Numerical simulation and experimental investigation of remelting processes.
The numerical simulation of remelting processes enables us to link the local solidification conditions to the operating parameters. Here, we discuss some recent studies aiming to develop specific aspects, e.g. the alternating current distribution during ESR of steels and superalloys, the ensemble...
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Інститут електрозварювання ім. Є.О. Патона НАН України
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irk-123456789-1032252016-06-15T03:02:47Z Numerical simulation and experimental investigation of remelting processes. Jardy, А. Пленарные доклады Международной конференции The numerical simulation of remelting processes enables us to link the local solidification conditions to the operating parameters. Here, we discuss some recent studies aiming to develop specific aspects, e.g. the alternating current distribution during ESR of steels and superalloys, the ensemble arc motion in a VAR furnace and the influence of electromagnetic stirring on the macrosegregation in remelted ingots 2013 Article Numerical simulation and experimental investigation of remelting processes. / А. Jardy // Автоматическая сварка. — 2013. — № 10-11 (726). — С. 83-88. — Бібліогр.: 27 назв. — англ. http://dspace.nbuv.gov.ua/handle/123456789/103225 621.793.18.06 en Автоматическая сварка Інститут електрозварювання ім. Є.О. Патона НАН України |
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Пленарные доклады Международной конференции Пленарные доклады Международной конференции Jardy, А. Numerical simulation and experimental investigation of remelting processes. Автоматическая сварка |
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The numerical simulation of remelting processes enables us to link the local solidification conditions to the operating parameters.
Here, we discuss some recent studies aiming to develop specific aspects, e.g. the alternating current distribution during
ESR of steels and superalloys, the ensemble arc motion in a VAR furnace and the influence of electromagnetic stirring on the
macrosegregation in remelted ingots |
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Jardy, А. |
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Jardy, А. |
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Jardy, А. |
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Numerical simulation and experimental investigation of remelting processes. |
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Numerical simulation and experimental investigation of remelting processes. |
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Numerical simulation and experimental investigation of remelting processes. |
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Numerical simulation and experimental investigation of remelting processes. |
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Numerical simulation and experimental investigation of remelting processes. |
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numerical simulation and experimental investigation of remelting processes. |
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Інститут електрозварювання ім. Є.О. Патона НАН України |
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Пленарные доклады Международной конференции |
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Numerical simulation and experimental investigation of remelting processes. / А. Jardy // Автоматическая сварка. — 2013. — № 10-11 (726). — С. 83-88. — Бібліогр.: 27 назв. — англ. |
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Автоматическая сварка |
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AT jardya numericalsimulationandexperimentalinvestigationofremeltingprocesses |
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8310-11/2013
UDC 621.793.18.06
NUMERICAL SIMULATION AND EXPERIMENTAL
INVESTIGATION Of REMELTING PROCESSES
A. JARDY
Institut Jean Lamour (UMR CNRS – Universite de Lorraine 7198) Parc de Saurupt, CS 50840, f-54011 Nancy Cedex,
france Laboratoire d’Excellence DAMAS, france. E-mail: alain.jardy@univ-lorraine.fr
The numerical simulation of remelting processes enables us to link the local solidification conditions to the operating param-
eters. Here, we discuss some recent studies aiming to develop specific aspects, e.g. the alternating current distribution during
ESR of steels and superalloys, the ensemble arc motion in a VAR furnace and the influence of electromagnetic stirring on the
macrosegregation in remelted ingots. 27 Ref., 1 Tabl., 5 figures.
K e y w o r d s : vacuum arc remelting, numerical simulation, electromagnetic stirring, current distribution, macrosegregation
I. Introduction
Consumable electrode remelting processes have
been developed to produce high-performance alloys
dedicated to critical applications, for which high met-
allurgical quality ingots are necessary. Consequently,
primary melting is not sufficient and remelting pro-
vides valuable advantages such as a fine grain struc-
ture, limited occurrence of solidification defects,
low level of micro- and macrosegregation and good
soundness of ingots.
The principle of the VAR (Vacuum Arc Remelt-
ing) process, as illustrated in figure 1-a, consists in
melting a consumable metallic electrode of the re-
quired grade under a high vacuum, in order to ob-
tain a sound ingot of good structural quality [1]. Dur-
ing remelting, an electric arc is maintained between
the tip of the electrode (which acts as the cathode)
and the top of the secondary ingot, in order to ensure
melting of the electrode. Liquid metal falls through
the arc plasma and progressively builds up the in-
got, which solidifies in contact with a water-cooled
copper crucible. In order to stabilize the arc, it can
be confined with the aid of an axial magnetic field
created by an external induction coil. The interaction
with the melting current stirs the liquid metal, the ro-
tation induced being in the orthoradial direction. By
reversing periodically the coil current, stirring can be
alternated.
