Modeling
feeding flow related shrinkage defects in aluminum castings
A
Reisa, Z. Xub, R.V. Tolb, R. Netoc
January 2012, Pages
1–7
Summary
The process modeling of shape casting
is geometrically complex and computationally very challenging. Besides the
three-dimensional complex shapes with multiple domains, the defects of interest
to industry arise as a consequence of the interaction amongst a range of
phenomena. Conventionally, the key phenomena and defect prediction are modeled
through empirical relations applied to the simulation results. Such approaches
are neither comprehensive nor reliable. This paper presents a 3-D model that is
capable
of predicting the formation of
shrinkage defects explicitly as a function of the interacting continuum
phenomena, i.e. free surface flow, heat transfer, and solidification, in
complex three-dimensional geometries which allows to identify the distinction between
surface depression, surface connected cavities and internal cavities. The model
solves the coupled macroscopic conservation equations for mass, momentum, and
energy
with a phase change during
solidification. In the model, the volume deficit due to solidification can
either be compensated by depression of the outside surface or by creating a
cavity that initiates either on the surface or in the interior of the casting.
The solidification morphology is taken into account by using a parameter, which
depends on the fraction solid, in the momentum equation. By using an adapted
free surface algorithm, it is suitable to predict surface connected defects:
depressed surfaces and caved surfaces. A critical pressure serves as a
criterion to open internal shrinkage cavities. The model does not need to
search for connected zones to feed shrinkage, but the shrinkage distribution
will automatically emerge from the continuity equation.
This advanced shrinkage model has
experimentally been validated successfully using two Al–Si alloys, a skin
freezing eutectic alloy and a mushy freezing hypo-eutectic alloy.
Recently, due to the development of
computer technology, an effort is done to predict casting defects directly as a
consequence of the physical phenomena that are involved. A modeling approach
based on an improved description of the physical processes
has become a more realistic practical
and straightforward option. Shrinkage related defects result from the interplay
of phenomena such as fluid flow, heat transfer with solidification, feeding
flow and its free surfaces, deformation of the solidified layers and
so on. Many attempts have been made to
model shrinkage related defects. However, common models do not take into
account feeding flow and therefore zone searching based on the solid fraction
is needed. Coupling heat transfer, feeding flow and mass conservation into
shrinkage defects, is an important approach. The first model that took into
account feeding flow dates back to the early 1D analytic work of Piwonka and
Flemings [1]. This early analytical work formed the basis of a category of
models based upon Darcy’s law. Darcy’s law relates the flow trough a porous
medium to the pressure drop across it. Kubo and Phelke [2] were the pioneers in
presenting a 2D numerical model by coupling Darcy’s law to the equations of
continuity estimating the fluid flow. Other 2D models were presented by Zhu [3]
and Huang [4]. In terms of 3D models,
Bounds [5] presented a model that
predicts macroporosity, misruns, and pipe shrinkage in shaped castings. Later
Sabau [6], Pequet [7] and Carlson [8] also present 3D models that included the
concept of pore nucleation and growth. This paper proposes a model to
explicitly calculate shrinkage defects as a result of deficiency in feeding flow.
A 3-D numerical problem that illustrates the ability to compute internal and
surface interconnected defects is presented and compared with experimental
results.
