Aerodynamic Optimisation of Highly Loaded Turbine Cascade ...

Universität der Bundeswehr München Fakultät für Luft- und Raumfahrttechnik

Institut für Strahlantriebe

Aerodynamic Optimisation of Highly Loaded Turbine Cascade Blades

for Heavy Duty Gas Turbine Applications

Dipl.-Ing. Pasquale Cardamone

Vollständiger Abdruck der bei der Fakultät für Luft- und Raumfahrttechnik

der Universität der Bundeswehr München zur Erlangung des akademischen Grades eines

Doktor Ingenieurs (Dr.-Ing.)

genehmigten Dissertation

Vorsitzender: Prof. Dr. sc. math. Kurt Marti 1. Berichterstatter: Prof. Dr. rer. nat. Michael Pfitzner 2. Berichterstatter: Prof. Dr.-Ing. Francesco Martelli

Tag der Einreichung: 04.10.2005 Tag der Annahme: 25.01.2006 Tag der Promotion: 03.02.2006

I

Preface This thesis is based on the investigations carried out during my activity as research engineer at the “Institute of Jet Propulsion” of the “University of the German Armed Forces Munich”.

I am truly grateful to Prof. Dr.-Ing. Leonhard Fottner, head of the “Institute of Jet Propulsion” until June 2002, because he gave me the opportunity to carry out this work. I will never forget his professional competence, guidance and support as well as the familiar atmosphere that he established as chief professor at the Institute. He unexpectedly passed away on June 21, 2002.

Prof. Dr. rer. nat. Michael Pfitzner, head of the “Institute of Thermodynamics” of the “University of the German Armed Forces Munich” is gratefully acknowledged for taking over the supervision of the present work after the death of Prof. Fottner. The beneficial suggestions of Prof. Pfitzner are thankfully acknowledged. I would like to thank Prof. Dr.-Ing. Francesco Martelli, chief of the “Turbomachinery Energy and Environment Group” of the Department of Energetics “Sergio Stecco” of the University of Florence, who kindly agreed to be part of the board of examiners of the present thesis. His valuable advices are thankfully acknowledged. Prof. Dr. Sc. Math. Kurt Marti is kindly acknowledged for being the chairman of the examination board of this thesis. Dr.-Ing. Michael Lötzerich of ALSTOM Power, is thankfully acknowledged for the valuable discussions and his precious suggestions during the development of the present work.

I would like to thank all the colleagues of the Institute of Jet Propulsion for the many interesting discussions (not only) on turbomachinery and for the years spent together in a motivating and friendly atmosphere. In particular I would like to thank Dr.-Ing. Peter Müller for the detailed work of revision and for the precious suggestion, which contributed to the successful conclusion of this work. For their support I would like to thank all the students who worked intensively within their thesis at the development of the present work.

The present investigations were mainly performed within the German research project “CO2 armes Kraftwerk. 500 MW auf einer Welle” of the research programme “AGTURBO II”. The funding by the German Federal Ministry of Economics and Labour (BMWA) and ALSTOM Power is gratefully acknowledged. For supporting the printing of this work (see Cardamone, 2006) the University of the German Armed Forces Munich is thankfully acknowledged as well.

Last but not least I would like to thank my family: my parents, who encouraged my choice to do this experience in Germany and my wife Katrin for her encouragement and her patience also in difficult moments and for being always at my side during these beautiful years spent in Munich. I am sure that without her support, this work would not have been possible.

Munich, February 2006 Pasquale Cardamone

II

to Professor Leonhard Fottner

Contents III

Contents

Nomenclature

Abstract

1. Introduction...............................................................................1

2. Scientific background and motivation....................................7

2.1 Boundary layer development on turbo machinery blade profiles ................................ 8

2.2 The choice of the optimal turbine blade profile velocity distribution ....................... 13

2.3 Automation possibilities of the aerodynamic blade design process .......................... 21

2.4 Recent progress in the field of the automatic aerodynamic blade design methods ... 25

3. Experimental investigations...................................................36

3.1 The reference turbine cascades T150, T151 and T152 .............................................. 36

3.2 The High Speed Cascade Wind Tunnel ..................................................................... 39

3.3 Measurement section set up ....................................................................................... 41

3.4 Measurement techniques and data evaluation............................................................ 43

3.5 Measurement programme .......................................................................................... 46

3.6 Experimental results and discussion .......................................................................... 47

4. Numerical optimisation environment ...................................58

4.1 The Parametric geometry generator PROGEN.......................................................... 59

4.2 Flow computations procedure.................................................................................... 61

4.2.1. The automatic grid generation method GRIDMOD ........................................ 61

4.2.2. The Navier-Stokes flow solver TRACE........................................................... 68

4.2.3. The automatic evaluation procedure AUSWERT............................................ 71

4.3 Validation of the flow solver ..................................................................................... 77

4.4 Optimisation techniques............................................................................................. 82

4.4.1. Multi-Island-Genetic algorithm........................................................................ 83

IV Contents

4.4.2. Adaptive Simulated Annealing ........................................................................ 84

4.5 Set up of the objective function and constraints ........................................................ 86

5. Results and discussion ............................................................93

5.1 Validation of the procedure at different aerodynamic loadings................................. 95

5.1.1. Results at the spacing of turbine cascade blade T151...................................... 97

5.1.2. Results at the spacing of turbine cascade blade T150.................................... 104

5.1.3. Optimisation results at varied blade spacing.................................................. 108

5.1.4. Modification of the geometrical and mechanical constraints......................... 109

5.2 Influence of the trailing edge on the aerodynamic behaviour.................................. 111

6. Summary and conclusions ...................................................117

7. Annex......................................................................................121

8. References..............................................................................124

Nomenclature V

( ) ( )0

1 E Eu u dyδ

ρ ρ⎛ ⎞

⎡ ⎤= − ⋅⎜ ⎟⎣ ⎦⎜ ⎟⎝ ⎠

∫

( ) ( )0

1 /E E Eu u u u dyδ

ρ ρ⎛ ⎞

⎡ ⎤⎜ ⎟= ⋅ − ⋅⎡ ⎤⎣ ⎦⎣ ⎦⎜ ⎟⎝ ⎠∫

δ

1δ

2δ

Nomenclature Symbols

a [m/s] Velocity of sound

α [°] Blade metal angle

b Generic variable, generic constraint

β [°] Angle

B Constraints vector

C [-] Generic constant

Cf [-] Wall shear stress

CL [-] Aerodynamic lift coefficient

d [m] Profile thickness

Dw [m2/s2] Destruction term at the wall

[m] Boundary layer edge

[m] Boundary layer displacement thickness

[m] Boundary layer momentum thickness

e [m] Cascade opening at the throat

eM [m] Distance of the wake traversing plane from the cascade exit plane

E [-] Internal energy

ε [m2/s3] Dissipation rate

f Generic function

ft Auxiliary function for the transition model

F Objective function

g Probability density (generating function of ASA-algorithms)

γ [°] blade wedge angle

h Probability density (acceptance function of ASA-algorithms)

H12 [-] Form factor ( )1 2δ δ=

l, L [m] Chord

κ [-] Isentropic exponent

k [-]; [m2/s2] Profile curvature; Turbulent Kinetic Energy

VI Nomenclature

Ma [-] Mach Number

ν [m2/s] Kinematical viscosity

νT [m2/s] Eddy viscosity

p [Pa] Pressure

p Probability

r [m] Radius

ρ [-]; [kg/m3] Aspect ratio of the profile curvature; Density

Re [-] Reynolds number

σ [-] Aspect ratio of the profile slope

t [m] Pitch

T [K]; [-] Temperature; ASA algorithm parameter “temperature”

Tu [-] Turbulence intensity

U [m/s] Flow velocity

x Generic design variable

X Design variables vector

y+ [-] Dimensionless wall distance

w [°]; [m/s] blade tangent angle; flow velocity

ω [s-1]; [s-1] Specific dissipation rate; Vorticity

ζ [-] Total pressure loss coefficient

Subscripts, Superscripts

* Sonic state

1 Inlet

2 Exit

ax Axial

crit Critical

E Boundary layer edge

hk, H Trailing edge

i Generic quantity

Nomenclature VII

Infl Inflection

Is Isentropic

K Tank (Kammer)

met Metal angle

N Nose

r clockwise direction on the blade

Ref Reference

s, SG Stagger

t Total

th theoretic

u local tangential position in the wake measurement plane

Umg Environment (Umgebung)

v counter-clockwise direction on the blade

Abbreviations

AG TURBO German National Research Association on Turbomachines

(Arbeitsgemeinschaft Turbomaschinen)

ANN Artificial Neural Network

ASA Adaptive Simulated Annealing

AVDR Axial Velocity Density Ratio (ρ2w2sinβ2/ρ1w1sinβ1)

BMWA Federal Ministry of Economics and Labour (Bundesministerium für

Wirtschaft und Arbeit)

CFD Computational Fluid Dynamics

CTA Constant Temperature Anemometry

DLR German Aerospace Center (Deutsches Zentrum für Luft- und

Raumfahrt)

DM Turbulence model destruction term by Menter

HFA Hot Film Anemometer

HGK High Speed Cascade Wind Tunnel (Hochgeschwindigkeits-

Gitterwindkanal)

VIII Nomenclature

HP High Pressure

IEA International Energy Agency

FSTI Free Stream Turbulence Intensity

GA Genetic Algorithm

LE Leading Edge

MIGA Multi Island Genetic Algorithm

MUSCL Monotone Upstream Scheme for Conservation Laws

NAG Numerical Algorithm Group

OEM Original Equipment Manufacturer

PS Pressure Side

RAM Reliability, Availability, Maintainability

RANS Reynolds Averaged Navier Stokes

RMS Root Mean Square

SA Simulated Annealing, Spalart-Allmaras turbulence model

SA2 Two layers version of the Spalart-Allmaras turbulence model

SAL Low Reynolds version of the Spalart-Allmaras turbulence model

SKE Secondary Kinetic Energy

SQP Sequential Quadratic Programming

SS Suction Side

TBC Thermal Barrier Coating

TE Trailing Edge

TRACE Turbomachinery Research Aerodynamic Computational Environment

TVD Total Variation Diminishing

UniBwM University of the German Armed Forces Munich (Universität der

Bundeswehr München)

VKI Von Karman Institute

WINPANDA Windows Software for the automatic measurement and evaluation of

the cascade wake and profile pressure distribution (WINdows

Programm zur Automatisierung von Nachlauf- und

Druckverteilungsmessungen inkl. Auswertung)

Nomenclature IX

WINSMASH Windows Software for the measurement and evaluation of hot-wire

anemometry signals (WINdows Software zur Messung und Auswertung

von Signalen der Heißfühler-Anemometrie)

X Abstract

Aerodynamic Optimisation of Highly Loaded Turbine Cascade Blades for Heavy Duty Gas Turbine Applications

Abstract

The present work deals with the development and validation of a method for the automatic

aerodynamic optimisation of turbine cascade blades for high pressure stages of heavy duty

gas turbines. This class of profiles features aerodynamic and geometric properties which can

strongly depart from typical conditions of turbine profiles for aero engines applications. In

fact, the Reynolds number and the trailing edge thickness of these profiles can be an order of

magnitude higher than the corresponding values of aeronautical gas turbines. In order to gain

better insight into these major differences, extensive experimental investigations were

performed at the High Speed Cascade Wind Tunnel of the University of the German Armed

Forces Munich on various turbine cascade blades designed by ALSTOM. These reference

profiles feature characteristics typical for high pressure turbine blades for heavy duty gas

turbines. The experimental results furnish an exhaustive database for the validation of the

flow solver applied within the developed design method. Furthermore, a comparison of the

optimisation results and the reference turbine cascades attests the high potential of the newly

developed procedure for the aerodynamic design of highly loaded turbine cascade blades.

The developed tool is conceived for the application in an industrial framework and design

time scales compatible with industrial requirements have to be considered as well. In this

context a method consisting of a two-dimensional RANS flow simulation approach combined

with a parametric geometry generator and an optimisation algorithm is proposed. For the

simulation of the turbine cascade flow a quasi three dimensional version of the Navier-Stokes

solver TRACE from the DLR in Cologne is applied. The parametrical representation of the

turbine profiles is realised using the blade geometry generator PROGEN, which is a tool

applied successfully for industrial blade design today. Various stochastic global optimisation

techniques were tested. The Adaptive Simulated Annealing algorithm demonstrated best

properties for a detailed investigation of wide parameter ranges in reduced timeframes.

Furthermore, this optimisation algorithm showed best capabilities in handling highly non-

linear objective functions, like the scalar objective function used within the present

investigations.

The main optimisation target in this work was the reduction of the cascade total pressure

losses by imposing a fixed operating point. Additional requirements on the profile pressure

distribution were introduced as well in order to allow optimal conditions for an efficient

cooling of the blade. This is a fundamental aspect for the generation of optimal blade profiles

which are of relevance for practical applications. In fact, a major goal of the present work was

Abstract XI

the development of an aerodynamic design method which does not merely optimise the

location of the transition zone on the blade suction surface, but also ensures profile velocity

distributions satisfying major aerodynamic requirements for the optimal cooling of the blade

(e.g. smooth acceleration on the suction and pressure surface). All these requirements were

integrated in a single value objective function. The form of the various components of the

scalar function was tailored ad hoc in extensive preliminary studies. Furthermore, some major

mechanic and geometric constraints were specified in order to restrict the search to a sub set

of realistic geometries. In this way the optimisation task was reduced to a single-objective,

constrained approach.

The results of the proposed numerical design system indicate that the present method is able

to generate automatically blade geometries with reduced losses and featuring profile velocity

distributions which ensure favourable conditions for the cooling of the blade. The reliability

of the method at changed geometric and mechanical boundary conditions was demonstrated

as well. In fact this is an aspect of major importance considering that the aerodynamic design

method has to be integrated into a more complex design process where various disciplines

with contrasting aims interact and modifications to the basic mechanical and geometrical

blade constraints often occur during an iterative blade design process.

1. Introduction 1

1. Introduction

Today the earth’s global warming is an undeniable phenomenon, confirmed by studies of

several independent scientific organisations. Over the last 140 years the global average earth

surface temperature has increased by about half a degree, as illustrated below in Figure 1.1.

Figure 1.1 Combined annual land-surface, air and sea-surface temperature anomalies (°C)

1861 to 2000, relative to 1961 to 1990 (Folland et al., 2001)

At present there is stronger evidence that most of the warming observed over the last 50 years

is of anthropogenic nature (Folland et al., 2001), deriving from increased emissions of

greenhouse gases.

This evidence has launched major intergovernmental efforts over the last two decades in order

to address the problem. At the beginning of the nineties the United Nations General Assembly

initiated negotiations leading to a framework convention on climate change. The convention

was opened at the UN Conference on Environment and Development, the so called “Earth-

Summit”, held at Rio de Janeiro, Brazil, in June 1992. The parties of the convention adopted a

protocol in December 1997, during a session held in Kyoto, Japan. This protocol outlines

clear objectives to limit the concentration of greenhouse gases in the atmosphere

(United Nations, 1997). The key point of the protocol is the reduction of the anthropogenic

carbon dioxide equivalent emissions of six major greenhouse gases1 to at least 5 per cent

below the 1990 level in the commitment period between 2008 and 2012. This goal represents

a worldwide challenge, that can only be met by new policies and approaches for a common

technological innovation. 1 The six gases addressed by the Kyoto protocol are carbon dioxide (CO2), methane (CH4), nitrous oxide (N2O), hydrofluorocarbons (HFCs), perfluorocarbons PFCs and sulphur hexafluoride (SF6)

2 1. Introduction

At the moment only two large major industrialised countries like the United States and

Australia, which together account for over one third of the greenhouse gases emitted by the

industrialised world, have not yet ratified the protocol. In November 2004, however, the

ratification of the treaty by the Russian Federation opened the door for the protocol to enter

into force in February 2005, thus becoming legally binding for its actual 128 parties.

The European union as a group has to reduce its equivalent CO2 emissions by 8% in the

commitment period. Internal European agreements establish specific national rates and a

Kyoto target of 21% for Germany represents one of the most challenging worldwide.

Germany, as the only country in the EU apart from the United Kingdom, can point to

considerable success in reducing emissions. In the period from 1990 to 2000 a reduction of

19% was achieved (BMWA, 2003).

Figure 1.2 World electricity generation (IEA, 2002)

In spite of these efforts, changing global boundary conditions have to be taken into account.

During the last two decades about three quarters of the anthropogenic carbon dioxide

emissions to the atmosphere were due to fossil fuel burning (Folland et al., 2001). At present

about 64% of the worldwide energy production arises from fossil fuelled power plants

(BMWA, 2003). For the first two decades of this century the International Energy Agency

IEA estimates an increase of the world demand for electricity by more than 70% (see

Figure 1.2). According to the IEA estimations, the use of conventional energy resources like

gas, oil and coal will remain constant or even increase over the examined period. The limited

increase in the use of renewable energy sources (wind, biomass, geothermal power, solar

energy etc.) is associated with high electricity generation costs. Furthermore, at present there

are still strong locality and time restrictions on the supply technologies associated with

renewable energy sources (BMWA, 2003).

1. Introduction 3

Other factors like the estimated increase in the dependence of Europe from energy imports

and, for countries like Germany, the planned nuclear power phase out must be considered as

well. In the actual political scenario, the high fluctuations in the gas and oil prices can assume

a principal role for the electricity generation costs. The large German reserves of lignite are of

particular significance for the development of advanced coal-fired power plants.

