metals

Article
Numerical Modeling of Open-Eye Formation and
Mixing Time in Argon Stirred Industrial Ladle
Eshwar Kumar Ramasetti 1, *, Ville-Valtteri Visuri 1 , Petri Sulasalmi 1 , Timo Fabritius 1 ,
Tommi Saatio 2 , Mingming Li 3 and Lei Shao 3
1 Process Metallurgy Research Unit, University of Oulu, PO Box 4300, 90014 Oulu, Finland
2 Outokumpu Stainless Oy, Terästie, 95490 Tornio, Finland
3 School of Metallurgy, Northeastern University, Heping District, Shenyang 11004, China
* Correspondence: eshwar.ramasetti@oulu.fi




Received: 28 May 2019; Accepted: 24 July 2019; Published: 26 July 2019


Abstract: In secondary metallurgy, argon gas stirring and alloying of elements are very important in
determining the quality of steel. Argon gas is injected through the nozzle located at the bottom of the
ladle into the molten steel bath; this gas breaks up into gas bubbles, rising upwards and breaking
the slag layer at high gas flow rates, creating an open-eye. Alloy elements are added to the molten
steel through the open-eye to attain the desired steel composition. In this work, experiments were
conducted to investigate the effect of argon gas flow rate on the open-eye size and mixing time.
An Eulerian volume of fluid (VOF) approach was employed to simulate the argon/steel/slag interface
in the ladle, while a species transport model was used to calculate the mixing time of the nickel
alloy. The simulation results showed that the time-averaged value of the open-eye area changed from
0.66 to 2.36 m2 when the flow rate of argon was varied from 100 to 500 NL/min. The mixing time
(95% criterion) of tracer addition into the metal bath decreased from 139 s to 96 s, when the argon
flow rate was increased from 100 to 500 NL/min. The model validation was verified by comparing
with measured experimental results.

Keywords: ladle metallurgy; CFD; open-eye; mixing time

1. Introduction
In the steel refining process, argon stirring is extensively employed to boost slag-steel reactions
and to homogenize the chemical composition of alloy elements and their temperature. The behavior of
the slag layer and mixing phenomena in the ladle are highly influenced by the argon stirring rates, the
number of nozzles, and their configurations. Over the years, many physical and computational fluid
dynamic (CFD) simulations [1–22] have been performed to investigate the effect of gas flow rate, slag
layer thickness, and number of nozzles on open-eye formation and mixing time in water models and
industrial-scale ladles.
Cao et al. [4] studied the fluid flow, mass transfer, and open-eye behavior in an industrial scale ladle
using both volume of fluid (VOF) and Euler-Lagrange modeling approaches. Cao et al. [5] extended
the work to investigate the mixing phenomenon using a species transport model. Valentin et al. [7]
studied the influence of stirring rate on the formation of the open-eye and mixing phenomena in a
170-t industrial ladle. Cloete et al. [8] investigated the fluid flow and mixing phenomena in full-scale
gas-stirred ladles by employing the VOF model for tracking the free surface of the melt. Cloete et al. [9]
extended the work of Cloete et al. [8] by studying the influence of various design variables on
mixing efficiency. Li et al. [10–12] investigated the fluid flow, bubble diameter, turbulent dissipation
rate, bubble movement, and open-eye fluctuation in a water model ladle through experiments and
numerical simulations.

