optimization of the rotor tip seal with honeycomb … · 2011. 6. 20. · labyrinth seal is...
TRANSCRIPT
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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
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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