In the case of Electro Slag Remelting (ESR), an
alternating current is passed from the electrode to the
water-cooled baseplate through a high-resistive calci-
um fluoride-based slag, thus generating Joule heating
[2]. The energy is both transferred to the electrode for
the melting and to the secondary ingot. Molten met-
al is produced in the form of droplets which fall and
build up the secondary ingot, as shown in figure 1-b.
Insulation from air and chemical refining, due to the
presence of slag, improve the inclusional quality.
Remelted materials are special steels and nick-
el-based superalloys. Vacuum Arc Remelting also
represents the final stage in the melting cycle of reac-
tive metals, such as zirconium and titanium. The stra-
© A. Jardy, 2013
figure 1. Schematic representation of (a) the VAR process, (b) the ESR process
84 10-11/2013
tegic importance of these products and their very high
added value make it essential to acquire a detailed un-
derstanding of the melting processes. Mathematical
modelling is a valuable tool to enhance fundamental
understanding, since it allows us to link operating pa-
rameters, such as the melting rate, ingot diameter or
cooling conditions, to local solidification conditions,
and thus to the ingot final quality. The work presented
here is part of a program initiated some twenty years
ago in Institut Jean Lamour to develop numerical
software for simulating the remelting operations, and
subsequently to help optimizing the processes. The
first version of the numerical model SOLAR (which
stands for SOLidification during Arc Remelting) was
applied to the simulation of VAR for reactive metals
[3]. Since then, the model has been constantly im-
proved. In the beginning of the century, it was adapt-
ed for nickel-base superalloys and special steels.[4,5]
More recently, a similar model has been developed
for the ESR process [6]. The development started in
2004 with a basic hydrodynamic model of the slag,
whose complexity was increased step by step. The
last model has several common bases with the SO-
LAR code, since ESR and VAR are quite similar in
terms of ingot growth and solidification.
A general description of both models (i.e. SO-
LAR and SOLECS, which stands for SOLar¬type Esr
Complete Simulation) and their validation was part
of a communication at the International Conference
on Welding and Related Technologies into the Third
Millenium, which was held in Kiev in 2008 [7]. Here,
we will focus our attention on 3 recent studies aiming
to develop some specific aspects of the behavior of
actual remelting processes.
II. Current distribution during electroslag
remelting
During the last years, several researches have been
presented, aiming to simulate the whole process in a
transient way, or discuss in more detail the electro-
magnetic fields in ESR [8–13]. Among these models,
the simulation software SOLECS was developed at
IJL, as stated in the Introduction. During the growth
of the ESR ingot, the slag is in contact with the wa-
ter-cooled mould, which is responsible for the for-
mation of a layer of solidified slag at the interface.
As the secondary ingot rises, this layer is partially re-
melted and crushed between the metal and crucible,
resulting in a slag skin which acts as a thermal insu-
lator and provides ESR ingots with a smooth lateral
surface [2].
In the paper by Weber et al. [6], it was written
that “we assume that the solidified slag skin insulates
electrically the slag and ingot from the mold. This as-
sumption is particularly questionable and needs to
be confirmed. Indeed, in some cases, the model pre-
dicts a discontinuous solid skin surrounding the slag
cap, implying a possible electrical contact between
liquid slag and mold”. While this strong assumption
is made classically in the literature devoted to ESR
simulation [14,15], it was sometimes claimed [16,17]
that a certain amount of current is able to flow into
the Cu crucible. This phenomenon could modify the
thermohydrodynamic behaviour of the slag and liq-
uid pool, hence influencing the solidification process.
Therefore, the goal of our study is to quantify this
phenomenon, and determine the impact of the solid
layer thickness and electric conductivity of the solidi-
fied slag on the current distribution during electroslag
remelting.
To reach the water cooled crucible and baseplate,
the melting current supplied to the electrode and liq-
uid slag can either flow in the ingot pool or directly
through the solidified slag skin. The resulting current
distribution depends on the electrical resistance of
that phase, hence the solid slag conductivity and skin
thickness. In this section, we present the computation
of electromagnetic phenomena with a simplified ge-
ometry. The thickness of the solidified slag skin is as-
sumed to be uniform and the assigned electrical con-
ductivities are estimated values. The main input data
are gathered in Table I.
