Plane Thermoelastic Waves in Infinite Half-Space Caused


FACTA UNIVERSITATIS  

Series: Mechanical Engineering Vol. 15, N
o
 3, 2017, pp. 397 - 411 

https://doi.org/10.22190/FUME170505022R 

Original scientific paper 

CASTING IMPROVEMENT BASED ON METAHEURISTIC 

OPTIMIZATION AND NUMERICAL SIMULATION 

UDC 621.7 

Radomir Radiša
1
, Nedeljko Dučić

2
, Srećko Manasijević

1
,  

Nemanja Marković
3,4

, Žarko Ćojbašić
3
 

1
Lola Institute Belgrade, Serbia

 

2
Faculty of Technical Sciences Ĉaĉak, University of Kragujevac, Serbia 

3
Faculty of Mechanical Engineering, University of Niš, Serbia  

4
Philip Morris Operations Serbia  

Abstract. This paper presents the use of metaheuristic optimization techniques to support 

the improvement of casting process. Genetic algorithm (GA), Ant Colony Optimization 

(ACO), Simulated annealing (SA) and Particle Swarm Optimization (PSO) have been 

considered as optimization tools to define the geometry of the casting part’s feeder. The 

proposed methodology has been demonstrated in the design of the feeder for casting 

Pelton turbine bucket. The results of the optimization are dimensional characteristics 

of the feeder, and the best result from all the implemented optimization processes has 

been adopted. Numerical simulation has been used to verify the validity of the presented 

design methodology and the feeding system optimization in the casting system of the 

Pelton turbine bucket. 

Key words: Metaheuristic Optimization, Sand Casting, Feeders, Numerical Simulation 

1. INTRODUCTION 

The task of the optimization is to find the variables in which the target (criterion) 

function has extreme (minimum or maximum) value, with the limits, which define the 

space of potential solutions. Optimization is an integral part of natural processes. From 

the phenomena that take place at the level of micro-scale (e.g. crystallization, in which the 

molecules occupy the minimum energy position), to the evolutionary process leading to, 

through the principle of survival of the fittest, the individuals that are better adapted to the 

                                                           
Received May 05, 2017 / Accepted August 04, 2017 

Corresponding author: Nedeljko Duĉić  

Faculty of Technical Sciences Ĉaĉak, University of Kragujevac, Svetog Save 65, 32000 Ĉaĉak  

E-mail: nedeljko.ducic@ftn.kg.ac.rs 



398 R. RADIŠA, N. DUĈIĆ, S. MANASIJEVIĆ, N. MARKOVIĆ, Ţ. ĆOJBAŠIĆ 

conditions in the "environment" – all this serves as an inspiration for several metaheuristic 

optimization techniques. The implemented metaheuristic optimization methods are based 

on the idea that, by imitating nature, what should be looked for is the optimum complex 

function of several variables that represent the mathematical abstraction of a complex 

engineering problem. The idea developed in this paper is to apply metaheuristic optimization 

and advanced simulation for improvement of the casting process, which is tested on the 

problem of design and optimization of the feeder for sand casting of the Pelton turbine 

bucket.  

When it comes to the implementation of metaheuristic optimization methods in the 

casting process, the spectrum of published research studies is very wide because of a large 

number of casting technologies and their respective complexity. Gravela et al. [1] presented 

ant colony optimization (ACO) for the solution of an industrial scheduling problem in an 

aluminum casting center. Santos et al. [2] presented the development of a computational 

algorithm (software) applied to maximizing the quality of steel billets produced by 

continuous casting. A mathematical model of solidification works integrated with a genetic 

search algorithm and a knowledge base of operational parameters. Surekha et al. [3] 

presented multi-objective optimization of green sand mould system using evolutionary 

algorithms, such as genetic algorithm (GA) and particle swarm optimization (PSO). 

