Squeeze casting, also known as liquid-metal forging, is a process by which molten
metal solidifies under pressure within closed dies positioned between the plates of a
hydraulic press [1,2]. The applied pressure and the instant contact of the molten metal with
the die surface produce a rapid heat transfer condition that yields a pore-free fine-grain
casting with mechanical properties approaching those of a wrought product. Due to the
elimination of air gap between the metal and die interface, the heat transfer
coefficient is increased, which enhances cooling rates and solidification. The squeeze
casting is easily automated to produce near-net to net shape high- quality components. The
process was introduced in the United States in 1960 and has since gained widespread
acceptance within the non ferrous casting industry. Aluminium, Magnesium, Copper alloys
components are readily manufactured using this process. Several ferrous components with
relatively simple geometry for example, Nickel hard-crusher wheel inserts have also been
manufactured by the squeeze casting process. Despite the shorter die life for complex life
for complex ferrous castings requiring sharp corners within the die or punch, the process
can be adopted for products where better properties and savings in labour or material costs
The process of mold design in the foundry industry has long been based on the
intuition and experience of foundry engineers and designers. To bring the industry to a more
scientific basis the design process should be integrated with scientific analysis such as fluid
flow, heat transfer and stress analysis. Perhaps the most effective way to do this is with the
aid of computer aided operation (CAO).
Starting with the original design, a computer model is used to stimulate the casting
process. Given a set of defect criteria, defects can be predicted modification to the original
design. After several iterations of this design cycle and optimum design, free of defects
should be produced.
From this procedure it will be possible to determine whether a given mold design
will produce a sound casting without having to discover this in the foundry through the
usual trial and error process, which can be very tedious, time consuming and expensive.
Figure 1.1 Schematic Diagram of Casting Design Process
Obviously the performance of this design cycle is based on the accuracy of the
casting simulation and the validity of the defect prediction criteria. The promise of CAO has
been that has we model the physical process closer to reality, the simulation process
becomes more accurate, the defect criteria simpler and more precise. However, this promise
comes at a price. First, as a model improves it becomes increasingly sensitive to the thermo
physical data. Often this data is difficult to obtain. Therefore several new experimental
techniques need to be developed. Second, as the mathematics becomes more complex there
is a need to either develop efficient solution algorithm or invest in more powerful computer
resources. It is a balance of all these factor that will result in a successful CAO application.
The numerical simulation has increasingly become an effective tool in the casting
manufacturing, by which some primitive and time-consuming procedures for finding the
appropriate set of process parameters are avoided. The aim of this thesis is to improve
the design cycle by investigating the heat transfer aspects of solidification during squeeze
1.2 Strategy of Thesis
Design Casting Simulation Defect prediction
Recently Sun  has carried out extensive experiments on squeeze casting process
of a different wall-thickness 5-step casting under different pressure conditions. Squeeze
casting of magnesium alloy AM60 was performed under an applied pressure 30, 60
and 90 MPa in a hydraulic press. With measured temperatures, heat fluxes and IHTCs were
evaluated using the polynomial curve fitting method and numerical inverse method. In this
thesis, solidification process during squeeze casting process is simulated using the
commercial CFD software FLOW-3D for the same set of parameters for which Sun [ ] has
carried out experiments. The heat transfer coefficients needed for metal/mold inteface is
taken from the polynomial fit developed by Sun [ ] which is explained in detail in chapter 4
of this thesis. The layout of the thesis is as follows:
A literature review related to modeling and experimental studies related to squeeze
casting process is presented in chapter 2. Chapter 3 explains the physics behind the
squeeze casting process, corresponding governing equations and method of
implementation using FLOW-3D,a commercial CFD software. Examination of
existing mathematical models to determine their suitability.
Chapter 4 explains in detail, the experimental setup used by Sun  to calculate heat
transfer coefficients at the metal/die interface during squeeze casting process under
different applied pressures. Construction and/ or importing of a mathematical model.
Chapter 5 deals with the results and discussion part of the simulations doen using
This is followed by conclusions in chapter 6.
1.3 Scope of Thesis
The scope of this thesis has been restricted to the investigation of solidification
process. In squeeze casting applied pressure plays an important role. The main advantage of
the deployment of high pressure is that it enhances the heat transfer coefficients between
liquid metal and mold surface by several orders of magnitude. This enhancement is realized
due to the establishment of direct contact between the liquid metal and the die wall. This
fact has been proved experimentally by Sun  where he has carried out extensive
experiments to record temperature profiles during squeeze casting process of different wall-
thickness 5-step casting under different pressure conditions. The alloy chosen for his
experiments were magnesium alloy AM60 for the casting and steel die for the mold. From
the experimental data, he back calculated the heat transfer coefficients at the metal/die
interface using inverse approach and by polynomianl fitting method. This work is directed
towards using these heat transfer coefficients at the metal/die interface for simulating the
solidification process of different wall-thickness 5-step casting under different pressure
conditions and to map the temperature profiles at different locations and try to compare the
results between simulation and experiments.
2.1 Squeeze Casting
Casting is the most economical route to transfer raw materials into readily usable
components. However, one of the major drawbacks for conventional or even more advanced
casting techniques, e.g., high pressure die-casting is the formation of defects such as
porosity. Furthermore, segregation defects of hot tears. New casting techniques have,
therefore, been developed to compensate for these shortcomings. Of the many such casting
techniques available, squeeze casting has greater potential to create less defective cast
Squeeze casting (SC) is a generic term to specify a fabrication technique where
solidification is promoted under high pressure within a re-usable die. It is a metal-forming
process, which combines permanent mould casting with die forging into a single operation
where molten metal is solidified under applied hydrostatic pressure. Although squeeze
casting is now the accepted term for this forming operation, it has been variously referred to
as "extrusion casting", "liquid pressing'', "pressure crystallization'' and "squeeze forming''.
