11 PETRUS-B Dynamic Thermal behavior...

CCC Annual ReportUIUC, August 14, 2013

Bryan Petrus

Department of Mechanical Science & Engineering

University of Illinois at Urbana-Champaign

Investigating Dynamic Thermal

Behavior with Conoffline

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Bryan Petrus • 2

Outline

• Brief introduction to Cononline and Conoffline

• Validating transient behavior of model– Advection versus conduction in the casting

direction (inherent in slice model assumption)

– Compare Conoffline with published strain gauge measurements

• Conoffline parametric study: effect of casting speed changes on metallurgical length


Cononline [1]

• Online control system for secondary cooling water sprays in caster

• Real-time model (“Consensor”) of heat transfer and solidification in the strand predicts surface temperature.

• Control algorithm (“Concontroller”) tries to keep the Consensorprediction constant


CON1D: heat transfer and solidification model

Thermal linear expansion


• In the axial (casting) direction, heat is transferred by:– Conduction– Material moving through the

caster at the casting speed (advection)

• The ratio of these two effects is described by the Peclet number:

– L = characteristic length– vc = casting speed– α = thermal diffusivity

• For a typical continuous caster, this is on the order of 103, which suggests advection dominates

• Neglecting axial conduction allows CON1D to run significantly faster

advection ratePeconduction rate

cLv

α= =

Cononlinesimulation

domain

Multiple slices traveling through the caster

CON1D model [2]


Conoffline

• However, we can also run Consensor offline, using casting conditions recorded from actual measurements, or fully made up

• For now, this still requires the two Linux servers to run, but we are working on a single-PC version

• This version has been used to:– Calibrate the model– Tune the controllers

• We would also like to use this to investigate the behavior of casters, particularly things like shell growth that cannot be easily measured

Recorded or invented casting

conditions


Example application of Conoffline [3]

Severe bulging noticed during trialLocation of

missing roll

Offline “replay” capability was used to compare re-calibrated Cononline model predictions to a previously performed trial. See 2012 CCC presentation for more details.

15:36 15:43 15:50 15:58 16:04 16:12 16:19 16:26

Conofflinepredicted ML

Casting speed


Conoffline Monitor

• Some options are available in a special version of the monitor program for changing simulated casting conditions on the fly

• More complicated scenarios with time-varying conditions require pre-written files

Change grade

Change casting speed

Change superheat

Change mold heat flux


Example of Conoffline “replay” file

Time Casting conditions

• The current way to generate scenarios for Conoffline replays is by editing a comma-separated value (CSV) file in Excel where each row contains all (83) CON1D casting conditions at that time

• This particular file is for a sudden drop in casting speed


Transient model [1]

• Cononline works by tracking multiple CON1D runs, and interpolating between them to get full transient behavior of the caster

• An implicit assumption in this is that each slice is independent of the other slices

• Questions:– Is this assumption valid for

transient case? (CON1D is steady)

– If so, does the assumption hold for conventional casters?(Cononline has so far been used for thin slabs)

Cononlinesimulation

domain

Multiple slices traveling through the caster


Strain gauge measurements from Gregurich et al [4]

• Plant measurements were taken at Burns Harbor Caster #1 using strain gauges attached to support rolls

• Roll loads were recorded during changes in casting speed

• Change in speed leads to change in liquid core position, which causes change in measured roll loads

• This is a quick step change in speed, on a conventional caster (thick slab, low speed). These are the conditions where conduction should matter the most. This makes it a good test case for Cononline

Low strain – solid core• No ferrostatic pressure• Thermal shrinkage pulls away from roll

High strain – liquid core • Ferrostatic pressure pushes shell into roll

Casting speed

Strain gauge measurements


CON1D model calibration: caster dimensions

• The goal is to1. Calibrate CON1D using steady state measurements in the paper2. Re-create the speed change in Conoffline3. Compare the results