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Metals 2019, 9, 829 2 of 12

Gonzalez et al. [13] investigated the fluid flow and open-eye behavior for a ladle under
non-isothermal conditions. Amaro-Villeda et al. [14] studied the effect of slag properties (thickness
and viscosity) on mixing time, open-eye, and energy dissipation in a 1:6 scale of a 140 tonne industrial
ladle. Zhu et al. [15] investigated the fluid flow and mixing phenomena in argon-stirred ladles with six
types of tuyere arrangement. The results concluded that mixing time is greatly influenced by a tracer
adding position, and mixing time decreases with increasing gas flow rate, but the effect is not great.
Lou et al. [16] performed numerical simulations to study the effect of different numbers and positions
of tuyeres on the inclusion behavior and mixing phenomena in gas-stirred ladles. Liu et al. [18] and
Li et al. [19] studied the effect of gas flow rate and slag layer thickness on open-eye formation and
mixing time in a water model ladle through physical and numerical modeling. Liu et al. [20] performed
simulations using an Large Eddy Simulation (LES) approach to study the effect of gas flow rate on
open-eye formation and slag entrapment.
Haiyan et al. [21] and Madan et al. [22] studied the effect of gas flow rate on the mixing phenomenon
in a bottom-stirring ladle with dual plugs. Wu et al. [23] and Thunman et al. [24] studied the effect of
gas flow rate and slag layer thickness on the open-eye formation and slag entrainment in water model
ladles. Li et al. [25] modeled the three-phase flows and behavior of the open-eye in an industrial-scale
ladle using the volume of fluid (VOF) approach. Liu et al. [26] investigated the effect of gas flow rate
and slag layer thickness on open-eye formation and mixing phenomena in an industrial-scale ladle.
Singh et al. [27] validated the simulation results of Liu et al. [26] and extended the model to investigate
the desulphurization behavior. Ramasetti et al. [28,29] investigated the effect of gas flow rate and slag
layer properties on open-eye formation in a water model ladle.
During the past years, studies were concentrated more on the modeling of water model ladles,
while studies related to industrial scale ladle modeling were limited. In the present work, a mathematical
model was developed to describe the three-phase flow in an industrial-scale ladle. The Eulerian VOF
model was used to track the slag/steel/gas interface behavior, and a species transport model was used
to calculate the mixing time. The industrial measurements for studying the effect of argon flow rate on
open-eye formation and mixing time were performed at Outokumpu Stainless Oy in Tornio, Finland.
The simulation results of open-eye area and mixing time were in good agreement with industrial data.

2. Materials and Methods

2.1. Model Description

A set of Navier-Stokes equations were used to solve the fluid dynamics in the system.
Continuity equation:
∂ρ ∂(ρui )
+ = 0, (1)
∂t ∂xi
Momentum equation:
 
∂(ρui ) ∂ ρui u j ∂p ∂ ∂ui ∂u j
" !#
+ =− + µe + + ρgi , (2)
∂t ∂t ∂xi ∂xi ∂x j ∂xi

where ρ is the fluid density; u represents the velocity; t is the time; p and g represent the pressure and
gravitational acceleration, respectively; and µe is the effective turbulent viscosity.
The volume of fluid (VOF) model tracks two or more phases by solving a single set of momentum
equations. In this work, it was used to track the liquid-steel/slag/argon-gas interface behavior. The
finite volume equation of the VOF model can be written in the following form:
 
n 
1  ∂    * 
X . . 

 αq ρq + ∇· αq ρq u q = Sαq + mpq − mqp , (3)

ρq  ∂t 
p=1
Metals 2019, 9, 829 3 of 12

. .
where mpq , mqp represent the mass transfer from phase p to q and phase q to p in unit time and volume,
respectively; αq is the volume fraction of phase q; ρq is the density of phase q; and Sαq is the source term
taken as 0 in Fluent software. The volume fraction of main phase is not calculated in Fluent software,
while it can be acquired by Equation (4). When the volume fractions are summed, the following
equation is satisfied:
Xn
αq = 1 (4)
q=1

The standard k − ε model is used to model turbulence, which solves two equations for the transport
of turbulent kinetic energy and its dissipation rate to obtain the effective viscosity field,
Turbulent kinetic energy, k:

∂ ∂ ∂ µt  ∂k
" #
(ρk) + (∂kui ) = µ+ + Pk − ρε, (5)
∂t ∂xi ∂x j σt ∂xi

The rate of dissipation of turbulent kinetic energy, ε:

