7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
COMPARISON OF 2D AND 3D MODELING OF MOLD FILLING OF ALUMINIUM CASTING
Kaushal P. Nishad, Lahbib Zealouk and Amsini Sadiki
Technische Universitat Darmstadt, Dept of Mechanical and Processing Engineering, Energy and Powerplant Technology,
Petersenstr. 30, 64287 Darmstadt, Germany
sadiki@tekt.tudarmstadt.de
Keywords: Mold filling, turbulence, free surface, oxide formation.
Abstract
In the present work, 2D and 3D simulations of moldfilling process are carried out using a mathematical model, built on a
multiphysics based commercial package STARCD. The simulation code has capability to solve multiphase problems
dominated by interface between two fluids in which parts of the interface break into regions filled by both fluids. The
numerical model addresses complicated dynamics of filling operation including free surface flow and subsequent flow
behavior and is based on conservation of mass and momentum. Free surface is modeled using the volume of fluid (VOF)
method.
The numerical model is validated by means of the benchmark experimental data from literature. The 2D and 3D results are
also compared to each other. Especially the role of turbulence and pouring rate on variables affecting sites prone to oxide film
formation is investigated using a simple but novel technique. It turns especially out that the inclusion of turbulence leads to a
substantial increase of the amount of the oxide film formation.
Introduction
The flow properties in the filling process during casting are
of great interest as they influence many important
phenomena, which have strong consequences on the end
product quality. These effects include among others the
formation, motion and entrapment of oxide film and gas
bubbles that may create defects if they become entrapped in
the solidifying material.
In last two decades, significant progress has been made in
the field of modeling of casting processes [13]. In
particular, effects of casting defects on the mechanical
properties of castings have been investigated by many
researchers (e.g. [15]) mostly based on experimental
techniques. Today, mathematical models practically touch
all aspects of casting process, from metal poring to
solidified cast products. With increase in computational
power, it is now possible to address processes involving
complex physics. With regard to the mold filling which is an
integral part of any casting operation, its modeling and
simulation are important from the point of view of design
optimization, i.e., volume and placement of riser, placement
of chill, etc. Mold filling is equally important from quality
point of view as origin of many casting defects can be
traced to mould filling stage. Entrapped air/gas pockets
originate during mold filling stage and can render a casting
useless. Similarly, excessive oxide film formation can take
place during the mold filling operation. As shown by
Campbell [4], porosity and other casting defects are linked
to oxide bifilms, which can originate during the mold
filling operation. Clearly, mathematical models for mold
filling operation can provide significant insight into the
process and can be used for control of several casting
related defects.
The main difficulty in modeling of mold filling operation is
its complex nature. Typical mold filling operation involves
unsteady, turbulent, multiphase flow along with free surface
movement. Besides these, heat transfer, phase change, oxide
films formation, etc need to be modeled. Simultaneous
occurrence of these phenomena while the mold is being
filled presents a formidable modeling challenge. In past,
therefore, models of mold filling have all been based on
simplified physics and these are used to address specific
issues [5].
In the present work, 2D and 3D simulations of moldfilling
process are carried out. The focus is to investigate the role
of turbulence and pouring velocity on oxide film formation
during mold filling operation. Oxide film formation is
directly related to evolving free surface and entrapped air.
Thereby the model is based on simplifying assumptions that
duration of mold filling is short compared to solidification
time and, therefore, heat transfer and phase change are not
considered. The numerical model addresses especially
complicated dynamics of filling operation including free
surface flow and subsequent flow behavior and is based on
conservation of mass and momentum. Free surface is
modeled using the volume of fluid method (VOF) integrated
in STARCD code. To validate the model the benchmark
experimental results from literature [5, 8] are used.
Mathematical modelling
As stated earlier, the mathematical model is built using
continuum formulation based multiphysics tool, STARCD,
with capability to handle free surface. Let us outline the
governing equations used.
