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OPTIMIZATION OF THE ROTOR TIP SEAL WITH
HONEYCOMB LAND IN A GAS TURBINE
W. Wróblewski, S. Dykas, K. Bochon, S. Rulik
Institute of Power Engineering and Turbomachinery,
Silesian University of Technology,
Konarskiego 18, 44-100 Gliwice, Poland
[email protected]
ABSTRACT
The goal of the presented work is an optimization of the tip
seal with honeycomb land in
order to reduce the leakage flow in the counter-rotating LP
turbine of an open rotor aero
engine. The goal was achieved in two ways: by means of the
commercial software delivered
by ANSYS with the Goal Driven Optimization tool and with the use
of an in-house
optimization code based on the evolutionary algorithm.
A detailed study including mesh generation, computational domain
simplification,
geometry variants and a comparison of both methods is presented.
The optimization methods
give very similar optimal geometry configurations, where a
significant mass flow rate
reduction through the seal was obtained. Moreover, a sensitivity
analysis and the results
verification are presented.
NOMENCLATURE
angle
μ mean deviation
σ standard deviation
v velocity
vax axial velocity component
vt circumferential velocity component
LE leading edge
LFA left fin angle
LFP left fin position
LGD left gap dimension
LGP left gap position
LPA left platform angle
RFA right fin angle
RFP right fin position
RGD right gap dimension
RGP right gap position
RPA right platform angle
TE trailing edge
INTRODUCTION
The competition among aircraft engine manufacturers has brought
about a significant reduction
in fuel consumption and pollutant emissions. Main efforts have
been associated with an increase in
the turbine cycle efficiency, e.g. by minimizing internal
leakages. The development of a new seal
design and gaining an insight into the flow phenomena are
therefore of particular importance. The
labyrinth seal is nowadays widely used in steam and gas turbines
where the possibility of the
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transient contact may occur. The major advantages of this seal
are its simplicity, tolerance to
temperature and pressure variations, and reliability. Honeycomb
seals are widely used due to the
ability to reduce the tendency towards rotordynamic
instabilities (Sprowl et al., 2007) and their
resistance to limited rubbing between the fins and the rotating
surface.
The need for a better understanding of the flow phenomena even
in the complex geometrical
configuration of the labyrinth seal enforced detailed
investigations and the use of more
sophisticated calculation models. Simulation methods based on
Computational Fluid Dynamics
have gained significant interest in recent years. The main
concern of many research works in the
past was to adjust the labyrinth discharge coefficients (e.g.
Takenaga et al., 1998, Denecke et al.,
2005).
Previous works were limited to simplified cases, where important
geometrical features (such as
a complete description of honeycomb cells) and/or flow
conditions (such as rotation) were not
included. For example, Vakili et al. (2005) presented CFD
computations on a simplified 2D knife on
a smooth land, i.e. without honeycomb cells. Choi and Rode
(2003) used a 3D model replacing
honeycomb cells with circumferential grooves. Most recent
investigations have shown a greater
possibility of flow structure modelling. Li et al. (2007)
presented an approach to include the effects
of honeycomb cells. The axial flow through a three-knife
configuration with stepped honeycomb
land was considered. The influence of the pressure ratio and of
the sealing clearance on the leakage
flow were investigated. It was concluded that the influence of
the pressure ratio on the leakage flow
pattern was negligible, and a similar leakage flow for cases
with rotating and non-rotating walls was
obtained. The leakage flow rate increased linearly with the
increasing pressure ratio.
A complete geometrical representation of honeycomb cells was
considered by Soemarwoto et
al. (2007). After the simulations of the leakage flow through
three selected configurations, the main
features of the flow were identified. A 2D mesh with 20000 cells
and, if necessary, a 3D mesh with
over 10 million cells were used. Fine grids of this kind which
take into account the honeycomb
structure can sufficiently capture the important flow features
with high gradients around the knife-
edge and in the swirl regions.
The purpose of this paper is to find the optimal geometrical
configuration of the blade tip
honeycomb seal to reduce the leakage flows in the
counter-rotating LP turbine of a contra-rotating
open rotor aero-engine.
