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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

wlodzimierz.wroblewski@polsl.pl

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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REFERENCES

Sprowl T.B., Childs D.W., (2004), A Study of the Effects of Inlet Preswirl on the Dynamics

Coefficients of a Straight-Bore Honeycomb Gas Damper Seal, ASME Paper GT2004-53328,

Takenaga H., Matsuda T., Yokota H., (1998), An Experimental Study on Labyrinth Seals for

Steam Turbines, Proceedings, 8th International Symposium on Flow Visualization, Sorrento, Italy

Denecke J., Farber J., Dullenkopf K., Bauer H.J., (2005), Dimesional Analysis and Scaling of

Rotating Seals, ASME Paper GT2005-68676

Vakili A.D., Meganathan A.J., Michaud M., Radhakrishnan S., (2005), An Experimental and

Numerical Study of Labyrinth Seal Flow, ASME Paper GT2005-68224

Choi D.C., Rhode D.L., (2003), Development of a 2-D CFD Approach for Computing 3-D

Honeycomb Labyrinth Leakage, ASME Paper GT2003-38238

Li J, Yan X., Li G., Feng Z., (2007), Effects of Pressure Ratio and Sealing Clearance on

Leakage Flow Characteristics in the Rotating Honeycomb Labyrinth Seal, ASME Paper GT2007-

27740

Soemarwoto B.I., Kok J.C., de Cock K.M.J., Kloosterman A.B., Kool G.A., Versluis J.F.A.

(2007) Performance Evaluation of Gas Turbine Labyrinth Seals Using Computational Fluid

Dynamics, ASME Paper GT2007-27905

Saltelli A., Ratto M., Andres T., Campolongo F., Cariboni J., Gatelli D., Saisana M.,

Tarantola S., (2008), Global Sensitivity Analysis, John Wiley & Sons Ltd, Chichester, England