The idea was initially suggested by Chernov  in 1878 to apply steam pressure to molten
metal while being solidified. However, in spite of its century old invention,
commercialization of squeeze casting has been achieved only quite recently and is mainly
concentrated in Europe and Japan. It is mainly used to fabricate high integrity engineering
components with or without reinforcement. Hartley  reported a technique developed by
GKN Technology in UK for the pressurized solidification of Al alloy in reusable dies. In
this process a die set is placed on a hydraulic press and preheated, and the exact amount of
molten alloy is poured into the lower half of the open die set, the press closed so that the
alloy fills the cavity and the pressure maintained until complete solidification occurs (31-
108MPa pressure). External undercut forms can be produced, and using retractable side
cores, through-holes are possible. Since the as-fabricated components can be readily used in
service or after a minor post-fabrication treatment, squeeze casting is also regarded as a net
or near net-shape fabrication route.
Parallel to commercialization, there are research centre throughout the world that are
actively researching further development and exploitation of this net or near net shape
fabrication process. This is evidenced by the publication of more than 700 papers in various
engineering and scientific journals. These are mainly related to Aluminium and Magnesium-
based alloys with special emphasis on metal matrix composites MMCs. According to
Crouch, squeeze casting is now the most popular fabrication route for MMC artifacts.
The annual 12±15% growth rate of MMCs in the automotive, aerospace, sport and leisure
goods and other markets is a clear indication of better usage of advanced manufacturing
routes such as squeeze casting.
In addition, since squeeze casting may be carried out without any feeding system,
runners, gates, etc., and shrinkage compensating units, risers, the yield is quite high with
almost no scrap for recycling. Finally, in contrast to forging, squeeze cast components are
fabricated in a single action operation with lesser energy requirements.
2.1.1. Process outline
The process of squeeze casting involves the following steps:
1. A pre-specified amount of molten metal is poured into a preheated die cavity, located on the
bed of a hydraulic press.
2. The press is activated to close off the die cavity and to pressurize the liquid metal. This is
carried out very quickly, rendering solidification of the molten metalunder pressure.
3. The pressure is held on till the metal is completely solidified. This not only increases the
rate of heat flow, but also most importantly can eliminate macro/micro shrinkage porosity.
In addition, since nucleation of gas porosity is pressure-dependent, the porosityformation
due to dissolved gases in the molten metal isrestricted.
4. Finally the punch is withdrawn and the component isejected out.
2.1.2.Mechanics of squeeze casting
22.214.171.124. The die
A most crucial aspect in permanent mould castings such as die-casting or squeeze casting is
the die itself and, most importantly, the design of the die including the selection of suitable
die material, the manufacturing process, appropriate heat treatment and the maintenance
practice. Squeeze casting dies are exposed to severe thermal and mechanical cyclic loading,
which may cause thermal fatigue, cracking, erosion, corrosion, and indentation. The nature
and features of die are greatly influenced by the particular alloy to be cast. Currently H13
tool steel is a widely used material of constructions but generally die steels should have
good hot hardness, high temper resistance, adequate toughness and especially a high degree
of cleanliness and uniform microstructure.
126.96.36.199. Different types of squeeze casting
Two basic forms of the process may be distinguished, depending on whether the pressure is
applied directly on to the solidifying cast product via an upper or male die (punch)or the
applied pressure is exerted through an intermediate feeding system as schematically shown
in Fig.2.1: (i) the direct squeeze casting mode, and (ii) the indirect squeeze casting mode.
Figure 2.1 Schematic diagram to illustrate the direct and indirect modes
of the squeeze casting process.
For the direct mode, two further forms may be distinguished based on liquid metal
displacement initiated by the punch movement: (i) without metal movement, and(ii) with
metal movement. As illustrated in Figure1.2, the first form is suitable for ingot type
components where there is no metal movement, whilst the second type involving metal
movement, also known as the backward process, is more versatile and can be used to cast a
wide range of shaped components.
Figure 2.2 Schematic diagram to show two forms of the direct squeeze casting process.
188.8.131.52. Various modes of squeeze casting
Squeeze casting can be classified according to type of equipment used as : (i)
vertical die closing and injection, (ii) horizontal die closing and injection, (iii) horizontal die
closing and vertical injection, and (iv) vertical die closing and horizontal injection. A further
classification may be envisaged as: (i) before the beginning of crystallization, and (ii) after
the beginning of crystallization, which may also be described as semi-solid pressing.
Figure 2.3 summarizes the various modes of the squeeze casting process.
Figure 2.3 Various modes of squeeze casting process
184.108.40.206 Process parameters
The most important process parameter is the alloy itself. The composition and
physical characteristics of the alloy are of paramount importance due to their direct effects
on the die life. These include the melting temperature, and thermal conductivity of the alloy
together with the combined effect of the heat-transfer coefficient and soldering onto the die
material. Furthermore, the alloy dictates the selection of casting parameters such as die
temperature, which has direct consequence on the die life. Therefore, squeeze casting is
usually employed for low melting point temperature alloys of Aluminium and Magnesium.
In addition to the composition of a casting alloy, which determines its freezing range and
affects the quality of finished components, the casting parameters should also be controlled
very closely to achieve a sound casting. The most dominant process parameters are die
temperature and pouring temperature, and superheat, although the level of applied pressure
is also important. Since the metal is cast under pressure, the inherent castability of the alloy
is of little or no concern. Other important parameters include the cleanliness of the metal in
relation to the presence of inclusions, metal movement within the die which may induce
turbulence, the die coat, and the time interval over which the pressure is applied, i.e., the so-
called dead time. The die temperature is usually held at between 200°C and 300°C for
Aluminium and Magnesium alloys, whilst the applied pressure varies between 50 and 150
MPa. The lubrication medium, i.e., the die coat, is usually graphite based. Heat-transfer
coefficients are extremely high due to the casting metal being pressed against the die wall.