Figure 1: Concept of “Direct Drive Open Rotor” and scheme of
blade tip honeycomb seal
Figure 1 presents the concept of a contra-rotating open rotor
aero engine and the tip blade
honeycomb seal applied in the LP turbine. In considered aero
engine propellers are directly driven
by the LP turbine without any gearing. In this case both the
”rotor” and the “stator” blades of the LP
turbine rotate in opposite directions. In consequence, in the
considered seal area, the shroud with
fins rotates in the direction opposite to the remaining area
including the honeycomb land, with the
same rotating speed.
In order to apply the tip seal optimization process based on
CFD, a special procedure was
developed including a Computer-aided Design (CAD) model, grid
generation, a CFD calculation
and an optimization technique based on the evolutionary
algorithm, where every individual has to
be calculated. The optimization was also performed with the use
of Goal Driven Optimization
implemented in Design Exploration which is part of ANSYS
Workbench. The optimization is based
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on the response surface, which is generated from a specified
number of design points calculated
using CFD. The second method is much faster, but the optimal
solution is obtained from an
approximation, and the results have to be verified with a direct
CFD calculation. Both procedures
were used to obtain the optimal solution due to the minimization
of the leakage flow. The use of two
independent optimization methods makes it possible to verify the
obtained results and to evaluate
their usefulness for this type of problem.
The geometry and the grid topology were simplified in order to
make possible and to speed up
the whole optimization process. The impact of the simplification
on the final solution was
investigated.
CFD MODEL
Basic Geometry and Its Simplification
CFD calculations are relatively time consuming. Therefore, the
maximally possible reduction of
the calculation domain is generally needed in order to lower the
calculation costs. It is especially
important in the case of an optimization which requires many
calculations. The CFD simulations
were made with the use of the ANSYS-CFX software.
The subject of the study was the tip seal with a honeycomb land
of the low pressure turbine. It
consists of two fins. The stepped honeycomb land above the fins
was applied (Figure 1).
Modelling the honeycomb land structure is very difficult, mainly
because of the large number of
small honeycomb cells in relation to the large area of the main
flow in the blade-to-blade channel.
The honeycomb cells are separated by walls. It means that the
boundary layer should be applied to
every single cell. Due to these facts, the number of the grid
elements increases significantly,
making the optimization process very difficult. In the first
step of the simplification, the main flow
domain including the blade-to-blade channel, was replaced by the
inlet and outlet chambers, where
the parameters from the main flow simulations were assumed. It
allowed a decrease in the pitch of
the domain, which is now determined by the honeycomb
circumferential periodicity instead of the
blade cascade pitch. In the second step, necessary for the
optimization purpose, the honeycomb
structure was replaced with rectangular cells (Figure 2). The
simplification made in the second step
allowed a replacement of the 3D unstructured mesh with the
extruded 2D unstructured mesh. It
reduced the number of the mesh nodes by approx. 5 times for the
same mesh settings and reduced
thickness of the simplified domain to 1.5mm, which is
approximately equal to the dimension of one
honeycomb cell size, instead of the full honeycomb structure
pitch.
After some preliminary calculations, the inlet and outlet
chambers were lengthened in order to
avoid the influence of close boundary conditions on essential
flow regions (see Figure 3).
The simplification steps were verified by CFD calculations,
which showed that their impact on
the results was small and acceptable.
Figure 2: Original and simplified structure of honeycomb
land
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Mesh
The hexa-dominant unstructured mesh for the optimization
controlled by the in-house code was
prepared by means of the ICEM CFD. According to the geometry
simplification, the prepared 2D
surface mesh is extruded with three elements in the direction
normal to the surface. The mesh
consists of about 0.13M elements and 0.1M nodes. The boundary
layer is built with 12 grid lines
with the ratio of 1.1. Due to the very low velocity inside the
honeycomb cells, the boundary layer in
this region was omitted.
Figure 3: Mesh topology used in the optimization studies
The Workbench environment required that the mesh for
optimization process, controlled by
Design Exploration, was generated with the use of the Meshing
tool implemented in Workbench.
Because of the lower number of required CFD calculations in this
method, a finer mesh could be
used. A similar mesh type was generated, but with five extruded
layers and 15 gridlines in the
boundary layer. The mesh had about 0.45M nodes.
The mesh applied for the evolutionary optimization is presented
in Figure 3.