∂(ρε) ∂(ρεui ) ∂ µt  ∂ε ε
" #
+ = µ+ + (C1 Pk − C2 ρε), (6)
∂t ∂xi ∂x j σε ∂x j k

where Pk is the generation term of turbulence kinetic energy due to mean velocity gradients, where k is
the turbulent kinetic energy, ε is the turbulent dissipation rate, and xi represents the spatial coordinates
for different directions. Pk is the turbulent kinetic energy source term caused by the mean velocity
gradient, and Pb is the turbulent kinetic source term caused by buoyancy. These terms are calculated
by Equations (7) and (8) respectively.

∂u j ∂ui ∂u j
!
Pk = µt + , (7)
∂xi ∂x j ∂xi

µt ∂ρ
!
Pb = −gi (8)
ρPri ∂xi
k2
µt = µ + ρcµ (9)
ε
The turbulent viscosity is calculated by Equation (9) using the equations k and ε from Equations (5)
and (6), respectively.
To calculate the mixing process in the ladle, the species transport model was solved throughout
the computational domain.

∂(ρc) µt
" ! #
+ ∇·(ρuc) = ∇· ρ D + ∇c (10)
∂t ρSct

where D is the mass diffusion coefficient and Sct is the turbulent Schmidt number with a value of 0.7
µ
(Sct = ρDt t where Dt is the turbulent diffusivity).

2.2. Experimental Details

The experiments were performed in an industrial ladle of 150-ton capacity at Outokumpu Stainless
Oy, Tornio plant in Finland. Argon gas was injected into the steel bath through a nozzle located at
the bottom of ladle. The measurements were conducted with gas flow rates varying from 100 to
500 NL/min. The thermo-physical and operating parameters are shown in Table 1.
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Table 1. Parameters for experiments and simulations.

Physical
TableProperties at 1812
1. Parameters K
for experiments Value
and simulations.Unit
Density of liquid steel [30] 6913 kg/m3
Physical Properties at 1812 K Value Unit
Viscosity of liquid steel [30] 0.005281 Pa s
Density ofDensity
liquid steel [30] 6913 kg/m 3
of slag 2746 kg/m 3
Viscosity of liquid steel [30] 0.005281 Pa s
Viscosity of slag 0.081 Pa s 3
Density of slag 2746 kg/m
Densityofofslag
Viscosity argon gas 0.8739
0.081 kg/m 3
Pa s
Viscosity
Density of argon
of argon gas gas 2.2616
0.8739× 10 −5 Pa s 3
kg/m
Temperature
Viscosity of bath
of argon gas × 10−5
2.26161812 KPa s
Temperature
Flow rate ofof bath
argon gas 100, 1812
300 and 500 NL/min K
Flow rate of argon gas 100, 300 and 500 NL/min
Slag layer height 35 cm
Slag layer height 35 cm

2.3. Numerical Details

2.3. Numerical Details
The computational domain and mesh system for the ladle configuration studied is shown in
FigureThe
1. computational
The number of cells domain
wasand mesh system
approximately for the A
1 million. ladle
meshconfiguration
size of 8 mmstudied
was setis shown in
throughout
Figure 1. The number of cells was approximately 1 million. A mesh size of 8
the domain, and a maximum mesh size of 4 mm was set for the inlet and slag layer. ANSYS Fluent mm was set throughout
the domain,
software wasand
useda to
maximum
perform themesh size of 4 mm
multi-phase flow was set for theAt
simulations. inlet
theand
inletslag layer.
of the ANSYS
ladle, Fluent
velocity inlet
software was used to perform the multi-phase flow simulations. At the inlet
boundary condition, pressure outlet condition at the ladle top surface, and no-slip boundary of the ladle, velocity inlet
boundary condition, pressure outlet condition at the ladle top surface, and no-slip
condition was used at the ladle walls. The finite volume technique was used for the discretization ofboundary condition
was used at theequations
conservation ladle walls. andTheSIMPLE
finite volume
scheme technique
was used was for
usedthe
forpressure-velocity
the discretization of conservation
coupling. The
equations and SIMPLE scheme was used for the pressure-velocity coupling.
volume of fluid (VOF) model was used to track the gas/steel/slag behavior and the species transport The volume of fluid
(VOF)
model model
was usedwasto
used to track
calculate thethe gas/steel/slag
mixing behavior
time of the nickeland theThe
alloy. species transport
variable time model
step ∆𝑡waswasused
usedto
calculate the mixing time of the nickel alloy. The variable time step ∆t was used by
by setting the Courant number to 2 and the convergence criterion was set to 10 for the residuals of−5 setting the Courant
number
dependent and the convergence criterion was set to 10−5 for the residuals of dependent variables.
to 2variables.