The effects of the variations of two parameters
(electrical conductivity and thickness of the solid slag
layer, written with italic characters in Table I) on the
current distribution and resulting Joule heating were
studied. The electrical conductivity was allowed to
vary in the range 10–3 — 400 Ω–1·m–1 (10–3 Ω–1·m–1
corresponds to a full insulation while 400 Ω–1·m–1 is
the conductivity of the liquid slag). The thickness of
the solidified slag skin was set to 4 or 6 mm. In the
literature, the computed current distribution is most
often represented by visualizing the magnitude of the
current density phasor (i.e. the maximum value for
each component of the current density), which clas-
sically leads to the observation of an important skin
effect in the electrode and ingot [6,11,14,18]. Indeed,
it is well known that the current distribution is related
Ta b l e I . Parameters used in the simulations
Melting current (maximum value) 10 kA
AC frequency 50 Hz
Electrode radius 26 cm
Mould external radius 30 cm
Mould thickness 2.5 cm
Electrode immersion depth 1 cm
Electrical conductivity of the metal 106 Ω–1·m–1
Electrical conductivity of the liquid slag 400 Ω–1·m–1
Electrical conductivity of the solid slag 10–3 — 400 Ω–1·m–1
Thickness of the solidified slag skin 4/6 mm
8510-11/2013
to the value of the skin depth into the different mate-
rials: if the latter is larger than the actual dimension
of the domain, the current distribution is homoge-
neous, e.g. into the liquid slag. However, within this
study, we chose to represent the instantaneous current
distribution at a precise moment in the alternating pe-
riod t = 0. In addition to the visualization of the skin
effect, such a representation also highlights the local
variation in the phase angle caused by the variation in
the induced magnetic field into the metallic conduc-
tors, as it was shown by Li et al. [13].
The first step of the study consists in confirm-
ing that part of the melting current is likely to flow
through the solidified slag layer and directly enter the
mould. figure 2 presents the computed results ob-
tained either when the solid layer behaves as a per-
fect insulator (such behaviour is reached as soon as
the electrical conductivity is lower or equal to 10–3
Ω–1·m–1) or when the electrical conductivity is set to
15 Ω–1·m–1. The solidified slag skin is supposed to be
4 mm thick. Clearly, when the electrical conductiv-
ity of the solid slag is set to 15 Ω–1·m–1, part of the
current actually flows through the skin to reach the
mould. The solidified slag layer does not act as a per-
fect electrical insulator and this modifies the current
distribution in the system. Our result confirms some
previous claims in the literature[16,17] and raises
new questions regarding the consequences of such a
loss of current on the process efficiency.
figure 3 summarizes the effects of a variation in
the electrical conductivity of the solid slag and in the
thickness of the solidified slag layer: it represents the
evolution of the total Joule heat generated accord-
ing to both parameters. The electrical conductivity of
the solid slag appears to be a crucial parameter of the
process. This observation emphasizes the necessity to
have access to actual measurements. The thickness
of the solidified slag layer also influences the current
distribution in the system. However, in the range of
tested values, the impact of this factor remains of sec-
ondary importance.
In its present state, this model considered a uni-
form layer thickness along the slag/crucible interface.
However, this parameter is liable to vary from a neg-
ligible value to few millimetres during a real remelt-
ing. To take into account this variation, as well as to
assess the influence of the electrical current distribu-
tion on the ingot solidification, the next step of our
study will consist in a full coupling of the model with
a numerical simulation of the whole ESR process.
Results obtained will be compared to actual experi-
mental observation.
III. Ensemble arc motion during vacuum
arc remelting
Knowledge of the electric arc behaviour in the
VAR process is based on visualization studies per-
formed first at Sandia National Laboratories [19]
during the remelting of steel or Ni-based superalloy
electrodes. Similar experiments have then been car-
ried out by Chapelle et al. on zr electrodes [20]. A
conclusion from these observations is that the behav-
iour of the arc is similar to the diffuse mode of a vac-
uum arc created between cold solid electrodes. The
arc consists of several dispersed clusters of cathode
spots moving over the whole surface of the cathode.
Such behaviour seems to imply that the total energy
transferred from the arc to the cathode tip is distribut-
ed uniformly; in particular, no azimuthal direction is
privileged, so an axisymmetric behaviour is expected
at the macroscopic scale, consistent with the flatness
of the cathode tip during full-scale melting.
However, it has been recently reported that the arc
often does not behave axisymmetrically at the mac-
roscopic scale. Based on measurements of the lumi-
nosity and magnetic field created by the arc [21, 22].