Boundary Conditions
The inlet total pressure, total temperature and the flow
direction were applied to both chambers,
as functions of the blade height. The radial distribution of the
circumferentially averaged static
pressure was used as a boundary condition at the outlets. Table
1 presents the average parameters in
the mean flow, which refer to the plane at the position of the
blade trailing edge in the previous row
(TE), and the plane at the position of the blade leading edge in
the next row (LE). The remaining
parameters (e.g. total pressure and total temperature at the
second inlet), necessary for the definition
of the boundary conditions of the model used during the
optimization (Figure 4), were taken from
the simulation of the mean flow including the blade-to-blade
channel. The symmetry condition was
used at the bottom walls of the chambers. In order to take into
account the circumferential
component of velocity, the periodic boundary conditions were
applied for both sides of the
calculation domain except the honeycomb cells, where the wall
was specified. This is important
especially when the inflow boundary conditions are set up
according to the results of the main flow
path computations. The rotating speed of 839rpm was applied to
the rotating wall which is part of
the rotor blade contour. The domain which is connected with the
drum contours rotates in the
direction opposite to the rotating wall at the rotating speed of
839rpm (Figure 4).
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TE (previous row) LE
(next row)
Total Pressure
(Absolute)
Total Temperature
(Absolute)
=arctan
(vt/v
ax)
Static
Pressure Mach
Static
Pressure
kPa K o kPa - kPa
58.51 699.08 -62.74 55.28 0.291 51.55
Table 1: Average values of parameters applied in CFD model
definition
Figure 4: Specified boundary conditions for the calculation
domain
A high resolution advection scheme was set up for the
continuity, energy and momentum
equations, and an upwind scheme was chosen for the turbulence
eddy frequency and the kinetic
energy equations. The gas properties were set up as air ideal
gas with the total energy heat transfer
option. The two-equation Shear Stress Transport turbulence model
was applied. The mass flow rate
through the tip seal was the objective function of the
optimization, so in the in-house code, the mass
flow rate was checked in order to control the computation
convergence. Preliminary calculations
showed that in the considered case it was a better solution than
controlling residuals. CFD
calculations were interrupted when the mass flow rate change
through the last two hundred
iterations was smaller than 0.2%. The value of the mass flow
rate change was selected after some
preliminary calculations and it ensures a satisfying convergence
of the computations and
stabilization of the mass flow rate. To make it possible, the
mass flow rate was exported to a text
file during the calculations and evaluated. In the optimization
controlled by Design Exploration, the
convergence of the computational process was controlled by the
continuity equation residual, and
the calculations finished at its maximal value of 1.0e-5.
OPTIMIZATION PROCEDURE
Parameters Description
In the presented case, the geometrical parameters of the tip
seal are the input design variables,
and the desired goal is to minimize the mass flow rate through
the tip seal. Ten geometry parameters
were selected for the optimization process. The parameters and
their range of changes are gathered
in Tab. 2. The established limits are given as relative values
in relation to the dimensions of the
initial geometry. The geometrical parameters selected for the
optimization of the tip seal are shown
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in Figure 5. All other geometrical parameters remain unchanged
during the whole optimization
process. The constraints related to the fins and the gap are
indicated as A, B, C and D in Fig 5.
No Parameter Abbrev. Limits of
changes, %
1 Left fin angle LFA -5.0 25.0
2 Right fin angle RFA -31.3 6.3
3 Left fin position LFP 0.0 22.5
4 Right fin position RFP 0.0 11.0
5 Left platform angle LPA -17.6 0.0
6 Right platform angle RPA -10.6 0.0
7 Left gap dimension LGD -17.6 17.6
8 Right gap dimension RGD -17.6 17.6
9 Left gap position LGP -12.8 3.4
10 Right gap position RGP -8.7 8.7
Table 2: Parameters review
Figure 5: Definition of constraints and geometrical parameters
to be optimized
In-house Optimization Code
For the purpose of the optimization studies using CFD
calculations, an in-house code was
developed. This code connects the external commercial tools with
the evolutionary optimization
algorithm.
The in-house code is written in the Visual Basic for
Applications language (VBA). The VBA
allows a direct access to the CAD software using macros, and a
straightforward visualization of the
results in Microsoft Excel. It also allows a proper connection
between the CAD environment and
CFD software. The calculation protocol which connects specific
commercial software to the in-
house code is presented in Figure 6.