Slavković et al. [4] presented application of learning machine methods in prediction and 

optimization of the wear rate of wear resistant casting parts. Duĉić et al. [5] presented 

optimization of chemical composition in the manufacturing process of flotation balls based 

on intelligent soft sensing. Duĉić et al. [6] presented optimization of the gating system for 

sand casting using genetic algorithm. The implementation of modern CAD/CAM software 

systems is frequent in the research projects of the casting process, as well as the combination 

of modern CAD/CAM software systems and methods of metaheuristic optimization. Dabade 

et al. [7] used MagmaSoft software for simulating the casting process and analyzing its 

various defects, by detecting the cause through simulation dimensionally and positionally 

different embodiments of the casting and the feeding systems. Jie et al. [8] used the Pro Cast 

software package to improve the casting process of aluminum alloy, and have concluded 

that the increase of molten metal temperature and of casting speed solves the problem of 

porosity. Nimbulkara and Dalu [9] presented the design of gating and feeding system with 

the objective of optimizing them by using the Auto-CAST X1 casting simulation software 

as well as of preparing the sand mold and casting the part, of comparing the simulated result 

and experimental results, of reducing the rejection rate and thus enabling the company to 

again start the production.   

Unlike these studies, in this paper four metaheuristic optimization techniques have 

been considered, while the obtained results have been tested and verified with the numerical 

simulation of casting processes using the advanced MAGMA
5
 software.  

2. OPTIMIZATION ASPECTS OF FEEDING THE CASTING PART 

Optimal design of some system is a goal in more or less every engineering discipline. 

The imperative of optimal design of the feeding system of the cast is to reduce material 

consumption so that the feeder can successfully compensate shrinkage of the material in 

the mold cavity. Unlike the filling of the mold cavity, feeding is a long, slow process that 



 Casting Improvement Based on Metaheuristic Optimization and Numerical Simulation 399 

is required during the contraction of the liquid that takes place on freezing. This process 

takes minutes or hours depending on the size of the casting. During freezing are present 

three different phases of the contraction volume, i.e. shrinkage: liquid contraction, 

solidification contraction and solid contraction (Fig. 1). 

 

Fig. 1 Schematic illustration of three shrinkage regimes:  

in the liquid; during freezing; and in the solid [10] 

Volume contraction is manifested in side effects: internal cavities, surface deformation, 

surface craters. One of the indicators of casting process quality is continuity of molten metal 

flow in the area of solidification that is fed and compensating deficit caused by solidification. 

Failure in this process will result in deficiencies of the solidification process that is called 

porosity. In Fig. 2 just a generalized classification of porosity is given, as a result of metal 

shrinkage. Open defects, as a result of metal shrinkage, are result of cooling while metal is 

in liquid state and during solidification. These defects are large-volumed, so they are called 

macro-shrinkage. Closed shrinkage defects manifest themselves as an internal macroporosity 

and internal microporosity. Open defects are exclusively related to the process of metal 

shrinkage, while closed defects, in addition to process of metal shrinkage, are directly related 

to nucleation and growth of grains, as the characteristics of crystallization. 

 

Fig. 2 Open and closed defects as a result of metal shrinkage  



400 R. RADIŠA, N. DUĈIĆ, S. MANASIJEVIĆ, N. MARKOVIĆ, Ţ. ĆOJBAŠIĆ 

The elimination of those side effects can be realized by the proper design of feeders 

which, after cooling, should be removed from the casting part. By exploring numerous 

literature references, as a general conclusion, the following sequence of activities in the 

cast feeding system design [11] is imposed: 

(a) Representation of the casting as a collection of simple, plate-like shapes  

 locate hot spots, and place a riser on each one  

 for each plate-like shape, determine edges with and without end effect  

(b) Determination of feeding zones, feeding paths and feeding dimensions.  

(c) Determination of feeding distances  

(d) Determination of riser sizes  

Within this sequence are incorporated rules on valid feeding of casting part, which 

Cambell systematically exposes in his book [10]. Numerous literature sources are mainly 

based on two rules of feeding the cast:  

(a) The feeder must solidify, at the earliest, at the same time as cast or, of course, later. 