Figure 1. Computational domain and mesh system of the industrial scale ladle.

3. Results and
3. Results and Discussion
Discussion

3.1. Effect of Gas Flow Rate on Open-Eye Formation

3.1. Effect of Gas Flow Rate on Open-Eye Formation
Figures 2 and 3 show the experimental and simulation results of the effect of argon flow rate on
Figures 2 and 3 show the experimental and simulation results of the effect of argon flow rate on
the open-eye area. The position and size of the open-eye were not constant throughout the process, the
the open-eye area. The position and size of the open-eye were not constant throughout the process,
Metals 2019,9,9,829
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the value of the open-eye area was averaged for a period of 60 s. The fluctuation of the open-eye area
value
the of the open-eye
value area waswas averaged for for a period of of
60 60
s. s.
The
Thefluctuation ofofthe open-eye area
with timeof forthe open-eye
flow rates ofarea100, 300,averaged
and 500 NL/min a period
for experimental fluctuation
and simulation the open-eye
results is shown area
with
with time
time for
for flow
flow rates
rates of
of100,
100, 300,
300,and
and 500
500 NL/min
NL/min for
for experimental
experimental and
and simulation
simulation results
results is
isshown
shown
in Figure 4. At the initial stage, the open-eye area expands rapidly, reaching peak values depending
in
inFigure 4.4.At the initial stage, the
the open-eye area
areaexpands rapidly, reaching peak values depending
onFigure
the flow At rate, theand
initial stage,
starts open-eye
to stabilize and fluctuateexpands
around rapidly, reaching
a constant level.peak
The peakvalues depending
values of the
on
on the
the flow
flow rate,
rate, and
and starts
starts to
to stabilize
stabilize and
and fluctuate
fluctuate around
around aaconstant
constant level.
level. The
The peak
peak values
values of
of the
the
open-eye area for flow rates of 100 NL/min, 300 NL/min, and 500 NL/min were 1.16 m 2 , 2.09 m
2 ,2 2.09 2 ,2 ,and
2 and
open-eye
open-eye area
area for
forflow
flow rates
rates ofof100
100 NL/min,
NL/min, 300
300 NL/min,
NL/min, and
and 500
500 NL/min
NL/min were
were 1.16
1.16 m m , 2.09m m , and
3.17 m2 2, respectively. The respective time-averaged values for the constant level of the open-eye area
3.17
3.17 m 2,, respectively. The respective time-averaged values for the
theconstant
constantlevel of thetheopen-eye area
werem0.66 respectively.
m 2 1.37 mThe
2 2, ,1.37 22, ,and
2 and respective
2.36 m2 2. time-averaged
The predicted values
trend offorenlargement level
of theofopen-eye open-eye
area with area
were
were 0.66 m m 2.36 m . The predicted trend of enlargement of the open-eye area with
argon0.66flowmrate , 1.37
wasmin, goodand 2.36 m . Thewithpredicted trend of enlargement ofetthe
al.open-eye area with
2
agreement the measurements of Valentin [7].
argon
argonflow
flowrateratewas wasiningoodgoodagreement
agreementwith withthe
themeasurements
measurementsofofValentin
Valentinetetal.al.[7].
[7].

