metals

Article
Optimizing the Gating System for Rapid Investment Casting of
Shape Memory Alloys: Computational Numerical Analysis for
Defect Minimization in a Simple-Cubic Cell Structure
Carlos E. S. Albuquerque 1 , Paulo C. S. Silva 2 , Estephanie N. D. Grassi 2 , Carlos J. De Araujo 2 ,
João M. P. Q. Delgado 3, * and Antonio G. B. Lima 2

1 Production Engineering Council, Federal University of the Vale do São Francisco, Campus Salgueiro,
Rua Antônio Figueira, 134, Salgueiro 56000-000, PE, Brazil; carlos.albuquerque@univasf.edu.br
2 Department of Mechanical Engineering, Center of Science and Technology, Federal University of Campina
Grande, Rua Aprígio Veloso, 882, Campina Grande 58429-900, PB, Brazil;
paulocesarsales@outlook.com (P.C.S.S.); end.grassi@hotmail.com (E.N.D.G.);
carlos.jose@professor.ufcg.edu.br (C.J.D.A.); antonio.gilson@ufcg.edu.br (A.G.B.L.)
3 CONSTRUCT-LFC, Civil Engineering Department, Faculty of Engineering, University of Porto,
4200-465 Porto, Portugal
* Correspondence: jdelgado@fe.up.pt; Tel.: +351-225081404

Abstract: With the aid of virtual prototyping and casting numerical simulation, this work presents
the optimization of an injection system used in a non-traditional investment casting process that
applies perpendicular centrifugal force to inject the molten metal into refractory plaster molds. In
this study, advanced techniques of simulation and production of complex geometries in Computer-
Aided Design CAD (Computer-Aided Design) are used in the design of the casting system of a
miniaturized simple-cubic cell structure. The cast part has a complex shape profile and needs a
high surface finish with strict dimensional tolerance. The alloy used to fill the mold is an aluminum
Citation: Albuquerque, C.E.S.; Silva,
bronze shape memory alloy (SMA). CAD was used to model the part and the proposed models for
P.C.S.; Grassi, E.N.D.; De Araujo, C.J.;
casting optimization. ProCAST software was used for the numerical simulation of the casting process.
Delgado, J.M.P.Q.; Lima, A.G.B.
Experimental parameters were used as input data for the numerical simulation. The simulation results
Optimizing the Gating System for
Rapid Investment Casting of Shape
were analyzed focusing on the identification of defects in the Cu–Al–Mn SMA simple-cubic structures.
Memory Alloys: Computational Different feeding systems have been designed to eliminate the identified defects. Concerning the
Numerical Analysis for Defect molten recirculation, the optimal nozzle model has a truncated cone profile, with a larger radius
Minimization in a Simple-Cubic Cell of 6.5 mm, a smaller radius of 2.0 mm and a height of 8.0 mm (called here model 3). Experimental
Structure. Metals 2023, 13, 1138. observations from cast SMA parts agree with the simulated results of the optimized nozzle model 3.
https://doi.org/10.3390/ In addition to the elimination of alloy recirculation with the nozzle optimization in this work, the
met13061138 shrinkage porosity at the upper base of the part was eliminated with the addition of a compensation
Academic Editor: Alexander volume close to the region where porosity is more intense. By exploring the possibilities offered
V. Shelyakov by commercial software, the work contributes to advance the knowledge and application of the
non-traditional investment casting process, highlighting its advantages and potential applications.
Received: 25 April 2023
Revised: 6 June 2023
Keywords: casting numerical simulation; investment casting; SMA; ProCAST; virtual prototyping
Accepted: 16 June 2023
Published: 19 June 2023

1. Introduction
Copyright: © 2023 by the authors. Metal cellular lattice structures (CLSs) have attracted much attention in biomedical
Licensee MDPI, Basel, Switzerland. (e.g., metallic implants) and industrial (e.g., aircraft fuselage and wings) applications due to
This article is an open access article their combination of mechanical, thermal and acoustic properties, creating opportunities for
distributed under the terms and
diverse cross-functional structural implementations [1]. These include ultralight structures
conditions of the Creative Commons
with high specific strength [2,3] and stress [4] and excellent impact absorption [5]. While
Attribution (CC BY) license (https://
CLSs can be manufactured as stochastic and periodic patterns, periodic CLSs have superior
creativecommons.org/licenses/by/
characteristics over stochastics; hence, their use in high-value engineering products is
4.0/).

Metals 2023, 13, 1138. https://doi.org/10.3390/met13061138 https://www.mdpi.com/journal/metals

Metals 2023, 13, 1138 2 of 23

preferred [6,7]. In addition, the mechanical properties of periodic CLSs can be adjusted
to the required level, which is not the case with stochastic structures [8]. So far, different
types of periodic CLSs have been investigated, including octet trusses [9], triangulated
faces of flat trusses [10], central pyramidal structure [10], simple-cubic and body-centered
cell structure (BCC) [11], BCC-Z [11], F2FCC [11] and F2FCC-Z [11].
Different materials have been used to produce CLSs, including stainless steel, Ti-6Al-
4V and NiTi [12,13]. NiTi, also known as Nitinol, is by far the most applied shape memory
alloy (SMA). SMA belong to a material class called intelligent or smart, which are a group of
new, state-of-the-art materials, that, over the last decades, have been developed and applied
in various sectors. Smart materials are capable of sensing changes in their environment and
responding to these changes in a predetermined way. SMA have the ability to return to a
predetermined shape after a pseudoplastic deformation through simple heating, which is
called shape memory effect (SME). On the other hand, the ability to recover large strains
(8% under isothermal tension) after a simple mechanical unloading is called superelasticity
or pseudoelasticity (SE) [14]. In addition, both phenomena are associated with a mechanical
hysteresis, which benefits dampening and shock absorption applications. There are two
main SMA composition groups: Ni–Ti-based alloys (Ni–Ti–Cu, Ni–Ti–Mo, Ni–Ti–Nb, etc.)
and Copper-based alloys (Cu–Zn–Al, Cu–Al–Ni, Cu–Al–Mn, Cu–Al–Be, etc.). Cu–Al-based
alloys have not only the functional characteristics of shape memory effect (SME) and
superelasticity (SE) but also are low cost and easier to manufacture compared to Ni–Ti-
based alloys [15]. Therefore, in addition to a high strength-to-weight ratio, relatively low
mass, low heat conductivity, high energy absorption and appropriate thermal and sound
insulation properties, CLSs made with SMA offer other benefits such as shape memory
properties [16,17], superelastic behavior [18] and low modulus of elasticity [19,20].
Until now, several conventional techniques have been applied to produce CLSs,
including casting, additive manufacturing and mechanical forming [21]. According to
Mun et al. [22], metal additive manufacturing processes that use laser or electron beam on
a metallic powder are completely capable of manufacturing complex 3D metallic CLSs.
Additive metal manufacturing methods consist of progressively depositing layers, one on
top of the other, until forming an object, following a 3D digital model. It is a relatively recent
technology, developed in the 1990s, which enabled new features such as rapid prototyping,
manufacturing of parts with complex geometries and customization of components that
would be difficult to manufacture by conventional routes [23].
However, despite these advantages, there are still restrictions in the process. Metal
parts produced by additive manufacturing are known to have macroscale defects such
as unmelted powder (i.e., lack of fusion), porosity, delamination and distortion [24–29].
On a microstructural scale, metal additive manufacturing processes are associated with
extreme temperature variations in their melting and solidification cycles [30]. Consequently,
they can generate parts with grains of different morphologies and anisotropic behavior
dependent on the construction direction [29,31–33]. This heterogeneous microstructure can
be further accentuated by cyclic recrystallization during repeated layer deposition [26].
Metal casting, on the other hand, allows for excellent microstructural and dimensional
control [34–38]. The investment casting process aided by 3D printing techniques is an
advantageous alternative for the production of CLSs manufactured with SMA. The invest-
ment casting process is one of the preferred casting methods used to produce components
with low dimensional tolerance, high degree of precision and excellent surface finish. Even
though it is a precision manufacturing process, at each manufacturing stage the investment
casting is subject to design and processing errors, resulting in defects in the obtained piece.
Casting defects are discontinuities that do not conform to design requirements with respect
to geometry (mismatches, undulations or dimensional defects); integrity (porosity, cracks,
oxides and inclusions); and material properties (hardness and mechanical resistance below
the specified standards). Broadly, defects in castings can be allocated into four categories:
filling defects; shape-related defects; thermal and appearance defects. Correctly identifying
such casting defects in the initial manufacturing phases significantly reduces the probability
Metals 2023, 13, 1138 3 of 23