This rule is called Chvorinov's heat-transfer criterion. 

(b) The feeder must contain sufficient molten metal to compensate to the casting part 

metal shrinkage, in the extent for which the aforementioned feeder is provided. 

Metaheuristic optimization of a feeder is a certain synthesis of exposed rules and activities 

in the feeding system design, embedded in standard optimization subjects, such as the fitness 

function, and appropriate limits. As optimization techniques were used nature-inspired 

metaheuristic algorithms: Genetic algorithm (GA), Ant Colony Optimization (ACO), 

Simulated annealing (SA) and Particle Swarm Optimization (PSO). 

3. METAHEURISTIC OPTIMIZATION TECHNIQUES 

Two major components of any metaheuristic algorithms are: intensification and 

diversification, or exploitation and exploration [12]. Diversification means to generate 

diverse solutions so as to explore the search space on a global scale, while intensification 

means to focus the search in a local region knowing that a current good solution is found in 

this region. A good balance between intensification and diversification should be found during 

the selection of the best solutions to improve the rate of algorithm convergence. The selection 

of the best ensures that solutions will converge to the optimum, while diversification via 

randomization allows the search to escape from local optima and, at the same time, increases 

the diversity of solutions. A good combination of these two major components will usually 

ensure that global optimality is achievable [13]. 

3.1. Genetic algorithm (GA) 

Genetic algorithms (GA) [13] are probably the most popular and widely used metaheuristic 

optimization technique. They represent abstraction model of biological natural selection, 

based on Darwin's theory of evolution. Application of genetic algorithms assumes the use of 

concepts from nature such as crossover, mutation, recombination and selection in adaptive 

and artificial systems. Such genetic operators are important elements of the each problem-

solving strategy by use of genetic algorithms. Genetic algorithms can be described by the 

following generic representation: 



 Casting Improvement Based on Metaheuristic Optimization and Numerical Simulation 401 

Data: population size N, crossover rate ηc and mutation rate ηm. 

Initialization: create initial population P={Pi}, i=1…N, and initialize the best solution 

Best ←void. 

WHILE {stoppingcriterion not met} 

 evaluate P and update the best solution Best. 

 initialize offspring population:R←void. 

 create offsprings: 

  FOR k=1 TO N / 2 DO 

  selection stage: select parents Q1 and Q2 from P, based on fitness. 

crossover stage: use crossover rate ηc and parents (Q1;Q2) to create 

offsprings (S1;S2). 

mutation stage: use mutation rate ηm to apply stochastic changes to S1 

and S2 and create mutated offsprings T1 and T2. 

Add T1 and T2 to offspring population: R ← R U {T1 and T2}. 

 Replace current population P with offspring population R: P ←R. 

 Elitism: replace the poorest solution in P with the best solution in Best. 

3.2. Ant colony optimization (ACO) 

Social ants foraging behavior was the role model for development of ant colony 

optimization (ACO) technique [13]. Ants use chemical messenger called pheromone, being 

social insects that live together in organized colonies and that interact and communicate 

among themselves. While foraging, ants lay scent chemicals or pheromone and are able to 

follow the pheromone routes marked by other ants, indicating the trail to food source. The 

ants follow the route with higher pheromone concentration, and as more and more ants 

follow the same route, it becomes the favored path with enhanced pheromone which is likely 

the shortest or more efficient path. Evolving, the system converges to a self-organized state. 

Generic representation of ant colony algorithm is: 

Data: Population size N, set of components C={C1,…, Cn}, evaporation rate evap. 

Initialization: amount of pheromones for each component PH = {PH1, …, PHn}; best 

solution Best. 

WHILE {stopping criterion not met} 

 initialize current population, P=void. 

 Create current population of virtual solutions P: 

 FOR i=1 TO N DO 

Create feasible solution S.  

Update the best solution, Best←void. 