This background points out the importance of extensive research activities for the reduction of

CO2 emissions of thermal power plant facilities. Thus major efforts are being made in the

development of the so called zero-emissions fossil fuelled power plants2. This concept can

only be achieved by the introduction of CO2 capture/storage technologies together with

increased energy conversion efficiencies. In Germany extensive research programmes have

been started and successfully carried out in the last decade in order to meet this challenge. The

present investigations were performed within a sub-research-project of the German national

cooperative project “CO2-armes Kraftwerk. 500 MW auf einer Welle” (AG Turbo Phase II).

Over time various innovative technologies can be listed, which allow major improvements in

the energy conversion efficiency. Among these the so-called hybrid-processes, consisting of a

combination of high temperature fuel cells and combined gas cycle power plants seem to be

the most promising today. Combined cycles on coal basis like pressurised fluidised-bed

combustion with partial gasification, externally fired combined cycles, pressurised pulverised

combustion and integrated gasification combined cycles are being currently tested and appear

to be a possible solution for the medium term. In a short period perspective, however,

substantial progresses can be only achieved by improving existing advanced technologies like

steam and gas combined power plants. In the nineties, in fact, extensive research efforts have

been performed in this field and great advances have been achieved already. Moreover the

components used within steam and gas combined cycle power plants present reliability,

availability and maintainability (RAM) which are in line with the market expectations for

energy production (Steel et al., 2004).

Today combined gas cycle processes show efficiencies slightly below 60%. By 2010 an

efficiency increase of the combined gas and steam turbine power plants to 62% is expected

(BMWA, 2003). This is a very challenging task which requires significant multidisciplinary

efforts both in the fluid mechanics research field and in the field of material technology.

Major improvement potential for increasing the efficiency is to be found in the gas turbine.

One of the key factors is the turbine inlet temperature. Figure 1.3 presents the development

trend of the maximum turbine inlet temperature as reported today by a leading original

equipment manufacturer (OEM) like Siemens Power Generation (Thien et al., 2004).

2 This denotation indicates power plants which release less than 0,1 kgCO2/kWh in the atmosphere by applying CO2 retention measures (BMWA, 2003)

4 1. Introduction

Figure 1.3 Development trend of the firing and material temperature over the last decades

in heavy duty gas turbines (Thien et al., 2004)

This diagram shows that firing temperatures higher than 1400°C are only possible through the

combined use of film cooling and thermal barrier coatings. Today flame temperatures above

1550°C are strived, but this challenge can be met only by developing materials with near gas

temperature capabilities. Additionally it must be mentioned that today typical life time

expectations for industrial gas turbines are higher than 100,000 hours (Madfeld, 2004). This

requirement limits the maximal admissible temperature in comparison to military or even civil

aero engine applications. Therefore a successful market placement of heavy duty gas turbines

requires advanced high temperature materials (nickel based alloys, nickel aluminides, ceramic

matrix composites) and optimised casting and machining processes (single crystal blades) for

the front turbine stages. Furthermore, protective coatings with improved temperature

capabilities and reliable life time prediction models have to be developed. All this has to be

done together with the development of more efficient cooling techniques. An idea of the

complexity of the technologies applied is shown in Figure 1.4, where a schematic

representation of the cooling system of a modern gas turbine TBC-coated vane and blade for a

heavy duty gas turbine is illustrated.

On the other hand it must be kept in mind that such an approach is associated with higher

manufacturing and operating costs. Therefore an obvious solution for decreasing the

manufacturing costs seems to be the reduction of the number of expensive parts in the high

pressure turbine. At the same time the resulting reduced wetted surface allows a saving of

compressed air flow for the cooling of the turbine components. Furthermore the necessary

high lift design approach has to deal with different challenges, like stronger shock structures,

higher secondary flow losses, higher tip clearance losses and higher profile diffusion

gradients. These undesirable effects, which are also negative with regard to the heat transfer

taking place on the profile, can be kept under control only through a better knowledge of the

1. Introduction 5

aerodynamic behaviour of the components operating at conditions typical for industrial gas

turbines. The challenge of a high lift blade/stage design methodology is confirmed by the fact

that at present important OEMs (IPG, 2004) prefer more conservative approaches for the

upgrade of modern industrial gas turbines even if higher reliability is obtained with a certain

loss of performance.

Figure 1.4 Cooling system for the first turbine row vane and blade of the

MITSUBISHI M501G gas turbine (Tsukagoshi et al., 2004)

A fundamental condition for the development of highly loaded turbine components is the

existence of appropriate design methods supported by reliable design tools which have been

extensively validated with experimental data. However, while over the last decade various

research activities have been successfully carried out with the aim of the development of

high-lift and ultra-high lift blading concepts for the application in low pressure turbines of gas

turbine engines, as described by Haselbach et al. (2001), there is still a certain information

deficit in the area of the components for modern heavy duty gas turbines. In fact, the

mechanical, geometrical and aerodynamic boundary conditions of heavy duty gas turbine

blade profiles differ considerably from those encountered in gas turbine aero engines. The

trailing edge thickness can be an order of magnitude higher than typical values encountered in

gas turbine aero engines. The operating Reynolds numbers are about ten times higher than the

Reynolds numbers of gas turbine for aeronautical applications and the resulting thinner

6 1. Introduction

boundary layers must be considered in appropriate form within the aerodynamic design

process. In order to address these major differences extensive experimental investigations

have to be carried out at typical boundary conditions of industrial gas turbines.

In this complex technological field automatic design procedures are gaining more and more

relevance, as they offer a high potential for the reduction of the design time and can

consequently contribute to a significant reduction of the design costs. A fundamental

condition that automatic design procedures have to fulfil is the possibility to react rapidly to

boundary condition changes deriving from other disciplines by adapting the design without

modifying the performance level. Various works in the literature give evidence of the huge

potential gains offered by automatic methods for the aerodynamic design of innovative, non-

standardised compressor and turbine blade profiles (Köller et al., 2000). However, an

essential requirement for the application of these procedures is a detailed validation work

supported by experimental data representative for realistic turbo machinery Mach and

Reynolds numbers. Furthermore, it must be kept in mind that in spite of the dramatic

evolution progress undergone by the computational resources over the last decades, today a

fully three dimensional aerodynamic optimisation analysis cannot be performed within

computational times reasonable for industrial applications yet.

The present work deals with the development and application of an automatic design

procedure for the aerodynamic optimisation of two-dimensional turbine blade profiles. This

method consists fundamentally of a Navier-Stokes solver (TRACE, DLR in Cologne), a

parametric geometry generator and an optimisation algorithm. The whole procedure was set

up within the commercial software package iSIGHT. This enabled a comparison between

different optimisation techniques and reduced the programming efforts for interfacing the

various components. The validation of the design method represents a fundamental point for

the successful application of the procedure itself. Thereby extensive experimental

investigations were performed on different turbine cascade blades representative for front

stage profiles of industrial gas turbines. The experiments were carried out in the High Speed

Cascade Wind Tunnel of the University of the German Armed Forces Munich. This allowed

the reproduction of similar operating conditions typical for turbo machinery and in particular

high Reynolds numbers, which were indispensable for the representation of this class of

profiles. The experimental data gave the opportunity to quantify the aerodynamic behaviour

of different blade design strategies at such operating conditions. The database was then used

both for the validation of the RANS solver TRACE and of the newly developed aerodynamic

optimisation method. A fundamental aspect distinguishing the present design procedure from

conventional two-dimensional optimisation methods is the direct control of the profile

velocity distribution. This major feature was introduced in order to ensure velocity

distributions on the optimised profiles featuring optimal characteristics for an efficient

cooling of the blade.

2. Scientific background and motivation 7

2. Scientific background and motivation

Today the components of modern gas turbines feature high aerodynamic efficiencies, so that a

further improvement represents a very challenging task for the turbo machinery aerodynamics

designer. The introduction of multidisciplinary aspects and of a three dimensional way of

thinking in the design process of the blading is fundamental for better engineered and more

clearly understood components. Moreover advanced methods are required which permit

higher levels of automation within the design process in order to reduce the development time

and costs. Over the last decades, the extraordinary development and improvement of

computing resources has been offering an ideal terrain for the design process to develop in

this direction. The use of Computational Fluid Dynamics (CFD) has been gaining even more

importance and covers a fundamental part within the aerodynamic design process today. A

fundamental aspect for the successful application of Navier-Stokes codes within the

aerodynamic blade design process is an extensive validation work based on experimental data

for operating conditions and aerodynamic loadings similar to those encountered in modern

turbo machinery blades. Moreover, the development of advanced optimisation techniques

handling large numbers of design parameters and eventually contrasting objectives could be

observed and a large amount of applications of these methods can be found in the literature.

The invention of splines in the 1960s followed by the introduction of more advanced

geometrical description systems based on spline- and Bezier-curves in the 1980s should not

be underestimated as this opened the way for the use of non conventional profile forms for

gas turbine blades.

On the other hand it must be kept in mind that in spite of the encouraging progress made in

the area of automatic aerodynamic optimisation of turbomachinery blade profiles, the

designer still plays a central role at present. Today, in fact the actual computational resources

do not permit the industrial use of three dimensional automatic methods for the aerodynamic

design of turbo machinery blades. This is due to the still high computational costs required by

three dimensional Navier-Stokes flow calculations, which restrict strongly the search space

for the optimisation and reduce the maximum number of design parameters.

The aim of the present chapter is firstly to give a theoretical background about the boundary

layer development in turbo machinery blades. In fact the knowledge of the boundary layer

development is a fundamental aspect for the design of turbine blade profiles with reduced

losses. Furthermore reliable numerical tools predicting with a reasonable accuracy the

transition phenomena and the turbulent boundary layer are the backbone for an accurate

assessment of the results obtained within the optimisation cycle. The question of the optimal

profile velocity distribution on high pressure turbine blade profiles for heavy duty gas turbine

applications and the question of the optimal turbine blade spacing will be discussed as well. In

fact, the former aspect is strictly associated to both the boundary layer development and to an

8 2. Scientific background and motivation

efficient blade cooling. The choice of the blade spacing is of major importance for the

improvement of the aerodynamic design of gas turbines components, featuring a reduced

number of parts. The blade spacing influences the profile Mach number distribution as well.

After the discussion of these fundamental physical aspects, a survey of recent progresses in

the area of automatic optimisation methods for aerodynamic blading design is illustrated. The

application of these procedures within the industrial design process is discussed as well.

Finally, a short overview about conventional aerodynamic design systems is given for a better

identification of the potentials offered by automatic methods for increasing the efficiency of

the design process.

2.1 Boundary layer development on turbo machinery blade profiles

Over the last few years the large amount of experiments performed on full- and large scale

compressor and turbine test facilities supported by cascade tests together with the

development of new high frequency measurement techniques and the introduction of

innovative calculation methods have produced extensive data for a better understanding of the

boundary layer behaviour in gas turbine engines. The state of the boundary layer influences in

a major way the loss development as well as the heat transfer to the gas turbine components.

Therefore, the detailed knowledge of the transition mechanisms and the distribution of

laminar and turbulent flow regimes over the blade profile is of fundamental importance for

the designer and the improvement of the aerodynamic design can only be achieved using

numerical solvers which ensure an accurate prediction of the profile boundary layer

behaviour.

The concept of a viscous boundary layer was first introduced by Prandtl (1904). When a real

fluid flows past a solid wall, the influence of the viscosity is confined to a relatively thin layer

in the immediate neighbourhood of the wall, called the boundary layer. At the wall the flow

velocity is zero in all directions (no slip condition) and it is the frictional, or viscous forces

acting within the boundary layer which reduce the fluid velocity from its free-stream value to

zero. The boundary layer flow can either be laminar or turbulent. In a laminar boundary layer,

fluid layers parallel to the blade surface slide over each other. The local fluctuations are

sufficiently damped so that they have negligible influence on the smoothness of the overall

flow. The initial portion of the boundary layer on turbine cascade blades is always laminar.

When increasing the Reynolds number the momentum exchange between the flow layers

increases and the laminar flow breaks down into a turbulent flow. Turbulent motion consists

of rapid random fluctuations which are superimposed on the mean motion. The zone over

which this change takes place is called transition region. The turbulent fluctuations cause high

momentum flow to be transported from the outer part of the flow field towards the wall. This

causes turbulent boundary layers to feature higher velocity gradients near the wall than

laminar boundary layers. The increased fluid exchange near the wall is associated with higher


wall shear stresses, higher friction losses and higher heat transfer coefficients (three to five

times higher) for a turbulent boundary layer in comparison to a laminar boundary layer. On

the other hand, the properties of a turbulent boundary layer lead to an increased stability and

to a higher diffusion capability, so that in a region of adverse pressure gradients turbulent

boundary layers have a lower tendency to separate than laminar boundary layers.

Figure 2.1 Reynolds effects on the boundary layer development on turbine cascade blades

(Hourmouziadis, 1989)

Figure 2.1 presents the qualitative distribution of the profile losses for the suction side of

typical turbine blades versus the Reynolds number as given by Hourmouziadis (1989). The

lower curve in the diagram (curve no. 2) represents the shear layer losses. At high Reynolds

numbers (configuration “a” in the figure) a turbulent boundary layer forms on the suction side

near the leading edge and turbulent separation at the trailing edge may occur, producing

further mixing losses (curve no. 3). Reducing the Reynolds number the transition region

moves further downstream on the profile suction side and the turbulent separation near the

trailing edge disappears (see configuration “b”). A further reduction of the Reynolds number

generates a short laminar separation bubble on the suction side (see configuration “c”). In this

case the losses are generated in the wall shear layer and the wake of the profile trailing edge.

Proceeding further to the left of the diagram, the transition region moves so far downstream

that no turbulent reattachment of the boundary layer is possible and the major part of the

losses is generated by mixing effects in the wake (curve no. 1).

The transition behaviour is affected by various parameters. The most important parameters are

Reynolds number, pressure gradient on the blade surface, free stream turbulence level, surface

curvature, surface roughness, temperature gradient between wall and fluid flow and the

history of these parameters as well. In real turbo machinery the transition position and


character is influenced by further parameters like steady and unsteady inhomogeneity of the

inlet flow, film cooling, acoustic disturbances and wall surface vibrations.

Mayle (1991), in an excellent review publication about transition in components of turbo

machines, distinguishes between three principal modes of transition: natural, bypass and

separated-flow transition. The development of the boundary layer and the transition process in

through-flow components of gas turbine engines, however, are stochastic, three dimensional

and unsteady phenomena so that they can hardly be described using a steady, two dimensional

approximation of this kind. On the other hand, only time-averaged loss and heat load

distributions are of relevance for the designer in the light of the actual computational

resources. The laminar-turbulent transition can take place in a reverse direction too, as usually

found on the pressure side of turbine blades, where the main flow accelerates under very high

velocity gradients. Furthermore, in gas turbine engines the transition may occur through

different transition modes at different locations at the same time on the same surface under

the influence of periodic unsteady wakes generated by an upstream blade row. This kind of

transition is indicated in the literature as periodic-unsteady transition (Mayle, 1991).

The natural transition process occurs in three main stages. In an initial phase the laminar

boundary layer is susceptible to small disturbances, a critical value of the momentum

thickness Reynolds number is reached and as consequence two dimensional Tollmien-

Schlichting waves develop (Schlichting et al., 1997). These instabilities grow and develop

into three dimensional highly fluctuating structures. Finally these structures develop into

turbulent spots which convect downstream into the transition region and merge together to

form the turbulent boundary layer. This mode of transition is of high relevance for external

aerodynamic applications, where low free stream turbulence levels are found.

For transition at free stream turbulence levels higher than 5-10 percent, like those encountered

in gas turbine engines, the first and second stage of the natural transition are completely

bypassed. This mode of transition, consisting exclusively of the production, growth and

convection of the turbulent spots is known in the literature as bypass transition.

Emmons (1951) developed a theory, introducing the concept of intermittency. This concept is

associated with the alternating appearance of turbulent spots within the transition region.

According to this idea, the transition zone is composed exclusively of fully turbulent spots

and laminar flow regions. In the transition zone the boundary layer presents therefore an

intermittent character, depending on the occurrence of laminar or turbulent regions of the

flow.

In adverse pressure gradients, if the laminar boundary layer separates, transition may take

place in a shear layer over the separation bubble. Since a turbulent shear layer has much

higher diffusion capability than a laminar one, the flow reattaches usually shortly after

transition. This mode of transition is known as separated-flow transition. For turbine blade

profiles of gas turbine engines a laminar separation bubble may occur near the leading edge


on the suction or pressure side or at the location on the suction side where the pressure

minimum is found. The separated flow transition is a very effective method to force the

development of a turbulent boundary layer. This method has been widely used for the design

of compressor blades and of low pressure turbine profiles (Hourmouziadis, 1989). Thereby

the idea consists in delaying the transition further downstream on the suction side through

continuous acceleration up to the pressure minimum, where transition takes place over a short

separation bubble. The challenge for this design task is the ability to predict the extension of

the bubble within the design phase, thus ensuring that a turbulent boundary layer reattaches in

the rear part of the suction side. If this does not happen, then the losses increase dramatically

(see Figure 2.1) and the prescribed flow deflection within the passage is not realised.