of product failure, raw materials expenditure, the release of gases into the environment,
and energy and time consumption. There are several ways to analyze the phenomena
that occur in the casting process, among which stand out real casting tests and process
numerical simulation. The later allows a much faster and cheaper analysis and is an advan-
tageous technique used to reduce the risk of defects. Simulation technologies are applied
extensively in casting industries to understand the effects of physical phenomena such as
chemical changes, phase transformation, heat transfer, fluid flow, microstructural evolution
and mechanical stresses on defect formation and final mechanical properties [39].
Although all casting processes are subject to design and processing errors, an early and
correct identification of defects significantly reduces the probability of product failure. In
this sense, numerical simulation of the casting process is an advantageous technique used
to reduce the risk of defects. Simulation technologies are applied extensively in foundry
industries to understand the effects of physical phenomena such as chemical variation,
phase transformation, heat transfer, fluid flow, microstructural evolution and mechanical
stresses on defect formation and final mechanical properties [39].
Numerical simulation of the casting and solidification consists of virtually reproducing
processes such as filling, solidification, defect formation and distribution characteristics
during the casting, which allows predictions and adjustments before performing real
experiments. For this purpose, a detailed knowledge of the casting and solidification
process is necessary, including the behavior of the material as a function of temperature,
the microstructural behavior of the material, the interactions between mold and material
and the appropriate calculation methods to represent the phenomena involved.
Virtual casting analysis has gained increasing attention in the scientific community
due to its advantages in terms of cost-effectiveness, shorter analysis time and reduced
environmental impact compared to real casting tests. Several authors have contributed to
this field by publishing studies employing numerical simulation to investigate fluid flow,
solidification and defect formation in each stage of the casting process, including filling,
injection and solidification [40–45]. These research efforts have played a significant role
in advancing knowledge in this area and improving casting processes. Furthermore, it is
worth mentioning the utilization of the ProCAST® finite element software by researchers,
such as the authors [46–51], to conduct these studies.
In this context, this work proposes a computational analysis of a non-traditional
rapid investment casting process that applies perpendicular centrifugal force to inject the
molten metal inside refractory plaster molds. Despite its relevance, the process is not well-
explored in the literature, offering a wide field to be explored. Therefore, this study’s main
contributions are the application of a non-traditional centrifugal precision casting process
coupled with the analysis of an alloy with distinct functional properties. By exploring the
possibilities offered by commercial software, the work seeks to advance the knowledge and
application of this casting method, highlighting its advantages and potential applications.
In a previous work [52], the potential of applying computational numerical analysis
methods combined with the fabrication of SMA by non-conventional precision casting was
used to study the castability of copper-based SMA, making it possible to estimate interface
heat transfer coefficients (IHTC). In this work, the analysis focuses on the manufacture of a
topologically optimized structure with complex geometry that requires great dimensional
tolerance and the absence of porosity defects that can harm the mechanical properties of the
part. The optimized functional structures are designed to allow experimental tests to aid
the development of vibration control devices. The topology of the cells is simple-cubic, and
the analysis is carried out with the aid of the ProCAST software. The virtual prototyping
analysis is used to optimize the molten metal injection system in the molds, thus reducing
defects and filling time of the Cu–Al–Mn SMA presenting the SME.

2. Methodology
The methodology used in this work is summarized in the flowchart of Figure 1.
The optimization process was divided in two steps: firstly focusing on the solution of
 software. The virtual prototyping analysis is used to optimize the molten metal injection
system in the molds, thus reducing defects and filling time of the Cu–Al–Mn SMA
presenting the SME.

Metals 2023, 13, 1138 2. Methodology 4 of 23

The methodology used in this work is summarized in the flowchart of Figure 1. The
optimization process was divided in two steps: firstly focusing on the solution of
recirculation during injection
recirculation during injection and
and afterwards
afterwards solving
solving the
the recurrent
recurrent porosity
porosity on
on the
the upper
upper
base of the desired casting geometry.
base of the desired casting geometry.

Figure 1.
Figure 1. Methodology
Methodology flowchart.
flowchart.

The addressed
The addressed problem
problem dealsdeals with
with the
the simulation
simulation of of the
the filling,
filling, solidification
solidification and
and
defect formation
defect formation process
process of of aa Simple-Cubic
Simple-Cubic (SC) (SC) metallic
metallic cellular
cellular lattice
lattice structure
structure using
using
the ProCAST
the ProCAST software
software (Version
(Version 16, 16, ESI,
ESI, Paris,
Paris, França).
França). The
The casting
casting process
process chosen
chosen for
for the
the
study
study uses
usescentrifugal
centrifugalforce
forceasasa ameans
meansofofforcing
forcing thethe
molten
molten metal
metalinto thethe
into mold. Figure
mold. 2a
Figure
schematically
2a schematically illustrates the simulated
illustrates casting method
the simulated casting for the production
method for the ofproduction
miniaturized of
shape memory
miniaturized alloymemory
shape components with the Power
alloy components withCast 1700 equipment
the Power [53]. Figure[53].
Cast 1700 equipment 2b
shows
Figurethe part and
2b shows themold
partdesign
and mold useddesign
in thisused
study. in The
this mold
study.hasThe a cylindrical
mold has ashape with
cylindrical
50 mm in diameter and 70 mm in height. The SC unit cell structure
shape with 50 mm in diameter and 70 mm in height. The SC unit cell structure has a strut has a strut diameter
and length
diameter of length
and 1 mm and of 1 2.5
mmmm, and respectively. A fillet radius
2.5 mm, respectively. A filletofradius
0.4 mm wasmm
of 0.4 used onused
was the
coincident edges. edges.
on the coincident The lattice structure
The lattice was generated
structure was generatedby repeating 5, 7 and
by repeating 5, 75and
unit5cells
unit
in thein
cells x, the
y andx, yz directions, respectively,
and z directions, with a spacing
respectively, of 2 mm,ofresulting
with a spacing in a porosity
2 mm, resulting in a
of approximately 59% (with respect to a dense rectangular block
Metals 2023, 13, x FOR PEER REVIEWporosity of approximately 59% (with respect to a dense rectangular block of 10.5 21 of 10.5 × 14.5 mm).
× ofIn
14.5
25
addition, dense blocks were added at the ends of the SC lattice
mm). In addition, dense blocks were added at the ends of the SC lattice structure, structure, measuring
10.5 mm of side
measuring and 3ofmm
10.5 mm sideofand
thickness.
3 mm of thickness.
The purpose of the analysis presented in this work is to reduce alloy loss by
recirculation, reduce the possibility of damage to the crucible tip and increase the
efficiency of the mold-filling flow. The model originally used to inject the desired cellular
compression structure shows signs of expulsion in counterflow from the alloy to the
interior of the equipment, and in many cases, the piece is joined to the crucible, leading to
the loss of the crucible tip. Figure 3 shows an example of such a joining between the part
and the mold generated during the injection.

(a) (b)
Figure 2. (a) Inside picture of the PowerCast 1700 equipment and illustration of the centrifuge
Figure 2. (a) Inside picture of the PowerCast 1700 equipment and illustration of the centrifuge system
system used in the studied casting process. (b) CAD of the studied part and mold.
used in the studied casting process. (b) CAD of the studied part and mold.

The purpose of the analysis presented in this work is to reduce alloy loss by recircu-
lation, reduce the possibility of damage to the crucible tip and increase the efficiency of
the mold-filling flow. The model originally used to inject the desired cellular compression
structure shows signs of expulsion in counterflow from the alloy to the interior of the
equipment, and in many cases, the piece is joined to the crucible, leading to the loss of the
crucible tip. Figure 3 shows an example of such a joining between the part and the mold
generated during the injection.
 (a) (b)
Metals 2023, 13, 1138 5 of 23
Figure 2. (a) Inside picture of the PowerCast 1700 equipment and illustration of the centrifuge
system used in the studied casting process. (b) CAD of the studied part and mold.

Figure 3.
Figure 3. Example
Example of
ofthe
thejoining
joiningbetween
betweenthe
thepart
part and
and thethe mold
mold generated
generated by by
thethe recirculation
recirculation of
of the
the alloy and the consequent tip fracture.
alloy and the consequent tip fracture.

The converging
The converging nozzle
nozzle studied
studied inin this
this work
work isis divided
divided inin two
two parts.
parts. The
The first is aa
first is
standard base used to support the parts in the mold. This base is 3D printed
standard base used to support the parts in the mold. This base is 3D printed in polylactic in polylactic
acid (PLA)
acid (PLA) and
andmeasures
measures12 12mmmmininheight,
height,2424
mmmmin in
thethe
larger diameter
larger diameterandand
13 mm
13 mmin the
in
smaller diameter. It was kept unchanged throughout the evaluated cases.
the smaller diameter. It was kept unchanged throughout the evaluated cases. The second The second part
of theofnozzle
part originally
the nozzle has the
originally shape
has of a half-sphere
the shape with a with
of a half-sphere diameter of 13 mm,
a diameter butmm,
of 13 for
the optimization
but study, this
for the optimization profile
study, this will be replaced
profile by moreby
will be replaced efficient profiles profiles
more efficient in relation
in
to the fluid
relation flow.
to the Therefore,
fluid for the analysis
flow. Therefore, of virtual
for the analysis ofprototyping, four models
virtual prototyping, four of parts
models
with
of simple-cubic
parts geometry
with simple-cubic cell-structure
geometry format were
cell-structure formatdesigned using Autodesk
were designed Inventor
using Autodesk
software.
Inventor software.
Table 1 displays the dimensional
dimensional and geometric
geometric characteristics of the converging
converging
nozzle models evaluated in this topic.

1. Dimensional
Table 1. Dimensional and geometric
geometric characteristics of the converging
converging nozzle models evaluated in
this topic.
this topic.