Add solution S to P: P ←P U S 

      Apply evaporation:  

FOR j=1 TO n DO  

PHj =PHj ·(1–evap) 

     Update pheromones for each component:  

FOR i=1 TO N DO  

FOR j=1 TO n DO 

 if component Ci is part of solution Pj, then update pheromones for this 

 component: PHj =PHj+Fitness(Pj) 



402 R. RADIŠA, N. DUĈIĆ, S. MANASIJEVIĆ, N. MARKOVIĆ, Ţ. ĆOJBAŠIĆ 

3.3. Simulated annealing (SA) 

Simulated annealing (SA) optimization was designed using analogy with metal 

annealing [14], and is a technique possessing main ability to avoid being trapped in local 

optima unlike deterministic optimization techniques. It is an optimization method which is 

alike the process of warming up a solid to melting, then followed by cooling it down until 

it crystallizes into a perfect lattice. Simulated annealing could be considered as Markov 

chain following search [12], which converges under appropriate settings. With each 

search move, moving trace a piecewise path, acceptance probability is assessed, accepting 

alterations improving the objective function and also keeping some changes that do not 

improve the objective [13]. Generic representation of simulated annealing is described by: 

Data: initial approximation X0, initial temperature T, number of iteration for a given 

temperature nT.  

Optimal solution: Xbest ← X0.  

WHILE {stopping criterion not met} 

n=0; i=0;  

WHILE (n<nT) DO  

Choose a new approximation Y  

Accept or reject the new approximation based on the Metropolis rule: Xi+1 

=G(Xi,Y,T) 

update optimal solution: if Xi+1 is better than Xbest, then Xbest ← Xi+1  

next n-iteration (n←n+1) 

update temperature T  

next T-iteration (i←i+1) 

3.4. Particle swarm optimization (PSO) 

Particle swarm optimization (PSO) is a technique developed on resembling swarm 

behavior, such as fish and bird schooling [13]. PSO has generated a lot of attention in the 

field of swarm intelligence. System is initialized with a population of random solutions 

and searches for optima by updating generations. The potential solutions, called particles, 

fly through the problem space by following the current optimum particles. Each particle 

keeps track of its coordinates which are associated with the best solution (fitness), and its 

value is also stored. Best fitness value is taken as final solution. Numerous PSO variants 

exist, as well as hybrid algorithms combining PSO with other algorithms. PSO is 

described by the following representation: 

Data: population size N, personal-best weight α, local-best weight β, global-best 

weight γ, correction factor ε.  

Initialization: create initial population P. 

WHILE {stopping criterion not met}  

Select the best solution from the current P: Best. 

Select global-best solution for all particles: B
G
.  

Apply swarming: 

FOR i=1 TO N DO  

Select personal-best solution for particle Xi:Bi
P
.  

Select local-best solution for particle Xi:Bi
L
.  



 Casting Improvement Based on Metaheuristic Optimization and Numerical Simulation 403 

Compute velocity for particle Xi: 

 FOR j=1 TO DIM DO  

Generate correction coefficients: a=α·rand(); b=β·rand(); 

c=γ·rand(). 

Update velocity of particle Xi along dimension j: 

Vij = Vij+a·(Bij
P
–xij) + b·(Bij

L
–xij) + c·(Bj

G
–xij) 

  Update position of particle Xi:Xi =Xi +ε·Vi 

4. OPTIMIZATION PROCESSES 

The proposed methodology of combining metaheuristic optimization and advanced 

casting simulation is applied to the problem of optimization of geometry of a feeder for 

casting Pelton turbine bucket (its CAD model is shown in Fig. 3). Optimization is based 

on the precise formulation of the objective function and constraints, and abovementioned 

techniques of metaheuristic optimization were implemented. 

 

Fig. 3 CAD model of buckets Pelton turbine  

4.1. Formulation of the optimization problem 

The formulation of the optimization problem is actually defining the fitness function. 

Defining the fitness function is one of the major steps of the optimization process. 

