Abstract

Continuous casting is an important process to solidify molten steel. Efficient and uniform heat removal by water spray without cracking or deforming steel slabs is a major challenge during continuous casting. With the aid of computational fluid dynamics (CFD), the current study presents a numerical model of spray cooling for process understanding and improvement. The Eulerian–Lagrangian approach is utilized to track the movement of water droplets that are injected from a hydraulic nozzle. The initial droplet size is predicted by the linear instability sheet atomization (LISA) model and the droplet distribution satisfies the Rosin-Rammler distribution. Droplet-slab impingement is modeled by the wall jet model and the associated heat transfer accounts for both heat conduction and radiation. Heat transfer coefficient (HTC) on slab surface is validated against a hot-plate benchmark experiment and shows good agreement. The significance of spray standoff distance and spray direction on heat transfer is also investigated. The results indicate the existence of the critical standoff distance beyond which the cooling effect becomes negligible. Spray direction plays an important role in determining the heat transfer rate as well, and insufficient cooling is observed when droplets are sprayed against gravity. Additional 10% to 15% of water will compensate for such low heat transfer. The current study should benefit the steel industry by providing fundamental insights into the process. The current model can also be applied to other types of spray nozzles and can further improve the efficiency of future simulations.

References

1.
Thomas
,
B. G.
,
2004
,
Continuous Casting (Metallurgy)
,
Yearbook of Science and Technology
,
McGraw-Hill Co.
,
New York
.
2.
Meng
,
Y. A.
, and
Thomas
,
B. G.
,
2003
, “
Heat-Transfer and Solidification Model of Continuous Slab Casting: CON1D
,”
Metall. Mater. Trans. B
,
34
(
5
), pp.
685
705
. 10.1007/s11663-003-0040-y
3.
Tang
,
L.
,
Yao
,
M.
,
Wang
,
X.
, and
Zhang
,
X.
,
2012
, “
Non-Uniform Thermal Behavior and Shell Growth Within Mould for Wide and Thick Slab Continuous Casting
,”
Steel Res. Int.
,
83
(
12
), pp.
1203
1213
. 10.1002/srin.201200075
4.
Zhang
,
X.
,
Chen
,
W.
, and
Zhang
,
L.
,
2017
, “
A Coupled Model on Fluid Flow, Heat Transfer and Solidification in Continuous Casting Mold
,”
China Foundry
,
14
(
5
), pp.
416
420
. 10.1007/s41230-017-7171-2
5.
Zappulla
,
M. L. S.
, and
Thomas
,
B. G.
,
2017
, “
Thermal-Mechanical Model of Depression Formation in Steel Continuous Casting
,”
Proceedings of 146th Annual Meeting & Exhibition Supplemental
,
San Diego, CA
,
Feb. 26–Mar. 2
, pp.
501
510
.
6.
Li
,
C.
, and
Thomas
,
B. G.
,
2004
, “
Thermomechanical Finite-Element Model of Shell Behavior in Continuous Casting of Steel
,”
Metall. Mater. Trans. B
,
35
(
6
), pp.
1151
1172
. 10.1007/s11663-004-0071-z
7.
Hibbeler
,
L. C.
,
Xu
,
K.
,
Thomas
,
B. G.
,
Koric
,
S.
, and
Spangler
,
C.
,
2009
, “
Thermomechanical Modeling of Beam Blank Casting
,”
Iron Steel Technol.
,
6
(
7
), p.
60
.
8.
Thomas
,
B. G.
,
Li
,
G.
,
Moitra
,
A.
, and
Habing
,
D.
,
1997
, “
Analysis of Thermal and Mechanical Behavior of Copper Molds During Continuous Casting of Steel Slabs
,”
Proceedings of 80th Steelmaking Conference
,
Chicago, IL
,
Apr. 13–16
, pp.
183
201
.
9.
Hibbeler
,
L. C.
,
Thomas
,
B. G.
,
Schimmel
,
R. C.
, and
Visser
,
H. H.
,
2014
, “
Simulation and Online Measurement of Narrow Face Mold Distortion in Thin Slab Casting
,”
Proceedings of 8th European Continuous Casting
,
Graz, Austria
,
June 23–26
, pp.
1
10
.
10.
Rackers
,
K. G.
, and
Thomas
,
B. G.
,
1995
, “
Clogging in Continuous Casting Nozzles
,”
Proceedings of 78th Steelmaking Conference
,
Nashville, TN
,
Apr. 2–5
, vol.