The control of following process parameters is important for a good quality squeeze casting
Melt Volume Precision control of the metal volume is required when filling the die cavity.
This ensures dimensional control.
Casting Temperature Depends on the alloy and part geometry. The starting point is
normally 10-100°C. above the liquidus temperatures.
Tooling temperatures ranging from 200-300 °C are normally used. The lower range is
more suitable for thick section casting. The punch temperature is kept 15 - 30°C below the
lower die temperature to maintain sufficient clearance between them for adequate vending.
Excess punch to die clearance allows molten metal to be extruded between them, eroding
Time delay is the duration between the actual poring of the metal and the instant the punch
contracts the molten pool and starts the pressurization of the thin webs that are incorporated
into the die cavity. Because increased poring temperature maybe required to fill these
sections adequately upon pouring, a time delay will allow for cooling of the molten pool
before closing of the dies to avoid shrink porosity.
Pressure levels of 50-140 MPa are normally used. There is an optimum pressure for each of
the systems after this there is no added advantage in mechanical properties.
Pressure duration varying from 30 - 120s has been found to be satisfactory for castings
weighing 9kg. However, the pressure duration is again dependant on part geometry. Applied
pressure after composite solidification and temperature equalization will not contribute any
property enhancements and will only increase the cycle times.
Lubrication for Aluminium, Magnesium and Copper alloys a good grade of colloidal
graphite spray lubricant has proved satisfactory when sprayed on the warm dies priority
casting. Care should be taken to avoid excess build-up on narrow webs and fin areas where
vent holes are used. Care must be taken to prevent plugging of these vents for ferrous
casting, ceramic type coatings are required to prevent welding between the casting and the
metal die surface.
2.1.3.Advantages of Squeeze Casting
With the current emphasis on reducing materials consumption through virtually net
shape processing and the demand for higher strength parts for weight savings, the
emergence of Squeeze casting as a production process has given materials and process
engineers a new alternative to the traditional approaches of casting and forging. By
pressurizing liquid metals while they solidify, near-net shapes can be achieved in sound
,fully dense castings. The near-net and net shape capabilities of these manufacturing process
are the key advantages of this process.Improved mechanical properties are additional
advantages of Squeeze cast parts.
The close contact with the die surface during solidification results in rapid
solidification of casting. This rapid solidification produces a fine secondary dendrite arm
spacing in the castings ,so that good strength and ductility can be attained. These excellent
properties are relatively high in the as cast condition and are enhanced further in the heat
treatable alloys by the excellent response to solution heat treatment. Since the process
minimizes both gas porosity and shrinkage cavities, excellent properties are attained. These
properties have been shown to be equivalent to wrought alloys in many instances. Although
this process has many advantages in producing parts of light metals that can be utilized in
structural applications ,the full potential can only be realized after the process has been
Squeeze casting has been successfully applied to a variety of ferrous and non ferrous
alloys in traditionally cast and wrought composition. Applications include aluminum alloy
pistons for engines and disc brakes; automotive vehicles, truck hubs, barrel heads, and
hubbed flanges; brass and bronzes bushings and gears; steel missile components and
differential pinion gears; and a number of parts in cast iron, including ductile iron mortar
shells . Squeeze casting is simple and economical, and efficient in its use of raw material,
and has excellent potential for automated operation at high rates of production. The process
generates the highest mechanical properties attainable in a cast product. The micro
structural refinement and integrity of squeeze cast products are desirable for many critical
Squeeze casting process gives new opportunities to fabricate advanced materials,
especially in the field of composites. Squeeze casting can also be used to fabricate bi-metals
where, for instance, cast iron inserts can be incorporated to increase wear resistance in
aluminum alloy components. Application to date have been wheels, pistons and brakes discs
2.1.4. Applications of Squeeze Casting
Squeeze casting process has been explored for number of application using various
metals and alloys. Due to low density and high strength-to-weight ratio, magnesium castings
in the automotive application increase rapidly. Currently, high pressure die
casting(HPDC) is the dominating production process for the most of magnesium
automotive components. Compared with the HPDC, the squeeze casting process with high
applied pressure is a promising solution for thick magnesium castings. The squeeze casting
has been commercially succeeded in manufacturing parts include an Aluminium dome ,
ductile Iron mortar shell, and a Steel bevel gear. Other parts that have been Squeeze cast
include stainless steel blades, super alloy discs, Aluminium automotive wheels and pistons,
and gear blanks made of brass and bronze.
Recently, this process has also been adopted to make composite material at an
affordable cost. A porous ceramic pre-form is placed in the preheated die which is later
filled with the liquid metal and pressure is then. The pressure, in this case, helps the liquid
metal infiltrate the porous ceramic perform, giving a sound metal ceramic composite. The
technological breakthrough of manufacturing metal-ceramic composites, along with the
ability to make complex parts by a near-net shapes Squeeze casting process, suggest that
this process will find application where cost considerations and physical properties of alloys
are key factors .However, rare squeeze cast magnesium components have been
used in real engineering applications.
2.1.5 Effect of pressure on the solidification behaviour during squeeze casting process
The application of pressure during solidification would be expected to affect phase relationships in
an alloy system. This may be deduced by considering the Clausius-Clapeyron equation ,
where Tf is the equilibrium freezing temperature, Vl and Vs are the specific volumes of the liquid
and solid, respectively, and ΔHf is the latent heat of fusion. Substituting the appropriate
thermodynamic equation for volume, the effect of pressure on freezing point may roughly be
estimated as follows :
where P0, ΔHf and R are constants. Therefore, Tf should increase with increasing pressure. On a
mechanistic approach, such change in freezing temperature is expected due to the reduction in
interatomic distance with increasing pressure and thus restriction of atomic movement, which is the
prerequisite for melting/freezing. The inter-solubility of constituent elements together with the
solubility of impurity and trace elements is also expected to increase with pressure.
