Group Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Title: 17.1.3 - Influence of an imposed Vertical Current on the Droplet Formation during a Melting Process
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 Material Information
Title: 17.1.3 - Influence of an imposed Vertical Current on the Droplet Formation during a Melting Process Droplet Flows
Series Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Physical Description: Conference Papers
Creator: Kharicha, A.
Ludwig, A.
Publisher: International Conference on Multiphase Flow (ICMF)
Publication Date: June 4, 2010
 Subjects
Subject: droplet formation
melting
MHD
VOF
Joule heating
electroslag
electric current
magnetic field
 Notes
Abstract: The droplet formation during the melting of an electrode under the action of strong vertical current is simulated with a multiphase-MHD approach. A VOF approach is used for the interface tracking, and a potential formulation is used for the electric and the magnetic field. The Lorentz force and the Joule heating is recalculated at each time step in function of the phase distribution. The first results provided by this model are presented. Two values of metal/slag surface tensions are explored. The effect of the presence of a horizontal magnetic field is also investigated.
General Note: The International Conference on Multiphase Flow (ICMF) first was held in Tsukuba, Japan in 1991 and the second ICMF took place in Kyoto, Japan in 1995. During this conference, it was decided to establish an International Governing Board which oversees the major aspects of the conference and makes decisions about future conference locations. Due to the great importance of the field, it was furthermore decided to hold the conference every three years successively in Asia including Australia, Europe including Africa, Russia and the Near East and America. Hence, ICMF 1998 was held in Lyon, France, ICMF 2001 in New Orleans, USA, ICMF 2004 in Yokohama, Japan, and ICMF 2007 in Leipzig, Germany. ICMF-2010 is devoted to all aspects of Multiphase Flow. Researchers from all over the world gathered in order to introduce their recent advances in the field and thereby promote the exchange of new ideas, results and techniques. The conference is a key event in Multiphase Flow and supports the advancement of science in this very important field. The major research topics relevant for the conference are as follows: Bio-Fluid Dynamics; Boiling; Bubbly Flows; Cavitation; Colloidal and Suspension Dynamics; Collision, Agglomeration and Breakup; Computational Techniques for Multiphase Flows; Droplet Flows; Environmental and Geophysical Flows; Experimental Methods for Multiphase Flows; Fluidized and Circulating Fluidized Beds; Fluid Structure Interactions; Granular Media; Industrial Applications; Instabilities; Interfacial Flows; Micro and Nano-Scale Multiphase Flows; Microgravity in Two-Phase Flow; Multiphase Flows with Heat and Mass Transfer; Non-Newtonian Multiphase Flows; Particle-Laden Flows; Particle, Bubble and Drop Dynamics; Reactive Multiphase Flows
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Bibliographic ID: UF00102023
Volume ID: VID00414
Source Institution: University of Florida
Holding Location: University of Florida
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Resource Identifier: 1713-Kharicha-ICMF2010.pdf

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7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


Influence of an imposed Vertical Current on
the Droplet Formation during a Melting Process
A. Kharicha, A. Ludwig
University of Leoben,
Franz-Joseph Strasse, 8. 8700 Leoben, AUSTRIA,
abdellah.kharicha@uni-leoben.at


Keywords: droplet formation, melting, MHD, VOF, Joule Heating, Electroslag, electric current, magnetic field




Abstract

The droplet formation during the melting of an electrode under the action of strong vertical current is simulated with a
multiphase-MHD approach. A VOF approach is used for the interface tracking, and a potential formulation is used for the
electric and the magnetic field. The Lorentz force and the Joule heating is recalculated at each time step in function of the
phase distribution. The first results provided by this model are presented. Two values of metal/slag surface tensions are
explored. The effect of the presence of a horizontal magnetic field is also investigated.


Introduction

The Electro-Slag-Remelting (ESR) process is an advanced
technology for the production of components of e.g. high
quality steels. An alternating current (Figure 1) is passed
from a conventionally melted and cast solid electrode
through a layer of molten slag to the baseplate. Because of
the electrical resistivity of the slag, Joule heating is
generated and the slag transfers this energy to ingot and
mould surfaces and to the melting electrode tip. The
molten metal produced in the form of droplets passes
through the slag and feeds a liquid pool from where
directional solidification takes place. The slag and the
ingot are contained in a water cooled copper mould. As
also the baseplate is water cooled, a heat flow regime is
imposed that gives controlled solidification, and this
results in improved structure characteristics of ESR ingots.

This process involves two liquids, a liquid metal and a
liquid slag. Each liquid is subject to a phase change due to
melting or solidification. From a fluid dynamic point of
view, the ESR process is clearly a multiphase process, with
free interfaces (slag/pool, gas/slag), and with a mixed area
(slag and falling steel droplets).

