Ci a ion: Walek, J.; Tkadleˇcko á, M.;
Veliˇcka, M.; Mach˚u, M.; Cupek, J.;
Huczala, T.; Cibulka, J.; R˚užiˇcka, J.;
Michalek, K. Physical Expe imen s
and Nume ical Simula ions o he
In luence o Tu bulence Inhibi o s
and he Posi ion o Ladle Sh oud on
he S eel Flow in an Asymme ic
Fi e-S and Tundish. Me als 2023,13,
1821. h ps://doi.o g/10.3390/
me 13111821
Academic Edi o : Jiehua Li
Recei ed: 5 Sep embe 2023
Re ised: 27 Sep embe 2023
Accep ed: 22 Oc obe 2023
Published: 29 Oc obe 2023
Copy igh : © 2023 by he au ho s.
Licensee MDPI, Basel, Swi ze land.
This a icle is an open access a icle
dis ibu ed unde he e ms and
condi ions o he C ea i e Commons
A ibu ion (CC BY) license (h ps://
c ea i ecommons.o g/licenses/by/
4.0/).
me als
A icle
Physical Expe imen s and Nume ical Simula ions o he
In luence o Tu bulence Inhibi o s and he Posi ion o
Ladle Sh oud on he S eel Flow in an Asymme ic
Fi e-S and Tundish
Jose Walek 1,* , Ma ké a Tkadleˇcko á2, Ma ek Veliˇcka 3, Ma io Mach˚u 3, Jiˇ íCupek 1, Tomáš Huczala 2,
Jiˇ íCibulka 2, Jan R˚užiˇcka 3and Ka el Michalek 1
1Depa men o Me allu gical Technologies, Facul y o Ma e ials Science and Technology, VSB—Technical
Uni e si y o Os a a, 17. lis opadu 2172/15, 70800 Os a a, Czech Republic; [email p o ec ed] (J.C.);
[email p o ec ed] (K.M.)
2Tˇ
RINECKÉŽELEZÁRNY, a.s., P ˚umyslo á1000, S a éMˇes o, 73961 Tˇ inec, Czech Republic;
[email p o ec ed] (M.T.); [email p o ec ed] (T.H.); [email p o ec ed] (J.C.)
3
Depa men o The mal Enginee ing, Facul y o Ma e ials Science and Technology, VSB—Technical Uni e si y
o Os a a, 17. lis opadu 2172/15, 70800 Os a a, Czech Republic; [email p o ec ed] (M.V.);
[email p o ec ed] (M.M.); [email p o ec ed] (J.R.)
*Co espondence: [email p o ec ed]; Tel.: +420-597323534
Abs ac :
The submi ed a icle deals wi h he use o physical and nume ical modelling o s udy
he p ocess o he s eel low in an asymme ic i e-s and undish ha con inuously cas s s eel. Fo
he pu poses o physical modelling, a 1:4-scale plexiglass model was used as he ope a ing undish,
and o nume ical modelling, he geome y o he ope a ing undish was c ea ed on a 1:1 scale. A
model liquid (wa e ) was used in he physical modelling o he mel low p ocess, while liquid s eel
was used as he s anda d lowing medium in he nume ical modelling. We assessed he ele an
ope a ing pa ame e s in luencing he cha ac e is ics o he low o he ba h in he undish— he shape
o he u bulence inhibi o , he posi ion o he ladle sh oud in ela ion o he u bulence inhibi o
and he dis ance be ween he ladle sh oud o i ice and he bo om o he u bulence inhibi o . The
p elimina y esul s show ha op imal s eel low cha ac e is ic esul s a e achie ed by using he TI3-C
con igu a ion. The esul s om bo h modelling me hods achie ed he same cha ac e is ics, he e o e
e i ying he esul s o each o he and demons a ing ha when aken oge he , he esul s o physical
and nume ical modelling can be conside ed su icien ly in o ma i e.
Keywo ds: undish; u bulence inhibi o ; s eel low; e en ion ime; modelling
1. In oduc ion
Du ing he con inuous cas ing o s eel, a undish is placed be ween he ladle and he
mould and is one o he mos impo an echnological nodes in he p ocess because i a ec s
he s abili y o he cas ing p ocess and he quali y o he con inuous cas p e o m. The
undish p ima ily se es as a ese oi o liquid s eel du ing sequen ial cas ing, p o iding
su icien ime o ladle changes wi hou ha ing o p ema u ely in e up he low o liquid
s eel in o he molds [1–3].
The undish can be used as a low- h ough eac o o ba h mixing, as, o a ce ain
ex en , i is s ill possible o modi y he p ope ies o he cas s eel a his poin . One o he
basic unc ions o he undish is o dis ibu e liquid s eel be ween he indi idual cas ing
s ands. The e en dis ibu ion o s eel needs o be ensu ed so ha he physical and chemical
p ope ies o he s eel a e app oxima ely he same in all s ands. The s eel in he indi idual
cas ing s ands should ha e he same empe a u e, he same chemical s uc u e and he
same pu i y in e ms o he con en o non-me allic inclusions. These indi idual p ope ies
Me als 2023,13, 1821. h ps://doi.o g/10.3390/me 13111821 h ps://www.mdpi.com/jou nal/me als
Me als 2023,13, 1821 2 o 18
a e closely ela ed o he cha ac e is ics o he s eel low in he undish. The s eel low is
in luenced by he in e nal a angemen s o he undish, and a ious objec s a e inse ed
in o he undish in o de o op imize he cha ac e is ics o he s eel low in a sui able way.