Fig 2.4The effect of rapid cooling and the application of pressure on the Al-Si phase diagram.
The above mentioned theoretical predictions have been proven experimentally where a
liquidus temperature rise of up to 90
C has been reported for pure Al/Si binary alloys at a pressure of
150 MPa. Furthermore, the eutectic point moves to the left, i.e., to higher Si contents as indicated in
Figure 2.4. The consequences of such changes in the phase diagrams area significant improvement
in the microstructure and mechanical properties of SC-fabricated components. The observed fine
grained structure of squeeze castings being principally due to the increase in heat-transfer
coefficients, i.e., greater cooling rates for the solidifying alloy due to reduction in the air gap
between the alloy and the die wall and thus more effective contact area. The size of the air gap
between the solidifying alloy and the die wall and the degree of undercooling, the two main
features for fine structure, are dependent on such process parameters as the pressure, the timing of
its application and the chemistry of the solidifying metal. Certainly, the application of pressure
reduces the air gap between the solidifying metal and the metallic mould and thus increases the
contact area; effecting improvement in the heat-transfer coefficient.
Cho and Hong (1996) studied heat transfer coefficients at the casting/die interface in
squeeze casting and applied a single load (50MPa) with die heating and concluded that heat transfer
coefficient increases with the application of pressure. Casting parameters, as studied by different
authors that have been known to have signiﬁcant inﬂuence on the squeeze cast products are applied
pressure, die pre-heat temperature and melt temperature. In the work of Maleki et al. (2006),
squeeze casting products decrease in density at lower applied pressure and increases with higher
applied pressures . They concluded that this increase becomes less signiﬁcant at applied
pressure of 100 MPa. In the report, it was also observed that with increase in applied pressure, the
cast specimens’ grain size becomes smaller coupled with improved hardness. The melt
temperatures of between 6900
C and 6600
C might just be enough for squeeze casting of Aluminium
and Aluminium alloys respectively, as observed by Yang (2003) . It was reported by Yang
(2007) that the shorter the solidiﬁcation time of casting, the higher is its density, yield strength and
ultimate tensile strength . Chattopadhyay (2007) applied a ﬁxed enthalpy formulation to model
solidiﬁcation for a cylindrical geometry and found that solidiﬁcation time decreased asymptotically
with increase in heat transfer coefﬁcient . This phenomenon, he sited was due to higher applied
pressure on the solidifying cast product. Investigating varying parameters of squeeze casting
process and its application, Ghomashchi and Vikhrov (2000) noted that many advances in squeeze
casting of Aluminium and low melting metals are leading to the application of the process to high
temperature alloys . Santos et al. (2001) observed an increase in the heat transfer coefﬁcients
with increasing melt superheat for horizontal directional solidiﬁcation and a reverse for a vertical
upward directional solidiﬁcation .
2.2 Definition of the problem
Recently Sun  has carried out extensive experiments on squeeze casting process of a
different wall-thickness 5-step casting under different pressure conditions. Squeeze casting
of magnesium alloy AM60 was performed under an applied pressure 30, 60 and 90 MPa in
a hydraulic press. With measured temperatures, heat fluxes and IHTCs were evaluated using
the polynomial curve fitting method and numerical inverse method. In this thesis,
solidification process during squeeze casting process is simulated using the commercial
CFD software FLOW-3D for the same set of parameters for which Sun [ ] has carried out
experiments. The heat transfer coefficients needed for metal/mold inteface is taken from the
polynomial fit developed by Sun [ ] which is explained in detail in chapter 4 of this thesis.
This work is directed towards using these heat transfer coefficients at the metal/die interface
for simulating the solidification process of different wall-thickness 5-step casting under
different pressure conditions and to map the temperature profiles at different locations and
try to compare the results between simulation and experiments. The cast material chosen for
this simulation is magnesium alloy AM60.
The chemical composition of AM60 is shown in Table I. The thermal properties
of the related materials in this study for performing the solidification simulation is
shown in Table II . Based on Yu(2007)’s work, the thermal conductivity(K) of AM60
has the linear relationship with its temperature and follows equations(K=192.8-0.187T) in
semisolid temperature range(540°C-615°C) ; (K=0.0577T+60.85) below the solidus
temperature(<540°C), and (K=0.029T+59.78) for the liquid temperature range(>615°C).
Table I Chemical composition of Magnesium Alloy AM60
Mg Al(%) Mn(%) Si(%) Cu()% Zn(%)
balance 5.5-6.5 0.13 0.5 0.35 0.22
Table II Thermo physical properties of magnesium alloy AM60
Properties Mg Alloy AM60
Thermal Conductivity (W/mK) 62 90
Specific Heat (J/Kg K) 1020 1180
) 1790 1730
Latent Heat (KJ/Kg) 373
Liquidus Temp at 0Mpa(°C) 615
Solidus Temp at 0Mpa(°C) 540
MATHEMATICAL MODELING OF CASTING PROCESS There are three
forms of energy transport : conduction (diffusion transport), convection (heat transmitted by
the mechanical motion of the fluid) and radiation (through space). All three are active
during solidification of casting. Energy diffusion and convection occurs within the casting
at the metal/mould interface and within the mould. Energy is transported by radiation from
the mould to its environment which is typically the air.
3.1 Heat transfer
Heat transfer is the single most important discipline in casting simulation. The
solidification process depends on heat transfer from the part to the mould and from the
mould to the environment. There are three possible modes of heat transfer (1) conduction
(2) convection and the (3) radiation. The partial differential equation describing the process
is given by
The solution of the above equation in a given domain requires knowledge of initial
and boundary conditions.