Ward et al. suggested that most of the time, the elec-
trical centre of the arc was rotating in a time-aver-
aged sense around the ingot centreline with a constant
speed (period equals typically 20 to 40 s when a su-
peralloy electrode melts under nominally diffuse con-
ditions). Then it was assumed that the distribution of
current flow and heat input followed the distribution
figure 2. Current density distribution (A·m–2) computed with two
values for the electrical conductivity of the solidified slag skin: 10–3
Ω–1·m–1 (a) and 15 Ω–1·m–1 (b)
figure 3. Evolution of the total resistive heating in the slag,
according to the electrical conductivity and the thickness of the
solidified slag skin
86 10-11/2013
of this location and a part of the arc was assimilat-
ed to a loosely focused rotating spot, radially located
away from the ingot centreline. A 3D model of the
ingot pool, using this representation as a boundary
condition, [23] enabled the authors to conclude that
the hydrodynamic behaviour of the melt pool and in-
got solidification process can be greatly influenced by
such an ensemble arc macroscopic motion.
In order to confirm the previous statements, the
dynamic behaviour of the arc in an industrial VAR
furnace has been investigated. Two synchronized vid-
eo cameras positioned in front of diametrically oppo-
site viewing glasses on top of the furnace chamber
were used to film the annulus gap between the elec-
trode and crucible wall. Video images were recorded
during the melt of a zy2 ingot with various stirring
conditions.
To help interpreting the recorded films, an im-
age processing procedure similar to that proposed by
Ward et al. [21] was developed. first, each film was
split into a series of images. Then a 2 s moving aver-
age was applied to suppress high frequency fluctua-
tions related to individual cathode spot behaviour and
the sampling frequency was reduced to 5 frames/s. A
given region of interest was extracted from each im-
age and all the results were put side by side to build a
temporal sequence (figure 4-a). finally, the luminosi-
ty in the extracted region was quantified and a fourier
analysis was performed to determine the frequencies
of fluctuations along the sequence.
An example of two sequences corresponding to
diametrically opposite regions is illustrated in figure
4-b. A plot of the evolution of the luminosity for both
sequences is also shown on the figure. The luminosity
fluctuates quite regularly, with an alternation between
very bright time periods and other time periods dur-
ing which it is notably reduced. The fluctuations of
luminosity in the two diametrically opposed regions
are essentially in phase opposition. A frequency anal-
ysis indicates that these fluctuations involve several
periods, with a dominating period of the order of 30
s, identical for the two cameras.
These fluctuations may be related to the arc be-
haviour. Indeed, it can reasonably be considered that
the luminosity fluctuates as a consequence of the evo-
lution of the spatial distribution of the arc, whose
centre of gravity moves across the electrode surface
with a period of about 30 s. This phenomenon was
observed for all the melt conditions tested. The dom-
inant period of the fluctuations was of the same or-
der of magnitude for all melt conditions (including
the conditions without any stirring). It seems in par-
ticular to be unconnected to the reversal period of the
magnetic field. Thus, an ensemble motion of the arc
seems to exist for all operating conditions and it ap-
pears to be relatively independent of the presence of
an external axial magnetic field.
This work enables us to confirm the conclusions
reached by Ward et al. [22] who reported a value of
the time constant of the arc motion very similar to the
one determined here. As discussed previously, the ex-
istence of a slow motion of the arc centre (with a time
period of around 30 s) could have important implica-
tions for the modelling of the VAR process.
IV. Electromagnetic stirring and macrosegrega-
tion in var zirconium ingots
Despite the use of electromagnetic stirring, chemi-
cal heterogeneities develop in the mushy zone during
the solidification stage. One of the main challenges
for zr and Ti producers is to master the VAR process
in order to control the macrosegregation in remelt-
ed ingots. Macrosegregation results from the associ-
ation of microsegregation and transport phenomena.
The latter are primarily due to the flow in the liquid
and mushy parts. It is now well established [24,25]
that the hydrodynamics of the melt pool depends on
figure 4-a. Temporal sequence used to study the fluctuations of luminosity above the ingot
figure 4-b. Typical temporal sequences obtained for two diametrically opposite regions
8710-11/2013
the combined action of the followings: thermal and
solutal buoyancy, self-induced electromagnetic force
and the periodic centrifugal force caused by the an-
gular movement generated by the stirring. The aim
of this section is to investigate numerically the action
of these forces on the macrosegregation of zircaloy 4
VAR ingots.