Physically, the development of the heat and mass transfer
at slag/droplet interface is important for the final ingot
quality, composition and cleanliness. Visual observations
of the droplet formation just under the electrode being
melted is almost impossible. Due to the presence of high
temperatures, opacity of the materials, and the presence of
the mould it is not possible to directly observe the
behaviour the slag/pool interface. Although usually
assumed flat, a previous work [1] using a Volume of fluid
(VOF) model has shown that the interface between a layer
of slag and steel layer in a cylindrical cavity is highly
coupled with the distribution of the electric current. A full
scale simulation of the ESR process using a VOF model


has shown that the shape of the pool interface is likely to
be non flat. Depending on whether a "flat" or "free"
interface is assumed, an appreciable difference was found
in the prediction of the pool shape and thickness [1]. This
difference was due to a different magnitude and
distribution of the Joule heat generated.

Usually the effects of the droplets are essentially taken into
account in the form of a momentum and energy source
applied to slag and pool regions [2-4]. Nevertheless this
approach needs an empirical or semi-empirical radial
droplet distribution, and droplet temperature. The latest
were selected according to the resulting pool shape.
However, as the steel/slag density and viscosity ratio are
neither very large nor very small, one can expect an
important transfer of momentum between the droplets and
the slag flow. And, as the electric conductivity of steel is
known to be much higher than that of the slag, the
distribution of the steel phase within the slag will be a
critical parameter to predict the distribution of the electric
current density which controls the Lorentz force magnitude.
From these physical facts, one can expect in this nonlinear
system a slight change in the distribution of the steel
droplets in the slag which can result in totally different
flow behavior.

For fundamental and technical reasons it is important to
study how the droplets forms and behaves in the slag. The
present work present the results given by a 3D
Magnetohydrodynamic (MHD) model coupled with a VOF
model for the phases (steel, slag) distribution. During the
process the electrode can develop a flat or a parabolic
surface, here it is assumed flat. The electric current
distribution is dynamically calculated from the transient
phase distribution. Then the electromagnetic forces and the
Joule heating are recalculated at each time step.





7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

Numerical Model
The deviation from the average resistance is defined by:
The calculation domain is a cylinder of 20 cm high and 5
cm radius. The electrode has a radius of 3.5 cm. The 1
container is filled with a layer of liquid slag (17 cm high) SRes(t) = Res(t) Res(t)dt,
and a quantity of liquid steel (3 cm high). The total number 2T
of volume elements is 3.4 Million cells.
where T is an averaging time large enough to include
Properties of steel and slag are assumed to be constant. The several dro let departures.
electrode supplies a total DC current oflo=1000 Amperes.

The interface between the two phases is tracked with the
geometric reconstruction VOF technique. A single set of
momentum equations is shared by the fluids, and the
volume fraction of each of the fluids in each computational
cell is tracked throughout the domain. According to the Po
local value of the volume fraction appropriate properties
and variables are assigned to each control volume within Supply
the domain.

In a two phase system the properties appearing in the
momentum equation are determined by the presence of the Electrode to be melted
component phase in each control volume. The local values
of a physical property 0 (such as density, viscosity, electric
conductivity) are interpolated by the following failing drolets
formula 0= 01f +f02 +f, 03, where the subscripts
1,2,3 indicate the corresponding phase. The value of the Liquid pool
surface tension is chosen to be equal to 0.1 or 1N/m. .r''
Depending on the dynamic of the interfaces, the typical _Mushy region
calculation time step lies in the range of 10 -10-o second. 'i .

Fluid flow The motion of the slag and liquid steel is totally solidified region
computed with the buoyant Navier-Stokes equations. The
effect of the turbulence is estimated with a Smagorinsky Water cooled mold
LES model. The no-slip condition is applied at the lateral (Cooper)
walls. The electrode and the bottom surface are modelled
as velocity inlets.

El,.. r ,,,,.... ,. The potential equation is computed from 'Baseplate
the equation of the conservation of the electric current: Figure 1: Schematic view of the ESR system.

V. = V(-oV ) = 0,
where V is the electric potential. A flux condition is applied
at the bottom surface, while a constant electric potential is
applied at the electrode. No current is allowed to enter the
later wall. The magnetic field is then extracted by solving
the magnetic potential equations. The computed
electromagnetic field is dynamically adjusted from the
space distribution of the electric conductivity, which is in
turn function of the predicted phase distribution. The
Lorentz force acting on both slag and steel is defined by:

FL =-, 1-B


The electric resistance can be calculated at each time from
the total joule heating generated in the domain:


Res(t) = a ,)
0J 2 (9, t)





7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


Results and Discussion

a) Surface tension of 1N/m

Figure 2 shows the evolution of the resistance around its
main value during the numerical melting experiment. The
curve shows several strong variations. The resistance
decreases with the decrease of the distance between the
accumulated liquid metal under the electrode and the
slag/pool interface. The minimum value of the resistance is
reached at the departure of the first droplet (-1-2 cm).
Then a slight increase occurs before a second minimum is
reached corresponding to the detachments of a second
large droplet. Then some secondary droplets are released,
that have smaller electric signature. The droplet departures
occur at a frequency of about 0.5 Hz.

