7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
Influence of inclusions and gas bubbles on the liquid metal flow: effect of rheology and
particle properties
Lahbib Zealouk*, Amsini Sadiki* and Jurgen Jakumeit**
(*)Technische Universitat Darmstadt, Dept. of Mechanical Engineering, Institute of energy and Power Plant Technology,
Petersenstr. 30, 64287 Darmstadt, Germany
(**) Access e.V, Materials+Processes, RWTHAachen, Intzerstr. 5, 52072 Aachen, Germany
sadiki@tekt.tudarmstadt.de
Keywords: VOF/EulerLagrangian coupled simulations, particleladen liquid metal flow
Abstract
Experience shows that the reliability of cast components depends strongly on the quality of the casting process. This lies on the
specific flow characteristics within the running system and mould cavity. The flow characteristics may include among others
the motion and entrapment of inclusions and gas bubbles (quoted as particles) that can create defects if they become entrapped
in the solidifying material. To avoid these defect mechanisms design process that includes often contradictory requirements
needs careful compromises. To achieve this purpose, an accurate prediction of the essential physical and rheology properties of
the liquid metal flow is a prerequisite.
In the present work focus is put on the transport of particles in a liquid Almetal flow at high temperature featuring a
multiphase flow system. Solidification processes are not taken into account at this stage. To mimic inclusions and bubbles
properties a turbulent polydisperse threephase flow is considered. First a VOF method is used to well capture the free surface
and entrapped air during the mold filling processes. The benchmark configuration of Campbell et al. (2006) is used for
validation.
An EulerLagrangian approach is then employed to model the liquid and to track the particles. To simulate the details of
transient turbulent flow and particle motion a simple first order turbulence model is applied using the commercial STARCD
code. First, the effect of polydispersed particles on the liquid metal flow are pointed out. Then, the effect of the rheology of the
fluid on the evolution of the mould filling process is investigated under different inflow conditions.
While the transport of particles is the focus here, the capture or entrapment of particles which touch the boundaries
representing the solidifying shell has to be next addressed. With respect to modeling and entrainment issues of inclusions and
bubbles in castings during form filling this method can be extended by including breakup phenomena of oxide film. This task
is left for future work.
Introduction
During casting processes the entrapment of inclusions,
bubbles, slag, and other particles into solidified steel
products is a critically important quality concern. These
particles require expensive inspection, surface grinding and
rejection of steel. The casting process itself can be
characterized by the robustness (repeatability) and specific
fluid flow properties within the running system and mould
cavity (Reilly et al., 2009). Such flow properties may
include among others the motion and entrapment of
inclusions and gas bubbles (quoted throughout as particles)
that can create defects if they become entrapped in the
solidifying material.
To avoid these defect mechanisms design process that
includes often contradictory requirements needs careful
compromises. To achieve this purpose, an accurate
prediction of the essential physical and rheology properties
of the liquid metal flow is a prerequisite. This is nowadays
possible by means of numerical modelling. Effects of
casting defects on the mechanical properties of castings
have been investigated by a number of researchers, with
unanimous conclusions being drawn about the role of
inclusions along with oxide films on the liquid metal. A
recent review has been provided by Pfeiler et al. (2008),
Ishmurzin et al. (2008).
In the present work focus is put on the transport of particles
in a liquid Almetal flow at high temperature featuring a
multiphase flow system. Solidification processes are not
taken into account at this stage. To mimic inclusions and
bubbles properties a turbulent polydisperse threephase flow
is considered. First a VOF method is used to well capture
the free surface and entrapped air during the mold filling
processes. Then an EulerLagrangian approach is employed
to model the liquid and to track the particles (Sadiki et al.,
2004, 2004, 2006). To simulate the details of transient
turbulent flow and particle motion a simple first order
turbulence model (Yun et al., 2005) is applied using the
commercial STARCD code. As first result, the effect of
polydispersed particles on the liquid flow is pointed out.