Feed Channels (mm)

Nozzle Model ShapeShape
Feed Channels (mm)
Nozzle Model Dinlet Doutlet
Dinlet Doutlet
Original Spherical (Half sphere with a radius of 6.5 mm) 3.0 2.5
Original Spherical (Half sphere with a radius of 6.5 mm) 3.0 2.5
11 Conical
Conical (Diameter
(Diameter equalequal
to 6.5to
mm6.5and
mm and of
height height of 6.1 mm) 3.0
6.1 mm) 3.0 2.5 2.5
ConeCone
trunktrunk
(Larger base
(Larger radius
base 6.56.5mm,
radius mm,smaller base radius 2.0 mm
smaller base
22 radius 2.0 mm and height 8.0 mm)
3.0 3.0 2.5 2.5
and height 8.0 mm)
Cone trunk (Larger base radius 6.5 mm, smaller base
3 Cone trunk (Larger base radius 6.5 mm, smaller base radius 2.0 mm 6.0 2.5
3 radius 2.0 mm and height 8.0 mm) 6.0 2.5
and height 8.0 mm)

Based on the dimensions and geometric characteristics presented in Table 1, Figure 4

illustrates the CAD models used to study the optimization of the converging nozzle that
directs the molten alloy to the interior of the mold.
After the nozzle optimization study, a porosity analysis was performed at the upper
base, a region identified as critical during numerical simulation due to the presence of
shrinkage porosities. In the porosity study, four riser models for shrinkage compensation
were evaluated. Table 2 summarizes the dimensions used in the design of these riser
models, and Figure 5 shows the compensation riser models used in this study.
Metals 2023, 13, x FOR PEER REVIEWdirects the molten alloy to the interior of the mold. 21 of 25

Based on the dimensions and geometric characteristics presented in Table 1, Figure 4

Metals 2023, 13, 1138 illustrates the CAD models used to study the optimization of the converging nozzle6 that
of 23

directs the molten alloy to the interior of the mold.

Figure 4. CAD models used to study the optimization of the converging nozzle which directs the
molten alloy to the interior of the mold.

After the nozzle optimization study, a porosity analysis was performed at the upper
base, a region identified as critical during numerical simulation due to the presence of
shrinkage porosities. In the porosity study, four riser models for shrinkage compensation
Figure 4.
4. CAD
CAD models used to
to study
study the
the optimization of
of the converging
Figure
were evaluated. models
Tableused
2 summarizes optimization
the dimensions the used in thenozzle
converging nozzle
designwhich
which directs the
directsriser
of these the
molten
molten alloy
alloy to
to the
the interior
interior of
of the
the mold.
mold.
models, and Figure 5 shows the compensation riser models used in this study.
After the nozzle optimization study, a porosity analysis was performed at the upper
Table 2. Dimensions
Table 2. Dimensions used
used in
in the
the design
design of
of the
the riser
riser models
models for
for porosity
porositycompensation.
compensation.
base, a region identified as critical during numerical simulation due to the presence of
RiserRiser
ModelModel shrinkage porosities. In the porosity study, Dimension
Dimension
four riser models for shrinkage compensation
1 1 were evaluated. Table 2Diameter
summarizes
of 6.0of
Diameter the
6.0dimensions
mm andand
mm height used
of 2.0
height in
mm
of 2.0 the design of these riser
mm
2 2 models, and Figure 5 shows the
Diameter compensation
Diameter
of 6.0ofmm6.0 mmandriser
and models
height
height of used
of 5.0 5.0
mmmmin this study.
3 3 Smaller diameter of 6.0 mm, larger diameter of
Smaller diameter of 6.0 mm, larger diameter of 8.0 and height 8.0 and heightof
of55mm
mm
4 Smaller
Table 2. Dimensions useddiameter of 6.0ofmm,
in the design largermodels
the riser diameter
for of 8.0 andcompensation.
porosity height of 8.0 mm
4 Smaller diameter of 6.0 mm, larger diameter of 8.0 and height of 8.0 mm
Riser Model Dimension
1 Diameter of 6.0 mm and height of 2.0 mm
2 Diameter of 6.0 mm and height of 5.0 mm
3 Smaller diameter of 6.0 mm, larger diameter of 8.0 and height of 5 mm
4 Smaller diameter of 6.0 mm, larger diameter of 8.0 and height of 8.0 mm

Figure 5.
Figure 5. Compensation riser models
models designed
designed for
for the
the study
study of
of shrinkage
shrinkage porosity.
porosity.

In addition to the models shown in Figures 4 and 5, it was also necessary to model
the crucible used for injection. This is because in simulations involving flow, the geometry
of the domain in which the fluid will travel is essential to accurately represent the fluid
dynamic phenomena. The external geometry of the crucible, which is complex and difficult
Figure 5. Compensation
to accurately measure,riser
wasmodels designed
digitized usingfor the study
Matter and of shrinkage
Form porosity.
Desktop 3D Scanner (Matter
and Form Inc., Toronto, ON, Canada). The scanner emits two beams of red light that, when
they fall on the surface of the object to be digitized, are detected by the equipment’s camera
and converted into points in a 3D coordinate system. The internal profile was obtained by
a 3 mm offset using Autodesk Inventor (Version 2019, AutoDesk, San Francisco, CA, USA),
 dynamic phenomena. The external geometry of the crucible, which is complex and
difficult to accurately measure, was digitized using Matter and Form Desktop 3D Scanner
(Matter and Form Inc., Toronto, ON, Canada). The scanner emits two beams of red light
that, when they fall on the surface of the object to be digitized, are detected by the
Metals 2023, 13, 1138 equipment’s camera and converted into points in a 3D coordinate system. The internal 7 of 23
profile was obtained by a 3 mm offset using Autodesk Inventor (Version 2019, AutoDesk,
California, EUA), assuming that the thickness of the crucible is constant. Figure 6 shows
the Matter that
assuming andthe
Form Desktop
thickness 3Dcrucible
of the Scanneris performing the process
constant. Figure 6 shows of
thedigitizing
Matter andofForm
the
crucible geometry.
Desktop 3D Scanner performing the process of digitizing of the crucible geometry.

Matterand
Figure6.6.Matter
Figure andForm
FormDesktop
Desktop3D
3DScanner
Scannerperforming
performingthe
theprocess
processofofdigitizing
digitizingofofthe
thecrucible
crucible
geometry.
geometry.

Havinggenerated
Having generatedthis
thisexternal
externalprofile,
profile,ititwas
waspossible
possibletotoobtain
obtainthe
theinternal
internalpart
partwith
with
aaroughing
roughingoperation
operationof of33mm,
mm,using
usingAutodesk
AutodeskInventor.
Inventor.At
Atthis
thispoint,
point,ititwas
wasassumed
assumedthat
that
the thickness of the real crucible is constant. After producing the geometries
the thickness of the real crucible is constant. After producing the geometries in Autodesk in Autodesk
Inventor,Visual-Mesh
Inventor, Visual-Meshwas wasused
usedtotodiscretize
discretizethe thestudy
studydomain
domainby bygenerating
generatingaamesh
mesh
composed of tetrahedral elements. The methodology sequence
composed of tetrahedral elements. The methodology sequence used in this work for used in this work for
domain discretization using Visual-Mesh:
domain discretization using Visual-Mesh:
I.I. Import
Importthe
theCAD
CADgeometry
geometry(using
(using.igs
.igsfile
fileformat);
format);
II. Repair, if necessary, the geometry imported
II. Repair, if necessary, the geometry imported from fromAutodesk
AutodeskInventor
Inventortotoensure
ensurethe
the
geometry has a closed volume (using the Repair
geometry has a closed volume (using the Repair tool); tool);
III. Create the mold with a cylinder geometry (Basic Shapes and Cylinder tools);
III. Create the mold with a cylinder geometry (Basic Shapes and Cylinder tools);
IV. Check for overlapping surface zones and create and merge volumes (Assembly tool);
IV. Check for overlapping surface zones and create and merge volumes (Assembly tool);
V. Create 2D mesh, which will be the basis for the volumetric mesh (Surface Mesh tool);
V. Create 2D mesh, which will be the basis for the volumetric mesh (Surface Mesh tool);
VI. Check for the quality of the surface mesh and eliminate cracking, overlapping, inter-
VI. Check for the quality of the surface mesh and eliminate cracking, overlapping,
section, poor-quality and coincident boundary nodes (Check Surface Mesh tool);
intersection, poor-quality and coincident boundary nodes (Check Surface Mesh tool);
VII. Create 3D mesh using tetrahedral elements (Tetra Mesh tool).
VII. Create 3D mesh using tetrahedral elements (Tetra Mesh tool).
The Figure 7 shows the mesh generated following the described methodology for one
The Figure 7 shows the mesh generated following the described methodology for one
of the studied cases.
of the studied cases.
The alloy selected to develop this work was the Cu-7.90Al-5.40Mn alloy. The choice
was made because it presents the SME both in the ingot and in the injected material,
according to previously performed studies. The properties of the alloy required to feed the
mathematical models were calculated using ProCAST via the right link to the CompuTherm
database. The mold material chosen was Resincast plaster.
Visual-CAST is the environment used to impose the process conditions and feed the
software the necessary information to properly perform the calculations. In this work, the
method chosen to establish the process conditions was through the “Cast” tab, and the
sequence used to model the casting processes:
I. Gravity Vector;
II. Volume Manager;
III. Interface HTC Manager;
IV. Process Condition Manager;
V. Simulate Parameters.
Metals 2023,13,
Metals2023, 13,1138
x FOR PEER REVIEW 8 of
21 of23
25

Figure7.7.Mesh
Figure Meshgenerated
generatedfor
foranalysis
analysisin
inthe
theProCAST
ProCASTsoftware.
software.(a)
(a)Complete
Completeset:
set: mold,
mold, part
partand
and
crucible.(b)
crucible. (b)Part
Part mesh
meshrefinement.
refinement.