78
, pp.
723
736
.
11.
Thomas
,
B. G.
,
Denissov
,
A.
, and
Bai
,
H.
,
1997
, “
Behavior of Argon Bubbles During Continuous Casting of Steel
,”
Proceedings of 80th Steelmaking Conference
,
Chicago, IL
,
Apr. 13–16
, pp.
375
384
.
12.
Chaudhary
,
R.
,
Ji
,
C.
, and
Thomas
,
B. G.
,
2010
,
Assessment of LES and RANS Turbulence Models With Measurements in Liquid Metal Gainsn Model of Continuous Casting Process
,
Technical Report No. CCC201013
,
University of Illinois at Urbana-Champaign
,
Urbana, IL
.
13.
Yuan
,
Q.
,
Vanka
,
S. P.
,
Thomas
,
B. G.
, and
Sivaramakrishnan
,
S.
,
2004
, “
Computational and Experimental Study of Turbulent Flow in a 0.4-Scale Water Model of a Continuous Steel Caster
,”
Metall. Mater. Trans. B
,
35
(
5
), pp.
967
982
. 10.1007/s11663-004-0091-8
14.
Thomas
,
B. G.
,
Bai
,
H.
,
Sivaramakrishnan
,
S.
, and
Vanka
,
S. P.
,
1999
, “
Detailed Simulation of Flow in Continuous Casting of Steel Using k-ε, LES, and PIV
,”
International Symposium on Cutting Edge of Computer Simulation of Solidification and Processes
,
Osaka, Japan
,
Nov. 14–16
, pp.
113
128
.
15.
Yuan
,
Q.
,
Vanka
,
S. P.
, and
Thomas
,
B. G.
,
2003
, “
Large Eddy Simulations of Transient Turbulent Flow During Continuous Slab Casting of Steel
,”
Proceedings of 3rd Symposium on Turbulence and Shear Flow Phenomena
,
Sendai, Japan
,
June 25–27
, pp.
681
686
.
16.
Liu
,
R.
,
Sengupta
,
J.
,
Crosbie
,
D.
,
Chung
,
S.
,
Trinh
,
M.
, and
Thomas
,
B. G.
,
2011
, “
Measurement of Molten Steel Surface Velocity with SVC and Nail Dipping During Continuous Casting Process
,”
Proceedings of 140th Annual Meeting & Exhibition Supplemental
,
San Diego, CA
,
Feb. 27–Mar. 3
, pp.
51
58
.
17.
Liu
,
R.
,
Thomas
,
B. G.
,
Sengupta
,
J.
,
Chung
,
S. D.
, and
Trinh
,
M.
,
2014
, “
Measurements of Molten Steel Surface Velocity and Effect of Stopper-Rod Movement on Transient Multiphase Fluid Flow in Continuous Casting
,”
ISIJ Int.
,
54
(
10
), pp.
2314
2323
. 10.2355/isijinternational.54.2314
18.
Thomas
,
B. G.
,
Zhang
,
L.
,
Yuan
,
Q.
, and
Vanka
,
S. P.
,
2004
, “
Flow Dynamics and Inclusion Transport in Continuous Casting of Steel
,”
Proceedings of NSF Conference on Design, Service, and Manufacturing Grantees and Research
,
Scottsdale, AZ
,
Jan. 6–9
, pp.
2328
2362
.
19.
Zhang
,
L.
, and
Thomas
,
B. G.
,
2003
,
Inclusion Nucleation, Growth, and Mixing During Steel Deoxidation
,
Technical Report No. CCC200206
,
University of Illinois at Urbana-Champaign
,
Urbana, IL
.
20.
Zhang
,
L.
,
Yang
,
S.
,
Cai
,
K.
,
Li
,
J.
,
Wan
,
X.
, and
Thomas
,
B. G.
,
2007
, “
Investigation of Fluid Flow and Steel Cleanliness in the Continuous Casting Strand
,”
Metall. Mater. Trans. B
,
38
(
1
), pp.
63
83
. 10.1007/s11663-006-9007-0
21.
Zhang
,
L.
,
Thomas
,
B. G.
,
Wang
,
X.
, and
Cai
,
K.
,
2002
, “
Evaluation and Control of Steel Cleanliness-Review
,”
Proceedings of 85th Steelmaking Conference
,
Nashville, TN
,
Mar. 10–13
, Vol.
85
, pp.
431
452
.
22.
Zhang
,
L.
,
Yang
,
S.