It is demonstrated that high levels of free surface turbulence
during mold filling (see ICMF 2010, Nishad et al., 2010)
lead to formation of extensive double oxide film casting
defect. Since the turbulence degree is strongly related to
flow viscosity, it is of interest to investigate how the
variation of theological properties, especially of the
viscosity, shall affect the mold filling process. By the way
the theological properties of a Newtonian fluid can be
modified by increasing the particle concentration giving rise
to a NonNewtonian behaviour. To capture these features a
simple coupling between the VOF method and the
EulerLagrangian approach is undertaken following the
technique proposed by Yang et al. (2_'1~4) and Dai et al.
'"' I4).
While the transport of particles is the focus here, the capture
or entrapment of particles which touch the boundaries
representing the solidifying shell has to be next addressed.
With respect to modelling and entrainment issues of
inclusions and bubbles in castings during form filling this
method can be extended by including breakup phenomena
of oxide film. This task is left for future work.
The paper is organized as follows. In the following section
we present the benchmark problem employed to validate the
VOF method. Next, the governing equations along with the
details of the submodels used and the EulerLagrange
approach are summarized. To evaluate the potential of the
models proposed, the basic configuration will be simulated.
In the next section, results obtained and parameter studies
are presented and discussed. The last section is devoted to
conclusions.
Benchmark problem
The mathematical model described above was tested
against experimental data provided by Campbell et al.
(2006). Figure 1 (left) shows schematic of the casting, used
in these experiments. The molten aluminum was allowed
to flow into the sprue by removing the stopper and the
interface positions were captured with the help of Xray
camera. These data were used for model validation.
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
Mathematical modelling
As stated earlier, the mathematical model is built using a
continuum formulation and a Lagrangian approach
available in the commercial code STARCD. Let us outline
the governing equations used.
Momentum
S(pu)+V(puu)= VpVu) + pg +S
at ax (1)
where u is the velocity vector in the Cartesian coordinate
and p is the pressure in the fluid, p and /u are the fluid
density and the dynamic viscosity, respectively. Influence
of the external forces is manifested in the form of the
momentum source terms, S.
Mass
+ V.(p)= 0
at
The above equation can be cast in volume conservation
form as follow:
0(ln p)_ +V 0
at (
Equation (3) is valid even when the density changes from
point to point, for example, across the liquidair interface.
Turbulence description
As the flow is expected to be turbulent especially at sprue
exit, a simple k turbulence model is used, and
requires solving two coupled conservation equations for
turbulence kinetic energy and dissipation rate (see in Yun
et al. 2005), respectively:
C(pk)+V (puk)= V r + = Vk + pv,G pe
(4)
t(ps) +V .(pus) = V Ia+P, V i pG C2p
8t LI or JK K
(5)
where k is turbulence kinetic energy and c is the
turbulence dissipation rate, vt is turbulence viscosity and
calculated as v,= C k / and c, 0k, o' C1, and
C,2 are all taken to be constants and are given
respectively the values 0.09, 1.0, 1.3, 1.44 and 1.92. The
quantity G is responsible for the production of turbulent
energy is expressed as:
G=[] +[ + 2 2+
La Lay Laz a ay ax az a) ay a
(6)
Free Surface
For free surface modeling, the volume of fluid method
(VOF) (Klein et al., 2002; Yang et al., 2004) is selected. It
deals with a single continuum whose properties vary in
Figure 1: Left: Benchmark test geometry.
Right: Numerical mesh
space according to its composition, the latter derived from
the solution of transport equations for the components. The
distribution of component fluids is defined by the volume
fraction, (, of each fluid. The variable takes the value 0.0
at the location fluid 1 and the 1.0 at the location in fluid 2.
The value of ( is obtained through the solution of the
scalar conservation equation:
Ot + V. (u)= 0 (7)
Ct
To mimic inclusions and bubbles properties a turbulent
polydisperse threephase flow is considered.
Type of inclusions Density Size [gnm]
[Kg/m^3]
Chloride Inclusion 2000 20
Aluminium Carbide 2360 10
Oxide Films 3700 50
Magnesium oxide 3800 300
Iron Oxide 5750 200
Table 2: Type and properties of inclusions used
Euler/Lagrange Approach
An EulerLagrange approach is employed. Thereby, the
particles are described by a Lagrangian transport through a
continuous carrier gas flow which is captured by an
Eulerian approach according to the numerical scheme
available in STARCD code. In fact, various numbers of
particles of different sizes and mass are employed as listed
in Table 2.