• Roll locations and roll gaps: Figure 3 in [4], shown below(BH1 line with adjusted roll gaps beyond 1000 in)

Reported roll locations

Distance below meniscus (in)

cold roll gap profile


CON1D model calibration with steady-state measurements

• A plain low-carbon (0.05%) steel was assumed

• CON1D was calibrated to match two steady state metallurgical lengths (ML) reported in the paper– Secondary cooling sprays

were assumed to be proportional to casting speed, vc

– Mold heat flux was assumed to be proportional to vc0.7 (see Prathiba’s work [5])

– The constants of proportionality for both were chosen to match reported MLs under steady conditions in the paper

Reported roll gap

Speed 0.9 m/min 1.1 m/min

Reported ML 23 m 28 m

CON1Dpredicted ML

23.2 28.1 m

Reported ML


Recreating trial conditions

20

30

40

50

-100

0 0

1000

2000

Cas

tin

g s

pee

d (

in/m

in)

Time after first speed change (s)

Casting speed history during the trial was re-created from Fig 18 in [4]

Figure 18 from [4] Recreated casting speed history


Steady-state results

Fast speed45 ipm (1.14 m/min)

ML = 26.6 m

Slow speed30 ipm (0.762 m/min)

ML = 18.6 m

Surfacetemperature

Shellthickness

Legend

0

20

40

60

80

100

120

0

500

1000

1500

0 10000 20000 30000S

hel

l th

ickn

ess

(mm

)

Su

rfac

e te

mp

erat

ure

(°C

)

Distance from meniscus (mm)

0

20

40

60

80

100

120

0

500

1000

1500

0 10000 20000 30000

Sh

ell t

hic

knes

s (m

m)

Su

rfac

e te

mp

erat

ure

(°C

)



Conoffline replay of trial

Sped up 60x

1300 s 1800 s

2700 s 3300 s


19202122232425262728

Dis

tan

ce f

rom

m

enis

cus

(m)

0.001 (liquidus)0.70.999 (solidus)roll 75 locationroll 76 locationroll 78 locationroll 79 location

ML for a particular solid fraction

Mo

del

p

red

icti

on

s

Changes in roll loads match best with Cononline predicted solidus location

Roll

Mea

sure

d

roll

load

Comparison of Conoffline with measurements: ML


-0.2

0

0.2

0.4

0.6

0.8

1

1.2

So

lid f

ract

ion

solid fraction at roll75 centerline

solid fraction at roll76 centerlinesolid fraction at roll78 centerline

solid fraction at roll79 centerline

Comparison of Conoffline with measurements: solid fraction

Roll

Changes in roll loads match best with Cononline predicted solidus location

Mo

del

p

red

icti

on

s

Mea

sure

d

roll

load


Cononline thermal shrinkage calculation

• Phase fraction at centerline only predicts the

• For further investigation, we modified Cononlineto estimate the thermal linear expansion (TLE) of the material

• Intuitive idea: shrinkage occurs after solid fraction in the entire strand is below a value chosen to represent coherency

Before coherency: liquid pool pushes shell against rolls, preventing shrinkage

After coherency: centerline is susceptible to segregation and other defects if the roll gap does not satisfy the desired shrinkage

Solid

Liquid


Cononline thermal shrinkage calculation

• Detailed method for Conlineshrinkage estimation1. At every location, calculate

density of present phases according to relationships from Harste, Jablonka, and Jimbo [7]

2. Before coherency, total TLE is set to 0

3. After coherency total TLE is based on the change in density (ρ) from the point of coherency (ρ0)

• Open question: what solid fraction represents coherency?