Figure 2.2 Topology of the different modes of transition in a Reynolds number,

acceleration plane (adapted from Mayle, 1991)

The different character of the fundamental modes of transition is shown in Figure 2.2. This

diagram presents the zones in which each mode of transition is expected to occur. Thereby an

acceleration parameter-momentum thickness Reynolds number plane is used. The

acceleration parameter accounts for the effects of free-stream acceleration and thus of the

profile velocity distribution on the boundary layer. This parameter is defined as

(ν/U2)/(dU/dx), while the momentum thickness Reynolds number is defined as (Uδ2/ν), where

U is the free-stream flow velocity, x is the surface coordinate in streamwise direction, ν the

kinematic viscosity and δ2 the boundary layer momentum thickness. The acceleration

parameter and the momentum thickness represented in the diagram are intended as the values

at the beginning of the transition zone. The curves at constant turbulence level represent the

momentum thickness Reynolds numbers for which transition takes place at the corresponding

value of the acceleration parameter for the present turbulence level. Natural transition can be

found only at low turbulence levels for negative acceleration parameters, which are associated


with adverse pressure gradients. The line indicated as “Stability criterion” represents in fact

the boundary above which Tollmien-Schlichting waves are possible. For reduced acceleration

parameters, as long as the turbulence level is not high enough, a separated-flow transition can

be encountered as well. The diagram shows that as long as the turbulence level is low,

increased acceleration parameters are associated with higher momentum thickness Reynolds

numbers at the beginning of transition. At higher turbulence levels, typically encountered in

turbomachinery components, the acceleration parameter has low influence on the momentum

thickness Reynolds number and thus the dependence of transition on the velocity distribution

on the profile is reduced.

Two further modes of transition are known from the literature. The first one indicated as

periodic-unsteady transition and also known as wake-induced transition

(Mayle et al., 1989), is caused by the periodic impingement of the wakes of upstream

aerofoils on the blade surface. As different modes of transition coexist at the same time on the

same surface this process is also called multimode transition. Over the last decade extensive

experimental investigations have been performed on compressor and turbine blade profiles in

appropriate test facilities (Tiedemann, 1998) and cascade wind tunnels (Schulte, 1995 and

Stadtmüller, 2001) for a better understanding of this complex phenomenon. A detailed

overview about blade row interference features and their effect on transition is given by

Hodson (1998). As in the present work steady aerodynamic investigations on turbine cascade

blades are carried out, this kind of transition will not be further considered.

A further mode of transition is represented by the transition process from turbulent to laminar

boundary layer, the so-called reverse transition or relaminarisation. It occurs in

turbomachinery components as well and is of particular importance for the gas turbine

designer, since it usually takes place on the pressure side of most profiles near the trailing

edge and may occur on the suction side near the leading edge in presence of strong

acceleration gradients. Mayle (1991) explains this process as the stretching of the streamwise

vortex lines associated with the turbulence in the boundary layer under the effect of a large

acceleration, so that the vorticity is dissipated through viscous effects. The relaminarisation

process is expected to occur at moderate turbulence levels if the acceleration parameter

exceeds a value of 3·106. This indirectly means that forward transition cannot take place as

long as the acceleration parameter does not fall below this value. The blade profiles class

examined within this work features reverse transition on the rear part of the pressure surface.

Some profiles feature reverse transition on the front part of the suction surface as well.

At the end of this section a short description of the possible boundary layer development on

high pressure turbine blades will be presented as described in the literature (Mayle, 1991).

Figure 2.3 presents the essential features of the profile boundary layer for this application on

the suction and on the pressure side. On the suction side it is usually expected that

downstream of an initial laminar part the boundary layer becomes turbulent (right side). The


length of the transition zone depends on whether the onset of transition is upstream or

downstream of the minimum pressure location. In the first case the transition zone will be

more extended. If a laminar separation bubble occurs in the front part of the suction side (left

side), then, in presence of extremely favourable pressure gradients, the boundary layer may

become laminar-like again and only marginally downstream a forward transition takes place.

Different authors show that reverse transition may occur on the suction surface (Hodson, 1984

and Warren et al., 1972). For film cooled blades the transition is expected at the injection

location. Downstream, however, a reverse transition process cannot be excluded. This

circumstance could strongly influence the heat transfer distribution on film cooled turbine

blades. On the profile pressure side two probable scenarios are illustrated as well. If a

separation bubble occurs the reattached turbulent boundary layer may become laminar like

again (right side). If no separation bubble is featured, a forward transition zone followed by a

reverse one, in the rear part of the profile, is expected (left side).

Figure 2.3 Boundary layer development on high pressure turbine blades (Mayle, 1991)

2.2 The choice of the optimal turbine blade profile velocity distribution

The form of the profile velocity distribution is essential for a satisfactory development of the

profile boundary layer and thus for the cascade loss and deflection as well as for the heat

transfer development on the blade. Moreover, various requirements on the profile pressure

distribution have to be taken into account in order to ensure optimal aerodynamic conditions

for the efficient action of the film cooling air on the blade profile. The form of the profile

velocity distribution is strictly dependent on the blade spacing. This parameter plays a


fundamental role within the design process since it influences directly the blade loading level

and the characteristics of the cooling as well.

Since the task of turbine cascades is to accelerate the flow from the inlet to the outlet, one

would imagine that an optimal turbine profile velocity distribution shows an ideal shape

without any deceleration region as presented in Figure 2.4. This distribution realises the

maximal enthalpy conversion. However, this distribution can not be realised not only because

it would lead, through the excessive length of the constant velocity region on the suction side,

to an unsatisfactory development of the boundary layer but also because it would require

blade shapes which do not satisfy major mechanical constraints.

Figure 2.4 Ideal velocity distribution for accelerating cascades (Hoheisel et al., 1987)

Figure 2.5 Mach number distribution for a subsonic turbine blade and boundary layer

development (Casey, 1994)


The essential features of the Mach number distribution on a turbine blade operating at

subsonic conditions are shown in Figure 2.5. The shape shown in this picture is a typical “aft-

loaded” profile velocity distribution. This means that the aerodynamic loading of the profile,

quantifiable through the area between the Mach number curves on the suction and the

pressure surface, is concentrated in the rear part of the blade. The flow on the suction surface

accelerates rapidly over the first third of the surface. This is followed by a more gradual

acceleration to the maximum velocity near to the passage throat and a subsequent deceleration

to the exit Mach number. A fully developed turbulent boundary layer is expected to form

slightly downstream of the blade passage throat. The deceleration and the amount of flow

turning in the rear part of the suction surface, which can be convex for subsonic applications,

can be limited by means of conventional diffusion criteria. The adverse velocity gradients in

the rear part of the suction surface contribute to the production of thicker boundary layers at

the trailing edge. When using transonic profiles the profile curvature beyond the throat should

be carefully controlled. On the pressure surface, instead, the flow accelerates almost

continuously from the leading to the trailing edge. The favourable pressure gradients lead to

the development of thin boundary layers which can eventually relaminarise. The small

diffusion region near the leading edge on the pressure surface, as a consequence of the change

of the blade curvature, is often found on turbine aerofoils and occurs on either the pressure or

suction surface or both.

In an excellent work about the influence of free stream turbulence and profile pressure

distribution on the boundary layer and loss development of turbine cascades,

Hoheisel et al., (1987) present a comparison between the front- and aft-loaded design

strategies, for low pressure turbine applications. The profile velocity distributions and blade

shapes of the three turbine profiles used within this study T104, T105 and T106 are shown in

Figure 2.6. The three profiles are designed for the same operating conditions (β1=127.7°,

Ma2th=0.59 and Re2th=500 000) and present the same aerodynamic loading. While T105 and

T106 feature an aft-loaded profile velocity distribution, the velocity maximum on the suction

side of T104 is shifted towards the leading edge as for a front loaded profile. The deceleration

taking place over the suction side of T104 is limited. T106 presents a lower peak velocity than

T105. This produces more limited pressure gradients in the rear part of the suction surface.

The pressure side distributions of T105 and T106 are almost identical. T104 features a

different velocity distribution on the pressure side. Since the boundary layer on the pressure

side is expected to be laminar for an extended region, the authors present the results of

detailed boundary layer investigations on the suction side. In this way a relation between

profile velocity distribution and boundary layer development as well as loss behaviour is

found.


Figure 2.6 Design velocity distributions and cascade geometries for the low pressure

turbine cascades T104, T105 and T106 (Hoheisel et al., 1987)

Figure 2.7 Effect of the deceleration factor wmax/w2th and Reynolds number Re2 on the

aerodynamic behaviour of the low pressure turbine cascades T104, T105 and

T106 (adapted from Hoheisel et al., 1987)


Figure 2.7 presents some of the results from these investigations. On the left hand side the

predicted influence of the suction side deceleration factor (defined as the ratio between the

suction side peak velocity wmax and exit isentropic velocity w2th) on the momentum thickness

at the suction side trailing edge is presented. The central diagram shows the effect of the

deceleration factor wmax/w2th on the cascade total pressure losses. In the right hand diagram the

effect of the Reynolds number Re2th on the boundary layer momentum thickness at the suction

side trailing edge is displayed. Both theory and experiments indicate that at the design

conditions and for free stream turbulence levels Tu1 higher than 0.8 %, an aft-loaded profile

velocity distribution with limited deceleration in the rear part of the suction side such as T106

leads to a lower momentum thickness at the suction side trailing edge and produces lower

losses. Furthermore, it must be mentioned that the front-loaded velocity profile featured by

T104 is associated with a boundary layer thickness lower than for the cascade T105. This lets

conclude that a front loaded design strategy like T104 cannot be excluded a priori within the

design process under a merely aerodynamic point of view. However, it must be pointed out

that both in the literature and in the practical design process there is a certain lack of

knowledge about the effectiveness of film cooling in presence of such velocity distributions.

This is the reason of the strong concerns of the designer to use front-loaded velocity

distributions for rotor blades and only extensive measurements in presence of film cooling

performed at realistic turbomachinery conditions can give a better insight (Lötzerich, 2004a).

A major advantage of a front loaded configuration is the possibility to reduce the maximal

suction side Mach number (see profile T104 in figure 2.6), which is of particular significance

for turbine vane applications, where higher blade spacing but lower deflection are featured

than for rotor blade applications. These considerations were integrated into the optimisation

process by providing the single value objective function with a supplementary term

accounting for the location of the maximal suction side Mach number with respect to the

passage throat. A comparison of the two formulations of the objective function is presented in

chapter 5.

All these considerations illustrate the key role of the profile velocity distribution for the

development of turbine blades with minimal losses. Hourmouziadis (1989) discusses the

optimal profile velocity distribution and specifies detailed rules for the aerodynamic design of

optimal turbine blades for low pressure turbine applications:

- Minimise boundary layer thickness at the trailing edge

- Minimise trailing edge thickness

- Avoid separation upstream of the trailing edge

- Select the highest pitch possible avoiding separation upstream of the trailing edge

- Select high acceleration on the pressure side upstream of the trailing edge

- Delay transition on the suction surface as far downstream as possible


- Use suction side acceleration to control transition

- Force suction side transition early enough to ensure reattachment

- Limit trailing edge diffusion to keep the flow attached

These rules apply for the design of high pressure turbine blades as well. However, some

additional aspects have to be considered. The reduction of the trailing edge thickness is not

imperative for these kinds of application for different reasons. First of all the necessary space

for the allocation of the cooling channels within the blades must be ensured. Moreover, an

excessive reduction of the trailing edge thickness leads to bigger exit passage areas and

consequently to reduced exit velocities. In this way the gradients between suction side peak

Mach number and exit Mach number become higher. This leads to increased back diffusion

and could make the cooling of the rear part of the blade more difficult. Moreover the losses

across a possible suction side profile shock increase, thus reducing the benefits of thinner

trailing edges. The use of aft-loaded profiles in high pressure turbine blades has benefits as

well, since the delay of transition on the suction side is associated with an increased extension

of the laminar boundary layer. However, this aspect should be realised ensuring adequate

acceleration gradients for an efficient action of the shower head cooling in the front part of the

profile suction side as well. Therefore, the acceleration to the peak suction side Mach number

should feature gradients high enough to ensure the cooling film to be uniformly distributed

over the surface. “Fuller” profile velocity distributions in this area are more beneficial for this

scope than distributions accelerating to the peak Mach number under low gradients.

Figure 2.8 Cooling effectiveness distribution from cascade tests (Yoshida et al., 1982)

Any kind of diffusion on the profile velocity distribution should be avoided, because it affects

the film cooling effectiveness negatively. A typical distribution of the film cooling


effectiveness on a turbine cascade blade is shown in Figure 2.8. The curves correspond to

different coolant mass flows. The distributions feature a rapid decrease of the cooling

effectiveness in the rear part of the suction side, independent on the coolant mass flow. The

diagram shows that as long as the flow accelerates, an increase of the cooling effectiveness is

achieved. Even though the best behaviour is observed at higher coolant mass flows, it must be

considered that the air mass flow used for cooling is limited by different factors. First of all it

does not experience the increase of enthalpy occurring in the combustion process and

therefore contributes only slightly to the enthalpy conversion in the turbine. Furthermore

aerodynamic losses due to mixing processes of cooling air and mainstream flow have to be

considered.

While for low pressure turbines in gas turbine aero engines excellent publications exist

(Hoheisel et al., 1987), dealing with the question of optimal profile velocity distributions and

where detailed rules are specified for the optimal design of these components

(Hourmouziadis, 1989), there is still a lack of information for high pressure turbine profiles in

heavy duty gas turbines. In fact, for these applications some geometrical and mechanical

properties of the profiles like leading and trailing edge thickness, due to cooling requirements,

assume values which cannot be classified as optimal from an aerodynamic point of view.

Furthermore, the boundary layer development at Reynolds numbers which are an order of

magnitude higher than in low pressure components of gas turbine aero engines have to be

investigated in more detail. Additional requirements associated with the need for an efficient

heat transfer rate and film cooling action on the blade surface also have to be taken into

account in the design process.

The choice of the blade spacing is another fundamental point within the design process of

turbine blades. Pioneer publications by Zweifel (1945) and some years later by

Ainley et al. (1951) specify rules for the choice of an optimal blade spacing, realising minimal

losses. In this context two main contrasting phenomena have to be considered. On the one

hand, a low blade spacing is associated with increasing profile losses due to high values of the

blade wetted surface. On the other hand, high blade spacing is associated with higher

aerodynamic loading which could lead to flow separation. Zweifel (1945) introduced an

aerodynamic loading coefficient, which is indicated in the literature with his name. The idea

behind this coefficient is to quantify the maximal opposite pressure gradient realisable within

the cascade. The Zweifel-loading-coefficient is defined as the ratio between the peripheral

force actually obtainable from the momentum theory, if the deflection diagram is given, and

the force obtainable from an ideal pressure distribution, featuring the value of the cascade

inlet total pressure on the pressure surface and the outlet static pressure on the suction surface.

Such a profile pressure distribution would be represented by a rectangle and it would feature

no deceleration region. The evaluation of various measurements on turbine cascades

(Scholz, 1977) indicates that for minimal drag-to-lift ratios this coefficient assumes a constant


value between 0.9 and 1.0 for accelerating profiles featuring high deflections. This empirical

loading limit has been widely used for the choice of the optimal spacing for turbine blades in

recent times as well. Ainley et al. (1951) presents a method for the determination of the

optimal blade spacing. The procedure is based on the interpolation of experimental data

obtained from tests performed on turbine blade profiles of “conventional” shape (e.g. RAF27

and C7 profile shapes) with circular and parabolic camber line, featuring thickness to chord

ratios between 10 and 25 percent. Figure 2.9 shows the profile-loss distribution versus the

blade spacing for different cascade deflections at a Reynolds number of 200 000 and a Mach

number lower than 0.5. The left hand diagram shows the family of curves obtained for

conventional nozzle blades, while on the right hand side a family of curves obtained from

conventional impulse blades are displayed. In order to obtain the profile losses for different

blade shapes the authors propose an interpolation formula using the results of nozzle and

impulse blades.

Figure 2.9 Profile-loss coefficients for conventional turbine blades (Ainley et al., 1951)

Obviously these experimental data cannot be used for the design of innovative turbine blade

profiles, since they are based on dated turbine profiles, featuring moderate aerodynamic

loading. Moreover, it must be considered that today a major trend in the gas turbine industry

is the design of high-lift blading. In fact, increasing the blade spacing and the deflection

reduces the number of parts and is thus associated with reduced manufacturing and

maintenance costs. This has particular benefits for high pressure turbine stages, where a

reduction of the number of blades means a reduction of the components for cooling and

therefore saves expensive compressed cooling air. Furthermore, the increase of the stage

loading is associated with higher temperature drops and the cooling of the following stages

can potentially be avoided. However, a remarkable increase of the stage loading can only be

achieved by introducing new design concepts (Haller et al., 2002) in order to address the

various challenges deriving from increased stage loading. An increase of the stage loading can

produce supersonic flow regions and therefore strong shock losses and increased trailing edge


losses. Therefore particular attention should be given to the curvature in the rear part of the

suction surface. Higher pressure gradients and higher deflections lead to the development of

more important secondary flow losses. This aspect is of particular importance for high

pressure turbine profiles, where low aspect ratio blades are found. Higher pressure ratios

across the stage increase tip leakage flows as well. When increasing the stage loading one has

to consider these challenges to ensure a high level of efficiency within the gas turbine.

Finally, it must be kept in mind that even if the existence of modern flow simulation tools can

reduce the experimental efforts and make the families of curves introduced by Ainley and

Mathieson or the Zweifel loading criteria superfluous, extensive experimental investigations

at typical heavy duty gas turbine operating conditions are needed in order to validate the

prediction tools applied.