Creating the fitness function is based on the rule: The heat-transfer requirement. The 

heat-transfer requirement for successful feeding can be stated as follows: the freezing time 

of the feeder must be at least as long as the freezing time of the casting [10]. Casting 

solidification time can be predicted using Chvorinov’s Rule shown by the equation [11]: 

 

2

s

V
t C

A

 
  

 
, (1) 

where ts is the total solidification time of the part or feeder, C is a mold constant, V is the 

volume of metal, and A is the total surface area of the part or feeder. As the feeder serves 



404 R. RADIŠA, N. DUĈIĆ, S. MANASIJEVIĆ, N. MARKOVIĆ, Ţ. ĆOJBAŠIĆ 

to compensate for the volume shrinkage in the casting part, it needs to be the final link of 

the solidification chain, i.e. it should be the last to solidify in directional solidification 

process. The longest solidification time for a given volume is the one where the shape of 

the part has the minimum surface area. Feeder module (Mfeeder) is taken to be for a minimum 

of 20% higher than the module of casting part, i.e. module of part which feeds [10]: 

 

_
1.2

feeder casting part
M M  . (2) 

The modulus of a designed feeder is given by Eq. (3), based on the dimensional 

characteristics (Fig. 4): 

 

2 2

2

2 2 2 2 2

( ) 2 ( )

3 ( ( ) ( )) 2
2

feeder

feeder

feeder

V H R R r r R l H R r H l
M

P R r
R r H R r R r l H

           
 

 
            

 

. (3) 

 

Fig. 4 CAD model of feeder and dimensional characteristics 

Based on the values of volume and surface of the casting part, obtained by analyzing 

the CAD model (Vc=4269327.33 mm
3
 and Ac=348116.32 mm

2
), the module of the 

casting part is Mcasting_part=12.26 mm. Eq. (4) gives the final expression of fitness function 

F(R,r,H,l), where all values are entered in [mm], that minimizes:  

 

2 2

2

2 2 2 2 2

( ) 2 ( )
12.26 0

3 ( ( ) ( )) 2
2

H R R r r R l H R r H l
F

R r
R r H R r R r l H

           
  

 
            

 

 (4) 



 Casting Improvement Based on Metaheuristic Optimization and Numerical Simulation 405 

4.2. Constraints of optimizations parameter 

First constraint is based on the rule Mass-transfer (volume) requirement. The fulfillment 

of the conditions given in rule “The heat-transfer requirement”, does not guarantee the 

fulfillment of the conditions given in rule “Mass-transfer (volume) requirement”. Although 

the feeder may have been provided of such a size that it theoretically would contain liquid 

until after the casting is solid, in fact it may still be too small to deliver the volume of feed 

liquid that the casting demands. Thus, it will be prematurely sucked dry, and the resulting 

shrinkage cavity will extend into the casting. This is because they are themselves freezing 

at the same time as the casting, depleting the liquid reserves of the reservoir. Effectively, 

the feeder has to feed both itself and the casting. We can allow for this in the following 

way. If we denote efficiency ε of the feeder as the ratio (volume of available feed metal) / 

(volume of feeder, Vf) then the volume of feed metal is, of course Vf. If the solidification 
shrinkage of the liquid is α, during freezing, then the feed demand from both the feeder 

and casting together is α(Vf,Vc), and hence [10]: 

 

( )
f f c

V V V   . (5) 

Solving for the feeder volume yields: 

 

2 2
0.4 ( ) 2 ( ) 0.25c

f c c

V
V V H R R r r R l H R r H l V



 
               


, (6) 

where α is the solidification shrinkage of the liquid during freezing (α =4, for steels the 

fcc structure applies above 0.1% carbon where the melt solidifies to austenite) and ε=20% 

for appropriate feeder. Relation (6) is a constraint 1 in the optimization process of geometry 

feeders. 

In addition to the abovementioned constraints, other constraints are referred to the 

mutual relations of values which are optimized and available space on the casting part. 