Solid

Liquid

0TLE =03 1TLE

ρρ

= −0ρ ρ=

Before coherency After coherency


-0.003

-0.002

-0.001

0

0.001

Pre

dic

ted

th

erm

al

linea

r ex

pan

sio

n

average TLEunder roll 75average TLEunder roll 76average TLEunder roll 78average TLEunder roll 79

Comparison of Cononline with strain gauges: thermal shrinking

Predicted thermal linear expansion provides a better match for the timing, and qualitatively predicts the undershoot and rebound in strain after the slowdown

Mo

del

p

red

icti

on

s

Roll

Mea

sure

d

roll

load

Coherency at 0.7 solid fraction


Model is verified

• If inter-slice effects were important, the time to reach steady state after the slowdown would be significantly longer, according to [6]

• This assumption about transient behavior is therefore valid for this caster

Mea

sure

d

roll

load

-0.003

-0.002

-0.001

0

0.001

Pre

dic

ted

th

erm

al

linea

r ex

pan

sio

n


Evolution of strain during slow down

The next slide shows snapshots of the strand while the caster was slowing down

Time after start of slow down:

-140 220 400 730 (s)


-0.200.20.40.60.811.2

-0.004-0.003-0.002-0.001

00.001

0 10000 20000 30000 Cen

terl

ine

solid

fr

acti

on

Ave

rag

e th

erm

al

linea

r ex

pan

sio

n


Snapshots of TLE and phase fraction profiles during slow down

-0.200.20.40.60.811.2

-0.004-0.003-0.002-0.001

00.001

20000 25000 30000 Cen

terl

ine

solid

fr

acti

on

Ave

rag

e th

erm

al

linea

r ex

pan

sio

n


coherency

Legend

TLE

Solid fraction

Colors indicate time of profile

Time related to start of slowdown

Note that TLE profile has same slope throughout speed-up.


Conoffline replay of trial

Sped up 60x

1300 s 1800 s

2700 s 3300 s


Evolution of strain during speed up

The next slide shows snapshots of the strand while the caster was speeding up

Time after start of speed up:

220 790 1150 1450 (s)1690


-0.200.20.40.60.811.2

-0.004-0.003-0.002-0.001

00.001

0 10000 20000 30000 Cen

terl

ine

solid

fr

acti

on

Ave

rag

e th

erm

al

linea

r ex

pan

sio

n


TLE

Solid fraction

Legend

Colors indicate time of profile

-0.200.20.40.60.811.2

-0.004-0.003-0.002-0.001

00.001

20000 25000 30000 Cen

terl

ine

solid

fr

acti

on

Ave

rag

e th

erm

al

linea

r ex

pan

sio

n


coherency

Note that TLE profile is steeper during slow-down than the speed-up. This is because the transient from the speed-up did not complete.

Snapshots of TLE and phase fraction profiles during speed up


Snapshot: 2070 seconds after start of speed change

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

-0.004

-0.003

-0.002

-0.001

0

0.001

20000 25000 30000

Cen

terl

ine

solid

fra

ctio

n

Ave

rag

e th

erm

al li

nea

r ex

pan

sio

n


TLESolid fraction

Estimated shrinkage:0.076 mm/m

Much less than reported machine taper (0.34 mm/m)

Most severe shrinkage happens after shell is fully solid


Thermal shrinkage

Conoffline predicts highest rate of shrinkage occurs after final solidification, because there is a sudden drop in temperature at that time.

• Before final solidification: latent heat is being removed, creating large temperature gradients in the material

• After final solidification: temperature quickly drops towards the average

Final solidification5 m after final solidification

5 m before final solidification


-0.004

-0.003

-0.002

-0.001

0

0.001

Pre

dic

ted

av

erag

e th

erm

al

linea

r el

on

gat

ion

Effect of coherency choice: comparison with measurements

Coherency choice changes where Conoffline predicts thermal shrinkage to start

Roll

Measured roll load

Coherency at 0.7 solid fraction

-0.004

-0.003

-0.002

-0.001

0

0.001

Pre

dic

ted

av

erag

e th

erm

al

linea

r el

on

gat

ion Coherency at 0.001

solid fraction


-0.2

0

0.2

0.4

0.6

0.8

1

1.2

-0.005

-0.004

-0.003

-0.002

-0.001

0

0.001

15000 20000 25000 30000

Cen

terl

ine

solid

fra

ctio

n

Ave

rag

e th

erm

al li

nea

r ex

pan

sio

n


Effect of coherency choice: snapshot of strand profile

Solid fraction

Estimated shrinkage:0.073 mm/min

Not significantly different from 0.7 coherency

Choice of coherency does not changed predicted rate of shrinkage, which is still smaller than reported machine taper (0.34 mm/m)