2.3 Automation possibilities of the aerodynamic blade design process

In this section a short overview of the conventional aerodynamic design process of turbo

machinery blades is presented in order to facilitate a better understanding of possible

application area for automatic blade design methods. Even though in the last years three

dimensional analysis methods have been gaining more and more importance, the backbone of

turbo machinery aerodynamic design systems remains still the quasi-three dimensional

approach introduced by Wu (1952). This general scheme assumes that the three dimensional

flow field can be approximated using two families of intersecting stream surfaces, as shown

in Figure 2.10.

Figure 2.10 Representation of the S1-S2 stream surfaces in the scheme by Wu (1952)

The stream surfaces indicated as S1 in the figure are the so-called blade-to-blade surfaces.

The S2-surfaces are the through-flow surfaces. The present technique is based on independent


flow calculations on each of the surface families. However, additional linkage terms between

the two surfaces, such as blade forces, are considered as well. The scheme introduced by

Wu (1952) ensures a quasi three dimensional description of the flow field within the blade

rows. The scheme in its original form is based on the assumption that the flow develops axis-

symmetrically within the machine. Over the last 50 years various modifications to the original

scheme have been developed and implemented in through-flow codes in order to account for

the mixing of flow properties occurring within a real machine.

The schematic representation given in Figure 2.11 contains the main elements used within the

aerodynamic design process as given by Jennions (1994). Links to other disciplines are

presented in the flux diagram as well. At the beginning of the design process basic

relationships, one-dimensional stream line methods, existing experience charts (Smith,

Swindell) and the designer experience are used to obtain a one-dimensional description of the

machine. The aerodynamic requirements prescribed in this introductory phase are passed to

the next design step, where a meridional (S2) through-flow code is used to compute a radial

distribution of the main aerodynamic properties within each row. The resulting model will

represent the desired flow conditions throughout the turbine. Developing this model the

designer must decide which aerodynamic conditions he wants to achieve in each blade row.

Thus at this point it can be decided if new aerodynamic concepts will be considered. For

example if previous rig tests have shown that a particular axial distance between aerofoils

reduces the blade row interaction, this has to be considered at this stage of the design process.

Figure 2.11 Elements of the turbo machinery aerodynamic design process (Jennions, 1994)

As indicated in figure 2.11 the through-flow code can be supplemented by information about

spanwise mixing effects occurring in the machine in order to consider secondary flow

phenomena in the basic physical model (Jennions, 1994). The design step following the


through-flow analysis is an iterative one, also known in the literature as direct design

problem. In this case the blade geometry is iteratively prescribed and a flow simulation tool

predicts the resulting aerodynamic data until the specified aerodynamic conditions are

fulfilled. The objective of this step is therefore to find −for each streamline− a blade shape,

which fulfils the aerodynamic boundary conditions of the S2 calculation. As a further

requirement the specified flow turning must be fulfilled while the goal of low aerodynamic

losses is pursued. The blade-to-blade (S1) code predicts loading, exit angle and losses for a

given blade geometry. This part of the design process can be quite time-consuming. Therefore

the application of automated reliable design procedure is particularly interesting for this task,

because of its potential to significantly reduce time and cost of the design. Additionally, it

must be mentioned that, since blade blockages and flow asymmetries will affect the position

of the stream lines and the target design values, the through-flow model has to be modified

iteratively. The two-dimensional blade shapes obtained using this quasi-three dimensional

process (with or without spanwise model extensions) are then stacked to a three dimensional

blade form. At this point of the process a full three dimensional CFD analysis is usually

performed. The resulting information is passed eventually to the through-flow model in order

to update loss and turning throughout the blade rows. However, it must be pointed out that

three dimensional calculations even using today’s available computational resources are very

time-consuming. Therefore a large part of the design task is still concerned with a two-

dimensional approach.

More automation within the design process is thus fundamental to reduce the development

costs by allowing the engineer to react rapidly to changes in functional requirements of the

gas turbine components. In this context, the present work aims to the development of a design

procedure for the aerodynamic optimisation of two-dimensional turbine cascade blades.

Aerodynamic design optimisation is distinguished in the literature into inverse and direct

design. In the following a comparison of the main features of inverse and direct optimisation

strategies is given, in order to underline the reasons which led to the exclusion of a pure

inverse method for the present task.

While the direct design considers the blade shape optimisation striving for low losses, the

inverse design approach consists of prescribing the profile velocity distribution and searching

for a blade shape which satisfies this condition. The main benefit of inverse design methods is

the low computational cost required. Usually few iterations are needed to obtain convergence

(Büche et al., 2003). The computational cost of direct design optimisation instead is a

multiple of a single flow calculation and could be very time consuming. On the other hand,

for inverse design methods, an iteration process for the prescribed profile velocity distribution

is needed in order to obtain an acceptable blade shape. Demeulenaere (1997) shows the

benefits of the application of inverse design strategies for the improvement of existing blade

designs. The shape of a given profile pressure distribution is locally improved using different


compressor and turbine cascade blades. The author points out that when prescribing the

pressure distribution only on a limited part of the suction and/or the pressure surface the new

design usually meets the specified mechanical constraints. Furthermore, a degree of freedom

in the target has to be introduced, in order to control the trailing edge thickness and the

prescribed outlet flow angle. Shahpar (2000) points out that the question on how to integrate

the mechanical and geometrical constraints in an inverse design approach is still open. The

success of this methodology is therefore strongly associated with the designer experience and

does not represent an optimal solution for automating processes which have to be applied for

innovative design tasks.

On the other hand, direct design methods aim to optimise the blade shape with respect to the

objectives (e.g. aerodynamic losses) specified by the design task. Mechanical and geometrical

constraints can be considered in various ways within the process. An originally constrained

minimisation problem can be modified into an unconstrained one by transforming the

constraints into penalty terms. This procedure is somewhat diffused in the literature

(Demeulenaere et al., 2004) and used within the present work for the treatment of some

specific requirements on the profile velocity distribution. Furthermore, dedicated

mathematical publications (Dennis et al., 1996) point out that the attempt to solve constrained

problems is always reduced either to solve a related unconstrained problem or to finding a

non-linear system of equations whose solution is the same as that of the constrained problem.

The main disadvantage of direct design methods is that the computational cost is represented

by the number of simulations needed by the optimisation algorithm until an optimal blade

shape is found. Time-consuming simulations with a high degree of modelling detail should

therefore be avoided.

The method developed within this work presents the same structure as common aerodynamic

optimisation methods for turbomachinery components consisting of three main components:

flow solver, parametric geometry generator and optimisation algorithm. A detailed description

of the specific components used within the present work is given in Chapter 4. At this point,

however, it must be pointed out that while the reliability of the flow solver and the flexibility

of the parametric geometry generator for reproducing a wide range of blade geometries can be

well assessed in a preliminary phase, the success of the optimisation algorithm depends

strongly not only on the specific problem but also on the interaction between the various

components and the form of the objective function. Furthermore, eventual misleading

information deriving from problems like network interruptions (with consequent erroneous

evaluation of the actual blade geometry) or erroneous interpretation of the actual results

caused by the evaluation procedure itself3 have to be taken into account for the choice of the

optimisation technique. Therefore stable algorithms are needed which perform well in 3 Shahpar (2000) points out how optimisation techniques are particularly suited to detect “weak points” of the design procedure producing geometries which are handled in erroneous way by the evaluation tools. This implies an extensive preliminary work, in order to debug “online” the design method.


presence of highly non-linear objective functions and are less sensitive to occasional

misleading information occurring during the optimisation loop. Optimisation algorithms for a

direct design can be divided into two main classes: gradient-based methods and stochastic

algorithms. Gradient-based methods rely on derivative information of all objectives and all

constraints for determining the search direction of the optimisation. Stochastic optimisation

algorithms comprise techniques like genetic algorithms, evolution strategies and simulated

annealing methods. This second class of algorithms is characterised by excellent properties in

coupling with “noisy” objective functions, thus ensuring a high degree of stability in the

design process. However, the computational effort associated with stochastic algorithms is

usually higher than gradient-based methods. On the other hand, results from the literature

show that for a number of variables higher than 14 some gradient-based methods become as

expensive as genetic algorithms (Shahpar, 2000). In contrast to the gradient-based methods,

stochastic techniques avoid focusing on local regions of the search space, evaluating designs

throughout the parameter space in search of global optima. These major considerations led to

the application of stochastic techniques for the present investigations.

2.4 Recent progress in the field of the automatic aerodynamic blade design methods

Over the last decade the scientific community has been striving for the development and

usage of optimisation techniques within the aerodynamic design process of turbo machinery

components. Turbo machinery design is in fact a mature field where the efficiencies featured

by the single components are already quite high and improvements are hard to achieve. In

addition there is a need for the designer to rely on dependable automatic design tools. These

have to ensure a reliable reaction in ever decreasing time scales to changes in the design

objectives and constraints. An extensive validation work of the simulation tools applied

within the process is essential as well, to ensure that consistent results are achieved. Recently

a large number of scientific publications highlight the potential of automatic optimisation

methods within the turbo machinery blade design. Köller et al. (2000) apply an automatic

design process for the development of a new family of subsonic compressor aerofoils for

heavy-duty gas turbine applications. In this publication the inviscid/viscous Q3D flow solver

MISES (Giles, 1985 and Drela, 1986) is coupled together with a parametric geometry

generator and an optimisation approach based on the combination of a random search

algorithm and a gradient-based method. The authors point out that apart from the reliability of

the flow solver and the quality of the search algorithm, the formulation of the objective

function is a key aspect for a successful optimisation. They combine the physical targets and

the geometrical/mechanical constraints in a single function using weighting coefficients for

each objective. This procedure is the already discussed method for reducing an initial

constrained direct problem to an unconstrained one. The choice of the weighting coefficients

requires extensive preliminary investigations to ensure that the specified targets are


appropriately fulfilled. In their investigation Köller et al. (2000) use an ad hoc formulated

objective function which contains the following elements: cascade total pressure losses at

design conditions, extension of the cascade operating range and stall margin, loss level over

the whole operating range and different geometrical constraints not directly specified in the

publication. The new family of aerofoils features reduced total pressure losses and a

significant extension of the operating range. The resulting profile Mach number distribution is

more front-loaded (Figure 2.12). The authors demonstrate that for the high Reynolds numbers

and turbulence levels characteristic of heavy-duty operating conditions, conventional CDA

aerofoils no longer represent an optimal solution. They associate the movement of the profile

loading towards the leading edge with the high Reynolds number of 2.5·106 and the high inlet

turbulence intensity of 3.5%. These operating conditions force the transition near the leading

edge, as it is expected in heavy duty gas turbine compressors. As a turbulent boundary layer

forms on the suction side very close to the leading edge, the optimisation method tends to

move the diffusion zone near the leading edge as well, where a thinner turbulent boundary

layer is found. The results of the optimisation method are confirmed experimentally

(Küsters et al., 2000).

Figure 2.12 Mach number distribution and total pressure losses for starting (CDA) and

optimised compressor blade profile (Köller et al., 2000)

The high potential offered by a combination of a three dimensional transitional flow

simulation and a gradient-based method are demonstrated by Nagel et al. (2003). Here an

experimental verification of the obtained results is given as well. The approach provides the

basis for a fully three dimensional design control over the whole wetted surface of a blade

passage. Starting from a low loss, low pressure turbine vane with linear diverging side-walls

an innovative geometry is obtained featuring non-axis symmetric end walls and reduced

integral total pressure losses. The main target of these investigations was the reduction of the

integral total pressure losses and secondary flows by fixed cascade deflection. Using a set of

40 design parameters the system converges after about 550 RANS computations, which


correspond to a real time of about four days on six 200 MHz processors of an ORIGIN 2000.

The resulting geometry, which is shown on the left hand side of Figure 2.13, underlines the

high potential offered by optimisation methods for exploring non conventional design spaces.

The advantages of the method in terms of total pressure losses is shown on the right side of

figure 2.13 where the spanwise total pressure loss distributions of the starting geometry

(dotted line) and the optimised geometry (continuous line) are compared. A good agreement

with the experimental data (circular symbols) is achieved as well. The total pressure losses

resulting from the optimised geometry are reduced with respect to the starting geometry and

the loss core is shifted towards the endwall. Even though the results obtained with this

optimisation method are very promising, the authors point out that the computational cost of

the three dimensional flow simulation is quite high. To save CPU time a relatively coarse

mesh has to be used within the optimisation process. Therefore further criteria to reduce the

mesh effects on the solution and the reliability of the numerical results have to be considered.

At least the final and initial geometries have to be computed using more refined grids and the

possible changes in flow patterns and efficiency gains have to be considered as well. The high

computational cost of three dimensional direct optimisation hinders the usage of stochastic

optimisation algorithms, thus restricting the search space, and makes an implementation of the

method difficult within an industrial aerodynamic design process. In this work the authors do

not consider constraints on the form of the profile velocity distribution. The resulting profile

Mach number distributions at different blade heights are shown in Figure 2.14. First of all an

excellent agreement between experimental and numerical results can be observed. However,

the profile pressure distributions feature significant intermediate diffusion zones on the

suction surface over the entire blade height. This aspect conflicts with the requirements on

film cooled blade profile Mach number distributions discussed in the previous section. The

investigations presented by Nagel et al. (2003) address two key aspects, which are still open

topics in the area of aerodynamic blade design optimisation. Firstly a three dimensional flow

simulation approach, due to limited computational resources, is hard to couple with global

optimisation searches and is associated with very high computational costs. Secondly,

requirements to the profile velocity distribution for a future cooling of the optimised blade are

not directly considered within the process. This aspect in particular is not yet addressed by

most of the aerodynamic automated blade design systems presented in the literature.

Shahpar (2000) addresses the problem of the large computational effort associated with three

dimensional flow simulations combined with heuristic approaches by introducing a linear

sensitivity matrix. This matrix results from the evaluation of the flow response for a number

of geometrical perturbations. The method gives the possibility to produce a very fast

alternative flow solution without the need to solve the full set of RANS equations. However,

this approach is based on the key assumption of the linearity of the flow response to large

changes of the parameters in the design space. The parameters used by the author at seven


different blade heights are the angle of rotation of the profile about the trailing edge (skew),

the circumferential and the axial movement of the profile.

Figure 2.13 Geometry of the optimised turbine cascade (left) and span wise loss

distribution for optimised and start geometry (right). (Nagel et al., 2003)

Figure 2.14 Comparison of experimental and numerical profile pressure distribution at four

blade heights (Nagel et al., 2003)

It must be pointed out that the set of 56 parameters used for this study corresponds to

established engineering modifications and the profile shape remains unaltered. The validity of


the linearity assumption for modifications of the profile form has to be proved. In this case

indeed curvature changes could produce flow phenomena like shocks, whose impact on the

flow solution is not expected to correlate in a linear way with the relative geometry

perturbations. The author demonstrates the validity of the linear assumption on the specified

parameter space in a previous publication (Shahpar et al., 1999). The optimisation target is the

minimisation of the secondary flow kinetic energy at the exit plane of a nozzle guide vane

maintaining the mass flow capacity between specified ranges. The results obtained with a

deterministic technique like the Sequential Quadratic Programming (SQP) algorithm are

compared with the results obtained from the application of two different heuristic approaches:

Genetic Algorithm (GA) and Simulated Annealing (SA). The most promising results are

obtained using the Simulated Annealing technique. Another important aspect resulting from

this comparison is that, when increasing the number of parameters to fourteen, the

computational cost required by the SQP-technique is comparable with that required using a

heuristic approach. Different optimisation results obtained using the SA-method are compared

with the results on the datum blade in Figure 2.15. The secondary kinetic energy SKE is used

here as a parameter which quantifies the passage vortex strength. Reduced SKE values

indicate a more uniform radial distribution of the exit flow angle and less overturning in the

region near the wall. The optimised geometries result from calculations performed using only

the section circumferential movement parameters (SA-1), the section circumferential and

axial movement parameters (SA-2) and the skew angles only (SA-3). All the configurations

obtained within the optimisation process, except the geometry SA-3, feature mass flow

capacity within the specified limits. The author points out that the obtained blade shapes do

not permit additional experimental validation, since discontinuities along the blade span occur

using only seven blade sections. No information about the Mach number distribution on the

blade is given.

Another methodology for the reduction of the computational efforts of a direct optimisation

process is given by the use of artificial neural networks (ANN) in combination with heuristic

optimisation algorithms (Pierret et al., 2000 and Demeulenaere et al., 2004). In this approach,

a database of individuals (blade geometries), whose flow solution has already been computed,

is interpolated using an ANN-method, in order to build an approximate model of the original

analysis problem. Thus the aerodynamic behaviour of new geometries is obtained by

evaluating the interpolating surface instead of performing a complete Navier-Stokes

calculation. At each step an intermediate optimum is found and a Navier-Stokes calculation of

this geometry has to be performed in order to actualise the network. The success of these

methods depends mainly on the knowledge of the neural network, which is fed by previous

designs of similar blades. Therefore a large preliminary database of solutions has to exist in

order to ensure a better accuracy in the approximation of the design problem. The results

obtained by Perriet et al. (2000) indicate great potential of this approach in order to speed up


the design process. The results of the aerodynamic optimisation of a high pressure turbine

rotor blade are shown in Figure 2.16.