In order to improve the description of the solid-
ification and related macrosegregation, a multiscale
model has been recently incorporated into SOLAR to
simulate the solidification of multicomponent alloy
VAR ingots. It is based on a volume-averaged Eul-
er-Euler two phases formulation [26, 27]. At the mac-
roscopic level, the permeability of the mushy zone
is given by the Carman-Kozeny law, depending on
a microstructure dimension typically of the order of
the secondary dendrite arm spacing (SDAS). A mac-
roscopic k-ε model that takes into account the actions
of both the thermosolutal buoyancy and the influ-
ence of the solid phase in the mushy zone is used to
simulate the turbulent nature of the flow. The phase
change is treated locally at the microscopic level,
either by assuming the lever rule or accounting for
grain growth controlled by finite diffusion of alloy el-
ements in both liquid and solid phases.
A zy4 electrode was remelted in a production fur-
nace. Two stirring sequences were successively applied:
a strong alternated stirring followed by a weak con-
tinuous one. In addition, a continuous and strong stir-
ring was temporarily used in order to mark several melt
pools in the ingot. The recording of the actual operating
process parameters provided input data for the model.
Thermosolutal buoyancy effects are simulated
thanks to the Boussinesq approximation. Thermal and
solutal expansion coefficients for zr alloys are not
available in the literature. Nevertheless, the thermal
expansion coefficient βT was estimated from data on
pure liquid zr. To investigate the influence of solutal
convection caused by Sn concentration gradients (Sn
is the major alloying element in zy4), we have simu-
lated 4 cases:
(a) βT = 0, βS
Sn = 0 ;
(b) βT > 0, βS
Sn = 0 ;
(c) βT > 0,βS
Sn < 0 and (d) βT > 0, βS
Sn > 0.
The positive value of the solutal expansion coef-
ficient βS
Sn (case d), was calculated from the volume
additivity assumption. The other value (case c) was
intentionally negative. Case a corresponds to the ab-
sence of all thermosolutal buoyancy, which means
that the flow is only caused by the electromagnetic
stirring.
for the four cases, the final maps of fe segrega-
tion computed by the model are shown in figure 5.
Because of the application of two successive stirring
sequences, two main segregation patterns can be ob-
served along the ingot height. In addition, we can
see two inclined depleted bands caused by the pool
markings. The enriched zone at the top of the ingot
was caused by the solidification of the last melt pool.
The average concentration of fe in the liquid pool in-
creases as the ingot grows because its partition coeffi-
cient is less than unity.
When thermosolutal buoyancy is not accounted
for (case a), the model predicts an iron enrichment in
the ingot central zone whatever the stirring employed.
Actually, the centrifugal force due to the angular flow
is predominant and generates a clockwise flow cell.
Consequently, iron-enriched liquid accumulates at the
bottom of the melt pool and in the mushy zone, caus-
ing a positive segregation near the axis. Alternated
stirring causes a weaker radial macrosegregation than
unidirectional stirring. for both stirring practices, ac-
counting for thermal convection (case b) increases
slightly the radial macrosegregation of the ingot cen-
tral part, as thermal buoyancy strengthens the centrif-
ugal force. In the mushy zone, the consequence is a
more intensive circulation resulting into more trans-
port of enriched liquid towards the centerline.
The effect of solutal convection on the centerline
macrosegregation is visible on figures 5-c and 5-d.
In case (c), radial segregation close to the centerline
is notably amplified because all the volumetric forc-
es cooperate. On the opposite, in case (d), the solu-
tal buoyancy is counteracting and reverses the flow in
the mushy zone at the bottom of the pool. The coun-
terclockwise upward flow in the mushy zone reduces
the segregation in the central region. When stirring
is alternated (bottom half of the ingot), iron concen-
tration is roughly uniform while a continuous stirring
figure 5. Maps of fe segregation in the zircaloy-4 VAR ingot for
the 4 cases studied
88 10-11/2013
(ingot top half) results in a positive segregation band
located at r/R ~ 0.25 (R is the total radius of the in-
got). This band forms due to the small counterclock-
wise flow loop induced by the solutal convection,
which carries iron-rich liquid from the center to the
outward radial direction.
The fe segregation profiles predicted by the mod-
el clearly show that thermosolutal convection affects
the macrosegregation only in the central region. In
the upper part, chemical analyses show the fe content
rises continuously in the inner half of the ingot. Com-
parison with the model predictions reveals that such
a behaviour is characteristic of case (d) where ther-
mosolutal buoyancy is considered and βS
Sn > 0. This
shows that the upward flow driven by solutal buoy-
ancy effects is partially responsible of the macroseg-
regation in zy4 VAR ingots. In the outer part, where
the centrifugal force is predominant, model and ex-
perimental results are in good agreement.
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