Table 1 The other constraints 

Constraint 2 2r+l<50 

Constraint 3 H<155 

Constraint 4 2R+ l<160 

4.3. Results of the optimization process 

The results of the carried out optimization processes are relatively similar and their 

overview is given in Table 2. Simultaneous application of several metaheuristic 

optimization techniques allows for efficient verification of obtained optimization results. 

Table 2 Results of optimization process 

Optimization value GA ACO SA PSO 

H 153 148 154 150 

R 61 58 55 57 

r 20 22 23 19 

l 26 24 28 27 



406 R. RADIŠA, N. DUĈIĆ, S. MANASIJEVIĆ, N. MARKOVIĆ, Ţ. ĆOJBAŠIĆ 

Based on the obtained results of taken optimizations, the following values of optimized 

sizes have been adopted: H=155 mm, R=60 mm, r=20 mm and l=25 mm. According to 

these values, CAD model of feeder was created and embedded into assembly of the entire 

gating system with a casting part. 

5. NUMERICAL SIMULATION AS A VERIFICATION OF THE OPTIMIZATION RESULT 

Instead of experimental trial-and-error, the results of mold cavity filling, solidification, 

critical spots, formation of residual stresses, etc. now optimized in a virtual computer 

environment with various conditions. Using numerical simulations in the development of 

casting technology not only shortens the time necessary for product development but also 

reduces expenditures, reduces risks from defects, etc. Modern digital tools enable a 

relatively fast attainment of optimized solutions for casting technology, which results in 

stable manufacture with lower expenditures [15−19]. Digital tools using for optimization 

of the technical parameters influence the macro and microstructure of a cast. Digital tools 

allow different technological parameters of a casting process to be tested. Hence, to 

perform the simulation, it is necessary to provide a 3D geometric model of the casting and 

other components (tools for casting, gating system, feeders, etc.) and technological 

parameters (casting temperature, casting time, alloy composition, etc.). Based on the results 

of experimental investigations, the optimization of relevant technological parameters and 

their implementation under industrial conditions showed that the properties of a casting, in 

practice, could be significantly improved. The results show that, under industrial conditions, 

digital tools provide satisfactory solutions in a short period, starting virtually from scratch. It 

was shown that the employment of these software packages brings great advantages 

compared to the conventional manner of adopting new products. For instance, the results 

obtained in a rapid generation of model elements significantly accelerated the work and 

improved the productivity of engineers, reduced the time for adopting new products, reduced 

the scope of traditional prototype testing (creating prototypes and their testing), which is 

expensive and time consuming, causing standstills in manufacture, and reduced expenditures 

for adopting new products. The digital tool (in our case used MAGMA
5
) package itself 

automatically generates a mesh. The software user can set the fineness of the mesh, i.e., the 

number of mesh elements by defining the minimum size of the desired elements in all three 

directions of the coordinate system (Fig. 5).  

 

Fig. 5 Mesh Quality 



 Casting Improvement Based on Metaheuristic Optimization and Numerical Simulation 407 

The finer the mesh, i.e., the more elements it has, the more accurate the calculation of 

the simulation is, but the simulation time is longer. The prepared mesh is used for further 

calculation. For each element, i.e., part of the mesh, differential equations used to calculate 

its physical and thermal parameters and the results obtained are boundary conditions for the 

calculation of the parameters in the neighboring element. Thus, the computer calculates 

element by element in 3D coordinates and finally integrates all the partial results for the 

overall geometry. The MAGMA
5
 software has many criteria for casting process simulation, 

part filling, but the results of two criteria are present in this paper:  

 Fill_Temp, whose results show the distribution of temperatures in the mold cavity 

from the start to the end of filling; this provides the possibility of monitoring the 

temperature distribution throughout the mold cavity at any time (Fig. 6).  