To date no methodology has been
proposed to quantify the extent of shrinkage porosity, coupling internal
(cavities) and external (surface connect or surface depression) shrinkage
defects which occur when solidification shrinkage cannot be compensated by
feeding flow. There are no validation
experiments that are suitable for this model regarding the factor that
determines whether shrinkage porosity is either internal or surface connected
or both
In this research, we did not use any
finite element analysis software. In fact we used the finite volume method to
solve the governing equations. Up to now no commercial software can simulate
the phenomenon perfectly. This is purely original research
work, we developed the core code to
solve the problem. But we used Experto-ViewCast to deal with pre-processing and
pro-processing. The finite volume method is used to discretize the governing
equations. A structured orthogonal mesh is employed to discretize the mold and
the casting. A staggered grid serves to discretize the governing equations for fluid flow
calculation. The Semi-Implicit- Method for Pressure Linked Equations, SIMPLE
method, described in detail by Patankar [10] is used to handle the velocity and
pressure coupling for the equations. The velocity field is calculated from the
momentum and continuity equations at each time step using the updated properties of each
volume element, such as solid fraction, density, and permeability. For every
time step, the temperature distribution, used to calculate solid fraction, was
obtained by solving the energy equation. Next the properties of each volume
element were updated again. Iteration is continued until the continuity
equation is satisfied. The movement of the free surface is evaluated by using
the velocity field. An adapted free-surface algorithm Xu [11] has been
developed to describe the external and internal shrinkage defects. An
element becomes a free surface depending on its pressure and solid fraction. At
each time step, if the conditions of P < Patm and fs < fs crit = 0.3 in
any of the outside layer elements are satisfied, this element becomes a free surface
element Also for internal elements, the condition of pore nucleation P <
Pcrit(T) = Patm × (1 − (Tl − T)/(Tl − Ts)) is tested. If this happens this
element will be treated as a free surface element that can act as a feeder. The
material properties used in the calculations are taken from Reis.
The governing equations are solved to
obtain the temperature, fraction solid, melt pressure and feeding velocity
throughout the casting. Before the start of solidification, unrestrained liquid
feeding occurs. Liquid contraction in the casting will be fed by the highest part of the system due to
gravity, resulting in “pipe shrinkage”. When the solidification starts at the
outer shell of the casting, the pressure in the liquid begins to drop due to
flow resistance caused by formation of solid crystals. As long as the pressure
in outside layer elements, besides the top part, drops to the atmospheric pressure they also become free surface
elements that can feed the solidifying casting to compensate the metal
contraction. In those elements that are emptying of liquid, the pressure is
forced to the atmospheric pressure. This will result in external shrinkage
defects, also called “caved surfaces”.
Result and
discussion:
When designing the geometry for the test case the idea has been to reproduce a
real casting condition, while maintaining the geometry as simple as possible.
With a simple geometry we can better identify the variables directly enrolled
in shrinkage feeding. Also the choice of the geometry has been
related with being prone to different types of shrinkage defects as to
illustrate the features of the developed model. In this paper results for short
freezing, AlSi12 and long freezingalloy, AlSi7, are presented. A comparison is
made between numerical and experimental.
Conclusion: This model and
corresponding validations have been applied to AlSi alloys. In this model
different types of defects can be predicted: porosity by surface initiation,
external porosity and internal porosity by nucleation. As expected, due to
freezing characteristics the short freezing material AlSi12 and the long
freezing AlSi7 presented a very different behaviour. Internal porosity by
surface initiation was found in both short and long freezing alloys, although
having different appearance. In the long freezing alloy AlSi7, what seems to be
a series of separate interdendritic pores, is in reality a single
interconnected pore with a highly complex shape. On the other hand, the short
freezing alloy AlSi12 reveals a single and
evident cavity. Numerical results showed that in the long-freezing-range alloy
this type of defect occurred at a late stage in solidification, when developing
the dendritic mesh (higher solid fraction-less permeability). This means that
drawing liquid from the nearby surface becomes easier than drawing liquid from
the more distant feeder. The point from which liquid may be drawn can be any
surface and a random point in a surface. However, in the short freezing alloy,
the initiation site begins at the surface and is much more localized. Surface
sinks (top and
side) were found in long freezing
alloys. They were particularly evident when the path from the feeder was
smaller. This means that the lowering in internal pressure happened very soon
and leads to an inward movement of the external surface of the casting, since
it was not solid enough to resist the pulling due to pressure drop. If the
movement is severe and localized it constitutes a defect known as a ‘sink’ or a
‘draw’. The expected shrinkage features were well described by the present
model and illustrate the capability of the “defect” model to predict the
shrinkage defects of interest to the foundry industry. The model
gives the correct trend in predicting the location, extent, and nature of the
shrinkage porosity defects. The way to avoid the shrinkage defect is to make
the riser neck larger. In this way it will form a direct solidification and
makes the feeding path open. The current method can also simulate this
situation
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