(a) (b) (c)

(a) (b) (c)
Figure 2. Open-eye size in the ladle from experimental results (Z = 3.37 m): (a) Q = 100 NL/min, (b) Q
Figure
Figure 2.2. Open-eye
Open-eye
= 300 NL/min, size
Qin
size
and (c) inthe
theladle
= 500 ladlefrom
NL/min. fromexperimental
experimentalresults (Z(Z
results = 3.37
= 3.37 m):m): Q =NL/min,
(a) Q(a)= 100 (b) Q
100 NL/min,
(b) Q =NL/min,
= 300 and (c)
300 NL/min, andQ (c) Q =NL/min.
= 500 500 NL/min.

(a) (b) (c)

(a) (b) (c)
Figure 3. Open-eye size in the ladle from simulation results (Z = 3.37 m): (a) Q = 100 NL/min,
Figure
(b) 3. Open-eye
Q = 300 size (c)
NL/min, and in the
Q =ladle from simulation results (Z = 3.37 m): (a) Q = 100 NL/min, (b) Q =
500 NL/min.
Figure 3. Open-eye
300 NL/min, and (c)size
Q =in500the ladle from simulation results (Z = 3.37 m): (a) Q = 100 NL/min, (b) Q =
NL/min.
300 NL/min, and (c) Q = 500 NL/min.
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Figure 4. Comparison between experimental and simulation results of time-averaged open-eye area.
Figure
Figure 4. Comparison between
4. Comparison between experimental
experimental and
and simulation
simulation results
results of
of time-averaged
time-averaged open-eye
open-eye area.
area.
3.2. Flow
3.2. Flow Field
Field Distribution
Distribution
3.2. Flow Field Distribution
Figures 5–7
Figures 5 to depict
7 depict thethe velocity,
velocity, turbulentkinetic
turbulent kineticenergy,
energy,and anddissipation
dissipationraterateprofiles
profileson on the
the
Figures
horizontalplane 5 to 7
planethat depict
thatpass the
passthroughvelocity,
through turbulent kinetic energy, and dissipation rate profiles on the
horizontal thethe position
position of the
of the plumes
plumes at heights
at heights 1.5 m1.5and
m and
3.0 m3.0 m from
from the
the bath
horizontal
bath bottom. plane
Thethat
flowpass through
velocity thethe position ofisthe plumes at heights 1.5 with
m and 3.0 m in from the
bottom. The flow velocity in theinplume plume
zoneszones very
is very high highincreases
and and increases
with increase increase
in the gas theflow
gas
bath
flow bottom.
rates, The flowsmall
whereas velocity
flowinvelocities
the plumeare zones is very in
observed high
the and
zoneincreases
around with increase
theTheplumes. in theflow
The gas
rates, whereas small flow velocities are observed in the zone around the plumes. flow velocities
flow rates,increase
velocities whereas small flow velocities are observed in the the
zone around theand plumes.
0.5attoa The flow
increase from 1.2 tofrom 1.2at
2.5 m/s toa2.5 m/s at
height of a1.0
height
m aboveof 1.0
thembath
above bottom, bathandbottom,
0.5 to 1.4 m/s 1.4 m/s
height at
of
velocities
a height ofincrease
3.0 m from
above 1.2
the to 2.5
bath m/s
bottom at a height
when of
the 1.0
gas m above
flow rate the
is bath
increasedbottom,
from and
100 0.5
to to
500 1.4 m/s
NL/min. at
3.0 m above the bath bottom when the gas flow rate is increased from 100 to 500 NL/min. The flow
aThe
height
flowoftend
3.0 m above
velocities tendthe bath
to as bottom
decrease when
asreaches
the flowthereaches
gas flow rate
the issurface
topof increased from
of bath.
the 100 bath.
ladle to 500 NL/min.
velocities to decrease the flow the top surface the ladle The sameThe same
trend is
The flow velocities
trend is followed tend to decrease
for the turbulence as the flow
kineticand reaches
energy the top
and dissipation surface of the
profiles, ladle bath. The same
followed for the turbulence kinetic energy dissipation profiles, which canwhich
be seen caninbe seen in
Figures 6
trend
Figures is 6followed
and 7. forpredicted
The the turbulence
velocity kinetic
fields energy
follow andsame
the dissipation
trends profiles,
of radial which canwhich
velocities, be seenwere,in
and 7. The predicted velocity fields follow the same trends of radial velocities, which were, measured
Figures
measured 6 and 7. The predicted
physically velocity fields follow the same trends of radial velocities, which were,
Xie et al. [31,32].
physically Xie et al. [31,32].
measured physically Xie et al. [31,32].