Figure 2.15 Blade geometries and secondary flow kinetic contours for baseline and SA

optimisation results (Shahpar, 2000)

Three sections equally distributed along the span (0%, 50% and 100% blade height) are

represented parametrically and an overall set of 97 parameters is used. The design goal is the

reduction of the cascade enthalpy loss coefficient maintaining a fixed pressure ratio, targeting

a given cascade deflection and considering further basic requirements on the profile pressure

distribution. Mechanical constraints as well as requirements on the profile Mach number

distribution are considered. The objective function is defined as a single value function

containing, in an appropriate form, the weighted contributions of the various objectives and

constraints. The terms related to the Mach number distribution which are considered are the

maximum Mach number on the suction side, the Mach number slope in the leading edge

region and the Mach number deceleration in the rear part of the suction side. The optimisation

procedure starts with a database containing 100 samples of similar rotor blades. The authors

point out that the time required for a design step is about 2.5 times higher than the time

needed for a three dimensional Navier-Stokes computation. A design step consists of the

network “learning process”4, the run time for the optimisation procedure (in this case a GA-

algorithm) and the Navier-Stokes computation performed on the temporary optimum

4 “Learning process” of the neural network is the process which is required to determine the free parameters of the network in order to fit the given database of samples.


geometry for the actualisation of the network. While the time required for the RANS-

computation is associated with the mesh size, the time required by the neural network and by

the GA-algorithm is proportional to the number of training samples and independent on the

mesh size.

Figure 2.16 Results of the aerodynamic optimisation of a high pressure turbine rotor blade

using a combined ANN / GA approach (Pierret et al., 2000)

Convergence is obtained after 9 design steps which correspond to a real time of about 24

hours. This represents a major improvement potential in design time of three dimensional

blades. However, for new design tasks preliminary computational efforts should be taken into

account as well, because an initial database has to be built and an additional preliminary

computational time of about 100 hours has to be taken into account. The upper left diagram of

figure 2.16 shows the distribution of the aerodynamic efficiency along the span, represented

as the difference between unity and the enthalpy loss coefficient. In the hub region, where the

original blade geometry features low efficiencies, major improvements are present. Along the

whole span an efficiency improvement of about 1% is obtained. In the upper right part of the

figure the outlet angle distribution along the span is shown. The target outlet angle is

indicated by the vertical dashed-dotted line. Even though the optimised geometry (continuous


line) realises a major improvement compared to the original geometry, there are still large

discrepancies (up to 3 degrees) between target and actual distribution. The isentropic profile

Mach number distribution of the initial database sample is shown at the bottom left of

figure 2.16, while the distributions on the optimised blade profile are shown at the bottom

right. An overall improvement of the distributions can be noticed. The diffusion region on the

pressure side near the leading edge at 50% and 95% blade height disappears and the large

deceleration region on the suction side of the initial geometry at 5% blade height is

suppressed as well. However, it must be pointed out that the initial distributions are quite poor

and not difficult to optimise. Further improvements in order to obtain more continuous

acceleration regions over the entire profile might be possible here.

The potential of the combination of ANN and heuristic optimisation techniques for the

reduction of the design time is also illustrated in a publication by Demeulenaere et al. (2004).

This work presents the results of a multipoint optimisation applied to a turbine rotor blade and

to a transonic compressor rotor blade. The multi-objective problem is reduced to a single-

objective task by introducing ad hoc tailored weighting coefficients for the different

objectives and constraints. Even if the ANN / GA combined method ensures a very low

computational requirement, it must be observed that the efficiency improvements presented

are quite moderate and the profile pressure distribution featured by the optimised geometries

can still be improved further. The authors point out that the choice of alternative approaches

such as multi-objective optimisation techniques would require a too large computational

effort. In fact during the search process these techniques generate families of solutions which

are usually indicated as pareto-front in the literature. The main advantage of multi-objective

techniques is the absence of any weighting function. Benini et al. (2002) show the large

potential of evolutionary multi-objective approaches for the development of a new class of

high-performance aerofoils for axial flow compressors. In this case, however, even using a

very fast quasi-three dimensional flow solver like MISES and limiting the number of

objectives to two, a large computational time has to be considered. The authors in fact state

that the final pareto front, compared with the original NACA65 cascades in the paper, is

obtained after 200 generations. For each generation 50 to 100 individuals are necessary.

Considering that the single-value approach developed within the present work requires, in

conjunction with an adaptive simulated annealing technique, 700 to 1000 evaluations for

convergence, the computational effort of a multi-objective approach becomes evident.

In an earlier publication, Goel et al. (1996) present a combined through-flow/blade to blade

quasi three-dimensional method for the aerodynamic design of turbine blades. This work

addresses in particular the question of a convenient profile Mach number distribution on

turbine blades. In this work the aerofoil quality is evaluated considering solely flow diffusion

and uniformity of flow changes of the predicted profile Mach number distribution. No profile

losses are considered, since the calculations are performed with an Euler flow solver. The


flow diffusion is computed analytically from the flow solution on the blade. The ratio

between peak Mach number on the suction side and exit Mach number is used as a criterion to

prevent flow separation in the unguided turning region. Moreover, the ratio between the

suction peak leading edge Mach number on the pressure side and the minimal Mach number

on the pressure side is considered in order to avoid the formation of a separation bubble in

this region. The uniformity of the velocity changes is measured by fitting polynomials to the

Mach number distribution on suction and pressure sides and evaluating the “error” between

actual Mach number distribution and fitted data. The authors point out that this approach is

different from an inverse design method, because the target created by fitting the data changes

with the actual Mach number distribution. Mechanical and geometrical constraints as well as

the aerodynamic constraints specified on the profile Mach number distribution form the

objective function. In order to explore a wide design space, a search strategy given by the

combination of a genetic algorithm and a hill-climbing deterministic technique is used. The

procedure is validated on two different turbine cases: the last stage of a high pressure steam

turbine is re-designed and the well known VKI LS59 rotor blade is used as further test case

for validation. For the steam turbine case the hub, mid-span and tip section of the blade are

independently optimised. In a further step the quasi three-dimensional optimised sections are

stacked and optimised in order to obtain a smooth radial geometry. The smoothness is then

measured by fitting splines to the geometry in the radial direction and measuring the

smoothness of the splines. In this second phase information regarding aerodynamic

parameters on the control sections is used as well in order to restrict the search in a region

including the sections which were just obtained. The upper part of Figure 2.17 presents a

comparison between initial and optimised blade geometry and profile Mach number

distribution at the three blade sections considered.

In all cases a more suitable profile velocity distribution is obtained with more uniform flow

acceleration and reduced diffusion. However, it must be pointed out that in absence of any

information about the boundary layer behaviour, more front-loaded solutions like the solution

obtained at mid-span are preferred even though, as discussed previously, this could negatively

influence the boundary layer development on the profile and the cascade total pressure

behaviour. Furthermore, the results obtained at the tip section indicate that the methodology

used does not recognise or classify an increased back diffusion in the rear part of the suction

side in appropriate form. In this case it can be supposed that the diffusion phenomenon taking

place in the leading edge region of the pressure side is rated as predominant by the present

polynomial fit approach. The results obtained at mid-span for the re-design of the VKI LS59

rotor blade are shown in the lower part of Figure 2.17. In this figure the profile Mach number

distribution of initial and optimised geometries are compared. In this case the method

recognises the predominant effect of the strong pressure gradients in the rear part of the

suction side and reacts consequently by reducing the ratio between peak Mach number on the

suction side and exit Mach number from 1.45 to 1.17.


Figure 2.17 Initial and optimised section geometries and Mach number distributions at tip,

mid-span and hub section (Goel et al., 1996)


The overview regarding automatic optimisation processes for the aerodynamic design of turbo

machinery blades presented in this section indicates that over the last decade large progress

was made in this area. Nevertheless different aspects have been pointed out which need

further improvement in order to be able to integrate these automatic procedures into an

industrial design environment. The computational costs associated with a fully three

dimensional aerodynamic blade optimisation are still too high for the industrial development

time-scales. Today, the aerodynamicist should be able to react rapidly to changes of the

design concept and constraints, as the design of turbomachinery blades is a challenging task

which takes into account different disciplines eventually with contrasting objectives. Fast and

reliable automatic methods are needed, which in addition to an increase of the aerodynamic

efficiency, should yield to good designs which can take into account various constraints and

basic requirements deriving from other disciplines.

In this challenging context an automatic design method for the aerodynamic optimisation of

two-dimensional cascade blades has been developed and is illustrated within the present

work. A method for the suitable evaluation of the profile Mach number distribution has been

developed and tested. Optimal profile velocity distributions for high pressure turbine blades

have been strived for. Cascade loss and deflection have been calculated using the state of the

art Navier-Stokes solver TRACE of the DLR in Cologne (Eulitz, 2000). In order to

investigate large design spaces an Adaptive Simulated Annealing optimisation algorithm has

been used. Extensive validation works have been performed on the basis of large

experimental data on high pressure turbine blades for heavy duty gas turbines obtained on the

High Speed Cascade Wind Tunnel of the University of the German Armed Forces in Munich

(Sturm and Fottner, 1985).

36 3. Experimental investigations

3. Experimental investigations

A fundamental condition for the successful application of automatic optimisation procedures

within the aerodynamic design process of turbomachinery blading is the assessment of the

reliability and application limits of the applied flow simulation tools. In this context extensive

experimental investigations were performed in the High Speed Cascade Wind Tunnel (HGK)

at the University of the German Armed Forces in Munich (UniBwM) on three different high

pressure turbine cascade blades designed by ALSTOM. These reference profiles feature

geometries and operating conditions typical for high pressure rotor blades of modern heavy

duty gas turbines. The High Speed Cascade Wind Tunnel ensures the reproduction of Mach-

and Reynolds numbers typical of heavy duty turbomachinery. The obtained data are used to

build an experimental database for the validation process of the developed aerodynamic

design method.

After a brief introduction of the reference geometries and the background leading to the

design of these cascades, the experimental setup will be presented. The main features of the

High Speed Cascade Wind Tunnel will be outlined as well as the applied measurement

techniques. The results obtained with the reference turbine cascade blades will be discussed in

order to identify detriments and benefits of the different design strategies.

3.1 The reference turbine cascades T150, T151 and T152

The datum profile, named T150, represents the mid-span section of a typical turbine rotor

blade for high pressure stages of large scale stationary gas turbines. The aerodynamic loading

of this profile is moderate. Starting from this reference profile, two further design approaches

were investigated. The resulting turbine cascade blades were indicated as T151 and T152.

Two different design strategies were strived for. While for the design of T151 the objective

was the reduction of the number of parts with a consequent increase of the blade spacing, for

T152 instead an optimisation of the profile Mach number distribution was pursued to enable

favourable conditions for the blade cooling. The reduction of the number of blades within the

stage is associated with reduced wetted surface, friction losses and reduced cooling air mass

flow per stage. Therefore the design strategy for T151 strived for the aerodynamic optimum.

On the other hand it must be kept in mind that increasing the aerodynamic loading produces

an increase of the cooling air mass flow per blade pitch since the increase of the adverse

pressure gradients influences the efficient action of the profile film cooling. This increases the

mixing flow losses. Furthermore, a reduced number of blades is associated with higher blade

sections for mechanical reasons. Thus, the internal cooling channels of the blade have to be

modified as well, with a consequent increase of the number of blade cooling channels

(Lötzerich, 2004b). As a consequence manufacturing costs increase. Furthermore, an

excessive increase of the blade aerodynamic loading is associated with higher pressure

3. Experimental investigations 37

gradients over the blade passage, which would lead to an undesirable increase of secondary

flow structures and leakage losses. These negative aspects deriving from an excessive

increase of the aerodynamic loading were considered for the design of T152, reducing the

blade loading to the level featured by the datum profile. Favourable conditions for the optimal

profile cooling were strived for as well. The gradients in the back diffusion region of the

suction side were reduced, the velocity magnitude on the whole pressure side was increased

and a continuous acceleration over the entire blade surface was realised. The design operating

conditions for the three cascades are quite similar. The design exit Reynolds number exceeds

two million and the design exit Mach number is slightly below 0.80. For the experimental

investigations the nominal reference exit Reynolds number and nominal reference exit Mach

number were fixed at Re2th=1 200 000 and Ma2th=0.75 respectively. The definition of the

theoretical exit Mach and Reynolds number is given by Ladwig (1989).

The geometries of the three cascades are presented in Figure 3.1. Here the profiles are scaled

to the same axial chord. The geometric and aerodynamic data for the reference cascades

T150, T151 and T152 at nominal operating conditions (Re2th=1 200 000 and Ma2th=0.75) are

presented in Table 3.1.

Figure 3.1 Geometries of the reference turbine cascade blades T150, T151 and T152


A parameter is introduced in order to quantify the aerodynamic loading of the profiles. This

coefficient CL, later referred to as compressible aerodynamic blade loading coefficient, is

defined as:

( )( )( ) ( )

2 2 2 2 2 1 1

1 2 1 2

sin cos sin 90

0.5 / 1Lax t

w w wtC

l p p h h

⎛ ⎞⋅ ⋅ ⋅ ⋅ − ⋅ −= ⎜ ⎟⎜ ⎟− ⋅ ⋅ +⎝ ⎠

ρ β β β (3.1)

The subscripts 1 and 2 indicate the inlet and outlet measurement plane respectively, the

symbol w represents the flow velocity, while β corresponds to the flow angle. The ratio h1/h2

corresponds to the axial velocity density ratio. The inlet total pressure is indicated as pt1 and

the exit static pressure as p2. The exit flow density is ρ2, while t and lax indicate respectively

the cascade pitch and axial chord.

Table 3.1 Geometric and aerodynamic data for T150, T151 and T152 at nominal

operating conditions (Re2th=1 200 000 and Ma2th=0.75)

Chord length (l)

Pitch to Chord ratio (t/l)

Trailing edge to Pitch ratio

(rTE/t)

Axial Chord length (lax)

Cascade opening to Pitch ratio

(e/t)

Cascade T150

150 mm 0.7320 0.028 138.98 mm 0.499

Cascade T151

120 mm 0.9572 0.014 94.58 mm 0.407

Cascade T152

140 mm 0.7266 0.016 123.68 mm 0.478

Inlet Flow Angle

(β1) Deflection (∆β)

Lift Coefficient (CL)

Inlet Mach Number (Ma1)

Cascade T150

133.9° 100.6° 0.876 0.42

Cascade T151

135.9° 110.9° 1.084 0.34

Cascade T152

131.5° 101.0° 0.893 0.40

The turbine cascades were manufactured using different chord lengths. Thus a trade-off

between large scale dimensions facilitating high Reynolds numbers and a high number of

blades for periodicity requirements within the test section was realised. For each cascade test

five blades were used.

Turbine cascade T151 features the highest aerodynamic loading among the reference cascades

and the largest blade spacing. The aerodynamic lift coefficient of T151 is about 24% higher

than for T150 and the pitch to chord ratio about 30% higher than for the datum profile T150.

Furthermore, cascade T151 realises about 10° more deflection than the other two cascades,


thus featuring a somewhat lower inlet Mach number in order to respect the specified mass

flow. The investigated cascades are characterised by high trailing edge to pitch ratios typical

for high pressure turbine blades in heavy duty gas turbines. The datum profile, however,

features a higher trailing edge thickness ratio than T151 or T152. This corresponds to a

trailing edge cooling design approach, while for the cascades T151 and T152 a pressure side

bleed approach was followed (Lötzerich, 2004b).

3.2 The High Speed Cascade Wind Tunnel

The aerodynamic investigation of turbine cascade models at Reynolds number levels typical

of heavy duty gas turbines requires appropriate experimental facilities. The High Speed

Cascade Wind Tunnel at the University of the German Armed Forces in Munich with its test

section dimensions and its power supply unit offers optimal conditions for this task.

Figure 3.2 shows a sectional drawing of the whole test facility. The High Speed Cascade

Wind Tunnel is a continuously operating closed loop test facility with an open loop test

section. The Wind Tunnel itself is contained in a cylindrical pressure tank, while its driving

unit is situated outside. The air flow supply is delivered by a six stage axial compressor. The

main feature of this experimental facility is the possibility to vary Mach and Reynolds number

independently from each other. The desired Mach number is obtained by adjusting the

number of revolutions per minute of the axial compressor. The Mach number range in the test

section can be varied between 0.2 and 1.05. By partly evacuating the pressure tank the

Reynolds number can be varied in the range 0.2·106m-1<Re/l<1.6·107m-1, where l is the

cascade chord length. A detailed description of the original configuration of the test facility in

Brunswick can be found in Scholz et al. (1959) while the modifications and extensions

featured by the test facility in Munich are described by Sturm et al. (1985). The following

provides a brief description of the main components of the test facility as shown in Figure 3.2.

The driving unit consists of an a.c. electric motor of about 1.3 MW power, a hydraulic

coupling and a gear box which is connected to the axial compressor. The axial compressor

working range and specifications are illustrated in the figure. Since each cascade works like a

throttle and corresponds therefore to a different working point in the compressor working

map, a variable bypass is used to prevent stalling phenomena. For reducing the air

temperature after compression, a system of lamella coolers for main flow and bypass air are

positioned downstream of the compressor. In order to increase the cooling efficiency a

diffusor precedes the main flow cooler. Although the cooler straightens the flow, a settling

chamber is located downstream to mix out the temperature and pressure non-uniformities.

The flow is then accelerated in a nozzle to the Mach- and Reynolds-number specified for the

test section.


The desired level of turbulence is achieved by locating a turbulence generator grid of proper

form at the inlet of the nozzle (Acton, 1994). Turbulence levels between 0.4% and 7.5% can

be achieved.