In thealloy
The Gravity Vector,
selected to the direction
develop thisof gravity
work waswasthe defined. In the Volume
Cu-7.90Al-5.40Mn alloy.Manager, the
The choice
materials
was madeofbecause
each volume of the the
it presents geometry are defined
SME both as well
in the ingot as their
and in theinitial
injectedtemperature
material,
and initial to
according filling percentage.
previously For the
performed mold, The
studies. the properties
initial filling
of is
theconsidered
alloy required 0%; for the
to feed
crucible, a volumetric percentage compatible with the total mass
the mathematical models were calculated using ProCAST via the right link to theneeded to fill the part and
the riser is used.database.
CompuTherm In the HTC TheManager Interface,
mold material the type
chosen was of contact plaster.
Resincast that the parts have can
be selected. In this is
Visual-CAST work, the COINC type
the environment usedcontact was the
to impose used for theconditions
process contact between
and feed mold
the
and metal,the
software and for this information
necessary contact, it is to
also necessary
properly to define
perform the heat transfer
the calculations. In thiscoefficient
work, the
between the elements
method chosen involved
to establish the in the contact.
process Boundary
conditions conditions
was through are created
the “Cast” in the
tab, and the
Process Condition Manager. In this work,
sequence used to model the casting processes: for each case, thermal conditions of heat transfer,
rotation geometry, fluid dynamics of wall pressure, etc., were imposed. Table 3 shows the
I. Gravity Vector;
summary of the input data used in this analysis.
II. Volume Manager;
III. Interface HTC Manager;
Table 3. Values used in the design of the riser models.
IV. Process Condition Manager;
V. Simulate Parameters.
Variable Input Data
In the GravitySMA
Cu-based Vector,
(%wt) theSMAdirection of gravity was defined. In the Volume Manager,
Cu-7.90Al-5.40Mn
the materials of each volume of the geometry are defined as wellplaster
Mold Resincast refractory as their initial
temperature and Filling method
initial filling percentage. For the mold, the initial Centrifugal
filling is considered 0%;
Rotation
for the crucible, speed (rpm)
a volumetric percentage compatible with the total 400mass needed to fill the
Rotation time (s) 11
part and the riser is used.
Superheat (◦ C)
In the HTC Manager Interface, the type of
5
contact that the parts
have can be selected. In this
Solidus temperature ( C) ◦work, the COINC 993 (calculated usingused
type contact was for the contact
CompuTherm)
between mold andtemperature
Liquidus metal, and for ◦
( C)this contact, it is also
1038 necessary
(calculated to define
using the heat transfer
CompuTherm)
coefficient between
Mold temperature (◦ C) involved in the contact. Boundary
the elements conditions are created
420 (constant)
in the Temperature outside the
Process Condition mold (◦ In
Manager. C) this work, for each case,Roomthermal
temperature
conditions of heat
Coefficient of heat exchange between the mold
transfer, rotation geometry, fluid2 dynamics of wall pressure, etc.,convection)
65 (forced were imposed. Table 3
and the environment (W/m ·K)
shows the summary of the input data used in this analysis.
Metal/mold interface heat transfer coefficient
535
(hi in W/m2 ·K)
Cast alloy mass (g) 25
Distance between mold inlet and center of
120
rotation (mm)
Metals 2023, 13, 1138 9 of 23

Finally, the simulation parameters are imposed through the “Simulate Parameters”
tool. For this work, we used a pre-definition for the centrifugal process; however, some
parameters were changed to better suit our specific case.
The software also presents three basic tabs with simulation parameters (General, Ther-
mal and Flow). In addition to these, in this work, we activated Turbulence model, choosing
the Realizable k-epsilon model, as it has already been proven in several experiments that
the realizable model k–ε provides better accuracy for flows involving rotations, strong
recirculation or separation [54].

3. Mathematical Modeling
Applicable to any transport phenomenon, the governing equations for solidification
modeling are the conservation of mass, conservation of momentum or momentum equation
and energy equation [55].
The equation for conservation of mass, or continuity equation, used in ProCAST is
given by [56–58]:
∂ρ →
+ ∇·(ρ u ) = 0 (1)
∂t
→
where u the velocity, t is the time, ρ represents the density and the operator ∇, referred
to as grad, nabla or del, represents the partial derivative of a quantity with respect to all
directions in the chosen coordinate system.
The linear momentum equation, derived from the Navier–Stokes equations, used by
ProCast is given by [57,58]:
" #
∂ui ∂ui ∂ ∂ui µ
ρ + ρu j + pδij (µ + µ T ) = ρgi − ui (2)
∂t ∂x j ∂x j ∂x j K

where p is the pressure, gi the gravity acceleration, δij the kronecker delta, µ the viscosity,
µT the turbulent viscosity and K is the permeability, which reflects the resistance of the
solid pattern to fluid flow, and is calculated using the Kozeny–Carmen equation [56].

(1 − gs (t))3 λ2 2 (t)
K ( gs (t), λ2 (t)) = (3)
gs ( t )2 180

where gs (t) is the solid volume fraction and λ2 (t) is the secondary dendrite arm spacing,
which can be evaluated at any point in the soft zone using a thickening law [46].
The ProCAST software uses four types of energy equation that are chosen depending
on how heat flows through the metal and mold and how it is released to the environment.
The methods are linear conduction transient, nonlinear conduction transient, transient lam-
inar advection–diffusion and transient turbulent advection–diffusion. Linear conduction
transient can be calculated by [57,58]:

δT
ρc p − ∇[k∇ T ] − q( x ) = 0 (4)
δt
where T represents the vectors of nodal temperatures, q(x) the spatially variable volu-
metric heat source, ρ the constant density, c p is the specific heat constant and k is the
conductivity constant.
The nonlinear conduction transient can be calculated by the equation [57]:

δH δT
ρ − ∇[k∇ T ] − q( x ) = 0 (5)
δT δt
Metals 2023, 13, 1138 10 of 23

in which case ρ = ρo f ( T ) is the temperature-dependent density, k = k o f ( T ) is the

temperature-dependent conductivity and H is the enthalpy as a function of temperature
calculated by:
Z T
H (T ) = c p dT + L[1 − f s ( T )] (6)
0
where L is the latent heat and fs is the solid volume fraction.
For transient laminar advection–diffusion, the used equation is [57]:

∂H ∂H
ρ − ρui − ∇(k∇ T ) − q = 0 (7)
∂t ∂xi

where ui = f l ui,liq is the surface velocity component, f l is the liquid volume fraction and
ui,liq is the current velocity of the liquid.
Finally, for transient turbulent advection–diffusion the equation used is [57]:
 
∂H ∂H µT
ρ − ρui − ∇ (k + )∇ T − q = 0 (8)
∂t ∂xi σT

where µ T is the turbulent viscosity and σT is the turbulent Prandtl number.

The turbulent vortex viscosity is calculated from the turbulent kinetic energy, k T , and
the turbulent dissipation rate, e, as follows:

Cµ ρk2T
µT = (9)
e
where Cµ = 0.09 is a default value.
The conservation equation for turbulent kinetic energy used by the software is given
by [46]: !
∂(ρk T ) ∂(ρk T ) ∂ µ T ∂k T
+ uj − = µ T G − ρe (10)
∂t ∂x j ∂x j σk ∂x j

where:
k T = 12 u2 + v2 + w2 ;

u, v, w = fluctuating velocity components;

σk = Prandtl number
 of turbulent kinetic energy, typically set to 1;
∂u
G= ∂ui
∂xj+ ∂xij ∂ui
∂xj = turbulence generation rate;
e = turbulence dissipation rate.
The turbulence dissipation rate used in Equation (10) can be calculated by:
!
∂(ρe) ∂(ρe) ∂ µ T ∂e e
+ uj − = (C1 µ G − C2 ρe) (11)
∂t ∂x j ∂x j σe ∂x j k T

where σe is the Prandtl number for the turbulence dissipation rate, normally defined as 1.3,
and the default constant values are C1 = 1.44 and C2 = 1.92.
The initial and boundary conditions for solving the previous equations are applied to
temperature, velocity, pressure, fixed turbulent kinetic energy, fixed turbulent dissipation
rate and specific, convective and radiation heat flux [58]. An iterative algorithm is used to
simulate solidification by solving the equations of motion and energy, finding a coherent
solution between the enthalpy and temperature results. More details on this strategy can
be found in [56,59].