,
Wang
,
X.
,
Cai
,
K.
,
Li
,
J.
,
Wan
,
X.
, and
Thomas
,
B. G.
,
2004
, “
Physical, Numerical and Industrial Investigation of the Fluid Flow and Steel Cleanliness in the Continuous Casting Mold at Panzhihua Steel
,”
Proceedings of AISTech Conference
,
Nashville, TN
,
Sept. 15–17
, p.
879
.
23.
Laitinen
,
E.
, and
Neittaanmäki
,
P.
,
1988
, “
On Numerical Simulation of the Continuous Casting Process
,”
J. Eng. Math.
,
22
(
4
), pp.
335
354
. 10.1007/BF00058513
24.
Hardin
,
R. A.
,
Liu
,
K.
,
Beckermann
,
C.
, and
Kapoor
,
A.
,
2003
, “
A Transient Simulation and Dynamic Spray Cooling Control Model for Continuous Steel Casting
,”
Metall. Mater. Trans. B
,
34
(
3
), pp.
297
306
. 10.1007/s11663-003-0075-0
25.
López
,
A. G.
, and
Olivares
,
I. M.
,
1990
, “
Heat Transfer Analysis During Water Spray Cooling of Steel Rods
,”
ISIJ Int.
,
30
(
1
), pp.
48
57
. 10.2355/isijinternational.30.48
26.
Nozaki
,
T.
,
Matsuno
,
J.
,
Murata
,
K.
,
Ooi
,
H.
, and
Kodama
,
M.
,
1978
, “
A Secondary Cooling Pattern for Preventing Surface Cracks of Continuous Casting Slab
,”
Trans. ISIJ
,
18
(
6
), pp.
330
338
. 10.2355/isijinternational1966.18.330
27.
Blazek
,
K.
,
Moravec
,
R.
,
Zheng
,
K.
,
Lowry
,
M.
, and
Yin
,
H.
,
2013
, “
Dynamic Simulation of Slab Centerline Behavior of the Continuous Casting Process During Large Speed Transitions and Their Effects on Slab Internal Quality
,”
Proceedings of 5th International Conference on Modelling and Simulation of Metallurgical Processes in Steelmaking
,
Ostrava, Czech Republic, Sept. 10–12
.
28.
Rayleigh
,
L.
,
1878
, “
On the Instability of Jets
,”
Proc. London Math. Soc.
,
1
(
1
), pp.
4
13
. 10.1112/plms/s1-10.1.4
29.
Zeoli
,
N.
,
Tabbara
,
H.
, and
Gu
,
S.
,
2011
, “
CFD Modeling of Primary Breakup During Metal Powder Spray
,”
Chem. Eng. Sci.
,
66
(
24
), pp.
6498
6504
. 10.1016/j.ces.2011.09.014
30.
Altimira
,
M.
,
Rivas
,
A.
,
Anton
,
R.
,
Sanchez Larraona
,
G.
, and
Ramos
,
J. C.
,
2007
, “
Fan-Spray Atomizers Analysis Through Mathematical Modeling
,”
Proceedings of Institute for Liquid Atomization and Spray Systems (ILASS)-Europe 21st Annual Conference on Liquid Atomization and Spray Systems
,
Mugla, Turkey, Sept. 10–13
.
31.
Koutsakis
,
K.
,
Gu
,
S.
, and
Vardelle
,
A.
,
2011
, “
Three Dimensional CFD Simulation of Liquid Copper Break up for the Liquid Precursor Spraying
,”
Surf. Coat. Tech.
,
220
(
15
), pp.
214
218
. 10.1016/j.surfcoat.2012.12.010
32.
Kalata
,
W.
,
Brown
,
K.
,
O'Donnell
,
S.
, and
Schick
,
R. J.
,
2016
, “
Transfer Efficiency for an Oil Spray Application
,”
Proceedings of 26th ILASS Americas Annual Conference on Liquid Spray and Spray Systems
,
Portland, OR, May 18–21
.
33.
Alkhedhair
,
A.
,
Jahn
,
I.
,
Gurgenci
,
H.
,
Guan
,
Z.
,
He
,
S.
, and
Lu
,
Y.
,
2016
, “
Numerical Simulation of Water Spray in Natural Draft Dry Cooling Towers with a New Nozzle Representation Approach
,”
Appl. Therm. Eng.
,
98
(
5
), pp.
924
935
. 10.1016/j.applthermaleng.2015.10.118
34.
