1 𝑠𝑙𝑖𝑔ℎ𝑡𝑙𝑦 < 𝑇2

Energy under batch, small overheating, spiral flow in 2nd

region → best conditions

𝑇1 ≥ 𝑇2

Overheating of the 1st region

𝑇1 > 𝑇2

batch

batch

batch

batch

batch

upper view side view1

2

Two spaces with different flow character and consideration of results reality

container furnace T-furnace (maximal ሶ𝑀𝑐𝑟𝑖𝑡, uF)

batchbatch

𝑇𝐺𝑎𝑣𝑒 = 1387°𝐶𝑉 = 100 𝑚3

ሶ𝑀𝑐𝑟𝑖𝑡 = 230 𝑡/𝑑𝑎𝑦 = 2.3 𝑡/ 𝑑𝑎𝑦 𝑚3 , 2.8 𝑡/(𝑑𝑎𝑦 𝑚2)ሶ𝑀𝑆𝑏𝑎𝑡𝑐ℎ = 0.087 𝑘𝑔/ 𝑚2𝑠 (spec. batch conversion rate)

𝐻𝑀0 = 4411𝑘𝐽/𝑘𝑔ሶ𝐻𝐽𝑜𝑢𝑙𝑒/ ሶ𝐻𝑡𝑜𝑡 = 0.07

𝑢𝐹 = 0.048𝑘1 = 0.52

Trajectories of critical bubbles.

1-st and 2-nd region: Character o flows and results

𝑇𝐺𝑎𝑣𝑒 = 1420°𝐶𝑉 = 30 𝑚3

ሶ𝑀𝑐𝑟𝑖𝑡 = 460 𝑡𝑜𝑛𝑠/𝑑𝑎𝑦 = 15.3 𝑡𝑜𝑛𝑠/ 𝑑𝑎𝑦 𝑚3

ሶ𝑀𝑆𝑏𝑎𝑡𝑐ℎ = 0.289 𝑘𝑔/ 𝑚2𝑠𝐻𝑀0 = 2552 𝑘𝐽/𝑘𝑔ሶ𝐻𝐽𝑜𝑢𝑙𝑒/ ሶ𝐻𝑡𝑜𝑡 = 0.76

𝑢𝐹 = 0.149𝑘1 = 0.92

Container: α=90 Wm-2K-1

T-furnace: α=400 Wm-2K-1

If α=200 Wm-2K-1, then

V=40 𝑚3,ሶ𝑀𝑐𝑟𝑖𝑡= 11.5 tons/ 𝑑𝑎𝑦 𝑚3

ሶ𝐻𝐽𝑜𝑢𝑙𝑒/ ሶ𝐻𝑡𝑜𝑡 = 0.58

ሶ𝑀𝑆𝑏𝑎𝑡𝑐ℎ𝑙 =𝛼𝑙 𝑡1 − 𝑡𝑙

𝐻𝑀𝑇

Problems and tasks

Only batch conversion, sand dissolution and bubble removal were

included.

The model of batch conversion was used ignoring the structure of

phase boundary between batch and melt. The values of ሶ𝑀𝑆𝑏𝑎𝑡𝑐ℎ

should be verified.

No melting reserve in the second region is considered in present

calculations (assessed around 10-20%).

The overheating of the first region at higher k1 should be restricted.

The very low space utilization is achievable in the first region.

In all-electric furnaces, lower values of batch conversion capacity

are expected.

The corrosion of RM in the first region was not assessed yet.

Variables to control the real process are not completely specified

(k1, ሶ𝐻𝐽𝑜𝑢𝑙𝑒1/ ሶ𝐻𝑐𝑜𝑚𝑏1…)

Thank you for your attention

This work has been supported by the Technology Agency of the Czech Republic in the

project TH02020316 “Advanced technologies in glass production”.

The overheating of the first region

Two surfaces are at disposal in the furnace with combined heating.

If the batch conversion in the first region is controlled by heat transfer:

It is significant for conversion whether the surface is „saturated“ or „unsaturated“ for heat

absorption. Saturated – batch extends, unsaturated – batch almost constant.

The lower surface appears saturated, and when increasing ሶ𝑀, the planned heat is not

absorbed and batch proceeds in the 2-nd region:

The ratio of ሶ𝐻𝐽𝑜𝑢𝑙𝑒1/ ሶ𝐻𝑐𝑜𝑚𝑏1 appears a significant factor of batch conversion.

𝐾𝐽 ሶ𝑀𝐻𝑀𝑇 = 𝑆𝑏𝑎𝑡𝑐ℎ𝐽𝛼𝐽∆𝑡𝐽 𝐾𝐶 ሶ𝑀𝐻𝑀

𝑇 = 𝑆𝑏𝑎𝑡𝑐ℎ𝐶 𝛼𝐶∆𝑡𝐶 , 𝐾𝐽+𝐾𝐶 =1

𝐾𝐽 ሶ𝑀 + ∆ ሶ𝑀 𝐻𝑀𝑇 > 𝑆𝑏𝑎𝑡𝑐ℎ𝐽𝛼𝐽∆𝑡𝐽

𝐾𝐽 − ∆𝐾𝐽 ሶ𝑀 + ∆ ሶ𝑀 𝐻𝑀𝑇 = 𝑆𝑏𝑎𝑡𝑐ℎ𝐽𝛼𝐽∆𝑡𝐽

The abundant energy partially heats

the melt in the 1-st region and

partially is transferred to 2-nd region

by circulation.

Proposed solution: A fraction of

Joule heat should be transferred to

burners where the surface appears

unsaturated. Equality is renewed on

the lower surface, overheating is

assumed to fade:

1 2

conversion in 2-nd region

compensation

of heat deficit

conversion

in 1-st region

overheating of 1-st region

transfer