Figure 3.2 The High Speed Cascade Wind Tunnel (HGK) of the University of the German

Armed Forces Munich


3.3 Measurement section set up

A sectional view of the wind tunnel measurement section is given in Figure 3.3. The

measuring positions and the fundamental instrumentation for one of the investigated turbine

cascades are shown in Figure 3.4. The test section height assumes values between 250 and

500 mm. This height corresponds to the distance between the horizontal test section side

walls. The test section height has to be adjusted in accordance with the desired inlet flow

conditions. The distance between the vertical test section side walls is fixed to 300 mm for

steady measurements. In order to achieve best homogeneity of the inlet flow variable guide

vanes are mounted on the upper and lower test section side walls. These vanes reproduce the

form of the blade camber line and are placed a half pitch above or below the blades at the

extremities of the cascade. During preliminary tests their position is adjusted until the

measured inlet static pressure (p1) features a uniform distribution over the test section height.

The inlet static pressure is measured using an array of pressure tappings aligned 140 mm

upstream of the cascade inlet plane, as displayed in Figure 3.4. The value p1 is an average of

the three tappings in the middle of this array. The inlet total pressure pt1 is measured using a

pitot probe 300 mm upstream of the cascade inlet plane on the same sidewall, where the inlet

pressure tappings are located. The distance of the pitot probe from the test section side wall is

50 mm. Additional measurements of the inlet flow conditions performed with a bent-head five

hole probe (cobra probe) for the three cascades indicate only slight differences (affecting the

third decimal place of the inlet Mach number) in the static and total pressure distribution

along the blade span at reference conditions. The results of these investigations are outlined in

detail in the reports of the reference cascades (Cardamone, 2002, 2003, 2004). The total inlet

temperature Tt1 is measured as an average of four PT 100 resistance thermometers, which are

located in the settling chamber. Assuming an adiabatic flow acceleration inside the nozzle and

the cascade this temperature is equal to the total temperature in the cascade measurement

plane. The pressure inside the tank pK is measured at a location within the tank where the flow

is undisturbed and the velocity is minimal. The only absolute pressure measurement concerns

the environment pressure pUmg outside of the tank. All the other absolute pressures are derived

from differential pressure measurements with respect to pUmg.

The described tests were performed positioning the same turbulence grid generator of the

Type IXgK in front of the nozzle. This turbulence grid is shown in Figure 3.5. Earlier

investigations by Kiock et al. (1982) indicate that inlet turbulence intensity values around 4%

are expected using a turbulence generator of this type, depending on Reynolds-, Mach number

and on the acceleration within the nozzle.


Figure 3.3 Sectional view of the turbine cascade built up

Figure 3.4 Turbine cascade as mounted in the test section and instrumentation equipment


Figure 3.5 Turbulence grid generator IXgK

3.4 Measurement techniques and data evaluation

In order to determine the profile pressure distribution the central blade in the test section

(blade number 3 in Figure 3.3) was instrumented with pressure tappings of 0.6 mm diameter

on the suction and the pressure side. The number of tappings and their distribution over the

profile was designed to catch the main gradients of the designed profile Mach number

distributions. The distribution on T152 is given in Figure 3.6. T150 was provided with 76,

T151 with 65 and T152 with 67 profile pressure tappings. The local pressure px, was

measured as a differential value with respect to the pressure within the tank pK using

Scanivalve equipment. The local pressure value is used to calculate the local isentropic profile

Mach number:

1

1,

21

1

k

kt

is xx

pMa

k p

−⎡ ⎤⎛ ⎞⎢ ⎥= ⋅ −⎜ ⎟⎢ ⎥− ⎝ ⎠⎢ ⎥⎣ ⎦

(3.2)

The profile distribution of this parameter was used to derive conclusions about the loading

distribution on the blade.

Wake traverses in a plane located at a distance of 40% chord length from the cascade outlet

plane (Figure 3.3) were performed using a five-hole-probe of 2.5 mm head diameter.


Figure 3.6 Distribution of the profile pressure tappings on the turbine cascade blade T152

in a bi-tangent coordinate system

At each traversing position the five pressure values measured by the probe are converted

using the calibration polynomials (Hoenen et al., 2001) to determine the local exit pressure

p2,u, the local exit flow angle β2,u and the local total pressure pt2,u. This last value is used to

calculate the local cascade total pressure loss coefficient:

1 2,

1

t t uu

t K

p pζ

p p

−=

− (3.3)

The integral cascade performance parameters are then obtained using the conversion

procedure by Amecke (1967), which consists mainly of applying the conservation laws for

mass, momentum and energy in order to obtain an integral constant value from a wake

distribution of the single flow quantities. The data acquisition was carried out using a pressure

scanner of the type 98RK (Esterline Pressure Systems, 2000). The control of the measuring

devices and evaluation was performed using the in-house software programme WINPANDA

(Ganzert et al., 1996).

A particularly interesting method for the flow visualisation over the blade surface is

represented by the oil flow pictures. Secondary flow structures can be investigated using this

technique without excessive effort (Weiß, 1993). Furthermore, this method can give useful

information about the boundary layer development on the blade surface, visualising the

position and extension of the transition zone (Engber, 1996). The surface of the measuring


blade is uniformly covered with a mixture of oil, petroleum and fluorescent powder. At the

desired operating conditions the visualisation of the flow structures on the painted surface is

possible due to the behaviour of the oil mixture depending on the local wall shear stresses. In

regions of high flow velocities, where no separation bubble occurs, the oil mixture is almost

completely removed from the blade surface. On the other hand, the oil mixture accumulates in

regions of local flow separation or in regions where low flow velocities occur (stagnation

point, pressure side), because of the lower wall shear stresses. In turbulent boundary layer

regions, due to the increased momentum and mass exchange near the wall, low quantities of

oil mixture are removed. This allows the recognition of the end of the transition zone on the

profile. The quality of the oil flow pictures depends strongly on the mixture composition. The

mixture has to remain liquid on the blade during the time taken for the tank evacuation (about

15 to 20 minutes) and should then rapidly dry at operating conditions in order to reduce the

experimental costs. The identification of separation bubbles requires particular attention. In

fact, in this case the relative high quantity of paint accumulated in the separation bubble

region has to be carefully removed towards the trailing edge. This is done by increasing the

compressor rotational speed for a short period of time. A possible alternative solution could

be to let the paint carefully flow back over the blade surface by shutting down the power

supply. In this way the two lines delimiting the separation bubble region can also be well

identified, but the flow configuration in the blade region upstream of the bubble is washed

away. Due to the higher gradients near the wall at higher Reynolds numbers the most evident

results were obtained at a lower Reynolds number level.

The inlet flow turbulence intensity was determined using the Constant Temperature

Anemometry (CTA). Assuming isotropic turbulence distribution, a single hot film probe of

the type “DANTEC HF-55R01” is mounted 500 mm upstream of the cascade inlet plane.

Wolff (1999) describes the CTA data acquisition system. The DANTEC anemometer system

“Streamline” is controlled by DANTEC software “Streamware” (DANTEC, 2001). The in-

house software WINSMASH (Wolff, 1999) controls the data acquisition. The probe is

calibrated for each local static pressure. A 4th order polynomial has been used for the

approximation of the calibration curve. The Hot Film Anemometer (HFA) signals were low-

pass filtered with a cut-off frequency of 10 kHz. Considering the generic quantity b, its mean

value is given by:

0

1 N

jj

b bN =

= ∑ (3.4)

where N is the number of samples and bj represents the generic quantity for each sample. The

standard deviation of b is then calculated using the RMS deviation given by:

( )2

0

1

1

N

jj

RMS b bN =

= ⋅ −− ∑ (3.5)


The turbulence level Tu is calculated using the RMS value of the velocity w measured by the

hot film probe and normalising it using the velocity in the cascade inlet plane w1:

1

100%RMS

Tuw

= ⋅ (3.6)

3.5 Measurement programme

The turbine cascades T150, T151 and T152 were investigated in a wide operating range at

various incidences. The effects of Mach- and Reynolds number on the aerodynamic behaviour

of the cascades were investigated as well. The exit Reynolds number Re2th was varied

between 600 000 and 1 200 000, while the exit Mach number Ma2th was varied in a high

subsonic region between 0.65 and 0.85. In this way the aerodynamic characteristics of the

different design strategies were quantified and an extensive database was provided for the

validation of the simulation tools.

Table 3.2 Measurement program for the turbine cascades T150, T151 and T152

Ma2th

Re2th 0.65 0.75 0.85

600 000 0 1 0 1 2 0 1

900 000 0 1 0 1 2 0 1 ∆β1=0°

1 200 000 0 1 2 0 1 2 0 1 2

Ma2th Re2th

0.65 0.75 0.85

600 000 0 1 2 0

900 000 1 2 ∆β1=+/−10°

1 200 000 1 2 0 1 2 0 1 2

Ma2th Re2th

0.65 0.75 0.85

600 000 0 1 2

900 000 1 2 ∆β1=+/−5°

1 200 000 0 1 2

Table 3.2 shows the measurement programme performed on the three turbine cascades. The

numbers indicate the cascade name (e.g. 1 means T151). In the left column information is

presented regarding the incidence at which the tests were performed (e.g. ∆β1 = +10° means

plus ten degrees incidence with respect to the reference cascade inlet flow angle). The inlet

flow angle is defined as in Figure 3.1 and positive incidences correspond to a rotation of the

inlet flow vector towards the pressure side (clockwise direction in Figure 3.1). The boxes


containing a number indicate a combination of incidence angle, Mach- and Reynolds number

at which a profile pressure distribution and wake traverse with a five hole probe were

performed. The wake traverses were performed at mid-span in a plane downstream of the

cascade at a distance of 40% chord from the cascade outlet plane. A shaded box means that

oil flow pictures were taken for the corresponding operating conditions. Bold characters

indicate the existence of inlet turbulence flow measurements.

For the turbine cascade T150 further measurements were performed at a higher exit Mach

number of Ma2th=0.90, a reference exit Reynolds number Re2th=1 200 000 and reference

incidence. These measurements were helpful for an additional numerical analysis of the

influence of the trailing edge thickness on the cascade total pressure losses (see Chapter 5).

3.6 Experimental results and discussion

The integral parameters quantifying the aerodynamic behaviour of the three cascades, the

measured turbulence levels and the extension of the transition zones, as read from the oil flow

pictures, are listed in the annex. The measured turbulence level confirmed the turbulence

range expected from the use of the turbulence grid generator of type XIgK, featuring values

around 4%. In the present section the influence of the inlet flow angle, the Reynolds- and the

Mach number on the cascade aerodynamic behaviour will be discussed.

A comparison of the isentropic profile Mach number distributions for the different turbine

cascades at reference operating conditions is shown in Figure 3.7. In the front part of the

suction surface of the datum-profile T150 the flow accelerates with quite high gradients to a

Mach number slightly below 0.8. In this initial zone, however, a well marked discontinuity in

the velocity gradients, associated with local diffusion phenomena can be identified. This zone

is followed by a second one in which the velocity level remains almost constant. A third

acceleration zone can be detected between 50% axial chord and the position of the peak Mach

number on the suction surface. In the following diffusion region a flow deceleration takes

place towards the exit Mach number. On the pressure surface near the leading edge T150

features a suction peak, indicating the presence of a short separation bubble. Downstream the

flow decelerates down to the pressure surface local minimum. Then a flow acceleration

occurs towards the exit Mach number. The pressure side acceleration features higher gradients

near the trailing edge, starting from 80% axial chord length. Numerical simulations indicate

that a boundary layer relaminarisation is expected to take place in this region on the pressure

side (see Chapter 5). The suction side acceleration for T151 and T152 takes place more

continuously than for the datum profile, presenting thus more advantageous conditions for an

efficient profile film cooling. However, the increased aerodynamic loading of T151 produces

a back diffusion region of higher gradients on the suction side. This results from the higher

suction surface peak Mach number, located as far downstream on the suction surface as for

T150, and from the lower exit Mach number featured by T151. The reduction of the exit


velocity level for T151 is a direct consequence of the increased blade spacing at a fixed

cascade mass flow. On the other hand, the profile velocity distribution on T152 features

improved characteristics with respect to the other two blade profiles. The deceleration to the

exit Mach number in the rear part of the suction surface of T152 occurs under quite moderate

gradients. The continuous acceleration and the higher velocity level featured by T152 on the

pressure surface are particular advantageous for an efficient action of the profile film cooling

in this region as well.

Figure 3.7 Comparison of the measured profile isentropic Mach number distributions for

T150, T151 and T152 at reference conditions (Re2th=1 200 000; Ma2th=0.75

and β1=β1ref)

Even if heavy duty gas turbines operate at fixed incidence for the most part of the working

time, it is usual to take into account the profile behaviour at different incidences within the

design process. In fact during transitional processes like start up and shut down of the turbine,

strong incidence variations occur, which could negatively influence an efficient film cooling

of the profile. This could lead to severe damage within the machine and it is therefore of

major importance to have knowledge of the aerodynamic behaviour of the investigated

profiles at different incidences as well.

The influence of the inlet flow angle on the development of the integral total pressure losses

of the three cascades is displayed in Figure 3.8. Here, the y axis is expressed as the ratio

between the actual total pressure loss coefficient and the measured total pressure loss

coefficient of the datum-profile at reference conditions. This will be used further on as a


reference value. An increase of the inlet flow angle means a rotation of the incidence vector

towards the pressure side. The diagram shows that the higher aerodynamic loading featured

by T151 produces a strong reduction of the level of the total pressure losses. At reference

conditions T151 presents a loss coefficient about 32% lower than the datum profile (T150).

T152 instead presents a loss reduction of about 10% with respect to T150 at reference

conditions. T150 and T151 react more sensitively to an inlet flow angle increase than T152.

Ten degrees more incidence produce about 30% higher total pressure losses for the datum

profile and for T151, while this increase is restricted to about 20% for T152.

Figure 3.8 Influence of the inlet flow angle onto the cascade characteristics of T150, T151

and T152 at reference conditions (Re2th=1 200 000; Ma2th=0.75 and β1=β1ref)

The influence of the Reynolds number on the aerodynamic behaviour of the cascades is

shown in figure 3.9 and figure 3.10.

Figure 3.9 presents the development of the measured cascade total pressure losses versus the

Reynolds number, while Figure 3.10 shows the behaviour of the cascade integral exit flow

angle versus the Reynolds number. In this diagram, because of the lower exit flow angles

featured by T151, the corresponding angles are represented on the right hand side y-axis of

the diagram. The Reynolds number influence in the range between 600 000 and 1 200 000 is

moderate, however the plots show some tendencies which are confirmed by the analysis of

the profile velocity distributions and oil flow pictures. In the following the cascade

aerodynamic behaviour at negative and positive incidences is discussed in order to evidence

these major features.


Figure 3.9 Influence of the Reynolds number on the total pressure losses of cascades

T150, T151 and T152 at reference conditions (Ma2th=0.75 and β1=β1ref)

Figure 3.10 Influence of the Reynolds number on the exit flow angle of cascades T150,

T151 and T152 at reference conditions (Ma2th=0.75 and β1=β1ref)

At negative incidences, where the blade aerodynamic loading is reduced, both T151 and T152

present a local minimum of the total pressure losses at the intermediate Reynolds number

Re2th=900 000. This is the result of two contrasting aspects. In fact, increasing the Reynolds

number to the nominal value of Re2th=1 200 000 moves the suction side transition region


towards the leading edge and therefore the turbulent boundary layer develops further

upstream. This produces a slight increase of the losses and an increase of the cascade exit

flow angle, which corresponds to a reduction of the cascade deflection because a thicker

turbulent boundary layer exists on the suction surface near the blade trailing edge. By

reducing the Reynolds number to Re2th=600 000 the total pressure losses of T151 and T152

increase. This is associated with the development of a short laminar separation bubble in the

region immediately downstream of the suction side Mach number peak. The existence of the

bubble is confirmed both by the measured profile pressure distributions and the related oil

flow pictures. Additional measurements, performed for T152 at Re2th=400 000, elucidate this

phenomenon even better. The presence of the laminar separation bubble does not influence

the cascade deflection behaviour, as confirmed by the curves in figure 3.10.

Figure 3.11 Profile velocity distribution for T152 at negative incidence ∆β1=−10° (upper)

and at positive incidence ∆β1=+10° at reference Mach number Ma2th=0.75


These observations are confirmed by the profile velocity distribution for cascade T152 at

negative incidence, as displayed in the upper part of Figure 3.11. The laminar separation

bubble featured at the lowest Reynolds number Re2th=400 000 is displayed in detail in the

upper right side of the figure. An analogous but less pronounced behaviour can be observed at

Re2th=600 000. At positive incidences, as presented in the lower part of the figure, the

diffusion region featured in the front part of the suction surface forces the transition further

upstream. Therefore the velocity distributions are almost independent on the Reynolds

number as shown in the lower part of figure 3.11. The distributions displayed in figure 3.11

qualitatively feature the same characteristics as T151, so that the same conclusions can be

drawn for this profile. However, for the datum profile T150 the existence of a velocity plateau

on the profile suction surface forces an earlier development of the turbulent boundary layer

even at negative incidences. Therefore the gradients existing in the suction side back diffusion

region do not lead to the development of a laminar separation bubble at Re2th=600 000. At

positive incidences T150 behaves similarly to T151 and T152, featuring a diffusion region in

the front part of the suction surface, which almost fixes the cascade deflection (see

figure 3.10).