Op imizing he ba h low in he undish is an impo an pa o he e icien ope a ion o
e e y con inuous cas ing. I is clea om an analysis o he li e a u e ha a p esen , he
mos common objec s inse ed in o he undish o imp o e he cha ac e is ics o he low
include u bulence inhibi o s, which a e inse ed unde he ladle sh oud, ba les, dams and
wei s, and a gon s i ing elemen s [2–6].
Tu bulence inhibi o s p e en s eel spa e ing when illing an emp y undish. They
signi ican ly educe he u bulence in ensi y o he inpu pou ing cu en . They di ec
he low o s eel, c ea e an a ea o he s eel o low h ough he plug low and assis he
lo a ion o inclusions. Tu bulence inhibi o s inc ease and equalize he e en ion ime o
he ba h in he undish, inc ease he p opo ion o olume wi h plug low and elimina e
sho -ci cui low. The use o he u bulence inhibi o s can no only educe he amoun o
en ained slag, bu also educe he eoxida ion o s eel du ing ladle eplacemen [7–12].
Ba les undamen ally change he cha ac e is ics o he s eel low in he undish due
o hei holes. They di ec he low o he ba h owa ds he su ace o he s eel in he
undish, he eby c ea ing mo e sui able condi ions o some non-me allic inclusions o
loa , while he adso p ion p ocess allows o he s o adhe e o he pa i ion su ace. Ba les
c ea e he mal homogeniza ion in he undish. They inc ease he esis ance o he s eel
low, he eby inc easing he minimum e en ion ime. Ba les elimina e sho -ci cui low,
inc ease he p opo ion o s eel olume wi h plug low and educe dead olume [13–17].
Dams and wei s aim o ex end and equalize e en ion imes, and elimina e dead
olumes and sho -ci cui low in he undish. Dams and wei s can imp o e he empe a u e
and chemical homogenei y o he s eel in he undish. The use o a wei alone could cause
sho -ci cui low and he o ma ion o dead olumes. The e o e, i is ad isable o combine
i wi h a dam, which should elimina e he sho -ci cui low issue. Dams a e mainly used
o di ec he liquid low owa ds he me al–slag in e ace o inc ease he e en ion ime o
he liquid s eel in he undish [18–20].
The a gon s i ing elemen in he bo om o he undish a o ably a ec s he cha ac-
e is ics o he low. I has a posi i e e ec on he p opo ion o olume wi h plug low
and on he educ ion o he ansi ion zone. I suppo s he empe a u e and chemical
homogeniza ion o s eel in he undish. Blown a gon ac s as a sc een ha di ec s he s eel
low, he eby g ea ly p omo ing he loa a ion o inclusions and elimina ing sho -ci cui
low. I is impo an o ensu e he app op ia e posi ioning o he a gon s i ing elemen and
he app op ia e low o a gon [21,22].
The op imiza ion o he me allu gical p ocesses o s eel low in he undish is di icul
unde ope a ing condi ions. The e o e, in labo a o y condi ions, modelling is used, whe e
he o iginal p o o ype is eplaced by a physical o nume ical model. In physical modelling,
he eal sys em is eplaced by a angible physical model ha is as iden ical o he beha io
o he eal sys em as possible. The pu pose o physical modelling is he a ge ed u iliza ion
o he simila i ies be ween he p ocesses ha ake place wi hin he ac ual de ice and
i s model. In his me hod, bo h he p o o ype and he model ha e he same physical
s uc u e and pu pose, and hese simila i ies ensu e ha he esul s om he model can
be applied o he p o o ype. One o he ad an ages o physical modelling is he abili y o
isualize he p ocesses aking place in he eal sys em. The second me hod o modelling
is nume ical modelling, which is ad an ageous o simula ing me allu gical p ocesses
because, unlike physical modelling, ex eme bounda y condi ions can be simula ed. Unlike
physical modelling, nume ical modelling has a di e en physical s uc u e o he p o o ype.
The o iginal echnological p ocess is eplaced by a ma hema ical model ha desc ibes he
gi en e en h ough pa ial di e en ial equa ions and con inui y equa ions. This ype o
modelling is a use ul ool, as he esul s achie ed on he model can p edic eal sys em
beha io du ing a ious p ocess changes. Compa ing he esul s o physical and nume ical
modelling is an e ec i e and op imal a ian o model esea ch [2,23–28].
Me als 2023,13, 1821 3 o 18
The aim o he p esen a icle is o e alua e he me hodology o labo a o y expe imen s
and simula ions, namely, physical and nume al modelling, ega ding he cha ac e is ics o
s eel low in a undish.
2. Ma e ials and Me hods
2.1. Expe imen al Condi ions o Physical Modelling
Physical expe imen s in es iga ing he cha ac e is ics o s eel low in a undish we e
pe o med in he Labo a o y o Physical and Nume ical Modelling a he Depa men o Me -
allu gical Technologies, Facul y o Ma e ials Science and Technology, a he VSB—Technical
Uni e si y o Os a a.
The physical model, consis ing o a ladle sh oud, indi idual u bulence inhibi o s and
molds, was made o anspa en o ganic glass (plexiglass) on a geome ic scale o 1:4 o
he ope a ing undish. This physical model also included wo ladles o ensu e he low o
wa e in o he undish h ough he ladle sh oud. Each cas ing s and was equipped wi h
a s oppe od, which, i necessa y, could egula e he low om he undish o he molds.
The cas ing s ands we e equipped wi h subme ge en y nozzles a he same le el as he
s eel in he molds. Figu e 1shows he schema o he ladle, undish and molds. Figu e 2
shows a gene al o e iew o he expe imen al equipmen .