The CAD environment allows a very precise geometry
parametrization and makes it possible to
include the relations among selected geometry parts. On the
basis of a prepared geometry an
automatic mesh generation process is activated, by means of a
prepared script. This script includes
all important features of the mesh, such as the boundary layer
properties and the size of the
elements at different locations. Afterwards, the boundary
conditions and other settings are updated
and the CFD simulation is launched. During the simulation the
objective function is monitored with
the use of an external procedure and the results are analyzed.
If a proper convergence of the
objective function occurs, the calculation process stops. After
the whole process is finished, the
objective function and the input parameters are gathered by the
evolutionary algorithm, and a new
set of input parameters is generated. In the case of an
optimization using CFD calculations, the most
time consuming aspect is the evaluation of the objective
function.
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Figure 6: Calculation protocol between the commercial software
and the in-house code
The optimization process was performed with 30 individuals per
generation. The number of the
individuals should be sufficient to obtain a proper diversity of
the population due to the number of
parameters. The initial population is generated by means of
random input variables. Other input
data for the evolutionary algorithm are presented in Figure
6.
Figure 7: Fitness function value in the course of the
optimization process
The evolutionary algorithm is well suited for parallel
calculations. This feature was also used
during the optimization process. Single individuals were spread
among different computers. Ten
computers were used during the whole process, what significantly
speeded up the computation.
Usually, about 70 generations were necessary to obtain a proper
fitness of the population. It means
that about 2100 individuals were analyzed. The fitness function
change during the optimization
procedure is presented in Figure 7. It is worth mentioning that
only individuals after crossing and
mutation have to be calculated. Others remain unchanged.
Goal Driven Optimization
Design Exploration is part of the Workbench environment which
offers parametric analyses,
Goal Driven Optimization and statistical analyses, collaborating
with other products gathered in
Workbench. Goal Driven Optimization (Figure 8) is a constrained,
multi-objective optimization
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technique in which tools such as: Design of Experiments (DOE),
response surface and common
optimization algorithms are used.
For input parameters and their ranges of change the same design
points are generated, as sets of
parameters with diverse values. The number of design points
depends on the number of input
parameters and the DOE type. Design points are calculated using
CFD tools (ANSYS-CFX) and,
on their basis, response surface are generated, with the use of
approximation methods or neural
networks.
The best proposed candidate is obtained from samples generated
by the optimization algorithm.
The available optimization algorithm, e.g. Genetic Algorithm or
Screening Method – Hammersley,
works on the basis of the previously generated response surface
so that additional CFD calculations
are not needed. The samples represent sets of parameters. It is
also possible to change the parameter
values manually to check or find a new sample. The best
candidate is generated using the response
surface so it is necessary to verify it with a direct CFD
calculation.
Figure 8: Scheme of Goal Driven Optimization
To generate design points, the Central Composite Design (CCD)
method was used with the VIF-
Optimality design type. To generate the response surface, mainly
the Standard Response Surface -
Full 2nd-Order Polynomials algorithm was used, but other
available methods were also tested. To
find the best candidate, all the described methods were used
(optimization algorithms and manual
change of parameter values).
At the beginning, all ten geometry parameters were optimized in
one step. In this case, 150
design points were calculated. The uncertainty connected with
proper approximation and the wide
spread of points for all ten parameters encouraged an attempt to
divide the task and optimize it in
three steps. In the first step, the angles and the position of
the fins were optimized. In the second
step, the fins were blocked in the optimal position and the left
gap dimension, its position, and the
left platform angle were optimized. In the third step, the right
gap and the platform were optimized
as well. For four parameters there are 25 design points which
were calculated, and for three
parameters – 15 design points. The results of the CFD
verification in the case of the three-step
optimization corresponded better with the results obtained with
the use of Goal Driven
Optimization than with those given by one-step strategy.
Moreover, a larger mass flow rate
reduction was obtained. It was also less time consuming because
of a lower number of design
points. Both approaches indicate the same tendencies of the
geometrical parameter configuration.
According to the facts described above, in the next part of this
paper the results of the step strategy
are presented.