When the horizontal magnetic field is applied in the y
direction, an additional Lorentz force acts on the liquid
metal and push it in the x direction (Figure 3). In fact the
droplet is not released from the centre of the electrode but
at mid distance from the electrode periphery. In the present
case the droplets collided on the lateral wall. The presence
of the magnetic field increases the droplet departure
frequency to almost 1 Hz. Since the melting rate is not
modified, the droplet size at departure is released at shorter
distance from the electrode leading to smaller minimum
pick in the electric resistance signal (Figure 2).

The melting rate is carefully controlled during the ESR
process. The control is achieved mainly by adapting the
amount of current imposed through the electrode. If during
the melting the imposed vertical current is suddenly
increased by a factor of 30 % (to 1300 Amps), the Lorenz
force is locally increased by a factor of 70 %. The liquid
metal faucet can be subject of a strong magnetic pinch
effect. In the present case the liquid metal faucet does not
survive and explode into multiple mini droplets (Figure 4).


Figure 3: Droplet formation with an axial magnetic field
coloured with electric current density magnitude [104
-109Amp/m2]


Figure 4: Splash of liquid metal when the imposed current is
suddenly increased by 30 %. Interface coloured with electric
current density magnitude [104 -109 Amp/m2].


Time (s)
Figure 2: Fluctuation of the resistance during droplet
departure without (t<4.5 s) and with horizontal magnetic
field (t > 4.5 s).






7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


b) Small surface tension of 0.1N/m


Properties of slags are known to vary strongly with
proportion of chemical components. From one slag to
another viscosity or the surface tension can differ by large
factors. In addition, strong variations with temperature
exist as well.

The same simulation than in the previous case is performed
with a small surface tension of 0.1 N/m. In this case it can
be observed that the computed resistance (Figure 5) doesn't
shows the same behaviour than for large surface tension
(Figure 2). The electric resistance is continuously
fluctuating but doesn't exceed 4% of the main value. It can
be seen that these variations are due to an almost
continuous release of small droplets (Figure 6). Here two
to three faucets form and cuts into droplets of about 0.5-4
mm diameter. Smaller droplets falls at smaller speed than
large droplets, new droplets depart before even the impact
of previous droplets on the slag/pool surface. This quasi
continuous presence of droplets in the slag height doesn't
allow the electric current distribution to find a steady state,
i.e. the resistance cannot reach a constant value in time.
Nevertheless, the picks corresponding to the lowest value
of resistance can still be attributed to some relatively large
droplets departure (larger than 2 mm).

4 -,


U' 2-


S-


S -2-


-4-

0,5 1,0 1,5 2,0 2,5 3,
Time (s)
Figure 5: Fluctuation of the resistance during melting
assuming surface tension of 0. N/m.

Since the liquid metal is not concentrated in an unique
faucet, the electric current can choose several "metallic
path" for travelling downward. Thus the faucets experience
smaller magnitude of electric current density (max 7e8
Amp/m2) than in the previous case (max 1010 Amp/m2).
This means that the Lorentz force is decreased by a factor
of 10. Then the effective ratio between the Electromagnetic
force over the surface tension force is not different from
the case where the surface tension was set to 1N/m. The
droplet formation is then controlled by a similar
mechanism than in previous case.


Figure 6: Droplet formation with small surface tension.
Interface coloured with electric current density magnitude
[103-108 Amp/m2]


Conclusions

A 3D VOF model was coupled with a
Magnetohydrodynamic model to simulate the droplet
formation during melting of a metallic electrode. The model
can predict the exact electric and magnetic field distribution
in function of the metallic distribution in a low conductivity
slag. The model was applied to the melting of small
electrode assuming a small and a large value of the
melt/slag surface tension. It was shown that with large
surface tension only one faucet forms and larger droplets are
released. The fluctuation of the resistance can easily be
interpreted as lower picks shown up during the release of
each primary or secondary droplet.

0 For small surface tension, two to three faucets appear from
which smaller droplets departs. In this case the space
between the electrode and the liquid pool surface is filled
with many mini droplets. The continuous release of droplets
generates constant electric resistance fluctuations. In this
configuration it is not possible to clearly link the resistance
signal with a phase distribution in the cavity.

Some additional effort must be given to configurations with
larger number of faucets. This corresponds to melting in
larger systems or to melting under smaller surface tension.

References

[1] A. Kharicha, W. Schiitzenhofer, A. Ludwig, R. Tanzer,
M.Wu Process Metallurgy Steel research international
77 (2006) No.7.
[2] B. Hernandez-Morales and A. Mitchell, Ironmaking &
steelmaking, Vol. 26 No. 6 (1999), p.423-438
[3] A. H. Dilawari and J. Szekely, Metall. Trans. B, Vol 8B,
(1997), p.227-236.
[4] K.M Kelkar, J. Mok, S.V Patankar and A. Mitchell,
Phys. IV France 120 (21 114) p 421-428






7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

[5] A. Jardy, D. Ablitzer and J. F. Wadier, Metallurgical and
Materials Transactions B Vol p111-120




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