The movement of the transition zone towards the front part of the profile suction surface with

increasing Reynolds number at negative incidences is illustrated in Figure 3.12, Figure 3.13

and Figure 3.14. The flow pictures at incidence ∆β1=−10° and reference Mach number

Ma2th=0.75 for the turbine profile T152 are displayed. The figures represent the unrolling on a

plane of the blade surface. The suction surface is shown in the right hand part of each figure

while the pressure surface is shown on the left. On the bottom of the figures the axial co-

ordinate is shown. Few interesting phenomena are revealed from the oil flow visualisation of

the pressure surface. Instead the visualisation of the suction surface reveals both the passage

vortex separation lines (S4-lines according to the nomenclature used by Sieverding, 1984) and

the extension of the transition zones. The transition zone on the suction side is located where

less paint is found and are indicated by the dashed white lines. At the lower Reynolds number

Re2th=400 000 a laminar separation bubble was observed on the suction surface during the

online monitoring. In order to avoid an upstream flow of the paint collected within this

recirculating zone during the shut down procedure of the wind tunnel the compressor was

driven shortly at higher rotational speed at the end of the test, thus pushing the collected oil

flow material towards the blade trailing edge.

A comparison of the profile velocity distributions for the three cascades at a higher operating

Mach number of Ma2th=0.85 is shown in Figure 3.15. From this figure it becomes clear that

the increased aerodynamic loading of T151 produces higher shock intensity. On the other

hand, even if a supersonic region occurs both on the suction surface of the datum-profile and

on the cascade T152, the peak Mach number on these profiles remains lower than for T151,

realising better conditions for the operation at higher Mach numbers. In the analysed Mach


number range, the effect of this phenomenon onto the cascade total pressure losses is quite

moderate. The measured behaviour at higher exit Mach numbers is confirmed by the

computations performed with TRACE (Martinstetter, 2004a).

Figure 3.12 Oil flow visualisation for T152 at Re2th=400 000, Ma2th=0.75 and ∆β1=−10°

Figure 3.13 Oil flow visualisation for T152 at Re2th=600 000, Ma2th=0.75 and ∆β1=−10°


Figure 3.14 Oil flow visualisation for T152 at Re2th=1 200 000, Ma2th=0.75 and ∆β1=−10°

Figure 3.15 Comparison of the measured profile isentropic Mach number distributions for

T150, T151 and T152 at operating conditions: Re2th=1 200 000; Ma2th=0.85

and β1=β1ref


In fact, while an increase of the exit Mach number from Ma2th=0.75 to Ma2th=0.85 produces

an increase of the integral total pressure loss coefficient for T150 and T151 of about 10%,

with respect to the reference operating conditions, the related increase for T152 is only 2%.

The sensitivity of the cascades to a reduction of the operating Mach number was investigated

as well performing tests at Ma2th=0.65. Under these operating conditions the profile Mach

number distributions feature an extended region of almost constant velocities, which forms

near the leading edge on the suction side. Thus it is to be expected that transition moves

upstream on the profile suction side and a thicker turbulent boundary layer develops over the

profile.

The influence of the Mach number onto the cascade deflection is discussed in the following.

From the literature (Scholz, 1978) it is well known that the sine rule is satisfied better as the

operating Mach number rises. This means that the deviation angle becomes smaller and the

cascade deflection rises. At choking conditions the sine rule applies almost exactly. This is

shown by applying the momentum theorem to the control volume of Figure 3.16. The

application of the momentum theorem at sonic conditions in the cascade passage throat leads

to the expression given in the figure. Since for sonic conditions in the throat the exit flow

velocity w2 and the sonic velocity of the Laval state a* are equal, the given expression obeys

the sine rule. Therefore rising the cascade operating Mach number leads to outlet flow angles

nearer to the outlet flow angle predicted by the sine rule.

Figure 3.16 Application of the momentum theorem to the rear part of the blade passage

(Scholz, 1978)


Figure 3.17 Influence of the Mach number on the cascade outlet flow angle at reference

∆β1=0° and positive incidence ∆β1=+10° at reference Reynolds number

Re2th=1 200 000

Scholz (1978) discusses another compressibility effect produced by the finite thickness of the

profile and the boundary layer thickness at the trailing edge. At near sonic conditions, in order

to compensate the increased cross-sectional area downstream of the blade trailing edge, the

fluid experiences velocity changes in a tangential direction to maintain the specified mass

flux. Higher velocity changes are required for higher changes in the cross sectional area (e.g.

produced by higher blade trailing edge thickness).

The measured influence of the operating Mach number on the exit flow angle is illustrated in

Figure 3.17. The diagram contains the measured integral exit flow angle at a reference

Reynolds number Re2th=1 200 000 and at a reference ∆β1=0° (continuous lines) and positive

incidence ∆β1=+10° (dashed lines). It can be observed that higher Mach numbers produce an

increase of the cascade deflection, resulting in an approach of the sine rule. Furthermore, this

occurs under higher gradients for the datum profile T150, which presents a thicker trailing

edge than the other two cascades. This aspect confirms the effects of profile trailing edge

thickness and Mach number on the cascade deflection observed in the literature. At increased

incidence, where the turbulent boundary layer forms more upstream and a higher

displacement thickness is expected at the trailing edge, the deflection changes become more

relevant for T151 and T152 even in the lower Mach number range between 0.65 and 0.75.


The experimental data quantifying the aerodynamic behaviour of the investigated cascades are

shown in the annex. In Table 7.1, Table 7.2, Table 7.3 and Table 7.4 the first column of

results refers to the datum cascade blade T150, while the second column contains the data of

T151 and the third column refers to T152. The data contained in Table 7.5 are all obtained at

the reference Mach number Ma2th=0.75.

58 4. Numerical optimisation environment

4. Numerical optimisation environment

The present chapter illustrates the numerical environment where the aerodynamic

optimisation procedure was developed. The structure of the automatic design method is

shown in Figure 4.1. The optimisation loop consists of three major components: parametric

geometry generator, Navier-Stokes flow solver and optimisation algorithm. The aim of the

optimisation process is to find the n-dimensional vector of design variables X=(x1, x2, …, xn)

which minimises a scalar function, indicated as the objective function F(X), and respecting a

set of m constraints expressed by the vector function B(X)=(b1, b2, …, bm). The generic ith

constraint bi(X) is violated, if bi(X) is located outside a specified range. For the present

application, the design variables correspond to the parameters describing the blade profile

geometry. The objective function is set up by combining various aerodynamic performance

coefficients which result from the flow simulation of the actual blade profile. Thereby the

main optimisation target is the reduction of the cascade total pressure losses by imposing a

fixed operating point. Requirements on the profile velocity distribution with regard to cooling

demands were integrated into the objective function as well. Furthermore, some major

mechanical and geometrical constraints were specified in order to restrict the search to a

subset of realistic geometries. In this way the optimisation task is reduced to a single-

objective, constrained approach.

Figure 4.1 Schematic representation of the optimisation loop and connections of the

components

As illustrated in Figure 4.1, the optimisation algorithm represents the core of the whole

process. It modifies the design parameters according to the information obtained by the

already evaluated parameter datasets.

4. Numerical optimisation environment 59

If the parameters satisfy the specified mechanical and geometrical constraints, the

corresponding blade geometry is transferred to the flow simulation process. Otherwise the

present parameter dataset is associated with an appropriately high value of the objective

function. The flow simulation process is performed in a sequence of automatic steps. The first

step is the grid generation. In this work a method was implemented which ensures reduced

dependence of the flow solution on the mesh by maintaining a fixed grid topology and

modifying, mainly, the mesh in the boundary layer region (Niß, 2002). The flow simulation is

performed using the Reynolds averaged Navier-Stokes solver TRACE developed by the DLR

in Cologne (Eulitz, 2000) in a quasi three dimensional version. In order to reduce the code

running time, each simulation restarts from a well converged solution on a reference mesh of

the reference geometry T150. Furthermore, a convergence criterion based on monitoring the

cascade total pressure losses, the exit flow angle and the total pressure ratio inlet/outlet during

the flow simulation was integrated within the solver. The third step of the flow simulation

process consists in the evaluation of the results obtained for the present set of design

parameters. The evaluation process (Jogwitz, 2002b and Groth, 2004) takes place both in a

plane downstream of the cascade and on the blade profile. The results are then used to build

the objective function, whose value is then computed by the optimisation algorithm. The

whole procedure is set up within the commercial software package iSIGHT

(Engineous Software, 2002). This facilitated the use of various optimisation techniques. The

present investigations were carried out using a probabilistic heuristic optimisation approach as

the adaptive simulated annealing algorithm ASA. Further investigations were performed

using the multi island genetic algorithm MIGA. Another major advantage of implementing

the optimisation procedure within iSIGHT was the reduced efforts to interface the single

components, thanks to the file parsing capabilities of this software package.

In the next sections the numerical tools used to set up the aerodynamic optimisation procedure

are described in detail. Furthermore, the results of the Navier-Stokes simulations are

presented, which were performed on the reference cascades.

4.1 The Parametric geometry generator PROGEN

The parametric representation of the blade geometry is realised using the software PROGEN

of ALSTOM. The three dimensional model of the blade is built up by interpolating the

profiles defined at different blade heights in a radial direction. The single blade profiles are

described as closed curves on conical surfaces. The straight lines used to generate the cones

represent the best fit approximation of the quasi three dimensional stream-surfaces on which

the different blade profiles are designed. Each blade profile consists of four curve segments

(suction side, leading edge, pressure side and trailing edge) which are linked by the profile

control points.


Figure 4.2 Definition of the control points and spline parameters within PROGEN

Each curve segment is a Bezier spline of fifth order and continuously differentiable twice at

the control points. The position of the control points is determined by using the geometric

system illustrated in the upper part of Figure 4.2. Specifying the blade chord length L and the

stagger angle βSG, two auxiliary points are defined. These are the central points of two short

auxiliary segments at trailing and leading edge of the blade. The length of these segments

corresponds to the trailing edge thickness dH and the blade nose thickness dN. The inclinations

of these segments are expressed by the blade metal angle at trailing edge and leading edge,

indicated as αH and αN, respectively. Thus the specification of these six parameters fixes the

position of the four control points unequivocally. The form of the Bezier-curves is then

determined by six additional parameters for each control point. These parameters correspond

to the profile tangent in the control point wi, the curvature ki, the aspect ratio parameters for

the profile slope in counter-clockwise direction ρvi and clockwise direction ρri and the aspect

ratio parameters of the profile curvature in counter-clockwise direction σvi and clockwise

direction σri. Therefore a blade profile section is described unequivocally using a complete set

of 30 parameters. In the case that the profile features symmetric leading and trailing edges the

parameter dataset reduces to 28. In this case in fact the blade wedge angles γH and γN can be

used instead of the blade tangents wi. The effects of the variation of the parameters ρ and σ on

the form of the Bezier-curves are illustrated in Figure 4.3. This figure illustrates that while the

parameter ρ influences the rear part of the spline segment, the influence of σ is more evident

in the front part of the curve. The different variation ranges of the two parameters have to be

considered in an appropriate way within the optimisation process.


Figure 4.3 Influence of the design parameters ρ and σ on the form of the Bezier-spline

4.2 Flow computations procedure

4.2.1. The automatic grid generation method GRIDMOD

A major requirement to the design method is the possibility of automation of the grid

generation process. A reduced mesh dependence of the flow solution is strived for as well. In

order to fulfil these requirements an automatic grid adaptation method, named GRIDMOD

(Niß, 2002) was set up. The automatic mesh generation process is based on the modification

of a low-Reynolds template mesh, which is adapted to fit the actual blade geometry. This

mesh corresponds to a grid of the datum profile T150, containing about 12 000 nodes. The

mesh quality represents a trade-off between accuracy of the solution and computational cost.

The template mesh used for the present investigations is shown in Figure 4.4. The inserts

showing the blade leading and the trailing edges indicate the high resolution of the boundary

layer ensured by this mesh. The present template mesh consists of a multi-block structured

grid featuring a standard O-H topology. The advantages of this topology, compared to more

advanced multi-block structured approaches (e.g. the OCGH topologies, Martinstetter, 2004a)

consist mainly of the possibility of parameterising the mesh in a simple way using a reduced

set of characteristic points at the block-boundaries as control points. On the other hand it must

be kept in mind that this topology does not feature the optimum for achieving high mesh

quality in the wake region for high cascade deflections. However, this aspect is not relevant

except for very high deflections, in a range 115°−120°. For the investigated deflection range,

between 100° and 115°, a satisfactory mesh quality could be achieved. The boundary layer

block of the template mesh contains about half of the mesh nodes. At reference operating

conditions the template grid ensured an average wall dimensionless distance y+ over the


suction side of around 2.5. This corresponds to a resolution which is accurate enough for the

one equation turbulence model approach used (Eulitz, 2000).

Figure 4.4 Template mesh for the automatic grid generation process

In a preliminary phase of the optimisation study, extensive investigations were performed to

quantify the mesh effects onto the flow solution and thus derive the most suitable parameters

for setting up the automatic mesh generation method. These investigations showed that the

integral cascade performance parameters (e.g. integral total pressure losses and exit flow

angle) are not significantly influenced by mesh modifications in the passage block and the

wake block. Since these coefficients are directly used to build the objective function, this

result has major significance for the development of the automatic mesh generator. On the

other hand changes within the boundary layer block (e.g. inclination of the mesh lines with

respect to the solid surface, overall number of nodes and distribution in a perpendicular

direction to the wall) showed stronger influence on the integral cascade coefficients. In order

to reduce the influence of the mesh quality in the O-block onto the flow solution, some major

rules have to be respected, as will be shown from the following mesh studies.

The effect of changes of the position of the boundaries of the wake block on the mesh

structure and on the relative total pressure losses is illustrated in Figure 4.5. The meshes on

which this study was performed are compared in the upper part of the figure. The original

mesh is called mesh A while the modified grid is indicated as mesh B. The major difference

between these meshes consists in the movement of the characteristic point P to the position P′, which corresponds to the position of this control point as calculated using the relationships


implemented within GRIDMOD. A comparison of the wake region of these meshes shows

reduced skewness of the cells in the wake block of mesh B. This feature is responsible for the

re-distribution of the calculated total pressure losses. However, no significant change of the

integral aerodynamic coefficients of the cascade was observed.

Figure 4.5 Influence of the mesh quality on the flow solution in the wake block

A comparison of calculated and measured total pressure loss distributions is displayed in the

lower part of Figure 4.5. The cascade integral total pressure loss coefficient for mesh B is

0.0003 points higher than for mesh A, corresponding to a variation of 0.7 %. Instead the

calculated integral exit flow angle is two hundredths of degree lower. These represent

admissible variations for the present investigations. However, it can be observed that the

computed total pressure loss curves of both cascades are shifted more towards the pressure


side branch of the wake (on the right hand side of the figure) than the measured curves. This

indicates that the predicted deflection is somewhat higher than the measured one. The

calculated total pressure losses are somewhat higher than the measured losses as well. These

discrepancies, however, were observed for all the reference cascades and remain

approximately constant over a wide operating range as will be shown in a further section of

this chapter regarding the validation of the flow solver.

Further investigations were performed both on the datum profile T150 and on the highly

loaded reference profile T151 in order to assess the influence of the angle between the j-lines

of the mesh in the boundary layer block and the blade solid wall on the cascade integral

performance parameters. In fact, a previous version of the automatic grid generation system

did not correct the slopes of the j-lines in the boundary layer block according to blade

geometry modifications. Thus the direction of the j-lines could depart strongly from the blade

orthogonal direction. This represented a major source of error for the calculation of the

integral boundary layer parameters, since the applied transition correlation by Drela (1995) is

based on these parameters. The correction of the j-lines slope implemented within

GRIDMOD is based on the modification of the distance between consecutive nodes,

distributed at specific positions over the entire blade suction surface. These modifications are

performed until a specific value, represented by the sum of the differences between the actual

slope and the direction orthogonal to the blade surface at specified locations, is minimised.

The slope correction is implemented only for the suction surface. In order to assess the

capability of the j-lines slope correction, two different meshes for the reference profiles T150

and T151 were analysed by changing the slopes of the mesh lines on the suction side. The

total number of nodes as well as their distribution law in the direction orthogonal to the wall

remained unchanged. While for T151 both meshes are obtained from the template mesh using

GRIDMOD with and without slope correction, for T150 the original mesh corresponds to the

template mesh itself. A comparison of the original and the modified mesh for T151 is

presented in Figure 4.6. The dashed lines in the zoom windows correspond to the mesh

obtained without slope correction. For T150 the differences between the two meshes are

somewhat reduced, because the template mesh presents j-lines which are orthogonal to the

blade surface. The difference between integral total pressure losses for the modified T150

mesh and template mesh is lower than 0.0001 points (about 0.1 %). The differences in terms

of exit flow angle are negligible. For T151 instead the differences are somewhat higher but

still limited. The integral total pressure loss coefficient calculated for the mesh without slope

correction is about 0.0005 points higher than using the mesh correction. This corresponds to a

difference of about 1.3 % of the calculated integral values. The difference in terms of exit

flow angle is limited to one hundredth of a degree. This underlines the importance of this

correction to increase the reliability of the information obtained from the flow simulation

procedure.