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OPTIMIZATION PROCESS AND RESULTS During the optimization process
local optima occur due to the assumed wide range of changes
of selected geometrical parameters. From each optimization
process, i.e. – the one using the in-
house code and the one conducted with Design Exploration, one
optimal geometry was chosen,
what is presented in Figure 9 and Tab. 3. The parameter changes
presented in the table are given as
values related to the initial geometry configuration.
In both cases the parameters tend to their limits. It is
especially visible in the geometry obtained
by means of Design Exploration, where all parameters reached
their minima or maxima. It can be
concluded that better results could have been achieved if the
ranges of parameter change had been
expanded.
The differences between geometrical configurations obtained with
the use of the in-house code
and Design Exploration are relatively small and concern only the
right part of the seal area. It can
be seen that the location of the right fin tip in both cases is
the same, which should be crucial for the
flow. Only the bottom part of the fin is slightly shifted to the
left, which is connected with the
change of the angle. There is also a difference in the right gap
dimension. It is worth pointing out
that the left platform was optimized in the third step of the
optimization performed by means of
Goal Driven Optimization, and that the mass flow rate reduction
was the lowest in this step, so the
changes in geometry in this area should influence the mass flow
rate marginally, which was the
objective function. The imperfections of optimization methods
and numerical models used in the
analyses could generate differences where the influence on the
objective function is slight.
Figure 9: Initial and two optimal geometry configurations
No Parameter Abbrev.
Optimal configuration
In-house
code, %
Design
Exploration,%
1 Left fin angle LFA 24.2 25
2 Right fin angle RFA -23.1 -31.3
3 Left fin position LFP 0,3 0.0
4 Right fin position RFP 5.1 0.0
5 Left platform angle LPA 0.0 0.0
6 Right platform angle RPA -10.5 -10.6
7 Left gap dimension LGD 12.9 17.6
8 Right gap dimension RGD 7.1 17.6
9 Left gap position LGP 3.4 3.4
10 Right gap position RGP 5.3 8.7
Table 3: Optimal geometry configuration
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The optimization shows that in comparison with the initial
geometry the fins should be leaned in
the direction opposite to the gas flow, the left fin should keep
its left limit position and the right fin
– the right limit position. The inlet and the outlet gaps should
be larger and shifted to the blade; the
left platform should be raised. The reduction of the mass flow
rate through the seal after the
optimization performed by means of the evolutionary in-house
code is about 14%. For the
optimization performed by means of Goal Driven Optimization, the
sum of the mass flow rate
reduction was 16.5% (11.6% after the first step, 4.3% after the
second and 0.5% after the third).
The optimization process also indicated an alternative geometry,
where the left fin is shifted to
the right and set upright, the inlet gap width is lower, and
instead of the right platform the left
platform is raised. However, the mass flow rate reduction was
substantially lower (10%) so the
geometry is not presented.
The flow structures in the seal area are shown in the streamline
plot in Figure 10. The two-
dimensional streamlines are not a projection of
three-dimensional streamlines. They were
constructed only with the use of the radial and axial velocity
components. The flow pattern is
characterized by two large vortices in the inlet cavity, above
the main flow of the leakage, and by
one vortex before the left fin. The size of the latter vortex
and the path of the leakage flow depend
on the left fin location. In the region between the fins, a more
significant domination of the main
vortex can be observed. In consequence for the proposed new
geometries, the main stream knee
between the fins is narrower, which can influence the mass flow
rate reduction. The flow structure
in the right cavity consists of two main vortices between which
the leakage is located. The vortex
behind the right fin is stretched more in the optimized
geometries. The leakage leaves the right
cavity only through a part of the right gap. The remaining part
of the gap is taken up by the
injection from the main flow domain. Generally, the streamlines
for the nominal and the optimized
cases look very similar.
Figure 10: Surface streamlines for: a) initial geometry, b) best
from in-house code, c) best
from Design Exploration
The fins configuration and the swirl structures in the optimized
cases change the path of the
leakage jet. The contact area of the jet with the honeycomb
structure is longer. Moreover, the angle
of the attack of the jet, as it passes the fins, is more acute.