Parametric Simulation Study

• We would like to use Conoffline to investigate the transient behavior of continuous casters

• In this presentation, we focus on the effect of casting speed changes on metallurgical length, on a thin-slab caster

• Based on standard conditions at Nucor Decatur: 90 mm thickness slab, low-carbon steel

• Future work will investigate additional conditions


Casting conditions

• Simulations are based on Nucor Decatur steel mill

• Thickness: 90 mm• Grade: Low-carbon (0.045%) steel• Speed: varies, depending on simulation

– 3.05 → 2.92 → 2.79 → 2.54 m/min

• Mold heat flux: varies with casting speed, based on average measured values– 2.17 → 2.09 → 2.00 → 1.82 MW/m2


Sudden slowdown in casting speed

2.752.82.852.92.9533.053.1

8.8

9

9.2

9.4

9.6

-100 0 100 200 300

Cas

tin

g s

pee

d (

m/m

in)

Met

allu

rgic

al le

ng

th

(m)

Time after speed change (s)

ML (water tied to speed) Casting speed

A problem with these simulations is that other conditions are strongly related to casting speed. In this simulation, when the casting speed dropped, two other conditions changed:

• Secondary cooling spray rates: changed according to current Nucor Decatur practice

• Mold heat removal rate: changed according to average of measured values at each speed at Nucor Decatur


2.75

2.8

2.85

2.9

2.95

3

3.05

3.1

8.4

8.6

8.8

9

9.2

9.4

9.6

9.8

-100 -50 0 50 100 150 200 250 300 Cas

tin

g s

pee

d (

m/m

in)

Met

allu

rgic

al l

eng

th (

m)


ML Casting speed

Effect of change in casting speed only

In this simulation, the casting speed is changed the same as during the slowdown, but heat flux and secondary cooling are constant.

The change in metallurgical length is gradual, begins roughly linear, and speeds up at the end.


Effect of change in heat flux only

1.95

2

2.05

2.1

2.15

2.2

8.4

8.6

8.8

9

9.2

9.4

9.6

9.8

-100 -50 0 50 100 150 200 250 300

Hea

t fl

ux

(MW

/m2 )

Met

allu

rgic

al l

eng

th (

m)

Time after heat flux change (s)

ML Broad face heat flux

The change in metallurgical length is small, sudden, and happens after the speed change according to the dwell time of the material.

In this simulation, the heat flux is changed the same as during the slowdown, but casting speed and secondary cooling are constant.


48

50

52

54

56

58

8.4

8.6

8.8

9

9.2

9.4

9.6

9.8

-100 -50 0 50 100 150 200 250 300

Flo

w r

ate

(L/s

)

Met

allu

rgic

al l

eng

th (

m)

Time after spray change (s)

ML Total secondary cooling

Effect of change in secondary cooling

In this simulation, the secondary cooling water is changed the same as during the slowdown, but casting speed and mold heat flux are constant.

The change in metallurgical length is gradual, and relatively small compared to the other effects.


