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Real-Time, Model-Based Spray-Cooling Control System for Steel Continuous Casting

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Abstract

This article presents a new system to control secondary cooling water sprays in continuous casting of thin steel slabs (CONONLINE). It uses real-time numerical simulation of heat transfer and solidification within the strand as a software sensor in place of unreliable temperature measurements. The one-dimensional finite-difference model, CON1D, is adapted to create the real-time predictor of the slab temperature and solidification state. During operation, the model is updated with data collected by the caster automation systems. A decentralized controller configuration based on a bank of proportional-integral controllers with antiwindup is developed to maintain the shell surface-temperature profile at a desired set point. A new method of set-point generation is proposed to account for measured mold heat flux variations. A user-friendly monitor visualizes the results and accepts set-point changes from the caster operator. Example simulations demonstrate how a significantly better shell surface-temperature control is achieved.

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Abbreviations

0 :

superscript to indicate initial time of creation (at meniscus)

Cp *steel :

effective specific heat of steel, including latent heat of solidification (J/kg K)

Δt :

time interval for control calculation (s)

Δt FD , Δx :

time step (s) and grid spacing (m) used in CON1D explicit finite difference scheme

ΔT j :

difference between estimated average surface temperature and set point in zone j (°C)

f roll :

fraction of heat removed through roll contact in zone

i :

subscript for CON1D slice number, used in CONSENSOR (N total)

j :

subscript for spray zone number (N zone total)

k P j , k I j , k aw j :

proportional, integral, and antiwindup controller gains

k steel :

thermal conductivity of steel (W/m K)

L j :

total length of zone j (m)

L roll contact,j :

length of zone j in which rolls are in contact with the steel surface (m)

Lspray,j , w j :

length and width of the area of the steel surface upon which all the sprays in zone j impinge (m)

n pattern :

index denoting desired spray pattern

p E :

weight percent of alloying element E

q :

surface heat flux at a particular time and location (MW/m2)

\( \bar{q}_{\text{mold}} \) :

average steel surface heat flux in mold (MW/m2)

Q sw,j :

spray water flux (L/s/m2) on surface of steel in zone j

ρ steel :

density of steel (kg/m3)

t :

real time (s)

t i (z):

time when slice i passes distance z from the meniscus (s)

T i (x,t):

temperature of CON1D slice i: 1-D transverse cross section moving along strand centerline at V c (°C)

Ts(z,t):

strand surface-temperature set point (°C)

\( \hat{T}\left( {z,t} \right) \) :

strand surface-temperature estimate (°C)

T amb :

ambient temperature (°C)

T pour :

measured temperature of molten steel in the tundish (°C)

T spray :

measured temperature of spray water (°C)

u j ′(t), u j (t):

spray water flow rate: measured, requested controller output (L/s)

u P j (t), u I J (t):

proportional and integral portions of requested spray water flow rate (L/s)

V c :

casting speed (m/s)

x :

distance through thickness of strand (m)

z :

distance from meniscus, in casting direction (m)

z i (t):

distance from meniscus of slice i at time t (m)

z m :

mold length (m)

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Acknowledgments

Ron O’Malley, Matthew Smith, Terri Morris, and Kris Sledge from Nucor Decatur are gratefully acknowledged for their unwavering support and help with this work. The TCP/IP programs in CONONLINE were written by Rob Oldroyd from DBR Systems on behalf of Nucor Decatur. We are grateful for work on CON1D calibration for the Nucor Decatur steel mill by Sami Vahpalahti and Huan Li from the University of Illinois. We are also very grateful for their work on CONONLINE. This work is supported by the National Science Foundation under Grants DMI 05-00453 and CMMI-0900138 as well as the Continuous Casting Consortium at UIUC.

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Authors and Affiliations

  1. Department of Mechanical Science and Engineering, University of Illinois, Urbana, IL, 61801, USA

    Bryan Petrus (Graduate Research Assistant), Kai Zheng (Graduate Research Assistant), X. Zhou (Graduate Research Assistant), Brian G. Thomas (Gauthier Professor) & Joseph Bentsman (Professor)

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  1. Bryan Petrus
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  2. Kai Zheng
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  3. X. Zhou
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Corresponding author

Correspondence to Brian G. Thomas.

Additional information

Manuscript submitted July 14, 2009.

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Petrus, B., Zheng, K., Zhou, X. et al. Real-Time, Model-Based Spray-Cooling Control System for Steel Continuous Casting. Metall Mater Trans B 42, 87–103 (2011). https://doi.org/10.1007/s11663-010-9452-7

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