3.1. Turbulence Modeling

According to [56], ProCAST models turbulence using the Reynolds-averaged Navier–
Stokes equations (RANS), where the additional turbulent stresses arising from the averaging
procedure are approximated using the vortex viscosity approach. In this approximation,
Metals 2023, 13, 1138 11 of 23

the Reynolds stresses are assumed to be proportional to the mean rate of the strain tensor in
an analogy to the laminar stress–strain relationship. The proportionality constant is called
the turbulent viscosity µ T .
There are several models in the literature to obtain turbulent viscosity. Popular among
these are the two-equation turbulence models, in which two additional transport equations
are solved for the kinetic energy of turbulence (k) and the rate of turbulence dissipation
(e). ProCAST has the following two-equation turbulence models [46]: Standard k–ε Model,
RNG k–ε Model and Realizable k–ε (RKE).
As aforementioned, for flows involving rotations, strong recirculation or separation,
it has been proven in several experiments that the realizable model k–ε provides better
accuracy [54]. The standard k–ε model is based on the model proposed by Launder and
Spalding [60].
The transport equations for k and ε are [54]:

" #
∂(ρk ) ∂ ρu j k

∂ µ T ∂k
+ = ρP − ρε + µ+ (12)
∂t ∂x j ∂x j σk ∂x j

"  #
∂(ρε) ∂ ρu j ε ε ε ∂ µ T ∂ε
+ = C1 ρP − C2 ρε + µ+ (13)
∂t ∂x j k k ∂x j σε ∂x j

with the turbulence production term P defined as:

!
∂ui ∂u j 2 ∂um 2 ∂um
P = µT + − δ − k (14)
∂x j ∂xi 3 ∂xm ij 3 ∂xm

The constants used in this model assume the following default values: C1 = 1.44 e and
C2 = 1.92.
The realizable k–ε turbulence model (RKE) is described and characterized as a variant
of the standard k–ε model. In particular, the RKE model can be distinguished from the
standard k–ε model by the following [54]:
I. Replacing the transport equation for ε in the standard k–ε model with a similar
transport equation that models the dissipation rate according to the dynamic behavior
of the mean square vorticity fluctuation in the high turbulent Reynolds Number limit;
II. Replacing the eddy viscosity equation of the standard k–ε model with an eddy viscos-
ity equation that ensures satisfaction of the realizability constraints (for the normal
and shear turbulent stress components).
The transport equation for turbulent kinetic energy, k, in the RKE model remains
unchanged from the standard k–ε model and the transport equation for ε, in the achievable
RKE model, can be written as [54]:

" #
ε2

∂(ρε) ∂ ρu j ε ∂ µ T ∂ε
+ = C1 ρSε − C2 ρ √
+ µ+ (15)
∂t ∂x j k+ ε ∂x j σε ∂x j
h i q
1
, η = S kε , S =
η
where: C1 = max 0, 43. η +5 , C2 = 1.92, Cµ = 2Sij Sij and
A0 + A5 U ∗ kε
s !
∼ ∼ ∼
U∗ = 2Sij Sij + Ωij Ωij , Ωij is the average rate of rotation seen in a rotating frame
√
with angular velocity ωk . The parameter A 5 is determined by A 5 = 6cos(φ), φ =
√  S S S ∼
r 
1
3 arccos 6W , W = ij ∼jk3 ki and S = (S ij Sij . The value of A0 is taken as 4.04.
S

3.2. Porosity Modeling

There are essentially two types of solidification porosity [54]:
Metals 2023, 13, 1138 12 of 23

- Shrink porosity: solidification shrinkage cannot be compensated by incoming liquid

flow when feed flow is no longer possible. Consequently, shrinkage porosity is formed.
- Gas porosity: gas porosity is the result of two concomitant mechanisms among solidi-
fication, shrinkage and segregation of gases. The higher density of the solid induces a
suction of the viscous liquid towards the pasty permeable zone, thus decreasing the
pressure in the liquid. Being segregated in the remaining part of the liquid, the gas in
the liquid can reach a concentration that exceeds the solubility limit, especially since
this limit decreases with the temperature, and the pressure of the liquid. Nucleation
and pore growth must be considered at this stage.
Two main equations are used to describe porosity formation during solidification [44].
The first governing equation is the conservation of alloy mass, which is a continuity
equation. Assuming that the solid phase is not moving and that there is no deformation
and, in addition, neglecting the specific mass of the bubbles, the average mass conservation
equation written for both phases gives [56]:

∂
[ρs gs + ρl gl ] + ∇(ρl gl vl ) = 0 (16)
∂t
where ρs is the specific mass of the solid and vl is the effective velocity of the fluid among
the solid cast (i.e., v = gl vl ). If porosity formation has already occurred, the volume fraction
of liquid, gl , is given by [55].
gl = 1 − gs − g p (17)
gs is the solid volume fraction and g p is the pore volume fraction.
The continuity equation can also be written as [54]:

∂g p ∂hρi ∂T
div(ρl gl vl ) − ρl =− (18)
∂t ∂T ∂t
where ρ = (ρs ·gs + ρl ·(1 − gs )) is the average mass of the solid–liquid mixture without
porosity. Solidification shrinkage and specific mass variations, the term on the right side of
the equation, can be compensated by interdendritic liquid feeding (first term on the left
member) or by microporosity formation (second term on the left member) [54].
The other equation is the Darcy flow equation, which is a flow moment equation,
that governs the resistance of a porous medium to the flow of viscous liquid. The porous
medium is the solid dendritic network in which the alloy solidifies. The Darcy flow
equation is [44]:
K
v = gl vl = − [ gradpl − ρl g] (19)
µ
where pl is the local pressure in the liquid, K is the permeability of the solid cast, µ is the
dynamic viscosity of the liquid and g is the gravity vector. Most terms are alloy properties.
Combining the continuity equations with Darcy flow:
 
K ∂g p ∂hρi ∂T
div ρl ( gradpl − ρl g) + ρl = (20)
µ ∂t ∂T ∂t

As it can be seen, two unknown scalar fields appear in this equation: the liquid
pressure, pl (x,t), and the microporosity volume fraction, gp (x,t). The terms pl and gp are
solved by applying boundary conditions.

4. Results and Discussion

4.1. Converging Nozzle Optimization: Simulation
Table 4 summarizes the fill time and nozzle recirculation results obtained in this
analysis. The assessment of whether or not there was recirculation in the nozzle refers
to the alloy that would be expelled from the mold when changing the flow direction
during filling.
Metals 2023, 13, 1138 13 of 23

Table 4. Values used in the design of the nozzle models.

Nozzle Model
Evaluated Parameter
Original Model 1 Model 2 Model 3
Filling time (s) 0.53 0.48 0.46 0.44
Recirculation in the converging nozzle Yes Yes Yes No
Shrinkage porosity (on the top base) 58.85% 61.18% 61.45% 62.62%

Observing the data presented in Table 4, the filling time improved by 17% and the
recirculation of the alloy was eliminated in the simulation with nozzle model 3. This
result was achieved by analyzing and identifying the defects present in the simulations
with the original nozzle profile and afterwards implementing new profiles, similar to the
methodology used by Kumar et al. [61].
In the simulations with the original profile, it was possible to identify that, under
the applied injection conditions, the molten metal is directed first to the wall on the right
side of the nozzle and, subsequently, flows to the center of the converging point of the
feed channels that ultimately inject the alloy inside the mold. In the case of the original
nozzle profile, due to the spherical curvature, a large part of the injected molten mass must
perform a curved trajectory, changing the flow direction by almost 90◦ . This, consequently,
leads a portion of the molten alloy on a tangent to the entrance of the feed channels and to
the opposite wall, which ultimately changed the flow direction of the molten mass by 180◦ ,
generating recirculation.
In view of this analysis, it is clear that the recirculation is primarily explained by the
lack of orientation provided by the geometry of the original nozzle, making it difficult for
the alloy to reach the feed channels and wasting a large part of the centrifugal flow inertial
energy. In order to overcome this problem, the nozzles designed in this work have a profile
directed towards the converging point of the feed channels, reducing the direction changes
in the molten flow. This result is supported by the reduction in filling time observed as
the nozzle models were optimized. The second point that favored recirculation was the
restriction generated by the small diameters of the feed channels. By increasing the feed
channel inlet diameter from 3 mm to 6 mm, this problem was solved, generating a feed
system without recirculation and with smaller filling time.
Figure 8 displays the filling time profile for each model. It can be seen that the original
model has more regions with longer filling times, whereas models 2 and 3 show great
improvements. It is also possible to infer that the upper base is the part of the piece that
takes the longest to fill.
Figure 9 shows the recirculation in each model. The software presented a limitation
when imposing an open boundary condition in the region where the alloy would be
expelled to the environment due to the counterflow, so the representation of material loss
due to recirculation is displayed as an alloy accumulation on the wall that, when colliding
with the standard base wall, returns to the correct flow direction. In the real injection, the
material is expelled out of the mold.
In the original model, the fluid begins to recirculate at 0.32 s but reaches a maximum
counterflow at 0.38 s (Figure 9a); in model 1, the fluid recirculation starts at 0.30 s and
peaks at 0.34 s (Figure 9b); model 2 exhibits a maximum recirculation at 0.35 s (Figure 9c);
and model 3 has no recirculation (Figure 9d). From these images, we can infer that the
nozzle model that presented the highest recirculation was the original model, and that the
improvements made in the nozzle design had gradual positive effects until reaching the
ideal model, which is model 3.
 increasing the feed channel inlet diameter from 3 mm to 6 mm, this problem was solved,
generating a feed system without recirculation and with smaller filling time.
Figure 8 displays the filling time profile for each model. It can be seen that the original
model has more regions with longer filling times, whereas models 2 and 3 show great
Metals 2023, 13, 1138 14 of 23
improvements. It is also possible to infer that the upper base is the part of the piece that
takes the longest to fill.

Metals 2023, 13, x FOR PEER REVIEWFigure 8. Color gradient for part filling time. (a) Original model. (b) Nozzle model 1. (c) 21 of 25
Nozzle
Figure 8. Color gradient for part filling time. (a) Original model. (b) Nozzle model 1. (c) Nozzle
model 2. (d) Nozzle model 3.
model 2. (d) Nozzle model 3.