Momentum
(pu)+V.(puu)= V\(pu) P+pg +S
At 9x (1)
where u is the velocity vector in the Cartesian coordinate
and p is the pressure in the fluid, p and /1 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
(p)0 (2)
+V (pu) = 0 (2)
iAt
The above equation can be cast in volume conservation
form as follow:
c(ln p) 0
at (3)
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 [11]),
respectively:
S(pk)+V(puk) =V Pam+ Vk +pv,G pe
(4)
C + = JVsj + ClpvG C2,p
(5)
where k is turbulence kinetic energy and c is the
turbulence dissipation rate, v, is turbulence viscosity and
calculated as v,=Ck /I and C,, k, O' Cl and
C2, 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:
F \81 [v 99 (u aw aw av
G +2 I +,,2 +raw11+( + i +i + 2 + 2
ax ayJ Laz j ay ax) y ax) ay a)
(6)
Free Surface
For free surface modeling [6, 7, 10], the volume of fluid
method (VOF) [7, 10] is selected. It deals with a single
continuum whose properties vary in 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, f, of
each fluid. The variable takes the value 0.0 at the location
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
fluid 1 and the 1.0 at the location in fluid 2. The value of
q is obtained through the solution of the scalar
conservation equation:
 + V. (u)= 0 (7)
9t
Calculation of area prone to oxide film formation:
The metal/air interfaces are considered prone to oxidation.
It is assumed that areas exposed to air contribute to
formation of oxide films. Owing to microscopic thickness,
these films do not have strength. These microscopic oxide
layers are at the dynamic moving surfaces during filling
operation and get incorporated in liquid all the time
making fresh liquid is available for further oxidation. In
other words, unlike the case of oxide films covering
stationary liquid metal, these oxide films do not prevent
further oxidation. Also, new surfaces generation and
merging of interfaces lead to incorporation of oxide films
into liquid. In order to get a comparative number for oxide
film formation under different processing conditions, the
following methodology is adopted. Areas exposed to air
are tracked. This includes free surface of liquid front as
well as metal interface enclosing entrapped air. Summing
these over time gives a measure of total oxide film in the
liquid. These are represented mathematically as follows: At
any time, t, St is the sum total areas at metal/air interface
[12]. Thus,
St = s1:
where S'is the total exposed surface at time t and s,'
the surface at different locations at time t. Amount of oxide
film formed and incorporated in liquid is given by
following equation
moj= lStAt (9)
0
The quantity m, is the oxide film formed during total
mold filling time, 91 is the rate of oxidation and is
dependent on metal properties, and At is the numerical
time step.
Benchmark problem
The mathematical model described above was tested
against experimental data provided in [5]. Figure la shows
schematic of the casting, used in these experiments. The
molten aluminum was allowed to flow in to 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.
Results and Discussion
Simulation of benchmark experiments:
The numerical model was used to simulate the benchmark
experiments as reported in [5]. For this purpose a series
of numerical simulations has been carried out.
Two dimensional (2D) computations with and
without turbulence consideration on the one hand
and under various pouring rates conditions on the
other hand, in order to assess the influence of
turbulence and pouring rates on the amount of
oxide formed
Three dimensional (3D) simulations under two
different theological conditions. Here two
different viscosities of the Almetal liquid are
used: the first viscosity value was set according to
experiments; the second was evaluated by means
of an appropriate expression provided in [9] that
relates the viscosity of Almetal liquid to the
temperature.
In Figures 14 the results of 2D simulations are presented.
Figure 5 focuses on the 3D results. Figure lb shows the
numerical grids, prepared by STARDESIGN, employed in
simulation. The total number of the cells used in the
calculation was 2122 in 2D case, 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
1 according to [5].
It may be noted that the benchmark test have been
simulated by many researchers [5, 8]. Furthermore,
different approaches have been taken by various
researchers for assigning the inlet boundary condition.
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.
Predicted mold filling pattern is compared with Xray data
of Benchmark test. Figures 2 and 3 show 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 = 0.24 second. 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 = 0.5
seconds. It is readily seen that the correspondence is
reasonably good.
This trend continues at other times. Comparison of
predicted and experimental melt front at different times
(Figs. 2 and 3) clearly show that model is able to capture
the essential free surface dynamics of mold filling
operation. These figures also show the complex nature of
free surface. With progress of mold filling, the metal level
rises and the front becomes more stable as seen in figures
3(a)(d). These features are also clearly observed in
Figure 5, where the results of 3D simulations are
displayed.