These phenomena increase energy
dissipation of the leakage jet and can be responsible for the
mass flow rate reduction.
a
b c
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Sensitivity Analysis
Beside the optimization studies, a sensitivity analysis was also
performed. For this purpose, the
Elementary Effects Method (EEM) was used. The selected method
makes it possible to find the
most important input factors among many others which may be
contained in a considered model
(Saltelli et al. (2008)).
The EEM provides two sensitivity measures for each input
factor:
• Mean deviation - μ, assessing the overall impact of an input
factor on the model output
• Standard deviation - σ, describing non-linear effects and
interactions
The sensitivity analysis was conducted for all 10 considered
geometry parameters of the tip seal.
All dimensions were referred to the established limits of
changes for selected geometry parameters.
Figure 11 presents a chart of mean and standard deviation for
different geometry parameters.
The values are referred to the averaged value of the mass flow
rate. The averaged value is
calculated on the basis of the initial vectors. The values of
mean and standard deviation lay more or
less on a straight line. It means that the parameters which have
a high overall importance are also
responsible for possible non-linear effects and interactions
among different geometry parameters.
However, mean and standard deviation should be read together.
The low values of both quantities
correspond to a non-influent geometry parameter.
The performed sensitivity analysis shows that the most
significant parameter is the right fin
angle. Also, the right and left fin position and the right gap
dimension seem to be quite important.
The less important parameters are: the left gap dimension and
position, and the left platform angle.
Some conclusions about the sensitivity of the considered
parameters can also be drawn from
Goal Driven Optimization. The largest mass flow rate reduction
obtained in the first step of the
optimization (see previous section) showed a higher importance
of the parameters connected with
fins, which corresponds to the results obtained by means of the
EEM presented in Figure 11. The
lowest importance of the parameters connected with the right
platform does not conform to the
results obtained in the sensitivity analysis. Probably, the
specified geometrical configuration
obtained after particular optimization steps causes that the
importance levels of some parameters do
not correspond to each other..
Figure 11: Mean and standard deviation for geometrical
parameters which were optimized
Results Verification
When the whole optimization procedure was completed, the results
were verified. In the first
step, the initial and the optimal geometries were calculated on
a finer mesh with 0.7M nodes. The
mass flow rate reduction was 1% lower than during the
optimization. In the second step, the inlet
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and the outlet chambers were replaced with a three-dimensional
blade-to-blade channel to include
detailed 3D structures in the calculation. The three-dimensional
structure and the simplified
structure of the honeycomb cells were considered. Tetra mesh was
used, with more than 8M nodes
in the seal area, and structured mesh with 0.25M nodes was
applied in the blade-to-blade channel.
Figure 12: Streamline plot for optimized geometry
In the case with the simplified honeycomb structure the mass
flow rate reduction differs only by
0.5%. For the three-dimensional honeycomb structure – the mass
flow rate reduction through the
seal is 6% lower than obtained during optimization, and the flow
structures differ only a little. The
streamlines presented in Figure 12 are a combination of
three-dimensional streamlines in the blade-
to-blade channel and two-dimensional streamlines in the seal
area.
CONCLUSIONS
A CFD optimization of the tip seal with a honeycomb land was
performed with the use of the
ANSYS commercial software with Goal Driven Optimization and an
in-house optimization code
based on the evolutionary algorithm. For both optimization
procedures their main features and
results were presented.
A calculation model was prepared to perform an efficient
optimization process, so the area of
interest was reduced, and the honeycomb structure was simplified
to a square shape. The obtained
solutions, i.e. the geometry configurations, the flow structures
and the mass flow rate were very
similar, and the mass flow rate reduction was 14% for the
evolutionary algorithm and 16.5% for
Goal Driven Optimization. The parameter values obtained with the
use of the in-house code
approximated their limits, while all the parameters in Goal
Driven Optimization reached their
limits, which means that with wider ranges of parameter changes
the result could have been
improved.
The sensitivity analysis shows that the parameters connected
with the fins and the right platform
have the largest impact on the mass flow rate reduction.
The performed two-step verification of the results confirms the
results obtained in the
optimization process, especially the mass flow rate reduction
for the new proposed geometry.
ACKNOWLEDGEMENTS
This work was made possible by the European Union (EU) within
the project ACP7-GA-2008-
211861 “DREAM” Validation of radical engine architecture
systems.
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