(a) (b)
(a) (b)
Figure 5. Velocity distribution
Figure 5. distribution profiles
profilesfor
fordifferent
differentgas
gasflow
flowrates
ratesfrom
fromthe
the ladle
ladle bottom:
bottom: (a)(a)
1.51.5 m
m (b)
Figure
(b)
3.03.0 5.
m. m. Velocity distribution profiles for different gas flow rates from the ladle bottom: (a) 1.5 m (b)
3.0 m.
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(a) (b)
(a) (b)
Figure 6. Turbulent kinetic energy profiles for different gas flow rates from the ladle bottom: (a) 1.5
Figure6.6. Turbulent
Figure Turbulentkinetic
kineticenergy
energyprofiles
profilesfor
fordifferent
differentgas flow
gas rates
flow from
rates thethe
from ladle bottom:
ladle (a) (a)
bottom: 1.5 1.5
m
m (b) 3.0 m.
(b) 3.0 3.0
m (b) m. m.

(a) (b)
(a) (b)
Figure7.7. Turbulent
Figure Turbulentdissipation
dissipationrate
rateprofiles
profilesfor
fordifferent gas
different flow
gas rates
flow from
rates thethe
from ladle bottom:
ladle (a) (a)
bottom: 1.5 1.5
m
Figure 7. Turbulent dissipation rate profiles for different gas flow rates from the ladle bottom: (a) 1.5
(b) 3.0 m.
m (b) 3.0 m.
m (b) 3.0 m.
3.3. Mixing Behavior
3.3. Mixing Behavior
3.3. Mixing Behavior
In this study, the mixing time is defined as the time to attain a 95% degree of homogenization
In this study, the mixing time is defined as the time to attain a 95% degree of homogenization in
in theInmolten
this study,
steel.the mixing
The time is
locations of defined
points toas calculate
the time to attain
the a 95%
mixing timedegree
in theofladle
homogenization
are shown in in
the molten steel. The locations of points to calculate the mixing time in the ladle are shown in Figure
the molten
Figure 8. In steel.
orderThe locationsthe
to simulate of addition
points toof
calculate the mixing
nickel alloy, timewas
the tracer in the ladle are
released shown
in the forminofFigure
circle
8. In order to simulate the addition of nickel alloy, the tracer was released in the form of circle with
8. In radius
with order to
of simulate the addition
0.196 m, located of nickel
just above alloy, of
the center thethe
tracer
plugwas released
where in the
the plume form the
breaks of circle with
slag layer
radius of 0.196 m, located just above the center of the plug where the plume breaks the slag layer and
radius
and of 0.196
creates the m, located The
open-eye. just above the centerand
shell formation of the plug where
subsequent the plume
melting of the breaks
alloy the
wasslag layer and
neglected in
creates the open-eye. The shell formation and subsequent melting of the alloy was neglected in the
creates
the the open-eye. The shell formation and subsequent melting of the alloy was neglected in the
simulations.
simulations.
simulations.
Figure 9 displays the concentration profiles of the tracer inside the ladle after an addition time of
0 s, 5 s, 10 s, 20 s, 40 s, or 60 s for different argon flow rates. At 0 s, the tracer is injected through the
generated open-eye which is located at the top-right side of the ladle furnace (see Figure 9a). As seen
in Figure 9b, the tracer started to dissolve into the molten steel at 5 s, but moved to the ladle surface
due to the direction of the high gas flow coming through the nozzle located at the bottom of the ladle.
The dissolution of tracer was higher at a gas flow rate of 500 NL/min, when compared to a low gas
flow rate of 200 NL/min. The same trend of tracer distribution in the molten steel was followed at 10 s
and 20 s (see Figure 9c,d). By 40 s, the tracer had spread out almost throughout the whole ladle at
a gas flow rate of 500 NL/min, while for a gas flow rate of 100 NL/min, it was still dissolving, with
approximately 65% dissolved. The tracer had almost spread out at 60 s for all gas flow rates as seen in
Figure 9f, and the tracer was completely spread out when the ladle furnace was operated at a high gas
flow rate of 500 NL/min.
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Figure 8.
Figure 8. Monitoring
Monitoring points inside
points the the
inside ladle.
ladle.
Figure 8. Monitoring points inside the ladle.