Me als 2023, 13, x FOR PEER REVIEW 3 o 18
eal sys em beha io du ing a ious p ocess changes. Compa ing he esul s o physical
and nume ical modelling is an effec i e and op imal a ian o model esea ch [2,23–28].
The aim o he p esen a icle is o e alua e he me hodology o labo a o y expe i-
men s and simula ions, namely, physical and nume al modelling, ega ding he cha ac-
e is ics o s eel low in a undish.
2. Ma e ials and Me hods
2.1. Expe imen al Condi ions o Physical Modelling
Physical expe imen s in es iga ing he cha ac e is ics o s eel low in a undish we e
pe o med in he Labo a o y o Physical and Nume ical Modelling a he Depa men o
Me allu gical Technologies, Facul y o Ma e ials Science and Technology, a he VSB—
Technical Uni e si y o Os a a.
The physical model, consis ing o a ladle sh oud, indi idual u bulence inhibi o s
and molds, was made o anspa en o ganic glass (plexiglass) on a geome ic scale o 1:4
o he ope a ing undish. This physical model also included wo ladles o ensu e he low
o wa e in o he undish h ough he ladle sh oud. Each cas ing s and was equipped wi h
a s oppe od, which, i necessa y, could egula e he low om he undish o he molds.
The cas ing s ands we e equipped wi h subme ge en y nozzles a he same le el as he
s eel in he molds. Figu e 1 shows he schema o he ladle, undish and molds. Figu e 2
shows a gene al o e iew o he expe imen al equipmen .
The cha ac e is ics o he s eel low in he undish we e simula ed in he physical
model using a model liquid (wa e ). The main ad an ages o using wa e a e p ima ily i s
low cos , good a ailabili y and i s physical p ope ies, which a e simila o liquid s eel.
The kinema ic iscosi ies o liquid s eel and wa e can be conside ed o be e y simila .
Table 1 shows he basic pa ame e s o he p o o ype and he model.
Figu e 1. Schema o he ladle, undish and molds.
Figu e 1. Schema o he ladle, undish and molds.
Me als 2023,13, 1821 4 o 18
Me als 2023, 13, x FOR PEER REVIEW 4 o 18
Figu e 2. Expe imen al de ice— he physical model o an asymme ic i e-s and undish.
Table 1. Basic pa ame e s o he p o o ype and he model.
Symbol Pa ame e P o o ype Model
V Volume o he ba h in he undish [m3] 4.64 37.12 × 10−3
m Weigh o he ba h in he undish [kg] 32,480 37.04
Tk A e age empe a u e o he ba h [K] 1520 + 273 20 + 273
ρk A e age densi y o he ba h [kg·m−3] 7000 998
νk Kinema ic iscosi y o he ba h [m2·s−1] 0.913 × 10−6 1.02 × 10−6
g G a i a ional accele a ion [m·s−2] 9.81 9.81
p P essu e abo e he ba h su ace [kg·m−1·s−2] 98.06 × 103 98.06 × 103
L1 In e nal leng h o he undish a he plane o he bo om [m] 6.387 1.597
L2 Dis ance be ween SEN [m] 1.5 0.375
D1 Inne diame e o he ladle sh oud [m] 0.085 0.021
H1 Ba h heigh app op ia e o weigh m [m] 0.925 0.231
H2 Dis ance o he ladle sh oud o i ice om he bo om o he TI [m] 0.525 0.131
Qm, k Mass low a e o he ba h o he undish [kg·min−1] 2779 12.39
Q , k Volume ic low a e o he ba h o he undish [l·min−1] 397 12.41
Q , k Volume ic low a e on he each SEN [l·min−1] 79.4 2.48
The physical model was equipped wi h a measu ing cen e , o measu e he conduc-
i i y and empe a u e o he model and i s egula o y sys em, as well as olume ic low
Figu e 2. Expe imen al de ice— he physical model o an asymme ic i e-s and undish.
The cha ac e is ics o he s eel low in he undish we e simula ed in he physical
model using a model liquid (wa e ). The main ad an ages o using wa e a e p ima ily i s
low cos , good a ailabili y and i s physical p ope ies, which a e simila o liquid s eel. The
kinema ic iscosi ies o liquid s eel and wa e can be conside ed o be e y simila . Table 1
shows he basic pa ame e s o he p o o ype and he model.
Me als 2023,13, 1821 5 o 18
Table 1. Basic pa ame e s o he p o o ype and he model.
Symbol Pa ame e P o o ype Model
VVolume o he ba h in he undish [m3]4.64 37.12 ×10−3
m Weigh o he ba h in he undish [kg] 32,480 37.04
TkA e age empe a u e o he ba h [K] 1520 + 273 20 + 273
ρkA e age densi y o he ba h [kg·m−3]7000 998
νk
Kinema ic iscosi y o he ba h [m
2·
s
−1
]
0.913 ×10−61.02 ×10−6
gG a i a ional accele a ion [m·s−2]9.81 9.81
p P essu e abo e he ba h su ace
[kg·m−1·s−2]98.06 ×10398.06 ×103
L1In e nal leng h o he undish a he
plane o he bo om [m] 6.387 1.597
L2Dis ance be ween SEN [m] 1.5 0.375
D1Inne diame e o he ladle sh oud [m] 0.085 0.021
H1
Ba h heigh app op ia e o weigh m [m]
0.925 0.231
H2
Dis ance o he ladle sh oud o i ice om
he bo om o he TI [m] 0.525 0.131
Qm, k
Mass low a e o he ba h o he undish
[kg·min−1]2779 12.39
Q , k Volume ic low a e o he ba h o he
undish [l·min−1]397 12.41
Q , k Volume ic low a e on he each SEN
[l·min−1]79.4 2.48
The physical model was equipped wi h a measu ing cen e , o measu e he conduc-
i i y and empe a u e o he model and i s egula o y sys em, as well as olume ic low
me e s, and conduc i i y and empe a u e p obes, which we e placed in he ladle sh oud
and in each subme ge en y nozzle. The conduc i i y p obes measu ed conduc i i y con-
inuously using wo opposi e pla inum elec odes, and he empe a u e p obes measu ed
in he ange 0–60 ◦C using a empe a u e Ni esis ance senso .