The turbulent fluid phase is described following a
URANSmodeling approach. The unsteady, general form of
the transport equation needed emerges as:
a(po ) a(pu) pv) (p  a(pw) a a aF a a S +s +K
at ax Oy a ax ax ay ay a z
in which q may represent the mean value of mass density p,
velocity components (u, v, w), turbulent kinetic energy and
turbulent dissipation rate, respectively. F represents an
effective diffusion coefficient and So the well known
turbulence source terms in single phase flows.
To better capture streamline curvature effects in turbulent
flows, it is well known that models of second order level,
nonlinear or algebraic kEpsilon models are very
appropriate. We apply therefore the simple (nonlinear)
kEpsilon (see in Yun et al., 2005) modified for twophase
flow description by including source terms for phase
exchange, S, This additional source terms in (1)
characterizes the direct interaction of mass, momentum and
turbulent quantities between the two phases and account for
the twoway coupling between the fluid turbulence and the
particles. Details about these terms can be found in Sadiki et
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
al. (2005). A simple twoway coupling is considered
through the momentum equation only.
To compute the properties of particles moving in turbulent
flow, the Lagrangian approach is employed. The trajectories
of individual particles are obtained from motion equations,
where all external effects, except drag force and gravity, are
neglected.
Coupled to the VOF method, this technique allows to point
out the effect of polydispersed particles on the liquid metal
flow. In order to study the effect of theological properties on
the mould filling process a variation of the fluid viscosity
has been achieved. For that purpose a typical viscosity value
of 0.01Kg/ms has been adopted. It has been derived from
the expression that relates the viscosity of Almetal liquid to
the absolute temperature (temperature range 9331270 K):
log,, (P / 0) = + (9)
T
where p/ =lmPas a1 =0.7324 and a, =803.49K. The
standard deviation of the above equation at the 95%
confidence level is 13.7% (Assael et al., 2006). This
viscosity is very high and mimics the behaviour of a
solidifying material, here considered as a non Newtonian
fluid. Even though a solidification model has not been used
the results in Figure 2 (right) seems to provide the state of
air entrapment during solidification as the temperature is
about 463.8 K.
Results and Discussion
Simulation of benchmark experiments
The VOF model was validated and applied to the
benchmark experiments as reported in Campbell (2006).
For this purpose simulations have been first carried out
without particle inclusions.
Figure 1 (right) shows the numerical grids, prepared by
STARDESIGN, employed in simulation. The total
number of the cells used in the calculation was 176300,
with the smallest cell size being 1.25 mm by 2.5 mm near
the sprue outlet. The thermophysical data used in
simulation are listed in Table 3 according to Campbell
(2006).
Liquid Al Air
(7200C)
Density P (kg/m3) 2580 1.0
Viscosity" (Ns/m2)) 0.0013 lx10
Viscosity (Ns@? )
Table 3: Thermophysical properties
It may be noted that the benchmark test have been
simulated by many researchers (Campbell, 2006, Nishad et
al., 2006). Furthermore, different approaches have been
taken by various researchers for assigning the inlet
boundary conditions. Constant velocity boundary condition
and constant stagnation pressure at the inlet are few of
them. In the present work, a constant velocity boundary
condition (0.75 m/sec) was specified at the inlet as
reference. For parameter studied purposes, this value will be
varied to 0.5 and Im/s, respectively.
Predicted mold filling pattern is compared with Xray data
of Benchmark test. Figure 2 shows the comparison of
experimental and simulated results at various times. Figure
2a shows the comparison of predicted melt front with
experimental melt front at t = 1.2 seconds. At this time the
metal is shown to flow through sprue. As mold filling
progresses, the metal stream enters runner. Fig. 2b shows
the experimental and predicted results at t = 1.5 seconds. It
is readily seen that the correspondence is reasonably good.