Figure 9. Cont.
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Figure 9. Tracer concentration profiles for different gas flow rates of 100 (left), 300 (middle), and 500
(right) NL/min with different time intervals: (a) 0 s (b) 5 s (c) 10 s (d) 20 s (e) 40 s (f) 60 s.
 flow rate of 200 NL/min. The same trend of tracer distribution in the molten steel was followed at 10
s and 20 s (see Figure 9c,d ). By 40 s, the tracer had spread out almost throughout the whole
Figure 9c; Figure 9d

ladle at a gas flow rate of 500 NL/min, while for a gas flow rate of 100 NL/min, it was still dissolving,
with approximately 65% dissolved. The tracer had almost spread out at 60 s for all gas flow rates as
seen in Figure 9f, and the tracer was completely spread out when the ladle furnace was operated at a
Metals 2019, 9, 829 10 of 12
high gas flow rate of 500 NL/min.
Figure 10a–c depict typical tracer response curves of four monitoring points and
Figure 10a; Figure 10b; Figure 10c;

the procedure
Figure 10a–c adopted
depictto evaluate
typical tracertheresponse
95% mixing time
curves of for
fourdifferent argon
monitoring flow and
points rates.
theThe average
procedure
mixing time
adopted value atthe
to evaluate Point
95%1mixing
from industrial measurements
time for different argon flow andrates.
numerical simulations
The average mixing aretime
shown
valuein
Figure 10d. During the experiments, steel samples of concentration were
at Point 1 from industrial measurements and numerical simulations are shown in Figure 10d. During taken from the ladle at
certain
the intervals steel
experiments, of time and atofa concentration
samples certain location. wereThetaken
nickel alloying
from to steel
the ladle was done
at certain at sampling
intervals of time
point
and at a0 certain
to reach case-specific
location. nickel
The nickel aim-content.
alloying to steel wasSteel
done samples were point
at sampling then 0used to evaluate
to reach the
case-specific
required
nickel mixing time
aim-content. for samples
Steel obtainingwereaim-nickel
then usedcontent, starting
to evaluate thefrom pointmixing
required of alloying. It can
time for be seen
obtaining
that with an
aim-nickel increase
content, in the argon
starting gas flow
from point rate, the Itmixing
of alloying. can betime seendecreased,
that with anand the same
increase trend
in the was
argon
followed in both experiments and simulations. The present results of mixing
gas flow rate, the mixing time decreased, and the same trend was followed in both experiments and times in the industrial
scale ladle are
simulations. Theinpresent
good agreement with the
results of mixing timessimulation results scale
in the industrial of Liuladle
et al.
are[26].
in goodThe agreement
numerical
simulation
with values for
the simulation mixing
results time
of Liu agree
et al. [26]. fairly well withsimulation
The numerical the industrial
valuesmeasurements,
for mixing timewith agreea
maximum error of 16.3%. The possible source for the error between the experiments
fairly well with the industrial measurements, with a maximum error of 16.3%. The possible source for and simulations
is the
the tracer
error addition
between the method and neglecting
experiments of shellisformation
and simulations the tracerand subsequent
addition method melting of the alloy
and neglecting of
in theformation
shell simulations.and subsequent melting of the alloy in the simulations.