Labo a o y expe imen s we e conduc ed in acco dance wi h he heo y o simila i y
be ween he p o o ype and he model, based on he iden i y o F oude’s c i e ion. I was
necessa y o ensu e, in pa icula , geome ical simila i y be ween he p o o ype and i s
model, and he dynamic simila i y o luid low h ough each. Be o e each expe imen ,
he ele an in e nal a angemen o he undish was se up, i.e., inse ing he ele an
u bulence inhibi o in o he undish and se ing he posi ion and heigh o he ladle sh oud
ela i e o he u bulence inhibi o , un il a s eady s a e o cas ing was eached. Subsequen ly,
he expe imen i sel was s a ed and an impulse o 50 mL o aqueous KCl solu ion was
injec ed in o he ladle sh oud. The esponse o he impulse was moni o ed by he subme ge
en y nozzles, pa icula ly he change in conduc i i y and empe a u e. As he esul s o
each expe imen we e a ec ed by mino low luc ua ions in he undish, each expe imen
was epea ed h ee imes o ensu e he ep oducibili y o he esul s. I a disc epancy was
no ed be ween he esul s, u he expe imen s we e pe o med un il h ee ma ching esul s
we e a ained. Fo u he e alua ion, he mean o all h ee co ec measu emen s was
calcula ed.
The main aim o physical modelling was o achie e insigh in o he in luence o
ele an pa ame e s on he cha ac e is ics o s eel low in he undish, in pa icula :
•The shape o he u bulence inhibi o ;
•The posi ion o he ladle sh oud in ela ion o he u bulence inhibi o .
Th ee a ian s o u bulence inhibi o we e used o modelling, e e ed o as TI1 (i.e.,
u bulence inhibi o 1), TI2 and TI3 (see Figu e 3). TI1 was a basic squa e a ian , loca ed a
he back wall o he undish; TI2 was a ec angula a ian and ex ended o e he en i e
wid h o he undish; and TI3 was a a ian TI2 wi h a con ex bo om.

Me als 2023,13, 1821 6 o 18
Me als 2023, 13, x FOR PEER REVIEW 5 o 18
me e s, and conduc i i y and empe a u e p obes, which we e placed in he ladle sh oud
and in each subme ge en y nozzle. The conduc i i y p obes measu ed conduc i i y con-
inuously using wo opposi e pla inum elec odes, and he empe a u e p obes measu ed
in he ange 0–60 °C using a empe a u e Ni esis ance senso .
Labo a o y expe imen s we e conduc ed in acco dance wi h he heo y o simila i y
be ween he p o o ype and he model, based on he iden i y o F oude’s c i e ion. I was
necessa y o ensu e, in pa icula , geome ical simila i y be ween he p o o ype and i s
model, and he dynamic simila i y o luid low h ough each. Be o e each expe imen , he
ele an in e nal a angemen o he undish was se up, i.e., inse ing he ele an u bu-
lence inhibi o in o he undish and se ing he posi ion and heigh o he ladle sh oud
ela i e o he u bulence inhibi o , un il a s eady s a e o cas ing was eached. Subse-
quen ly, he expe imen i sel was s a ed and an impulse o 50 mL o aqueous KCl solu-
ion was injec ed in o he ladle sh oud. The esponse o he impulse was moni o ed by he
subme ge en y nozzles, pa icula ly he change in conduc i i y and empe a u e. As he
esul s o each expe imen we e affec ed by mino low luc ua ions in he undish, each
expe imen was epea ed h ee imes o ensu e he ep oducibili y o he esul s. I a dis-
c epancy was no ed be ween he esul s, u he expe imen s we e pe o med un il h ee
ma ching esul s we e a ained. Fo u he e alua ion, he mean o all h ee co ec meas-
u emen s was calcula ed.
The main aim o physical modelling was o achie e insigh in o he in luence o ele-
an pa ame e s on he cha ac e is ics o s eel low in he undish, in pa icula :
• The shape o he u bulence inhibi o ;
• The posi ion o he ladle sh oud in ela ion o he u bulence inhibi o .
Th ee a ian s o u bulence inhibi o we e used o modelling, e e ed o as TI1 (i.e.,
u bulence inhibi o 1), TI2 and TI3 (see Figu e 3). TI1 was a basic squa e a ian , loca ed
a he back wall o he undish; TI2 was a ec angula a ian and ex ended o e he en i e
wid h o he undish; and TI3 was a a ian TI2 wi h a con ex bo om.
(a) (b) (c)
Figu e 3. Va ian s o u bulence inhibi o s used o physical modelling: (a) TI1; (b) TI2; (c) TI3.
The indi idual u bulence inhibi o s we e loca ed in he undish be ween he hi d
and ou h cas ing s ands (see Figu e 4). The o he moni o ed pa ame e , based on
Figu e 3. Va ian s o u bulence inhibi o s used o physical modelling: (a) TI1; (b) TI2; (c) TI3.