Senecal
,
P. K.
,
Schmidt
,
D. P.
,
Nouar
,
I.
,
Rutland
,
C. J.
,
Reitz
,
R. D.
, and
Corradini
,
M. L.
,
1999
, “
Modeling High-Speed Viscous Liquid Sheet Spray
,”
Int. J. Multiphase Flow
,
25
(
6–7
), pp.
1073
1097
. 10.1016/S0301-9322(99)00057-9
35.
Fung
,
M. C.
,
Inthavong
,
K.
,
Yang
,
W.
, and
Tu
,
J.
,
2012
, “
CFD Modeling of Spray or a Nasal Spray Device
,”
Aerosol Sci. Tech.
,
46
(
11
), pp.
1219
1226
. 10.1080/02786826.2012.704098
36.
Nijdam
,
J. J.
,
Guo
,
B.
,
Fletcher
,
D. F.
, and
Langrish
,
T. A.
,
2006
, “
Lagrangian and Eulerian Models for Simulating Turbulent Dispersion and Coalescence of Droplets Within a Spray
,”
Appl. Math. Model.
,
30
(
11
), pp.
1196
1211
. 10.1016/j.apm.2006.02.001
37.
Ogawa
,
H.
,
Matsui
,
Y.
,
Kimura
,
S.
, and
Kawashima
,
J.
,
1997
, “
Three-Dimensional Computation of In-Cylinder Flow and Combustion Characteristics in Diesel Engines—Effect of Wall Impingement Models of Fuel Droplet Behavior on Combustion Characteristics
,”
JSAE Rev.
,
18
(
2
), pp.
95
99
. 10.1016/S0389-4304(96)00065-3
38.
Naber
,
J. D.
, and
Reitz
,
R. D.
,
1988
, “
Modeling Engine Spray/Wall Impingement
,”
SAE Int. J. Engines
,
97
(
6
), pp.
118
140
. 10.4271/880107
39.
Bai
,
C.
, and
Gosman
,
A. D.
,
1995
, “
Development of Methodology for Spray Impingement Simulation
,”
SAE Int. J. Engines
,
104
(
3
), pp.
550
568
.
40.
Grover
,
R. O.
, and
Assanis
,
D. N.
,
2001
, “
A Spray Wall Impingement Model Based upon Conservation Principles
,”
Proceedings of 50th International Symposium on Diagnostics and Modeling of Combustion in Internal Combustion Engines
,
Nagoya, Japan, July 1–4
, pp.
551
559
.10.1299/jmsesdm.01.204.75
41.
Kalantari
,
D.
,
2013
, “
Evaluation of Some of the Existing Models for Droplet and Spray/Wall Interactions
,”
Fluid Dyn. Mater. Process.
,
92
(
2
), pp.
169
182
.
42.
Mundo
,
C.
,
Tropea
,
C.
, and
Sommerfeld
,
M.
,
1997
, “
Numerical and Experimental Investigation of Spray Characteristics in the Vicinity of a Rigid Wall
,”
Exp. Therm. Fluid Sci.
,
15
(
3
), pp.
228
237
. 10.1016/S0894-1777(97)00015-0
43.
Liu
,
H.
,
Cai
,
C.
,
Yan
,
Y.
,
Jia
,
M.
, and
Yin
,
B.
,
2018
, “
Numerical Simulation and Experimental Investigation on Spray Cooling in the Non-Boiling Region
,”
Heat Mass Transfer
,
54
(
12
), pp.
3747
3760
. 10.1007/s00231-018-2402-7
44.
Zuckerman
,
N.
, and
Lior
,
N.
,
2006
, “
Jet Impingement Heat Transfer: Physics, Correlations, and Numerical Modeling
,”
Adv. Heat Transfer
,
54
(
12
), pp.
3747
3760
. 10.1016/S0065-2717(06)39006-5
45.
Menter
,
F. R.
,
1993
, “
Zonal Two Equation k-ω Turbulence Models for Aerodynamic Flows
,”
Proceedings of AIAA 24th Fluid Dynamics Conference
,
Orlando, FL
46.
Liu
,
A. B.
,
Mather
,
D.
, and
Reitz
,
R. D.
,
1993
, “
Modeling the Effects of Drop Drag and Breakup on Fuel Sprays
,”
SAE Int. J. Engines
,
102
(
3
), pp.
83
95
. 10.4271/930072
47.
Gosman
,
A. D.
, and
Ioannides
,
E.