This trend continues at other times. This comparison of
predicted and experimental melt front at different times
clearly shows that model is able to capture the essential
free surface dynamics of mold filling operation. With
progress of mold filling, the metal level rises and the front
becomes more stable as seen at t=2seconds.
Based on this prediction confidence of the numerical
model, a series of parameter studies have been carried out.
Especially the effect of rheology via viscosity change has
been pointed out. This is outlined in Figure 3 that presents
comparisons between experimental (left) and numerical
(right) results at (a) t=1.2; (b) t=1.5; (c) t=1.7 und (d) t=2s
with two different viscosities. The results (middle) with the
first value of 0.001Kg/ms that corresponds to the
experimental value agree in a satisfactory way with
experimental data at all the different times recorded.
Further studies have been achieved in order to point out the
influence of polydispersed particles on the liquid metal
flow. Figures 47 show clearly this effect having in mind
the simulation result and experimental data without particle
displayed in Figure 2.
In particular the study was achieved at different
viscosities also in Figures 4 and 5 as well as in
Figures 6 and 7 using the same inlet velocity of 0,5
and Im/s, respectively. So, besides the result in
Figure 3 where comparison with experimental is
shown, the effect of the rheology of the fluid on the
evolution of the mould filling process by changing
the fluid viscosity along with the particle
concentration is obvious
Furthermore, Figures 4 and 6 as well as Figures 5
and 7 exhibit the effect of polydispersion assuming
a constant viscosity of 0.001 and 0.01Kg/ms,
respectively, under variation of the inlet velocities.
This comparison makes clear how the inlet
conditions influences the evolution of the mold
filling process.
Conclusions
A computational model has been developed to simulate the
transport of particles (inclusions and bubbles) in a liquid
Almetal flow at high temperature featuring a threephase
flow system. The model could capture the essential free
surface dynamics of mold filling operation according to the
VOF method. Next, it could compute the transport of over
36,000 particles using a Lagrangian approach to track the
trajectories. Thereby, the transient turbulent flow in the
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
mold region was simulated using a simple (nonlinear)
Kepsilon model. Solidification processes were not taken
into account.
A series of parameter studies allowed to point out:
the influence of particle polydispersion on the
liquid metal flow. This was achieved at different
viscosities and inlet conditions.
the effect of the rheology of the fluid on the
evolution of the mould filling process by changing
the fluid viscosity along with the particle
concentration.
the effect of the inlet conditions on the evolution of
the mold filling process.
While the transport of particles was the main focus here, the
capture or entrapment of particles which touch the
boundaries representing the solidifying shell has to be next
investigated.
Acknowledgements
The authors recognize the financial support by the german
council of research (DFG).
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7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
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Figure 3: Comparison between experimental (left) and
numerical (right) results at (from top to bottom) times (a)
1.2, (b) 1.5, (c) 1.7 and (d) t=2s, respectively, with
different viscosities 0.001Kg/ms corresponding to
experiment (middle) and 0.01 Kg/ms (right). Red:
Alliquid; Blue: air
IV 1 (a)
(b)
U1
(c)
(d)
Figure 2: Comparison between experimental (left side)
and simulated results (right side) for time (a) 1.2, (b) 1.5,
(c) 1.7, and (d) 2 sec, respectively from top to bottom
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
Figure 4: Effect of polydispersion on the mold filling
process (viscosity 0.001Kg/ms, inlet velocity: 0.5m/s) at
(a) 1.2, (b) 1.5, (c) 1.7 and (d) t=2s, respectively.
Figure 6: Effect of polydispersion on the mold filling
process (viscosity 0.001Kg/ms, inlet velocity: lm/s) at
(a) 1.2, (b) 1.5, (c) 1.7 and (d) t=2s, respectively.
figure 3: iiect oi poiyaispersion on me moia iiling
process (viscosity 0.01Kg/ms, inlet velocity: 0.5m/s) at
(a) 1.2, (b) 1.5, (c) 1.7 and (d) t=2s, respectively.
Figure 7: Effect of polydispersion on the mold filling
process (viscosity 0.01Kg/ms, inlet velocity: lm/s) at (a)
1.2, (b) 1.5, (c) 1.7 and (d) t=2s, respectively.