Figure 9 shows the recirculation in each model. The software presented a limitation
when imposing an open boundary condition in the region where the alloy would be ex-
pelled to the environment due to the counterflow, so the representation of material loss
due to recirculation is displayed as an alloy accumulation on the wall that, when colliding
with the standard base wall, returns to the correct flow direction. In the real injection, the
material is expelled out of the mold.

Figure 9. Maximum recirculation in each model (a) t = 0.38 s original profile, (b) t = 0.34 s modified
Figure 9. Maximum recirculation in each model (a) t = 0.38 s original profile, (b) t = 0.34 s modified
profile with nozzle model 1, (c) t = 0.35 s modified profile with nozzle model 2 and (d) t = 0.34 s
profile with nozzle model 1, (c) t = 0.35 s modified profile with nozzle model 2 and (d) t = 0.34 s
modified profile with nozzle model 3.
modified profile with nozzle model 3.
In the original model, the fluid begins to recirculate at 0.32 s but reaches a maximum
counterflow at 0.38 s (Figure 9a); in model 1, the fluid recirculation starts at 0.30 s and
peaks at 0.34 s (Figure 9b); model 2 exhibits a maximum recirculation at 0.35 s (Figure 9c);
and model 3 has no recirculation (Figure 9d). From these images, we can infer that the
Metals 2023, 13, 1138 15 of 23

Another parameter affected by changing the filling nozzle construction parameters

was the maximum gas pressure inside the mold. Figure 10 shows the points of maximum
pressure of the gas inside the mold. The original model (Figure 10a) presented points with
maximum pressure distributed in the center of the part, with a maximum value of 2.81 bar.
Model 1 showed a similar behavior (Figure 10b), with a maximum pressure of 3.98 bar in
one segment of the cell structure. Models 2 and 3 (Figure 10c,d) also presented maximum
pressure points on the upper base of the part but compared to the previous models showed
Metals 2023, 13, x FOR PEER REVIEW 21 of 25
a reduction in maximum gas pressure, showing maximum pressure points of 2.24 and
2.06 bar, respectively.

Figure 10. Maximum gas pressure inside the mold. (a) Original profile. (b) Modified profile 1. (c)
Figure 10. Maximum gas pressure inside the mold. (a) Original profile. (b) Modified profile 1.
Modified profile 2. (d) Modified profile 3.
(c) Modified profile 2. (d) Modified profile 3.

In addition
The pressure to variation
the pressure of the trapped
observed gas, the
in each case pressure
is due to gasofentrapment.
the alloy was also
The eval-
results
uated, and in this analysis, it was possible to verify that the pressure of the
presented in Figure 10 show that the optimization of the feeding system, in addition to alloy becomes
higher at points
improving far of
the flow from the inlet
molten metalgate,
intoprobably
the mold,duehas to the effectinfluence
a positive of the centrifugal force
on the removal
that
of airtakes
frominto account
the mold, thereducing
thus distancethe
from the rotation
internal axis.
pressures ofThis pressure
the mold and increase
improving in the
the
outermost
filling segments
of the canin
part details cause the mold to rupture, consequently leading to filling fail-
the mold.
ures.In Figure 11 shows
addition to thean exampleofofthe
pressure thetrapped
pressuregas,
gradient of the alloy
the pressure in alloy
of the the mold. The
was also
gradient displayed was generated in the simulations of model 3, but all evaluated
evaluated, and in this analysis, it was possible to verify that the pressure of the alloy cases
show a similar
becomes higherbehavior.
at points far from the inlet gate, probably due to the effect of the centrifugal
force that takes into account the distance from the rotation axis. This pressure increase
in the outermost segments can cause the mold to rupture, consequently leading to filling
failures. Figure 11 shows an example of the pressure gradient of the alloy in the mold. The
gradient displayed was generated in the simulations of model 3, but all evaluated cases
show a similar behavior.

Figure 11. Alloy pressure inside the mold. (a) Nozzle model 3 at 0.44 s. (b) Nozzle model 3 at 0.71 s
 uated, and in this analysis, it was possible to verify that the pressure of the alloy becomes
higher at points far from the inlet gate, probably due to the effect of the centrifugal force
that takes into account the distance from the rotation axis. This pressure increase in the
outermost segments can cause the mold to rupture, consequently leading to filling fail-
ures. Figure 11 shows an example of the pressure gradient of the alloy in the mold. The
Metals 2023, 13, 1138 16 of 23
gradient displayed was generated in the simulations of model 3, but all evaluated cases
show a similar behavior.

Metals 2023, 13, x FOR PEER REVIEW 21 of 25

such as11.
Figure mold geometry,
Alloy material
pressure inside properties
the mold. and operating
(a) Nozzle model 3 at conditions, it indicates
0.44 s. (b) Nozzle model 3the abil-s
at 0.71
Figure 11. Alloy pressure inside the mold. (a) Nozzle model 3 at 0.44 s. (b) Nozzle model 3 at
ity of the injection system to correctly fill all regions of the mold, ensuring proper for-
time.
0.71 s time.
mation of the casting. We can notice that the original model is the one that presents more
Regarding
points with a high
Regarding therisk
the misrun
misrun sensitivity,
of filling failures
sensitivity, Figure
and, as
Figure 12the
12 compares the risk
geometries
compares the risk that
were eachoptimized,
being
that each nozzle model
nozzle model
the
generates. Misrun
number of points
generates. sensitivity
Misrunofsensitivity is a measure
high risk decreased. used by the ProCAST software
is a measure used by the ProCAST software to assess the to assess the
probability
probability of occurrence
This occurs
of occurrence
because,of of filling
asfilling failures
shownfailures in aa casting
in the previous
in casting process.
analyses,
process. Taking
the nozzle
Taking into account
models
into account factors
with high
factors
levels of recirculation also have higher internal gas pressures and reduced
such as mold geometry, material properties and operating conditions, it indicates the ability flow inertia,
which
of hinders the
the injection filling
system to of the partfill
correctly details in theof
all regions mold. In addition
the mold, to the
ensuring internal
proper pressure
formation of
of the
the gas and
casting. Wepressure
can notice drop,
that another point
the original that must
model is the be
oneconsidered is that
that presents morethe recircula-
points with
ation reduces
high risk ofthe temperature
filling at which
failures and, as thethe alloy comes
geometries intobeing
were contact with the mold,
optimized, decreas-
the number of
ing its of
points viscosity
high riskand consequently its castability.
decreased.

Figure 12.
Figure 12. Misrun
Misrun sensitivity.
sensitivity. (a)
(a) Original
Original profile.
profile. (b)
(b) Nozzle
Nozzle model
model 1.
1. (c)
(c) Nozzle
Nozzle model
model profile
profile 2.
2.
(d) Nozzle model 3.
(d) Nozzle model 3.

4.2. Converging
This occursNozzle Optimization:
because, as shown inExperiments
the previous analyses, the nozzle models with high
levelsThe
of recirculation also13have
image in Figure higher
shows internal gas between
the comparison pressuresthe
and reduced
real flow inertia,
parts injected with
the original feeding system (Figure 13a) with the designed model 3 feeding system (Figure
13b). Both pieces showed signs of cracking in the casting as some regions that should have
been empty close to the upper base were filled. A hypothesis for this problem was dis-
cussed in the analysis of the virtual prototyping and presented in Figure 11. In this dis-
Metals 2023, 13, 1138 17 of 23

which hinders the filling of the part details in the mold. In addition to the internal pressure
of the gas and pressure drop, another point that must be considered is that the recirculation
reduces the temperature at which the alloy comes into contact with the mold, decreasing
its viscosity and consequently its castability.
Metals 2023, 13, x FOR PEER REVIEW 21 of 25
4.2. Converging Nozzle Optimization: Experiments
The image in Figure 13 shows the comparison between the real parts injected with the
observedfeeding
original in the system
experimentally castwith
(Figure 13a) part.the
On the other
designed hand,
model the realsystem
3 feeding component manu-
(Figure 13b).
Both pieces
factured showed
with signsmodel
the nozzle of cracking in thean
3 showed casting as some regions
improvement thattoshould
in relation haveofbeen
the filling the
empty
details close
of theto thesince
part upperits base weredid
structure filled.
not A hypothesis
show a lack offor this As
filling. problem
shownwas discussed
in Figure 12d,
in the results
these analysis of the
were virtual
pointed prototyping
out and presented
in the simulation inthe
results as Figure 11. Insignaled
software this discussion, it
high risks
was identified that the most distant points from the feed channels presented the
of filling failure in a few internal elements of the cellular structure and limited risk in the highest
pressures,
rest of the and this could harm the structure of the mold.
piece.

Figure 13. Photo of the parts injected with the feeding systems. (a) Original. (b) Modified model 3.