3.1.1. Initial and Boundary Conditions
The initial conditions define the temperature distribution throughout the domain at
some initial point in time. The simplest option is to set the initial temperature depending on
the estimated loss of superheat during mould filling. The initial mould temperature depends
on the type of casting. Hence the mould temperature has to be fixed accordingly. For
investment castings, the mould is preheated to a specified temperature which depend on the
metal to be cast.
Initial conditions (t=0) used for the simulation are:
The pouring temperature of the molten alloy (MP of pure metal),Tmelt = 993K
Temperature of the mould material , Tmould = 483K
The boundary condition describe the condition that must be satisfied on the
boundaries of the domain. There are different types of boundaries viz., mold exterior walls,
metal/mold ,metal/insulator, metal/chill, and metal/core interface and the metal free
surfaces while simulating the casting process .
Boundary condition used for the simulation:
At the metal mold interface, the heat flux is governed by
Thermal conductivity of the cast metal
- Thermal conductivity of the mold
- interfacial heat transfer coefficient
Hence the boundary condition to be specified at the metal mold interface is a heat transfer
coefficient value 3.1.2 Mold exterior
During the casting process, the mold’s exterior surface is in contact with air. Hence
there exists a thermal boundary layer where the temperature varies from the surface
temperature to the fluid free stream temperature. Either the temperature or heat flux can be
prescribed as a boundary condition at this surface. But the most common approach is to
approximate the heat flux at the solid surface (mold exterior) using Newton’s law of cooling
am TThq (3.3)
This is commonly referred to as the convective boundary condition. In equation (3.3) the
terms Tm, Ta, q and h corresponds to the mold exterior temperature, ambient temperature,
flux and convective heat transfer coefficient respectively.
3.1.3. Metal/mold or metal/chill or metal/insulator or metal/core interface
These boundaries are often referred to as interior boundaries. Generally there is a
temperature discontinuity at these boundaries. For metal/mold interface the common
approach is to express the interfacial heat flux as
where Tc, Tm, hgap are the temperatures of the casting surface, mold surface and the gap heat
transfer coefficient. Generally the gap heat transfer coefficient varies with respect to time or
temperatures which are usually determined either by experiments or by an inverse heat
3.1.4. Metal free surfaces
At the metal free surface, the cast metal is exposed to the ambient. The heat transfer
at these surfaces can be modeled using a convective boundary condition as given by
Solidification modeling involves the application of the heat transfer concept along
with the technique to account for the release of latent heat during solidification. The
mold and any other solid materials like chill, insulators etc. are modeled using the standard
heat conduction equation (equation 3.1). For the solidifying metal, a special procedure is
required to accurately model the latent heat release.
3.2.1. Fraction of solid
The extent of solidification at any location within the casting is represented by the
fraction of solid, fs. At temperatures greater than or equal to the liquidus temperature, the
cast metal is in a completely liquid state with a solid fraction value of zero. As the latent
heat is removed, the fraction of solid increases and reaches a value of unity when the metal
is in completely solid state. The temperature at this point is called the solidus temperature.
The region where the solid fraction is between zero and unity is referred to as the mushy
There are several ways to describe the solid fraction variation between the liquidus
and solidus temperatures. The simplest approach is to assume that the solid fraction varies
linearly in the mushy zone. Alternatively, an analytical expression such as Scheil’s equation
may be used. The best approach is to determine the solid fraction-temperature relationship
using experimental measurements.
The more accurate method is using the solidification kinetics approach which
involves the time integration of a solid fraction evolution equation. However solidification
kinetics approach requires detailed metallurgical data which may not be known.
3.2.2 Latent Heat
The release of latent heat during solidification is accounted for by a heat generation
where ΔHf represents the latent heat of solidification. This term is treated as a source term
and is determined from known parameters which is explained as:
The latent heat release rate is expressed as
This term can be included in the left hand side of equation (3.1) by defining an apparent
specific heat as
For the case where the solid fraction is assumed to vary linearly between liquidus and
solidus, the above expression will be
Hence the governing differential equation for solving solidification and heat transfer
during casting process becomes
with appropriate initial and boundary conditions.
3.3 Assumptions for the simulation
(1) The die was assumed to be fully filled with liquid alloy at the start of
simulation. This is a valid assumption when the cavity filling time is
reasonably small so that the heat loss during filling time is negligible.
(2) A uniform mold temperature was assumed for the simulation
3.4 Flow 3D- An Overview
FLOW-3D is a powerful and highly accurate commercial CFD software that gives engineers
valuable insight into many of the physical processes. With special capabilities for accurately
predicting free-surface flows, FLOW-3D is the ideal CFD software to use in design phase as well
as in improving production processes [ ]. It employs specially developed numerical techniques to
solve the equations of motion for fluids to obtain transient, three-dimensional solutions to multi-
scale, multi-physics flow problems. An array of physical and numerical options allows users to
apply the code to a wide variety of fluid flow and heat transfer phenomena. It is an easy-to-use
simulation software designed to:
Accurately simulate filling and solidification processes
Pinpoint probable defects and problems – before casting
Identify viable designs more quickly
Decrease the number of design iterations
Improve scrap rates
Reduce overall casting costs
Flow-3D employs specially developed numerical techniques to solve the equations of
motion for fluids to obtain transient, three-dimensional solutions to multi-scale, multi-physics flow
problems. An array of physical and numerical options allows users to apply the code to a wide
variety of fluid flow and heat transfer phenomena. Fluid motion is described with non-linear,
transient, second-order differential equations. The fluid equations of motion must be employed to
solve these equations. The science (and often art) of developing these methods is called
computational fluid dynamics. A numerical solution of these equations involves approximating the
various terms with algebraic expressions. The resulting equations are then solved to yield an
approximate solution to the original problem. The process is called simulation. An outline of the
numerical solution algorithms available in FLOW-3D follows the section on the equations of
motion. Typically, a numerical model starts with a computational mesh, or grid. It consists of a
number of interconnected elements, or cells. These cells subdivide the physical space into small
volumes with several nodes associated with each such volume. The nodes are used to store values
of the unknowns, such as pressure, temperature and velocity. The mesh is effectively the numerical
space that replaces the original physical one. It provides the means for defining the flow parameters
at discrete locations, setting boundary conditions and, of course, for developing numerical
approximations of the fluid motion equations. The FLOW-3D approach is to subdivide the flow
domain into a grid of rectangular cells, sometimes called brick elements. A computational mesh
effectively discretizes the physical space. Each fluid parameter is represented in a mesh by an array
of values at discrete points. Since the actual physical parameters vary continuously in space, a mesh
with a fine spacing between nodes provides a better representation to the reality than a coarser one.