The indi idual u bulence inhibi o s we e loca ed in he undish be ween he hi d and
ou h cas ing s ands (see Figu e 4). The o he moni o ed pa ame e , based on ope a ional
cases, was he posi ion o he ladle sh oud in ela ion o he u bulence inhibi o (see
Figu e 4).which we e based on ope a ional cases
Me als 2023, 13, x FOR PEER REVIEW 6 o 18
ope a ional cases, was he posi ion o he ladle sh oud in ela ion o he u bulence inhib-
i o (see Figu e 4).which we e based on ope a ional cases
The posi ions o he ladle sh oud in ela ion o he u bulence inhibi o in he model
we e as ollows:
• Rea posi ion 1 (R1)—iden ical o all a ian s;
• Rea posi ion 2 (R2)—iden ical o all a ian s;
• Cen e posi ion (C)— o TI1; Rea posi ion 3 (R3) o TI2 and TI3;
• F on posi ion 1 (F1)— o TI1; iden ical o Cen e posi ion (C) o he TI2 and TI3.
(a)
(b)
(c)
Figu e 4. In e nal a angemen o he undish model including he indi idual posi ions o he ladle
sh oud o he indi idual u bulence inhibi o s: (a) TI1-R1, R2, C, F1; (b) TI2-R1, R2, R3, C; (c) TI3-
R1, R2, R3, C.
2.2. Expe imen al Condi ions o Nume ical Modelling
As pa o nume ical modelling, pa allel nume ical simula ions we e pe o med in
he CFD (Compu a ional Fluid Dynamics) en i onmen o he ANSYS Fluen p og am,
e sion 19.2, which is pa o he ANSYS Wo kbench so wa e package. Nume ical simu-
la ions aimed o e i y he esul s o he physical modelling o selec ed a ian s. Va ian s
wi h all ypes o he u bulence inhibi o s, TI1, TI2 and TI3, we e chosen o e i ica ion.
The ladle sh oud was in i s cen al posi ion, i.e., always abo e he geome ic cen e o he
espec i e u bulence inhibi o (posi ion C). Figu e 5 shows he 3D geome y o he un-
dish using TI3. Fo he nume ical simula ions, a undish model was c ea ed a a scale o
1:1. The componen s o he undish model we e he app op ia e u bulence inhibi o , ladle
sh oud, s oppe ods and ou le nodes, including he subme ge en y nozzles.
Figu e 5. 3D geome y o he modelled a ea using TI3.
Figu e 4.
In e nal a angemen o he undish model including he indi idual posi ions o he ladle
sh oud o he indi idual u bulence inhibi o s: (
a
) TI1-R1, R2, C, F1; (
b
) TI2-R1, R2, R3, C; (
c
) TI3-R1,
R2, R3, C.
The posi ions o he ladle sh oud in ela ion o he u bulence inhibi o in he model
we e as ollows:
•Rea posi ion 1 (R1)—iden ical o all a ian s;
•Rea posi ion 2 (R2)—iden ical o all a ian s;
•Cen e posi ion (C)— o TI1; Rea posi ion 3 (R3) o TI2 and TI3;
•F on posi ion 1 (F1)— o TI1; iden ical o Cen e posi ion (C) o he TI2 and TI3.
Me als 2023,13, 1821 7 o 18
2.2. Expe imen al Condi ions o Nume ical Modelling
As pa o nume ical modelling, pa allel nume ical simula ions we e pe o med in
he CFD (Compu a ional Fluid Dynamics) en i onmen o he ANSYS Fluen p og am,
e sion 19.2, which is pa o he ANSYS Wo kbench so wa e package. Nume ical simula-
ions aimed o e i y he esul s o he physical modelling o selec ed a ian s. Va ian s
wi h all ypes o he u bulence inhibi o s, TI1, TI2 and TI3, we e chosen o e i ica ion.
The ladle sh oud was in i s cen al posi ion, i.e., always abo e he geome ic cen e o he
espec i e u bulence inhibi o (posi ion C). Figu e 5shows he 3D geome y o he undish
using TI3. Fo he nume ical simula ions, a undish model was c ea ed a a scale o 1:1. The
componen s o he undish model we e he app op ia e u bulence inhibi o , ladle sh oud,
s oppe ods and ou le nodes, including he subme ge en y nozzles.
Me als 2023, 13, x FOR PEER REVIEW 6 o 18
ope a ional cases, was he posi ion o he ladle sh oud in ela ion o he u bulence inhib-
i o (see Figu e 4).which we e based on ope a ional cases
The posi ions o he ladle sh oud in ela ion o he u bulence inhibi o in he model
we e as ollows:
• Rea posi ion 1 (R1)—iden ical o all a ian s;
• Rea posi ion 2 (R2)—iden ical o all a ian s;
• Cen e posi ion (C)— o TI1; Rea posi ion 3 (R3) o TI2 and TI3;
• F on posi ion 1 (F1)— o TI1; iden ical o Cen e posi ion (C) o he TI2 and TI3.
(a)
(b)
(c)
Figu e 4. In e nal a angemen o he undish model including he indi idual posi ions o he ladle
sh oud o he indi idual u bulence inhibi o s: (a) TI1-R1, R2, C, F1; (b) TI2-R1, R2, R3, C; (c) TI3-
R1, R2, R3, C.