 

Fig. 6 Fill_Temp – filling: a) 25 %, b) 50 %, c) 75 %, and d) 100 % 

 Fill_Tracer, which shows which portion of the metal in the casting passed through 

ingate. The distribution of the melt in the simulation is visible because the respective 

melt fractions from each ingate are highlighted in different colors. This means that 

possible changes of the gate positions and gate cross sections as well as changes in the 

angles at which different sections of the gates are connected could be simulated and 

the resulting impact on the filling of the mold could be made easily visible, thus 

substantially facilitating an optimized gating design (Fig. 7). 



408 R. RADIŠA, N. DUĈIĆ, S. MANASIJEVIĆ, N. MARKOVIĆ, Ţ. ĆOJBAŠIĆ 

 

Fig. 7 Fill_Tracer – filling: a) 25 %, b) 50 %, c) 75 % and d) 100 % 

In order to define the solidification, i.e., the cooling process of bucket casting, necessary 

parameters and boundary conditions are entered (the time or temperature at which the 

solidification simulation stops specified). Generally, it is possible to perform simulation 

without the results of casting solidification. However, if casting simulation is performed 

before solidification simulation, then the results and temperatures reached at the end of mold 

filling are taken as the basis for solidification simulation (the Fill_Temp file) [15]. In the 

used MAGMA
5
 version presented in this paper, this Fill_Temp file exists in the system, 

which considerably simplifies the procedure. The solidification results are also shown 

through several criteria: Solid_Temp (shows temperature distribution within the selected 

material in the casting system during solidification), Hotspot (determines isolated regions of 

residual melt at any time during solidification), and Porosity (can visualize porosities in the 

casting). Using the Solidification Criteria Results after the simulation is terminated, the 

program automatically calculates several criteria that can be selected at each point. 

Displaying the criteria results helps find defects in the casting and analyze the solidification 

behavior. The solidification time is 50 min. This paper presents the results of the following 

criteria: Solid_Temp (Fig. 8), Hotspot and Porosity. 



 Casting Improvement Based on Metaheuristic Optimization and Numerical Simulation 409 

 

Fig. 8 Solid_Temp – solidification, a) 25 %, b) 50 %, c) 75 % and d) 100 % 

The results show that the solidification process develops in a directed way and that the 

last parts that solidify are pour cup and feeder. Using the Hotspot criterion, isolated 

regions of residual melt (Fig. 9a) are determined at any time during solidification. If the 

feeding calculation option in the simulation setup is checked, this criterion helps to detect 

porosities in these residual melt regions. The unit is solidification time in seconds (s, 

color scale). This can determine the time during solidification at which a particular hot 

spot develops. It can be clearly seen in Fig. 9b that    the solidification process develops 

according to expectations and that the last points of solidification are in feeders. In this 

case, the solidification time is 47 min.  

 

Fig. 9 Solidification results, a) Hotspot and b) Porosity 



410 R. RADIŠA, N. DUĈIĆ, S. MANASIJEVIĆ, N. MARKOVIĆ, Ţ. ĆOJBAŠIĆ 

Using the Porosity criterion, porosities in the casting can be visualized (Fig. 9b). The 

portion of porosities at the end of solidification simulation is displayed. The unit is 

percent (%, color scale). The unfilled and thus porous regions are displayed in white. An 

analysis of porosity problems is the most reliable when using this criterion. 

6. CONCLUSION 

This paper presents a methodology for improvement of casting process, demonstrated 

on the problem of design and optimization of the feeder’s geometry in the process of 

casting Pelton turbine bucket. Four methods of metaheuristic optimization were used: 

Genetic algorithm (GA), Ant Colony Optimization (ACO), Simulated annealing (SA) and 

Particle Swarm Optimization (PSO), which gave satisfactory and very similar results, 

mutually confirming validity of the obtained solution. Based on the obtained results 

geometry of feeder was dimensioned and CAD model of feeder was created. Performed 

numerical simulations confirm the correctness of the designed optimized feeding system 

according to all criteria. 

Acknowledgement: The paper is a part of the research done within the projects TR35037, TR35015, 

TR35016 and TR35005.  

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