The part injected

In addition to the with
fillingthe original feeding
improvement, it was model (Figure
possible 13a) shows
to identify in theregions
injectionwith
ex-
filling defects
periments thatinrecirculation
the upper base,
was mainly
eliminatedin the
in left corner and
the designed in themodel
nozzle lower 3.base, but with
As shown in
weaker
Figure 3,intensity. These the
when injecting experimental
alloy with results are similar
the original feedingtomodel,
the results presented
the tip in the
of the crucible
virtual prototyping
was damaged duringshown in Figureas12,
the process which
the alloyindicate high risks
recirculated of filling
and joined failure
the pieceinwith
several
the
regions in the upper base and some points of the cell structure. The numerical
crucible. As a result of this joining, the riser of the injected part with the original model simulation
did not predict,
presents a markhowever, the risk
of the shape of filling
of the diameterfailure in the
of the lower tip,
crucible base,aswhich
can bewas observed
seen in
in Figure
the experimentally cast part. On the other hand, the real component manufactured
14a. In Figure 14b, however, we can see that this mark is not present, confirming that the with the
nozzle modelwas
recirculation 3 showed
indeedan improvement
reduced with theinoptimized
relation tomodelthe filling
3. of the details of the part
since its structure did not show a lack of filling. As shown in Figure 12d, these results were
pointed out in the simulation results as the software signaled high risks of filling failure in
a few internal elements of the cellular structure and limited risk in the rest of the piece.
In addition to the filling improvement, it was possible to identify in the injection
experiments that recirculation was eliminated in the designed nozzle model 3. As shown
in Figure 3, when injecting the alloy with the original feeding model, the tip of the crucible
was damaged during the process as the alloy recirculated and joined the piece with the
crucible. As a result of this joining, the riser of the injected part with the original model
presents a mark of the shape of the diameter of the crucible tip, as can be seen in Figure 14a.
Metals 2023, 13, 1138 18 of 23
Metals 2023, 13, x FOR PEER REVIEW 21 of 25

Metals 2023, 13, x FOR PEER REVIEW 21 of 25

In Figure 14b, however, we can see that this mark is not present, confirming that the
recirculation was indeed reduced with the optimized model 3.

Figure 14. Signs of recirculation in the riser of the pieces. (a) Original. (b) Modified model 3.

Figure 14. Signs of recirculation in the riser of the pieces. (a) Original. (b) Modified model 3.
Figure 14. Signs of recirculation in the riser of the pieces. (a) Original. (b) Modified model 3.
4.3. Shrinkage Porosity Simulation
4.3.
4.3. Shrinkage
As shownPorosity
Shrinkage in TableSimulation
Porosity 4, all studied models in the nozzle optimization showed shrinkage
Simulation
porosityAs in the upper base, includingmodelsthe modelthe with the best filling results (nozzle model
As shown in Table 4,
shown in Table 4, all
all studied
studied models in in the nozzle
nozzle optimization
optimization showed
showed shrinkage
shrinkage
3). Model
porosity 3 presented shrinkage porosity in the upper base with a maximum of 62.62%.
porosityin inthe
theupper
upperbase,
base,including
includingthe themodel
model with
withthethebest filling
best results
filling (nozzle
results model
(nozzle 3).
model
Observing
Model 3 these results,
presented it is clear
shrinkage that thein
porosity upper
the base is base
upper a critical
with point
a concerning
maximum ofporosity
62.62%.
3). Model 3 presented shrinkage porosity in the upper base with a maximum of 62.62%.
defects.
Observing It can also be noted clearthat as thethe injectionbase
systems were optimized, the percentage
Observingthese theseresults,
results,ititis
is clear that
that the upper
upper base is is aa critical
critical point concerning
point concerning porosity
porosity
of shrinkage
defects. It can porosity
also be was high.
noted that This
as theis injection
because the optimization
systems were of the feed
optimized, the models allows
percentage of
defects. It can also be noted that as the injection systems were optimized, the percentage
ashrinkage
faster filling and consequently
porosity was high. This a greater
is because thermal load to be dissipated
the optimization of the feedduring
modelssolidifica-
allows a
of shrinkage porosity was high. This is because the optimization of the feed models allows
tion
fasterinside
fillingthe mold.
and This favors
consequently the formation
a greater thermalofload
contraction porosities
to be dissipated in thesolidification
during upper base,
a faster filling and consequently a greater thermal load to be dissipated during solidifica-
which does
inside the not This
mold. present anythe
favors compensation mechanismporosities
formation of contraction and is one of the
in the lastbase,
upper regions to
which
tion inside the mold. This favors the formation of contraction porosities in the upper base,
solidify.
does not present any compensation mechanism and is one of the last regions to solidify.
which does not present any compensation mechanism and is one of the last regions to
Figure 15 15 shows
shows the
theposition
positionand andaasectional
sectionalview
viewthat that shows
shows thethe maximum
maximum shrink-
shrinkage
solidify.
points
age pointsin thein virtually molded
the virtually molded partpart
withwiththe optimized
the optimized nozzle.
nozzle.
Figure 15 shows the position and a sectional view that shows the maximum shrink-
age points in the virtually molded part with the optimized nozzle.

Figure 15. Shrinkage

Figure 15. Shrinkage porosity
porosity in
in the original model
the original model with
with optimized
optimized converging
converging nozzle.
nozzle. (a)
(a) Position
Position
of
of porosities.
porosities. (b)
(b) Section
Section showing
showing region
region of
of maximum
maximum porosity.
porosity.
Figure 15. Shrinkage porosity in the original model with optimized converging nozzle. (a) Position
of porosities. (b) Section showing region of maximum porosity.
According
According toto Rajkolhe
Rajkolhe and
and Khan
Khan [62]
[62] and
and Ingle
Ingle and
and Sorte
Sorte [63],
[63], shrinkage
shrinkage defects
defects such
such
as porosity-considered closed shrinkage
shrinkage defects
defects occur
occur when there feed metal supply is
According to Rajkolhe and Khan [62] and Ingle and Sorte [63], shrinkage defects such
insufficient
insufficient to compensate for shrinkage
as porosity-considered closed shrinkageasdefects
the metal solidifies.
occur when there feed metal supply is
insufficient to compensate for shrinkage as the metal solidifies.
Metals 2023, 13, x FOR PEER REVIEW 21 of 25
Metals 2023, 13, x FOR PEER REVIEW 21 of 25
Metals 2023, 13, 1138 19 of 23

This type of porosity can be reduced or eliminated with geometric modifications such
This type of porosity can be reduced or eliminated with geometric modifications such
as changes in the feeding system, insertion of mass to compensate for shrinkage, modifi-
This type
as changes of feeding
in the porositysystem,
can be insertion
reduced of or mass
eliminated with geometric
to compensate modifications
for shrinkage, modifi-
cation of the part geometry and with manipulation of injection parameters such as rota-
such
cationasofchanges
the partin the feeding
geometry and system, insertion ofofmass
with manipulation to compensate
injection parametersfor suchshrinkage,
as rota-
tion speed, injection
modification of the partpressure and temperature,
geometry thermal insulation,
and with manipulation of injection among others. The fo-
parameters
tion speed, injection pressure and temperature, thermal insulation, among others. such as
The fo-
cus of
rotationthis work,
speed, however,
injection was
pressure notandto modify the
temperature, injection
thermal parameters,
insulation, mainly
among because
others. the
The
cus of this work, however, was not to modify the injection parameters, mainly because the
data used
focus of thisas boundary condition and input parameters were replicated from preliminary
data used aswork, however,
boundary was not
condition and to input
modify the injection
parameters wereparameters,
replicatedmainly because the
from preliminary
physical
data used experiments.
as boundary Therefore,
condition in
and order
input to reduce
parameters the porosity
were in the part,
replicated fromcompensation
preliminary
physical experiments. Therefore, in order to reduce the porosity in the part, compensation
volumes were added Therefore,
physical and were designed to move the the porosity in to its part,
interior. These vol-
volumesexperiments.
were added and were designed in order to toreduce
move the porosity
porosity to the compensation
its interior. These vol-
umes
volumes were
were positioned on
added andonwere the upper base and centered around the region identified as
umes were positioned the designed
upper base to move the porosity
and centered to itsthe
around interior.
region These volumes
identified as
being
were the most critical concerning the presence of shrinkage porosity. All porosity cases
beingpositioned on the concerning
the most critical upper base and centered around
the presence of shrinkage the region identified
porosity. as being
All porosity the
cases
evaluated
most inconcerning
critical this topic werethe made from
presence of the optimized
shrinkage porosity. convergent
All porositynozzle
casesmodel (nozzle
evaluated in
evaluated in this topic were made from the optimized convergent nozzle model (nozzle
model
this 3). were made from the optimized convergent nozzle model (nozzle model 3).
topic
model 3).
Figures 16–19
Figures show
16–19 show
showthe the results
theresults obtained
resultsobtained
obtained for each type of projected compensation vol-
Figures 16–19 forfor
eacheachtype type of projected
of projected compensation
compensation vol-
ume. In riser
volume. models
In riser models 1 and 2, the
1 and shrinkage
2, the shrinkage compensation
compensation volumevolumehas hasthe shape
the shape of a of
cyl-
a
ume. In riser models 1 and 2, the shrinkage compensation volume has the shape of a cyl-
inder. In Figure 16, we can see that the riser model 1 displaced the
cylinder. In Figure 16, we can see that the riser model 1 displaced the porosity to its interior,porosity to its interior,
inder. In Figure 16, we can see that the riser model 1 displaced the porosity to its interior,
but aa large
but large part
part is
is still
still present
present in in the
the part
part because
because thethe volume
volume does does notnot have
have enough
enough mass mass
but a large part is still present in the part because the volume does not have enough mass
to compensate
to compensate for the shrinkage of the alloy nor to change the
the shrinkage the alloy nor to change the temperature field in that temperature field in that
to compensate for the shrinkage of the alloy nor to change the temperature field in that
region. In model 2, the height of the
region. the volume
volume was was increased by 3 mm mm in in order
order to to increase
increase
region. In model 2, the height of the volume was increased by 3 mm in order to increase
the compression mass. As
the Asititcan
canbe beseenseenininFigure
Figure17, 17,it itcaused
caused a greater
a greater displacement
displacement of
the compression mass. As it can be seen in Figure 17, it caused a greater displacement of
porosity
of porosity compared
compared to the riser
to the model
riser model 1, but a part
1, but a partof the
of theporosity
porosityis still present
is still presentin the cell
in the
porosity compared to the riser model 1, but a part of the porosity is still present in the cell
structure.
cell structure.
structure.