2.2. Expe imen al Condi ions o Nume ical Modelling
As pa o nume ical modelling, pa allel nume ical simula ions we e pe o med in
he CFD (Compu a ional Fluid Dynamics) en i onmen o he ANSYS Fluen p og am,
e sion 19.2, which is pa o he ANSYS Wo kbench so wa e package. Nume ical simu-
la ions aimed o e i y he esul s o he physical modelling o selec ed a ian s. Va ian s
wi h all ypes o he u bulence inhibi o s, TI1, TI2 and TI3, we e chosen o e i ica ion.
The ladle sh oud was in i s cen al posi ion, i.e., always abo e he geome ic cen e o he
espec i e u bulence inhibi o (posi ion C). Figu e 5 shows he 3D geome y o he un-
dish using TI3. Fo he nume ical simula ions, a undish model was c ea ed a a scale o
1:1. The componen s o he undish model we e he app op ia e u bulence inhibi o , ladle
sh oud, s oppe ods and ou le nodes, including he subme ge en y nozzles.
Figu e 5. 3D geome y o he modelled a ea using TI3.
Figu e 5. 3D geome y o he modelled a ea using TI3.
This c ea ed and de ined geome y was subsequen ly impo ed in o he meshing
p ep ocesso en i onmen , whe e a egula s uc u ed mesh was gene a ed using he cu
cell me hod. A e c ea ing he geome y and gene a ing he compu a ional mesh, he
model was de ined in Fluen . The s anda d k-epsilon u bulence model was chosen o he
calcula ion o he s eady low ield, aking in o accoun he cha ac e is ics o he s eel low in
he undish. A s anda d wall unc ion was de ined on he walls o he undish. Subsequen ly,
he ma e ial p ope ies o he ollowing mediums we e de ined. To e i y he esul s om
he physical expe imen s, s eel was simula ed as a ma e ial in he nume ical simula ions.
The he mophysical p ope ies o s eel we e de ined as a unc ion o empe a u e o h ee
alues using a linea unc ion. The de ined he mophysical p ope ies o s eel a e shown in
he Table 2.
Table 2. The mophysical p ope ies o s eel o nume ical simula ions.
Tempe a u e
(K)
Densi y
(kg·m−3)
Speci ic Hea
(J·kg−1·K−1)
The mal Conduc i i y
(W·m−1·K−1)
Viscosi y
(kg·m−1·s−1)
1793 6970 821 35 0.0055
1773 6985 813 35 0.0057
1753 7001 805 35 0.0059
In he nex s ep, he bounda y condi ions we e se . The ope a ing condi ions o he
nume ical simula ions we e also se wi hin he bounda y condi ions. Values o hea loss
h ough he walls o he undish we e se based on he li e a u e [
29
,
30
]. The de ined
bounda y condi ions a e lis ed in he Table 3. Calcula ions o he cha ac e is ics o he low
in he undish basin ook place in SW ANSYS Fluen and we e sol ed by he nume ical
ini e olume me hod. In o de o achie e a con e gen calcula ion solu ion, which is he
goal in nume ical simula ions, i was necessa y o de e mine he sizes o he esiduals and
he numbe o i e a ions. Fo he ansien calcula ion, i was also necessa y o de e mine
he ime s ep size, he numbe o ime s eps and he maximum numbe o i e a ions pe
ime s ep.
Me als 2023,13, 1821 8 o 18
Table 3. Model se up bounda y condi ions o nume ical simula ions.
Pa ame e Value
Mass low a e o he s eel h ough he ladle sh oud [kg
·
s
−1
]
46.32
Cas ing empe a u e [K] 1773
Tu bulence in ensi y [%] 10
Hyd aulic diame e [m] 0.085
Hea lux o he ee su ace [W·m−2]15,000
Hea lux h ough he walls o he undish [W·m−2]2500
G a i y [m·s−2]−9.81
Ope a ing p essu e [Pa] 101,325
Ope a ing empe a u e [K] 1773
3. Resul s and Discussion
The e alua ion o he physical expe imen s was ca ied ou in h ee phases. In he
i s phase, e en ion ime esul s we e compa ed; in he second phase, he esul s we e
compa ed on he basis o he dis ibu ion o indi idual olumes in he undish; and in
he las e alua ion phase, isualiza ion pho os we e aken, wi h injec ed dye showing he
cha ac e is ics o he ba h low in he undish. As he esul s o each ial we e a ec ed
by mino low luc ua ions in he undish, each ial was epea ed h ee imes o ensu e
he ep oducibili y o he esul s. Fo u he assessmen , he mean o all h ee co ec
measu emen s was calcula ed.
The cha ac e is ics o s eel low in he undish we e s udied as pa o nume ical
simula ions. A basic calcula ion o s eady low was pe o med in o de o ob ain a s a iona y
low ield o he s eel in he undish. Wi h his s eady low ield, a ansien calcula ion o
RTD cu es was subsequen ly pe o med using he species model.
3.1. E alua ion Me hodology o he Physical Expe imen s
In he case o undish me allu gy, i is impo an o know he amoun o ime a ce ain
elemen o he mel spends in he undish. The aim is o achie e cha ac e is ics ha allow
each elemen o he mel o s ay in he undish o as long as possible. The pe iod o
ime ha a ce ain pa o he s eel s ays in he undish is e e ed o as he e en ion ime.
The dis ibu ion o e en ion imes is e e ed o as he RTD ( esidence ime dis ibu ion).
Re en ion imes we e de e mined by he conduc i i y me hod, which uses he di e ences
in he conduc i i y o liquids. An aqueous solu ion o KCl, which is cha ac e ized by
ionic conduc i i y, was used as an indica o medium in he indi idual expe imen s. The
conduc i i y was measu ed wi h a conduc i i y p obe a he inpu and ou pu poin s o he
undish. The calcula ed esul s o med RTD C-cu es [2].