Comparison of the three cases: steady state effects

Casting speed Metallurgical length

(m) (%) (m) (%)

Before change 3.05 9.57

After change 2.79 91.7 8.57 89.6

Difference 0.25 8.3 1.00 10.4

Mold heat flux Metallurgical length

(MW/m2) (%) (m) (%)


After change 2.00 92.4 8.72 101.6

Difference 0.17 7.6 0.15 1.6

Secondary cooling Metallurgical length

(L/s) (%) (m) (%)


After change 49.2 85.8 9.79 102.2

Difference 8.1 14.1 0.21 2.2

In terms of proportional effect on steady-state metallurgical length …

… casting speed has more effect than mold heat flux …

… and mold heat flux has more effect than secondary cooling.


Comparison of the three cases: transient effects

8.4

8.6

8.8

9

9.2

9.4

9.6

9.8

10

-100 -50 0 50 100 150 200 250 300

Met

allu

rgic

al l

eng

th (

m)

Time after condition change (s)

speed is decreased heat flux is decreased spray water is decreased

Change due to speed is gradual, starts immediately

Change due to spray water is gradual, has a delay before beginning

Change due to heat flux is sudden, has a long delay


Sudden slowdown in casting speed

2.75

2.8

2.85

2.9

2.95

3

3.05

3.1

8.8

8.9

9

9.1

9.2

9.3

9.4

9.5

9.6

-100 -50 0 50 100 150 200 250 300

Cas

tin

g s

pee

d (

m/m

in)

Met

allu

rgic

al l

eng

th (

m)


ML (water tied to speed) Casting speed

Returning to the first (realistic) simulation, with all three effects (decrease speed, spray water, and mold heat flux) happening at once:

Initial decrease is mostly response to speed...

Decrease slows due to effect of secondary cooling…

Late increase is due to effect of mold heat removal


2.75

2.8

2.85

2.9

2.95

3

3.05

3.1

8.68.78.88.9

99.19.29.39.49.59.69.7

-100 0 100 200 300

Cas

tin

g s

pee

d (

m/m

in)

Met

allu

rgic

al l

eng

th (

m)


ML (look-up table) ML (surface temperature control)

ML (constant water) Casting speed

Different spray water control systems

• In all following simulations, the look-up table (speed-tied) method is used to set water sprays

“no control”Settling time

look-up table 179 s

surf. temp. control 161 s

no control 176 s


Comparison of slowdown and speed up

2.72.82.933.1

8.89

9.29.49.6

-100 0 100 200 300 Cas

tin

g s

pee

d

(m/m

in)

Met

allu

rgic

al

len

gth

(m

)


ML Casting speed

2.72.82.933.1

8.89

9.29.49.69.8

-100 0 100 200 300 Cas

tin

g s

pee

d

(m/m

in)

Met

allu

rgic

al

len

gth

(m

)


ML Casting speed

• Final speed: 2.79 m/min

• Final ML: 8.95 m• Time to reach steady

state: 179 s

• Final speed: 3.05 m/min

• Final ML: 9.57 m• Time to reach steady

state: 180 s

Time to reach steady state does not depend on casting speed


Comparison of different size speed decrease

2.5

2.6

2.7

2.8

2.9

3

3.1

8

8.2

8.4

8.6

8.8

9

9.2

9.4

9.6

9.8

-100 0 100 200 300

Cas

tin

g s

pee

d (

m/m

in)

Met

allu

rgic

al l

eng

th (

m)


ML (5 ipm) ML (10 ipm) ML (20 ipm)Casting speed (5 ipm) Casting speed (10 ipm) Casting speed (20 ipm)

183 s

192 s

179 s

Time to reach steady state does not depend on casting speed


Comparison of different size speed increases

2.5

2.6

2.7

2.8

2.9

3

3.1

8

8.2

8.4

8.6

8.8

9

9.2

9.4

9.6

9.8

-100 0 100 200 300

Cas

tin

g s

pee

d (

m/m

in)

Met

allu

rgic

al l

eng

th (

m)


ML (5 ipm) ML (10 ipm) ML (20 ipm)Casting speed (5 ipm) Casting speed (10 ipm) Casting speed (20 ipm)