We arrive then at a fundamental property of a numerical approximation: any valid numerical
approximation approaches the original equations as the grid spacing is reduced. If an approximation
does not satisfy this condition, then it must be deemed incorrect.
Reducing the grid spacing, or refining the mesh, for the same physical space results in more
elements and nodes and, therefore, increases the size of the numerical model. But apart from the
physical reality of fluid flow and heat transfer, there is also the reality of design cycles, computer
hardware and deadlines, which combine in forcing the simulation engineers to choose a reasonable
size of the mesh. Reaching a compromise between satisfying these constraints and obtaining
accurate solutions by the user is a balancing act that is a no lesser art than the CFD model
development itself. Rectangular grids are very easy to generate and store because of their regular, or
structured, nature. Nonuniform grid spacing adds flexibility when meshing complex flow domains.
The computational cells are numbered in a consecutive manner using three indices: i in the x-
direction, j in the y-direction and k in the z direction. This way each cell in a three-dimensional
mesh can be identified by a unique address (i, j, k), similar to coordinates of a point in the physical
space. Structured rectangular grids carry additional benefits of the relative ease of the development
of numerical methods, transparency of the latter with respect to their relationship to the original
physical problem and, finally, accuracy and stability of the numerical solutions. The oldest
numerical algorithms based on the finite difference and finite volume methods have been originally
developed on such meshes. They form the core of the numerical approach in FLOW-3D. The finite
difference method is based on the properties of the Taylor expansion and on the straightforward
application of the definition of derivatives. It is the oldest of the methods applied to obtain
numerical solutions to differential equations, and the first application is considered to have been
developed by Euler in 1768. The finite volume method derives directly from the integral form of
the conservation laws for fluid motion and, therefore, naturally possesses the conservation
properties. Rather than point wise approximations on a grid, FVM approximates the average
integral value on a reference volume. FVM partitions the computational domain into control
volumes (which are not necessarily the cells of the mesh).It then discretizes the integral formulation
of the conservation laws over each control volume (making use of the Gaussdivergence theorem). It
then solves the resulting set of algebraic equations or updates the values of the dependent variables.
The key to the method is that the integral form of the conservation law can be rewritten; using the
Gauss Divergence Theorem. In other words, the rate of change of mass in the control volume is
equal to the net mass flux through its boundary. The domain of the current problem is divided into
finite control volumes using cubic cells.
The steps involved in simulating the casting solidification process using FLOW3D are
shown in the flowchart:
Geometry modeling of the casting
Identification of the material type of
Activating physical models
Applying Initial and Boundary
Meshing the geometry
Figure 3.1 Flowchart for implementation of solidification simulation in FLOW-3D
As a first step the solidification simulation of 5-step casting with the following dimensions
for the steps: step 1 of dimensions 100 X 30 X 3 mm, step 2 of dimension 100 X 30 X 5 mm,
step 2 of dimension 100 X 30 X 8 mm, step 4 of dimension 100 X 30 X 12 mm, step 2 of
dimension 100 X 30 X 20 mm, is carried out using FLOW-3D. The whole casting geometry
was created as a solid model in AutoCAD along with the bottom cylindrical shape sleeve of
diameter 100 mm. This solid model was first converted to an .stl file . This file was used as
the computational domain in the CFD software FLOW 3-D.
The implementation of solidification simulation in FLOW -3D is briefly explained here:
3.5.1 Geometry modeling of the casting
The first task is to create the computational domain for casting and mold. The
mold box is created as a rectangular component using the primitive Box in FLOW-3D.
Appropriate dimensions were chosen so that it covers the casting geometry in all
directions. For the present simulation the dimensions of the mold box chosen was 160 X
140 X 270 mm. This is identified as component 1 and is a solid component. The 5-step
casting geometry was then imported as an .stl file in FLOW-3D as a subcomponent to
component 1 and this is identified as subcomponent 1. Since it is easier to work with SI
units, appropriate transformations were done to convert the scale of the geometry from mm
to m. Once the stl file is imported, the somponent type is transformed from solid to
complement as shown in Figure 3.2.
Figure 3.2 FLOW-3D GUI for creating computational domain
3.5.2 Identification of the material type
The component1 is chosen as mold material and is made of steel and hence the material type
loaded is Steel AISI P- 20 from the materials tab - solid database. The fluid 1 which
corresponds to metal cavity (subcomponent 1 ) is chosen as the cast alloy and for the present
simulation it was chosen as AM60 Magnesium alloy. The schematic view of the material
database of FLOW-3D is shown in Figures 3.3 and 3.4 .
Figure 3.3 FLOW-3D GUI for material selection - solids
Figure 3.4 FLOW-3D GUI for material selection - fluids
3.5.3 Meshing the geometry
The first step in defining a particular domain is to determine the type of coordinate
system to use for the mesh. Two types are available in FLOW-3D: Cartesian and cylindrical.
The choice of mesh (cylindrical or Cartesian) does affect some of the geometry definitions.