Figure 5 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. A further comparison with the 2D
computations in Figure 3 emphasizes the three dimensional
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
character of turbulence that is better captured only by 3D
computations. See also [10].
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 we used a typical viscosity
value of 0.01Kg/ms that has been derived from the
expression that relates the viscosity of Almetal liquid to
the absolute temperature (temperature range 9331270 K)
[11]:
logo (P / P)= a, + a
T
(10)
where p' =lmPas a, =0.7324 and a =803.49K. The
standard deviation of the above equation at the 95%
confidence level is 13.7%. 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
5 (right) seems to provide the state of air entrapment
during solidification as the temperature is about 463.8 K.
An interesting finding from this work is the ability of the
model to show the entrapped air during the mold filling
operation using 2D simulations. The 3Dbased analyses are
left for future work. This aspect did not receive adequate
attention in earlier simulations of this experiment, though
entrapped air pockets were clearly visible in experimental
data. More air pockets lead to more chances of oxide film
formation and therefore, conditions leading to its
minimization would enhance quality of the casting.
10 1015
x0 xIcs ]150 ii
Figure 1: Left: Benchmark test geometry.
Right: Numerical mesh
Importance of turbulence
Mold filling operations are usually turbulent. However,
simulation of molding filling with consideration of
turbulence is highly computation intensive. Two
simulations, one with turbulence [11] and another without
turbulence, were carried out. The influence of turbulence
on to, a quantity related to amount oxide film formation
(equations 8 and 9) was assessed. Figure 4(a) shows the
comparison. It is clearly seen that inclusion of turbulence
leads to substantial increase of the value of nmo. This
result gives an indication that turbulence suppressing
devices will work towards minimization of oxidation
formation.
Liquid Al Air
(7200C)
Density P 2580 1.0
(kg/m )
Viscosity U 0.0013 lxl0
(Ns/m2)
Table. 1. Thermophysical properties
Effect of pouring rate
Pouring rate is a crucial parameter in mold filling operation.
In order to investigate the role of pouring rate on oxide
formation, four simulations were performed. Fig. 4(b)
shows the influence of poring rate on mn A very
interesting result is obtained. At low poring rate, mn is
high. With increase in poring rate it goes down. However,
with further increase in pouring rate, mo goes up again.
Initial decrease in mo is on account of decreased time for
filling operation and consequently for oxidation. However,
as pouring rate increases, the surface becomes more
chaotic and free surface profile changes. These contribute
to increase inm,. Thus, beyond certain pouring rate, mo
goes up again.
Conclusions
2D and 3D computations of the moldfilling process have
been presented and compared. For this purpose the
benchmark configuration of Campbell has been used.
During mold filling operation, many defects originate. The
role of few important variables on parameter affecting
oxide film formation has been investigated. The
phenomenon of air entrapment and its transport has been
depicted. The role of turbulence and pouring rate on
parameters affecting oxide film formation has also been
investigated. Corresponding parameter studies based on 3D
calculations are left for future work.
Acknowledgements
The authors recognize the financial support by the german
council of research (DFG) as well as the Graduate School
on Computational Engineering.
References
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7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
Assessment of Casting Filling methods, Modeling
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[8] lulp \\ \\ fe\iu.s s.co.uk
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7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
Figure:2 Comparison between experimental (left side) and simulated results (right side) for time
(from top to bottom) (a) 0.24, (b) 0.5, (c) 0.74, and (d) 1.0 sec respectively from top to bottom
Sr
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
(a)
(b)
(c)
(d)
Figure:3 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
Q)
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
04 05 06 07
Pouring rate (m/sec)
08 09
Figure: 4 (a) Importance of turbulence: oxide formation for cases with and without turbulence (b) Effect of
pouring rate: oxide film at different pouring rate
a 1.8
S1.6
S1.4
S1.2
! 1
0.8
0 0.6
0 0.4
= 0.2
0
Swithoutturbulence
SAwith turbulence
0 0.5 1 1.5 2 2.5
Time (sec)
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
Figure 5: 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