Comparison of different rates of speed decrease

2.7

2.75

2.8

2.85

2.9

2.95

3

3.05

3.1

8.6

8.8

9

9.2

9.4

9.6

-50 50 150 250 350

Cas

tin

g s

pee

d (

m/m

in)

Met

allu

rgic

al l

eng

th (

m)

Time after start of speed change (s)

ML (1 s) ML (1 min) ML (2 min)Casting speed (1 s) Casting speed (1 min) Casting speed (2 min)

179 s 227 sSettling time from start of change:

Settling time from end of change: 178 s 167 s

290 s

170 s


Comparison of different rates of speed increase

2.7

2.75

2.8

2.85

2.9

2.95

3

3.05

3.1

3.15

3.2

8.8

9

9.2

9.4

9.6

9.8

-50 50 150 250 350

Cas

tin

g s

pee

d (

m/m

in)

Met

allu

rgic

al l

eng

th (

m)

Time after start of speed change (s)

ML (1 s) ML (1 min) ML (2 min)

Casting speed (1 s) Casting speed (1 min) Casting speed (2 min)

180 s 232 sSettling time from start of change:

Settling time from end of change: 179 s 172 s

287 s

167 s


Conclusions

• Cononline generalizing CON1D modeling framework to transient cases is valid

• Conoffline predicted thermal shrinkage is a good qualitative match to roll loads

• Cononline should be an accurate tool to adjust location of soft reduction during transient conditions

• However, predicted amount of thermal shrinkage is an order of magnitude smaller than typical soft reduction amounts – soft reduction cannot be explained by centerline shrinkage alone

• For typical variations of casting speed, the settling time of metallurgical length does not vary much

• This may not be true for more severe changes in casting speed


Future Work

• Extend CON1D/Cononline to investigate and predict ideal machine taper

• We want to complete a full parametric study (in coordination with Prathiba’s work)

• Study the effect of changing …– casting speed– spray rate

• … on …– metallurgical length– shell thickness– thermal shrinkage

• … for different …– thicknesses– grades

• Any other suggestions?• Does anyone want us to include their caster in the study?


Acknowledgments

• Continuous Casting Consortium Members(ABB, ArcelorMittal, Baosteel, MagnesitaRefractories, Nippon Steel, Nucor Steel, Postech/ Posco, Severstal, SSAB, Tata Steel, ANSYS/ Fluent)

• National Science Foundation Grant CMMI-09-00138

• Ron O’Malley, Bob Williams of Nucor Decatur

• Rudolf Moravec of ArcelorMittal Global R&D


References

1. Petrus, B., K. Zheng, X. Zhou, B.G. Thomas, and J. Bentsman, “Real-Time Model-Based Spray-Cooling Control System for Steel Continuous Casting”, Metallurgical and Materials Transactions B, Vol. 42B:2, 87- 103, 2011

2. Meng, Y. and B. G. Thomas, “Heat-Transfer and Solidification Model of Continuous Slab Casting: CON1D,” Metallurgical & Materials Transactions B, 34B:5, 685-705, 2003

3. Petrus, B. “Implementation Issues in Cononline”, CCC 20124. Gregurich, N., Flick, G., Moravec, R., and Blazek, B. “In-Depth Analysis of

Continuous Caster Machine Behavior During Casting With Different Roll Gap Taper Profiles”, Iron & Steel Technology, December 2012

5. Duvuuri, P. “Mold Heat Transfer”, CCC 20136. R.A. Hardin, K. Liu, A. Kapoor, and C. Beckermann, “A transient simulation and

dynamic spray cooling control model for continuous steel casting”, Metallurgical & Material Transactions B, 2003, vol. 34B, pp. 297–306

7. Li, C. and B. G. Thomas., “Ideal Taper Prediction for Billet Casting,” ISSTech2003 Steelmaking Conference Proceedings, Indianapolis, IN, Apr. 27-30, 2003, ISS-AIME, Warrendale, PA, 685-700, April 2003

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