Metallurgical and Materials Transactions B

, Volume 42, Issue 1, pp 87–103 | Cite as

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

  • Bryan Petrus
  • Kai Zheng
  • X. Zhou
  • Brian G. Thomas
  • Joseph Bentsman
Article

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.

Nomenclature

0

superscript to indicate initial time of creation (at meniscus)

Cpsteel*

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

Δt

time interval for control calculation (s)

ΔtFD, Δx

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

ΔTj

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

froll

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 (Nzone total)

kjPkjIkjaw

proportional, integral, and antiwindup controller gains

ksteel

thermal conductivity of steel (W/m K)

Lj

total length of zone j (m)

Lroll contact,j

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

Lspray,j, wj

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

npattern

index denoting desired spray pattern

pE

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)

Qsw,j

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

ρsteel

density of steel (kg/m3)

t

real time (s)

ti(z)

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

Ti(x,t)

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

Ts(z,t)

strand surface-temperature set point (°C)

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

strand surface-temperature estimate (°C)

Tamb

ambient temperature (°C)

Tpour

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

Tspray

measured temperature of spray water (°C)

uj′(t), uj(t)

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

ujP(t), uJI(t)

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

Vc

casting speed (m/s)

x

distance through thickness of strand (m)

z

distance from meniscus, in casting direction (m)

zi(t)

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

zm

mold length (m)

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Copyright information

© THE MINERALS, METALS & MATERIALS SOCIETY and ASM INTERNATIONAL 2010

Authors and Affiliations

  • Bryan Petrus
    • 1
  • Kai Zheng
    • 1
  • X. Zhou
    • 1
  • Brian G. Thomas
    • 1
  • Joseph Bentsman
    • 1
  1. 1.Department of Mechanical Science and EngineeringUniversity of IllinoisUrbanaUSA

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