Figure 16. Shrinkage porosity riser model 1 with optimized converging nozzle. (a) Position of po-
Figure
Figure Shrinkageporosity
16. Shrinkage porosityriser
riser model1 1with
with optimized converging nozzle. (a) Position of
rosities.16.
(b) Section showing region model optimized
of maximum porosity. converging nozzle. (a) Position of po-
porosities.
rosities. (b)(b) Section
Section showing
showing region
region of of maximum
maximum porosity.
porosity.

Figure 17. Shrinkage porosity riser model 2 with optimized converging nozzle. (a) Position of po-
Figure 17.
(b)Shrinkage
rosities.17. porosityregion
Section showing riser model 2 with porosity.
optimized converging nozzle. (a) Position of po-
Figure Shrinkage porosity riserofmodel
maximum
2 with optimized converging nozzle. (a) Position of
rosities. (b) Section showing region of maximum porosity.
porosities. (b) Section showing region of maximum porosity.
 The riser models 3 and 4 have volumes in the shape of a truncated cone (Figure 5).
Model The riser models
3 generated 3 and 4 havethat
a displacement volumes
almostinremoved
the shapeallofthe
a truncated
porosity ofcone
the (Figure 5).
upper re-
Model 3 generated a displacement that almost removed all the porosity of
gion of the part (Figure 18). Based on this result, the riser model 4 was designed with the the upper re-
gion of
same the partdimensions
diameter (Figure 18).butBased
withon this result,
a greater theinriser
height model
relation to 4model
was designed with the
3, approximately
same diameter dimensions but with a greater height in relation to model
3 mm. In the case of the riser model 4, the displacement generated by the compensation3, approximately
Metals 2023, 13, 1138 3 mm. In thesufficient
case of the riser modeldisplace
4, the displacement 20 of 23
volume was to completely the porositiesgenerated by the
to its interior, compensation
leaving the part
volume
free was sufficient
of shrinkage to completely
porosities, as can bedisplace the porosities
seen in Figure 19. to its interior, leaving the part
free of shrinkage porosities, as can be seen in Figure 19.

Figure 18. Shrinkage porosity riser model 3 with optimized converging nozzle. (a) Position of po-
Figure
Figure 18.
18. Shrinkageporosity
porosityriser
risermodel
model3 3with
withoptimized
optimized converging nozzle.
(a) (a) Position of
rosities. (b) Shrinkage
Section showing region of maximum porosity. converging nozzle. Position of po-
porosities. (b) Section showing region of maximum porosity.
rosities. (b) Section showing region of maximum porosity.

Figure 19. Shrinkage porosity riser model 4 with optimized converging nozzle. (a) Position of po-
Figure 19.
Figure
rosities. 19.
(b) Shrinkage
Shrinkage
Section porosity
porosity
showing riser model
riserof
region model4 4with
maximum withoptimized
optimized
porosity. converging nozzle.
converging (a) (a)
nozzle. Position of po-
Position of
rosities. (b) Section showing region of maximum porosity.
porosities. (b) Section showing region of maximum porosity.
5. Conclusions
5. Conclusions
The riser models 3 and 4 have volumes in the shape of a truncated cone (Figure 5).
In this work, virtual prototyping is used to optimize the efficiency and accuracy of a
Model In3this
generated
work, a displacement
virtual prototyping that is
almost
used removed all the
the porosity of the accuracy
upper region
non-traditional precision casting process that to optimize
uses centrifugal efficiency
force to and inject the molten of a
of the part
non-traditional(Figure 18).
precision Based on this result, the riser model 4 was designed with the same
alloy into the mold. This casting
modified process
castingthat usesfrom
differs centrifugal forceprocesses
traditional to inject the molten
because it
diameter dimensions but with a greater height in relation to model 3, approximately 3 mm.
uses centrifugal force in the perpendicular direction to the rotation axis to inject the mol-it
alloy into the mold. This modified casting differs from traditional processes because
In thecentrifugal
uses case of the riser in model 4, the displacement generated by the compensation volume
ten metal inside force the mold; thewhile
perpendicular
traditionaldirection
processes to use
the rotation
centrifugal axisforce
to inject
in thethe mol-
same
was
ten sufficient
metal to
inside completely
the mold; displace
while the porosities
traditional processesto its
useinterior, leaving
centrifugal the
force part
in thefree
sameof
direction of the rotation axis.
shrinkage
direction porosities,
of the rotation as can be seen in Figure 19.
The virtual castingsaxis.
carried out in this work enabled the analysis and design of the
feedingThe virtual castings carried outofina this
systems for the production work enabled
simple-cubic cellularthestructure
analysis with and design
complex of ge-
the
5. Conclusions
feeding
ometry systems
manufactured for the production
with of
a copper-baseda simple-cubic
shape cellular
memorythe structure
alloy. with
The numerical complexsimula-ge-
In this
ometry work, virtual
manufactured withprototyping
a is used
copper-based to optimize
shape memory efficiency
alloy. The and accuracy
numerical simula- of
tion
ation of the processprecision
non-traditional allowed casting
reducing and correcting
process that uses possible
centrifugal defects
force that
to may the
inject impair the
molten
of the process
production and allowed
integrity of reducing
the part, and correcting
especially possibleand defects that may impairthat the
alloy into the
production mold.
and This modified
integrity of the casting
part, differsrecirculation
especially from traditional
recirculation and
shrinkage
processes
shrinkage
porosity
because
porosity it uses
that
mechanically
centrifugal weaken
force in thethe component.direction to the rotation axis to inject the molten metal
perpendicular
mechanically weaken the component.
inside the mold; while traditional processes use centrifugal force in the same direction of
the rotation axis.
The virtual castings carried out in this work enabled the analysis and design of the feed-
ing systems for the production of a simple-cubic cellular structure with complex geometry
manufactured with a copper-based shape memory alloy. The numerical simulation of the
process allowed reducing and correcting possible defects that may impair the production
and integrity of the part, especially recirculation and shrinkage porosity that mechanically
weaken the component.
Metals 2023, 13, 1138 21 of 23

The results showed that gas circulation inside the mold has a strong influence on the
filling process. Badly designed feeding systems tend to make it difficult for the gas to return
and generate high pressures that can trap the gases, forming voids in the parts or causing
damage such as cracking and mold rupture. Regarding the design of the studied part in
this article, it is possible to conclude that the convergent nozzle proposed in model 3 is a
better design to reduce filling time and eliminate recirculation, but due to the presence of
retraction pores, it is necessary to add compensation for volume shrinkage. The shrinkage
compensation volume that presented the best results has the shape of a truncated cone
with a larger diameter of 8 mm, a smaller diameter of 6 mm and a height of 8 mm, such as
the riser proposed in model 4 in this work.

Author Contributions: Conceptualization, C.E.S.A. and C.J.D.A.; methodology, C.E.S.A. and P.C.S.S.;
software, C.E.S.A.; validation, C.E.S.A., C.J.D.A. and A.G.B.L.; formal analysis, C.E.S.A.; investigation,
C.J.D.A. and P.C.S.S.; resources, C.J.D.A. and A.G.B.L.; writing—original draft preparation, C.E.S.A.;
writing—review and editing, E.N.D.G. and J.M.P.Q.D.; visualization, E.N.D.G.; supervision, C.J.D.A.
and A.G.B.L.; project administration, C.J.D.A.; funding acquisition, J.M.P.Q.D., C.J.D.A. and A.G.B.L.
All authors have read and agreed to the published version of the manuscript.
Funding: This research was funded by Brazilian National Council for Scientific and Technological
Development (CNPq) for the scholarship PQ-1C, grant number 302740/2018-0; the Paraíba State
Research Support Foundation (FAPESQ-PB) for the project NISMArt, grant number 044/2023; and the
Brazilian Coordination for the Improvement of Higher Education Personnel (CAPES) for the doctoral
scholarship to Paulo César Sales da Silva and for the post-doctoral scholarship to Estephanie Nobre
Dantas Grassi. In addition, this work is a result of the project “BlueWoodenHouse”, with the reference
POCI-01-0247-FEDER-047157, co-funded by the European Regional Development Fund (ERDF)
through the Operational Programme for Competitiveness and Internationalization (COMPETE 2020),
under the Portugal 2020 Partnership Agreement, and the project “BlueHouseSim”, with reference
2022.06841.PTDC, funded by national funds (PIDDAC) through FCT/MCTES. Furthermore, this
work was financially supported by Base Funding-UIDB/04708/2020 and Programmatic Funding-
UIDP/04708/2020 of the CONSTRUCT-Instituto de I&D em Estruturas e Construções-funded by
national funds through the FCT/MCTES (PIDDAC); and by FCT—Fundação para a Ciência e a
Tecnologia through the individual Scientific Employment Stimulus 2020.00828.CEECIND.
Data Availability Statement: Not applicable.
Acknowledgments: The authors acknowledge the authors cited in the text that helped in the im-
provement of this paper as well as the ESI Group for granting the license for the ProCAST program
(Ref: CA/ARDS/RSD_2007_01BR).
Conflicts of Interest: The authors declare no conflict of interest.

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