,
1983
, “
Aspects of Computer Simulation of Liquid-Fueled Combustors
,”
J. Energy
,
7
(
6
), pp.
482
490
. 10.2514/3.62687
48.
Ranz
,
W. E.
, and
Marshall
,
W. R.
,
1952
, “
Evaporation From Drops
,”
Chem. Eng. Progress
,
48
(
3
), pp.
141
146
.
49.
Schmidt
,
D. P.
,
Nouar
,
I.
,
Senecal
,
P. K.
,
Rutland
,
C. J.
,
Martin
,
J. K.
,
Reitz
,
R. D.
, and
Hoffman
,
J. A.
,
1999
, “
Pressure-Swirl Spray in the Near Field
,”
SAE Int. J. Engines
,
108
(
3
), pp.
471
484
. 10.4271/1999-01-0496
50.
O’Rourke
,
P. J.
,
1981
, “
Collective Drop Effects on Vaporizing Liquid Sprays
,”
Ph.D. thesis
,
Princeton University
,
Princeton, NJ
.
51.
Reitz
,
R. D.
,
1987
, “
Modeling Spray Processes in High-Pressure Vaporizing Sprays
,”
At. Spray Tech.
,
3
(
4
), pp.
309
337
.
52.
Birkhold
,
F.
,
2007
, “
Selektive Katalytische Reduktion von Stickoxiden in Kraftfahrzeugen: Untersuchung der Einspritzung von Harnstoffwasserlösung
,”
Ph.D. thesis
,
University of Karlsruhe
,
Karlsruhe, Germany
.
53.
Akao
,
F.
,
Araki
,
K.
,
Mori
,
S.
, and
Moriyama
,
A.
,
1980
, “
Deformation Behaviors of a Liquid Droplet Impinging Onto Hot Metal Surface
,”
Trans. ISIJ
,
20
(
11
), pp.
737
743
. 10.2355/isijinternational1966.20.737
54.
Bernardin
,
J. D.
, and
Mudawar
,
I.
,
1999
, “
The Leidenfrost Point: Experimental Study and Assessment of Existing Models
,”
J. Heat Transfer
,
121
(
4
), pp.
894
903
. 10.1115/1.2826080
55.
Issa
,
R. J.
,
2004
, “
Numerical Modeling of the Dynamics and Heat Transfer of Impacting Sprays for a Wide Range of Pressures
,”
PhD dissertation
,
University of Pittsburgh
,
Pittsburgh, PA
.
56.
Yao
,
S. C.
, and
Cox
,
T. L.
,
1998
, “
Investigation Into the Use of Large-Drop Sprays for Hot Strip Rolling Mills
,”
Proceedings of Mechanical Working and Steel Processing Conference
,
Pittsburgh, PA
, pp.
359
366
.
57.
Koric
,
S.
, and
Thomas
,
B. G.
,
2006
, “
Efficient Thermo-Mechanical Model for Solidification Processes
,”
Int. J. Numer. Methods Eng.
,
66
(
12
), pp.
1954
1989
. 10.1002/nme.1614
58.
Horsky
,
J.
,
Raudensky
,
M.
, and
Tseng
,
A. A.
,
2005
, “
Heat Transfer Study of Secondary Cooling in Continuous Casting
,”
Proceedings of AISTech Conference
,
Charlotte, NC, May 9–12
.
59.
Blazek
,
K.
, and
Moravec
,
R.
,
2019
, “
The Effect of Standoff Distance on the Cooling Efficiency of Air Mist and Hydraulic Nozzles
,”
Proceedings of AISTech Conference
,
Pittsburgh, PA
,
May 6–9
.
60.
Ji
,
C.
,
Cai
,
Z. Z.
,
Wang
,
W. L.
,
Zhu
,
M. Y.
, and
Sahai
,
Y.
,
2014
, “
Effect of Transverse Distribution of Secondary Cooling Water on Corner Cracks in Wide Thick Slab Continuous Casting Process
,”
Ironmaking Steelmaking
,
41
(
5
), pp.
360
368
. 10.1179/1743281213Y.0000000161
61.
Ma
,
H.
,
Lee
,
J.
,
Tang
,
K.
,
Liu
,
R.
,
Lowry
,
M.
,
Silaen
,
A.
, and
Zhou
,
C. Q.
,
2019
, “
Modeling of Spray Cooling With a Moving Steel Slab During the Continuous Casting Process
,”
Steel Res. Int.
,
90
(
4
), p.
1800393
. 10.1002/srin.201800393
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