The e alua ion o he expe imen s was based on he measu ed da a om he RTD
cu es. The minimum (c
min
) and maximum (c
max
) concen a ions we e de e mined om he
measu ed cou se o he concen a ion change. F om his, he dimensionless concen a ions
we e calcula ed [2].
−
c=(c−cmin)/(cmax −cmin)(1)
The heo e ical a e age e en ion ime was calcula ed using he liquid olume in he
undish and he olume ic liquid low a e h ough he undish [2].
−
τ=V/QV(2)
The heo e ical e en ion ime conside s a s eady s a e when he olume ic liquid low
a e inpu in o he undish is he same as he olume ic liquid low a e ou pu . Since he
s eel low in a mul i-s and asymme ic undish is associa ed wi h a dispe sion o e en ion
imes, i was necessa y o calcula e he eal e en ion ime in o de o e alua e he ba h low
in he undish [2].
−
τ eal =Zc·τ·dτ/Zc·dτ(3)
Me als 2023,13, 1821 9 o 18
Fu he mo e, he minimum e en ion ime (
τmin
) was de e mined om he measu ed
cou se o he concen a ion change, which was de ined as he ime o he i s appea ance
o he ma ke a he ou pu , and he maximum e en ion ime (
τmax
), which was he ime
i ook o each maximum concen a ion a he ou pu o he undish. The coe icien o
a ia ion ( ) was de e mined om he e en ion imes, which indica es he a iabili y o he
e en ion imes in he indi idual cas ing s ands. The coe icien o a ia ion is exp essed
as he quo ien o he s anda d de ia ion and he mean [2].
=s/−
x·100(4)
The undish was assessed as a whole and he non-uni o mi y o he low was e alua ed
acco ding o he alues o he indi idual minimum e en ion imes and he app op ia e
coe icien s o a ia ion. The highe he coe icien o a ia ion, he less equal he minimum
e en ion imes we e, esul ing in la ge di e ences. This condi ion is no op imal. The aim
is o achie e he highes possible minimum e en ion imes and, a he same ime, low
coe icien s o a ia ion. The ob ained e en ion imes can be used o calcula e pa ame e s
ha u he e ine he cha ac e is ics o he low in he undish. The o al olume o he
undish basin was sepa a ed in o h ee pa s: mixed olume (V
m
), olume wi h plug low
(V
p
) and dead olume (V
d
), all o which ha e di e en low cha ac e is ics [
2
]. In he mixed
olume a ea, he e was an in ensi e mixing o s eel, which was caused by he kine ic ene gy
o he inpu cas ing cu en . The p opo ion o he mixed olume in he undish was always
ensu ed. Only du ing he eplacemen o cas ing ladles du ing sequen ial cas ing, when
he supply o s eel o he undish is in e up ed, does he mixed olume d op o ze o. The
p opo ion o mixed olume in he undish was de e mined as an addi ion o he o al
olume [2].
(Vm/V) + (Vp/V) + (Vd/V) = 1 (5)
This mixed olume a ea was ollowed by he a ea wi h plug low, which was uni o m
wi h he ba h low, whe e no elemen o he mel o e akes ano he elemen . In his olume,
he s eel low al eady had a lamina cha ac e is ic, and he e o e mo e a o able condi ions
we e c ea ed o he loa ing o inclusions [2].
Vp/V=τmin/−
τ(6)
The hi d olume a ea o he undish was he so-called dead olume. In his a ea, he
s eel lows e y slowly and he mel has wice he a e age e en ion ime. The dead olume
educes he ac i e olume o he undish, hus sho ening he e en ion ime o he s eel
low. Local solidi ica ion o s eel can occu in his a ea [2].
(Vd/V)=1−(−
τ eal/−
τ(7)
3.2. E alua ion o he Flow Cha ac e is ics om he Physical Modelling
Since he inpu o he undish is posi ioned be ween cas ing s ands 3 and 4, i is
impo an ha he highes possible minimum e en ion imes o hese s ands a e achie ed,
in o de o elimina e sho -ci cui low. The measu ed cha ac e is ics RTD C-cu es show
he dependence o he impulse change o concen a ion on ime, he ladle sh oud and all
i e cas ing s ands o he selec ed a ian s, as can be seen in Figu e 6. All measu ed and
calcula ed low cha ac e is ics a e summa ized in he Table 4. Fo be e cla i y, he low
cha ac e is ics a e g aphically displayed in Figu es 7and 8.
Me als 2023,13, 1821 16 o 18
Table 5.
Minimum e en ion imes and hei coe icien s o a ia ion o a ian s in he nume -
ical simula ions.
Va ian CS1
τmin (s)
CS2
τmin (s)
CS3
τmin (s)
CS4
τmin (s)
CS5
τmin (s)
Ø
τmin (s)
(%)
TI1-C 135 79 45 44 85 78 48
TI2-C 120 54 44 45 59 64 49
TI3-C 155 60 49 46 55 73 63
3.5. Compa ison o he Resul s o he Physical Expe imen s and Nume ical Simula ions
Table 6shows he minimum e en ion imes om he esul s o he physical expe i-
men s o he selec ed a ian s, hei con e sion o he condi ions o he p o o ype ( ime
scale M
τ
= 0.5) and he minimum e en ion imes de e mined om he esul s o he nu-
me ical simula ions. These esul s also show he pe manen change in concen a ion o he
impulse and he ans o ma ion o he ob ained F-cu es in o C-cu es. When using TI2
and TI3, he con e ed minimum e en ion imes o he p o o ype we e always highe han
he minimum e en ion imes ound in he nume ical simula ions. When using TI1, he
con e ed minimum e en ion imes o he p o o ype we e also highe , wi h he excep ion
o cas ing s ands closes o he ladle sh oud, CS3 and CS4, whe e he highe minimum
e en ion imes we e equal o hose om nume ical simula ions.