The selection of coordinate system applies to all mesh blocks. Cartesian meshes
accommodate general geometries rather well and are therefore best for most problems. They
are the default setting as indicated in the Mesh Type drop-down box. Cylindrical meshes can
provide considerable improvements over Cartesian meshes for certain geometries that lend
themselves to a cylindrical description, especially when the problem can be considered
axisymmetric. Existing mesh block definitions may be modified in the tree structure. The
resolution is controlled by the value specified for either the size of cell, or the total number of
cells, or the number of the cells specified in each coordinate direction.
When the geometry becomes complex shaped , intermediate mesh planes can be
defined, as well as cell sizes for the domain between any two mesh planes. Figure 3.5(a)
depicts the mesh domain in FLOW-3D and Figure 3.5(b) shows the mesh information for the
Fig 3.5 (a) Meshed computational domain (b) mesh information dialog box
For the present simulation, cell size chosen is 2 mm in each direction. Hence the total
number of cells in the computational domain was around 245000 cells in the mesh.
3.5.4 Activating physical models
The physical models were activated from physics tab where the gravity, heat transfer and
solidification models were activated for the current simulation. In the gravity model the value
of acceleration due to gravity was entered in the desired direction. For the present simulation
a value of -9.8 m/s2
was given in the y -direction. In the heat transfer model the full energy
equation option is chosen with implict numerical approximation Figure 3.6 shows the GUI of
FLOW-3D for implementation of physics.
Fig 3.6 Dialog box of FLOW-3D where the physical models are activated.
3.5.5 Applying initial and boundary conditions
For the present simulation it was assumed that the cavity was initially filled with liquid
alloy. Hence the whole cavity which is considered as fluid domain was assigned the same
initial temperature. The initial temperature of the fluid was specified as 993K using the initial
conditions setting tab of FLOW-3D. The mold temperature was specified as 483 K using the
initial conditions setting tab of FLOW-3Dfor mold material. All the external boundaries
which corresponds to mold exterior was set to symmetry boundary condition. The interface
between mold and metal is treated as a boundary and a typical value of heat transfer
coefficient is specified .
3.5.6 Numerics Tab
The user can adjust parameters associated with the numerical methods used during a
simulation in the Numerics Tab of FLOW-3D. There are six control options;
(i) Time step controls - use the entry boxes in this group to change the initial time step size ,
minimum time step and the maximum time step.
(ii) Pressure solver options - radio button to choose the desired pressure iteration scheme.
(iii) Explicit / Implicit solver options - To change the numerical options associated with
viscosity, heat transfer,elastic stress,surface tension,and the bubblepressure. Also the user can
use the convergence controls buttons to modify the default convergence criteria if desired,
when implicit options are selected.
(iv) Volume of Fluid Advection - radio button option for choosing advection scheme for
volume of fluid
(v) Momentum Advection Group - radio button option for choosing the approximations for
partial derivatives in momentum equations. (vi) Fluid Flow Options - radio button option
through which the user can opt either for fluid flow or no fluid flow. The user has the option
to choose either constant fluid velocity or zero fluid velocity for the fluid domain. Otherwise
the full momemtum equations will be solved. Figure 3.7 shows the GUI corresponding to
numeric option in FLOW-3D.
Figure 3.7 GUI for numerics in FLOW-3D
3.5.7 Output Tab
The output tab of FLOW-3D is used for generating results for post processing. The user
has the option to generate result files based on either time, or fill fraction or solidified
fraction. The user also has the option to choose what data he needs to store in the results file
like temperature, solid fraction, liquid fraction, wall temperature, wall heat flux etc. Also
through probes GUI, the user can generate data corresponding to a particular location at all
time intervals of the simulation. The GUI correponding to output tab of FLOw-3D is shown
in Figure 3.8.
Figure 3.8 GUI for output tab in FLOW-3D
3.5.8 Simulation Manager
The GUI corresponding to the Simulate tab of FLOW-3D is shown in Figure 3.9. Using
this tab, the user can either start the "preprocess simulation" or "run simulation" option. If the
user chooses "preprocess simulation", FLOW3D solver checks whether there are any errors
associated with physics setting, meshing, property setting etc. If there are any errors , the
solver comes out with error messages. If there are no errors, a file by name "flsgrf.*" is
created and this file is the one which is used for running the solver.
Figure 3.9 GUI for output tab in FLOW-3D.
Once the pre-processing is done the user can use the "run simulation" option to start the
solver run. The "run simulation" option opens another window as shown in Figure 3.10 which
shows the progress of the simulation and the data files available for post processing is also
shown in this window.
Figure 3.10 Simulation window of FLOW-3D.
One of the most valuable additions to the "Simulation Manager" tab is the introduction
of a robust "Queue Manage tab" which is shown in Figure 3.11. The "Queue Manager" is
especially useful for managing many simulations with changing priorities. For example, the
"Queue Manager" allows simulations to be added to the queue, reordered, paused, restarted,
and terminated. These actions are performed using the buttons located below the Queue
Figure 3.11 Queue manager tab FLOW-3D.
The post processing option in FLOW-3D is carried out using the "analyze tab" which is
shown in Figure 3.12. Here the user has to load the simulation file for which post processing
has to be done. The post processor of FLOW-3D can generate one dimensional, two
dimensional and three dimensional contour plots, history plots like cooling curves at specified
locations or spatial plots of temperature etc. If the user wants to generate text files of the data
generated through simulation, he can do so by exporting the data as .txt file. Further movies
can be generated for visualizing the mold filling, solidification profile etc. The post
processing window of FLOW-3D is shown in Figure 3.13.
Figure 3.12 Analyse tab FLOW-3D.
Figure 3.12 GUI for choosing options for post processing in FLOW-3D.