Metals 2019, 9, x FOR PEER REVIEW 11 of 13

(a) (b)

(c) (d)
Figure
Figure10.10. Tracer
Tracer concentration
concentration change
change for
for different
different gas
gas flow
flow rates
rates of
of (a)
(a) 100
100 NL/min
NL/min (b)
(b) 300
300 NL/min
NL/min
and
and(c)
(c) 500
500 NL/min.
NL/min. (d)
(d) Comparison
Comparison of
of simulated
simulated average
average mixing
mixing time
time for
for different
differentgas
gas flow
flow rate
rate with
with
the
the experimental
experimentalvalues.
values.

4.
4. Conclusions
Conclusions
In
In this
this study,
study,the
theeffect
effectof
ofargon
argonflow
flowrate
rateon
on the
the fluid
fluid flow,
flow,open-eye
open-eyesize,
size,and
andmixing
mixing time
time were
were
numerically
numerically investigated. The Eulerian
investigated. The Eulerian VOF
VOF model
model waswas used
used to
to track
track the
the slag/steel/argon
slag/steel/argon interface
interface
behavior,
behavior, andand aaspecies
speciestransport
transportmodel
model was
was used
used to calculate
to calculate the mixing
the mixing time.time. The simulation
The simulation results
results of open-eye size and mixing time showed good agreement with the industrial
of open-eye size and mixing time showed good agreement with the industrial measurements. The measurements.
The following
following conclusions
conclusions can can be drawn
be drawn fromfrom
the the numerical
numerical simulations.
simulations.
1. The flow patterns of the molten steel inside the ladle furnace are largely dependent on the argon
flow rate. The flow velocity is very high at heights near to the bottom of the ladle furnace, and
it tends to decrease as the flow moves upwards.
2. The increase in the flow rate of argon gas from 100 to 500 NL/min enlarges the open-eye size
from 0.66 to 2.36 m2.
3. The simulated mixing time (95% criterion) of tracer addition into the metal bath decreased from
139 s to 96 s when the argon flow rate was increased from 100 to 500 NL/min.
Metals 2019, 9, 829 11 of 12

1. The flow patterns of the molten steel inside the ladle furnace are largely dependent on the argon
flow rate. The flow velocity is very high at heights near to the bottom of the ladle furnace, and it
tends to decrease as the flow moves upwards.
2. The increase in the flow rate of argon gas from 100 to 500 NL/min enlarges the open-eye size from
0.66 to 2.36 m2 .
3. The simulated mixing time (95% criterion) of tracer addition into the metal bath decreased from
139 s to 96 s when the argon flow rate was increased from 100 to 500 NL/min.

Author Contributions: Investigation: E.K.R.; methodology, T.S. and M.L.; supervision, V.-V.V., P.S., T.F., and L.S.
Funding: The authors are grateful for the financial support of the European Commission under grant number
675715-MIMESIS–H2020-MSCA-ITN-2015, which is part of the Marie Sklodowska-Curie Actions Innovative
Training Networks European Industrial Doctorate Program.
Acknowledgments: The authors are grateful to Sapotech Oy for the support to capture the formation of the
open-eye process in the ladle at very high temperatures.
Conflicts of Interest: The authors declare no conflict of interest.

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