Table 6.
Compa ison o minimum e en ion imes om he physical expe imen s and nume -
ical simula ions.
Va ian Condi ions CS1
τmin (s)
CS2
τmin (s)
CS3
τmin (s)
CS4
τmin (s)
CS5
τmin (s)
Ø
τmin (s)
TI1-C
Model 87 48 19 19 47 44
P o o ype 174 96 38 38 94 88
NS 135 79 45 44 85 78
TI2-C
Model 108 52 23 23 48 51
P o o ype 216 104 46 46 96 102
NS 120 54 44 45 59 64
TI3-C
Model 93 43 25 25 57 49
P o o ype 186 86 50 50 114 98
NS 155 60 49 46 55 73
De ia ions in he alues o he minimum e en ion imes in he physical and nume ical
model can be explained by di e en in luences, such as using wo di e en me hods o
de e mine e en ion imes. This is he eason o implemen ing an ins an aneous impulse
(Di ac impulse—C-cu e) in he physical expe imen s, in con as o pe manen change o
ma ke concen a ion (Hea iside uni s ep—F-cu e) in he nume ical simula ions. In he
nume ical simula ions, he selec ed u bulence model (e.g., k-epsilon, k-omega), in some
cases, a ec ed he esul ing e en ion ime alues.
Nume ical modelling con i med he esul s om he physical modelling, and wi h
ega d o de e mining he minimum e en ion imes on indi idual cas ing s ands, he
e i ica ion o he esul s can be conside ed su icien ly de e mining. Wi hin all modelled
a ian s, he minimum e en ion imes we e de ec ed i s on CS3 and CS4, hen on CS2
and CS5, and las ly on he u hes , CS1.
4. Conclusions
In he case o his asymme ic undish, i is impo an o inc ease he alues o he
minimum e en ion imes o cas ing s ands 2, 3, 4 and 5, and, a he same ime, educe
he minimum e en ion ime o cas ing s and 1. This was pa ially achie ed in ega d
o he he coe icien s o a ia ion by using TI3. The V
p
/V
d
a io has p o en o be a

Me als 2023,13, 1821 17 o 18
de e mining ac o o he cha ac e is ics o he low o he ba h in he undish. In ega d o
he emo al o non-me allic inclusions and o he possible impu i ies, i is ad an ageous
o he alue o he a io o be as la ge as possible. In acco dance wi h he li e a u e,
he shape o he u bulence inhibi o and he posi ion o he ladle sh oud in ela ion o
he u bulence inhibi o appea ed o be c ucial pa ame e s in luencing he cha ac e is ics
o he s eel low in he undish. I is impo an ha he en i e olume o he low alls
inside he u bulence inhibi o and o a oid posi ions whe e he low alls mainly on he
on edge o he u bulence inhibi o . As pa o he model esea ch solu ion, geome ic
modi ica ions o exis ing u bulence inhibi o s and o he echnological pa ame e s used
in he ope a ing condi ions we e p oposed and e i ied, in o de o op imize s eel low in
he undish. The op imiza ion o he s eel low in he undish using TI3 has been p o en
h ough physical and nume ical modelling. The compa ison o he esul s o physical and
nume ical modelling is an e ec i e and op imal a ian o model esea ch, p o iding a
mode n app oach o sol ing p ac ical indus ial p oblems.
Au ho Con ibu ions:
Concep ualiza ion and me hodology, cha ac e iza ion, isualiza ion and
w i ing—o iginal d a , J.W.; me hodology, cha ac e iza ion and w i ing— e iew and edi ing, M.T.;
w i ing— e iew and edi ing, M.V., M.M., J.C. (Jiˇ íCupekand), T.H., J.C. (Jiˇ íCibulka) and J.R.;
me hodology, cha ac e iza ion and w i ing— e iew and edi ing, K.M. All au ho s ha e ead and
ag eed o he published e sion o he manusc ip .
Funding:
This s udy was conduc ed wi h he suppo o a s uden g an compe i ion un by he
VSB—Technical Uni e si y o Os a a, p ojec numbe SP2023/034—Resea ch and De elopmen o
Composi e Mul i unc ional Ma e ials o Sus ainable P og ess.
Da a A ailabili y S a emen : No applicable.
Acknowledgmen s:
This esea ch was unde aken hanks o p ojec No. CZ.02.1.01/0.0/0.0/17_049/
0008399 o he EU, and CR inancial unds p o ided by he Ope a ional P og amme Resea ch,
De elopmen and Educa ion, Call 02_17_049 Long-Te m In e sec o al Coope a ion o ITI, Managing
Au ho i y: Czech Republic—Minis y o Educa ion.
Con lic s o In e es : Ma ké a Tkadleˇcko á; Tomáš Huczala and Jiˇ íCibulka we e employed by he
company Tˇ
RINECKÉŽELEZÁRNY, a.s. The au ho s decla e no con lic o in e es . The unde s had
no ole in he design o his s udy; in he collec ion, analyses o in e p e a ion o da a; in he w i ing
o he manusc ip ; o in he decision o publish he esul s.
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