EXPERIMENTAL RESULTS REPORTED BY SUN ET AL FOR ESTIMATION OF
HEAT TRANSFER COEFFICIENT DURING SQUEEZE CASTING PROCESS
In this chapter, the experimental results of Sun et al [ ] is presented where they have done
experiments to record the thermal histories at certain locations and how they back calculated
the heat transfer coefficient between metal/die interface by using polynomial extrapolation
method. 4.2 EXPERIMENTAL SETUP
4.2.1 5-Step Casting
A 5-step shape casting was designed by Sun et al specifically to record the thermal histories
at certain locations during squeeze casting process.. Figure 4.1 shows the 3-D model of 5-
step casting used for their experimental study. It consists of 5 step casting, with dimensions
of 100 x 30 x3 mm, 100 x 30 x 5 mm, 100 x 30 x 8 mm, 100 x 30 x12 mm, 100 x 30 x 20
mm accordingly. The molten metal was allowed to fill ths cavity from the bottom by a
cylindrical shape sleeve with diameter 100 mm.
Fig 4.1 3-D model of 5-step casting with the round-shape gating system [ Sun et al., [ ]]
(a) XZ view; (b) YZ view; (c) isometric view
2.2 Configuration of die and installation of measurement unit.
To measure the temperatures and pressures at the casting-die interface accurately and
effectively, a special thermocouple holder was developed. It hosted 3 thermocouples
simultaneously to ensure accurate placement of thermocouples in desired locations of each
step. The thermocouple holders were manufactured using the same material P20 as the
die to ensure that the heat transfer process would not be distorted. Figure 4.2 illustrates
schematically the configuration of the upper die (left and right parts) mounted on the top
ceiling of the press machine. It also reveals the geometric installation of pressure
transducers and thermocouple holders. Pressures within the die cavity were measured using
Kistler pressure transducers 6175A2 with operating temperature 850°C and pressures up to
200 MPa. As shown in Figure 4.2, pressure transducers and temperature thermocouples
were located opposite to each other so that measurements from sensors could be directly
correlated due to the symmetry of the step casting. Five pressure transducers and
temperature measuring unit were designated as PT1 through PT5, TS1 through TS5,
respectively. Each unit was inserted into the die and adjusted until the front wall of the
sensor approached the cavity surface. The geometry shape of thermocouples holders
was purposely designed the same as the pressure transducer, so that they could be
exchangeable at different locations.
Figure 4.2 Configuration of the upper die and the geometric
installation of hermocouple and pressure transducers. (Sun et al., [ ])
Figure 4.3 Installation of upper - die and geometric installation of thermocouples
and pressure transducers. (Sun et al., [ ])
As shown in Figure 4.3, the thermocouple head was bent down to 90 degree and attached to
the die surface tightly. The designed installation method minimized the disturbance of the
temperature field in the step casting cavity. On the right part of the die, the
thermocouples was installed to measure casting surface (T-surf) and inside die
temperatures(T1,T2,T4). To ensure the accuracy, temperature measurements were also
carried out simultaneously in both the right and the left parts of the die. This thermocouple
head bending method enables to acquire relatively accurate data of the casting surface
4.2.2 Casting Process
The integrated system included a 75 tons laboratory hydraulic press, upper-lower die, an
that the mold assembly is composed of three parts. The two upper dies of the casting cavity
is split along the center. The bottom sleeve has a diameter of 0.1016 m and a height of 0.127
m. The chill vent was located on the top of the step casting, which can discharge the gas
inside the upper die cavity. Both the upper die and the bottom sleeve were heated by
Fig 4.4 Schematic diagram of squeeze casting machine used by Sun et al., [ ]
Before pouring, the dies were pre-heated to 210°C using four heating cartridges installed
inside the dies. The experimental procedure included pouring molten magnesium alloy
AM60 into the bottom sleeve with a pouring temperature 720°C, closing the dies, cavity
filling, squeezing solidification with the applied pressure, lowering the sleeve die,
splitting the two parts of the upper die. Finally the 5-step casting can be shaken out
from the cavity. The temperatures inside the die and casting were measured by
Omega KTSS -116U thermocouples with response time below 10 ms. Real-time in-cavity
local pressures and temperature data were recorded by a Lab VIEW based data acquisition
system. The mold coating used in step castings is Boron Nitride lubrication (Type Sf) which
was sprayed manually onto the surface of the mold cavity before heating the dies to the
initial temperature. To minimize the thermal barrier effect of mold coating, the coating
thickness applied in this study was relatively thin (below 50 m).
4.3. Determination Of IHTC by Polynomial Curve Fitting Method.
To evaluate the IHTC effectively as a function of solidification time in the squeeze
casting process, the finite difference method (FDM) was employed as follows based on the
heat transfer equations. Since the thickness of each step is much smaller than the width or
length of the step, it can be assumed that the heat transfer at each step is one-dimensional.
The heat transfer across the nodal points of the step casting and die is shown in Figure 4.5.
The temperatures were measured at 2, 4, 6, 8 mm beneath die surface and the heat
flux transferred to the die mould can be evaluated by heat transfer equations.
Fig 4.5 One-dimensional heat transfer at the interface between the casting and die, where
temperature measurements were performed (Sun et al. [ ])
Fig 4.6 5-step castings solidifying under applied pressure 30, 60, and 90MPa. (Sun et al., [ ]
From the temperature versus time curves obtained at each position inside the die, the
temperature at the die surface (X0 = 0mm) can be extrapolated by using polynomial curve
fitting method. After the completion of filling, by selecting a particular time of
solidification process, the values of temperatures were read from the temperature-time
data at position X1, X2, X3, and X4 as shown in Figure 4.5. A polynomial curve with
various measured temperatures against distance X were plotted and extrapolated by a
polynomial trend line. The temperature at the die surface was determined by substituting the
value of X=0 in the polynomial curve fitting. The polynomial equation thus obtained is
given below which predicts the temperature values at various distances inside the die at a
y = 0.0635x3
- 16.495x + 308.43
This procedure is repeated for a number of time increments to get series of such
temperatures with corresponding times at metal - die interface, at metal surface, die
surface, and at various positions inside the die.