Figure 4.6 Correction of the j-lines slope in the boundary layer block for T151

The choice of the optimal number of nodes in the O-block used in the template mesh is based

on additional preliminary computations performed on the turbine cascade T150. A concept

was sought which reduces the number of mesh variables to be controlled in the boundary

layer block. Thereby the nodes distribution law (Robert’s distribution law,

CFD Norway, 2003) and the boundary layer block thickness were fixed and the minimal

number of nodes was determined which is necessary in the O-block to resolve the boundary

layer correctly (Martinstetter, 2004b). The results of these computations showed that at least

thirty nodes in the j-direction are necessary in order to obtain reliable results. The results of

this mesh sensitivity study are shown in Figure 4.7. On the left hand side the influence of the

mesh onto the distribution of the wall shear stress on the suction side is shown. Slight

discrepancies can be observed between 32 and 40 nodes in j-direction, while the distribution

obtained using 20 nodes departs strongly from the other two. The variation in the computed

total pressure losses with changing number of nodes in j-direction is illustrated on the right

hand side of the figure. The curve shows that the template mesh requires at least 30 nodes in

j-direction in order to ensure reproducible results.


Figure 4.7 Mesh sensitivity study for the choice of the number of nodes in j-direction

Based on the information obtained from these preliminary mesh studies, a system for the

automatic mesh generation was set up. This procedure adapts an existing template mesh to the

new blade geometry. The template mesh is represented by an ASCII file containing a list of

commands for the multi-block mesh generator Threemesh (CFD Norway, 2003). These

instructions specify the form of the block-boundary curves and the nodes distribution law

along the boundaries. GRIDMOD modifies the mesh ASCII file in order to adapt the template

mesh to a new arbitrary blade geometry. So that the grid topology remains unchanged and the

overall number of nodes remains constant. The distance of the nodes from the solid wall and

their distribution within the O-block remains unchanged as well. This is achieved by

extruding the profile using the angle information derived from a spline-representation of the

blade geometry itself. In this way the external boundary of the O-block presents a form which

is quite similar to the profile. The blade is represented by four spline segments (trailing edge,

suction side, leading edge and pressure side) obtained by the interpolation of the blade points.

The extrusion process takes place for each of these segments. The external O-block boundary

is divided into four spline segments as well. The interpolation technique implemented within

GRIDMOD for the treatment of these boundary curves is based on appropriate algorithms of

the NAG numerical libraries (Numerical Algorithms Group, 2005). The iterative procedure

for the slope correction of the j-lines follows, which checks the slope of the j-lines within the

O-block at particular locations and changes the distribution of the nodes along the profile (i-

direction) in order to control the slope of the j-lines. In this way the nodes distribution in the

boundary layer block is almost independent from blade geometry modifications. Furthermore,

a quite high grid resolution in the direction along the blade was chosen, so that strong changes

of the profile thickness could be performed. Further parameters (see Figure 4.8) are used to

adapt the position and form of the block boundary curves in order to reduce possible grid

quality changes in the inlet, passage and wake blocks. It must be considered also that a

generic block boundary curve is defined within the mesh generator by specifying the start and

end point as well as derivatives (angles) and influence factors of the curve angles at these


points. However, GRIDMOD considers only the parametric modification of coordinates and

angles at start and end points of the mesh boundary curves.

The schematic representation of the parameters used within GRIDMOD is illustrated in

Figure 4.8. Once the new O-block is generated, the position of the different control points, Pi,

and the form of the boundary curves is determined. The location of P1 is expressed as a

function of the blade point at minimal axial x-coordinate B1, indicated as the cross point in

the leading edge region. P2 is positioned at a fixed distance from P1 and at the same axial

position. The point P3 is located at the lowest y-coordinate on the O-block external boundary.

The control curves P3-P4 and P3-P5 start from this position. The tangents of these curves

form an angle α3b and α3a with the horizontal axis respectively. While the curve P3-P4 ends

with a horizontal tangent, the curve P3-P5 terminates orthogonal to the O-block. While P4 is

located at a fixed distance from the point at the maximal x-coordinate on the blade B2

(indicated in the figure as the cross point in the trailing edge region), the position of the

control point P5 is fixed by the number of nodes on the lower side of the passage block,

which is related, for boundary conditions, to the number of nodes on the suction side segment.

The code requires a mesh featuring an equal number of nodes on the periodic boundaries.

Figure 4.8 Geometric system for the automatic mesh generation process GRIDMOD


Figure 4.9 Application of GRIDMOD for the mesh generation of the turbine blade T152

Finally P6 is located at the position in the front pressure side region of the O-block where a

horizontal tangent is featured. The block boundary curve P6-P2 forms an angle α2 with the O-

block, which remains unchanged during the mesh adaptation process.

Changes of the trailing and leading edge thickness and of the pitch are treated within

GRIDMOD as well. In this case, however, the overall number of nodes changes within the

mesh adaptation process in order to avoid local mesh overlapping in the trailing and leading

edge regions. The position of P5 changes accordingly in order to respect the condition of an

equal number of nodes on the upper and lower periodic boundaries of the mesh

(Martinstetter, 2004a). Even if trailing and leading edge thickness were not considered as

design parameters within the automatic optimisation procedure, these features of GRIDMOD

reduced the mesh generation efforts considerably allowing extensive investigations of the

influence of the trailing edge thickness on the aerodynamic behaviour of the cascades (see

Chapter 5). The results of the application of GRIDMOD for meshing the reference profile

T152 are shown in Figure 4.9. Where the datum-profile geometry T150, on which the

template mesh is based, is shown as well.

4.2.2. The Navier-Stokes flow solver TRACE

The flow computations were performed using a two dimensional MPI-parallelised version of

the Reynolds-Averaged Navier-Stokes flow solver TRACE of the DLR in Cologne

(Eulitz, 2000). The flow solver TRACE is widely used in various German research and


industrial departments. Recent publications document the major cooperation activities

between the DLR in Cologne and the University of the German Armed Forces in Munich for

the validation and further development of the RANS solver TRACE for different application

fields (e.g. Acton, 1998, Cardamone et al., 2002, Hilgenfeld et al., 2003). The present section

describes the most important numerical features of the flow solver and the major

characteristics of the turbulence and transition models used for the present investigations. For

a more detailed description of the numerical approaches used for the solution of the Navier-

Stokes equations the reader can refer to Hirsch (1988), while an excellent review on

turbulence modelling can be found in Wilcox (1993).

The Reynolds-averaged Navier-Stokes equations and the turbulence model are discretised on

multi-block structured grids. The space discretisation of the convective fluxes is based on the

TVD (Total Variation Diminishing) scheme by Roe, (1981), which is combined with a

MUSCL extrapolation scheme by Van Leer, (1979) in order to obtain second order accuracy

in space. The viscous derivatives are discretised using a second order central-differences

scheme. The present calculations were performed by neglecting the viscous diffusion in the

direction parallel to the shear surfaces using a thin-layer approximation (Hirsch, 1988). The

flow governing equations are solved in time using an implicit time integration technique as

described by Engel (1997). Non-reflecting boundary conditions formulated by Giles (1992)

are implemented at the inlet and outlet boundaries.

For the prediction of the boundary layer development on the blade surface a turbulence

closure based on the one-equation model by Spalart and Allmaras (1992) was used. Even

though many authors argue that two-equation turbulence models represent the minimum

acceptable level of closure for the Reynolds stress tensor (Speziale et al., 1998), in the

nineties the development of a new generation of one-equation turbulence models represented

a major trend in the scientific community. The goal was a simpler model ensuring an

equivalent level of computational accuracy as established two-equation models and at the

same time higher numerical robustness. Recent successful implementations of these models

attest the progresses achieved in this area (Eulitz, 1999, Arnone et al., 2001).

The major advantage of a one-equation turbulence model based on the formulation of Spalart-

Allmaras is that in this approach a simple transport equation for the eddy viscosity νT is used.

In this way any conceptual difficulty associated with the algebraic specification by empirical

means of a turbulent length scale is avoided. Furthermore, the eddy viscosity features lower

gradients near the wall than typical variables used for two-equation models like the turbulent

kinetic energy, k, or the dissipation rate, ε. This should ensure a mesh independent resolution

of the laminar sub-layer using a reduced number of nodes near the wall. Eulitz (2000)

indicates that while a mesh independent solution for two-equation turbulence models require

y+ values below 1, the usage of a one-equation model based on the transport of the eddy

viscosity requires y+ values below 3. These characteristics render this model an optimal


choice for the application at high Reynolds numbers. For the present investigations a Spalart-

Allmaras turbulence model was used in the modified version by Eulitz (2000). The original

Spalart-Allmaras model can be written in the form:

1 2T T T T

Prod T Destr w Diff T Diffi i i i

Dv v v vC ω v C D C v C

Dt x x x x

⎡ ⎤∂ ∂ ∂ ∂= − + +⎢ ⎥∂ ∂ ∂ ∂⎣ ⎦ (4.1)

The transport model for the eddy viscosity is therefore set up of a convection term (on the left

hand side), a production term depending on the vorticity ω, a destruction term and additional

diffusion terms. The modifications introduced by Eulitz concerned the production and the

destruction terms. For the present investigations these modifications were all adopted with

exception of the additional production term introduced for a better modelling of the free

stream turbulence intensity introduced by incoming wakes. In fact, preliminary investigations

on the reference turbine cascade T150 (Jogwitz, 2002a) indicated that this formulation was

responsible for an un-physically large increase of the total pressure losses and was therefore

no further used for the present class of profiles.

Since the Spalart-Allmaras model, as with any other model based on the Boussinesq eddy

viscosity hypothesis, is completely void of any transition physics, the start of transition has to

be indicated. This is done by coupling the turbulence model with a transition correlation by

Abu-Ghannam and Shaw (1980) in the formulation by Drela (1995). In this model the

transition onset is located where the local momentum thickness Reynolds number, Reδ2,

exceeds a particular value, defined as

( )5/ 42,

12

1 10155 89 1 tanh 5.5

4 1δ Start critRe nH

⎡ ⎤⎛ ⎞= + + −⎢ ⎥⎜ ⎟−⎝ ⎠⎣ ⎦

% (4.2)

with

( )8.43 2.4 ln 0.027 tanh / 2.7critn Tu= − − ⎡ ⎤⎣ ⎦%

This correlation expresses the value of the momentum thickness Reynolds number, Reδ2,Start,

at which the transition begins as a function of the boundary layer shape factor, H12, and the

turbulence intensity at the boundary layer edge, Tu. The shape factor H12 is thereby defined as

the ratio between boundary layer displacement thickness, δ1, and momentum thickness, δ2.

Both quantities are calculated within TRACE by integrating along mesh j-lines between the

solid wall and the boundary layer edge δ. This circumstance underlines the importance of

orthogonal j-lines within the boundary layer block for the accurate simulation of the boundary

layer characteristics. Furthermore, it must be noted that the integration takes place exclusively

within the O-block. This is done in order to avoid expensive communications between

different processors. For this reason the O-block thickness cannot be reduced below a certain

value, as would be desirable to improve the mesh quality in the passage block at higher

cascade deflections. The boundary layer edge, δ, is determined using the method by

Stock et al. (1989).


The coupling between turbulence model and transition correlation occurs by activating or

deactivating the turbulence production terms according to the information derived from the

transition correlation. Specifically, the production term is controlled by means of an auxiliary

function, ft. The value of this function is set to zero if the momentum thickness Reynolds

number is lower than Reδ2,Start and becomes positive if this value is exceeded. As long as the

auxiliary function, ft, is zero the convective term of the transport equation for the turbulence

production is zero, too. Therefore, monitoring this auxiliary function, ft, gives information on

the boundary layer state. If ft is zero the boundary layer is laminar, while positive values of ft

indicate transitional or turbulent boundary layers. Eulitz (2000) shows that for a completely

developed turbulent boundary layer, ft assumes the value 0.3 in accordance with the Bradshaw

hypothesis (Bradshaw, 1996).

In order to reduce the computational time required for each flow simulation within the

optimisation loop, the solution on the new blade geometry is generated by restarting from a

well converged solution obtained on the template mesh. Thereby the solution is passed

together with the adapted mesh to the new blade geometry. The flow computation is

interrupted if an ad hoc developed convergence criterion integrated within the flow solver in

the present work is fulfilled. The convergence criterion is based on the cascade total pressure

ratio, exit flow angle and total pressure losses. If these three quantities vary in a fixed range

for a certain number of consecutive iterations the calculation is converged. Extensive

preliminary investigations showed that a well converged solution is obtained if the integral

exit flow angle varies in a range of 0.01° and the cascade total pressure ratio and losses in a

range of 0.0001 for three consecutive iterations.

4.2.3. The automatic evaluation procedure AUSWERT

The post-processing procedure has to provide the objective function with appropriate

parameters qualifying the flow solution for the actual blade geometry. The evaluation method

developed within the present system, named AUSWERT, handles both the cascade wake and

the profile velocity distribution. The wake evaluation makes available the cascade integral

performance coefficients (e.g. total pressure losses, exit flow angle, total pressure ratio etc.)

while the treatment of the profile velocity distribution provides information about maxima,

minima and inflection points featured on the suction and the pressure side.

The wake evaluation process takes place in a plane positioned at the same distance from the

cascade exit plane as the measurement plane (eM/l=0.4). In order to reduce the mesh

dependence, a two-dimensional interpolation of the flow solution is set up, using the modified

method of Shephard (1968) implemented in the NAG-C numerical libraries

(Numerical Algorithm Group, 2005). The treatment of the solution in the wake region is

schematically illustrated in Figure 4.10. The interpolating surface is constructed through a set

of scattered data points, corresponding to the nodes of a mesh region located around the


evaluation plane. Thus, for each flow variable, a curve is obtained by intersecting the

particular flow solution interpolating surface with the evaluation plane. The effective

evaluation process uses the same flow homogenisation procedure implemented for the post-

processing of the experimental results (Amecke, 1967). This procedure applies the

conservation laws for mass, momentum and energy between the evaluation plane and a plane

so far downstream that the flow quantities are homogenised. The homogenisation is supposed

to take place adiabatically. The usage of the Amecke procedure ensures that the integral

values for the generic flow quantity are independent from the position of the evaluation plane.

These values are then combined to calculate integral flow parameters like cascade total

pressure losses, exit flow angle and axial velocity density ratio.

The evaluation of the profile velocity distribution plays a fundamental role within the design

process. In this context some basic ideas for an efficient cooling of the profile have been

integrated in the design procedure and considered as optimisation targets as well. A

continuous acceleration has to take place in the front part of the suction side in order to

generate the favourable conditions for the coolant flow to follow the profile smoothly.

Figure 4.10 Treatment of the wake region within AUSWERT

Diffusion regions along the suction surface have to be avoided and adverse pressure gradients,

taking place downstream the cascade passage throat, have to be limited as well. Furthermore

the presence of suction peaks or short separation bubbles in the front part of the pressure side,

where high heat transfer is expected, has to be prevented (Wolff, 2003).

All these phenomena were quantified within the post-processor AUSWERT by interpolating

the calculated isentropic profile Mach number distribution on the pressure and the suction


sides by means of cubic spline curves, obtained using the NAG-C numerical libraries

(Numerical Algorithm Group, 2005). The knowledge of the derivatives of these interpolation

curves up to the third order allows the determination of maxima, minima and inflection points

featured by the profile velocity distribution. Thereby, indicating the isentropic profile Mach

number distribution with f(x), the following conditions have to be fulfilled for a local

maximum to be featured at the position xi:

1 1 1

0 0 0 0i i i i i i

df df df df df df

dx dx dx dx dx dx− − +

⎡ ⎤ ⎡ ⎤⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞⋅ < ∧ > ∨ ⋅ < ∧ >⎢ ⎥ ⎢ ⎥⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎢ ⎥ ⎢ ⎥⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠⎣ ⎦ ⎣ ⎦

(4.3)

2 2 2

2 2 21 1

0 0 0i i i

d f d f d f

dx dx dx− +

⎡ ⎤⎛ ⎞ ⎛ ⎞⎛ ⎞ ⎛ ⎞ ⎛ ⎞⎢ ⎥⎜ ⎟ ⎜ ⎟< ∧ < ∧ <⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎢ ⎥⎝ ⎠ ⎝ ⎠ ⎝ ⎠⎝ ⎠ ⎝ ⎠⎣ ⎦

(4.4)

The conditions for a local minimum are derived in similar way. For the determination of the

inflection points the maxima and minima of the first derivatives were searched for. The

treatment of the inflection points was undertaken only on the suction surface.

Figure 4.11 Second derivative distribution of the isentropic Mach number

Preliminary investigations showed that, using this approach, the interpolating spline has to be

evaluated at a number of points not lower than 10000 in order to avoid under-sampling

phenomena and ensure the prediction of all the local peaks of the examined distribution and

their derivatives. The problem associated with cubic spline interpolation curves, however, is

the discontinuity of their second derivatives. These discontinuities are even higher for the


third derivates and influence the exact prediction of the inflection points for the profile Mach

number distribution. In order to avoid this, approximating polynomials were used to fit the

second derivative distributions obtained from the interpolation process. The polynomial

approximation approach was not directly used for the profile velocity distribution, because it

leads to an incorrect prediction of the position of the local peaks and thus to an incorrect

interpretation of the results. On the other hand, since only the presence of zones with

curvature changes is relevant for the present investigations and not the exact position of the

related inflection points, the approximation approach is applicable best to the treatment of the

second derivatives. Regions between two inflection points have to be avoided, because they

lead to a discontinuous acceleration on the profile. This is illustrated by a comparison of the

suction side of the datum-profile T150 with the suction side of T151 or T152 (see Figure 3.7).

T150, in fact, features a curvature change between thirty and sixty percent of the blade axial

chord, while the other two profiles accelerate continuously over the suction surface.

Figure 4.11 shows the second derivative of a generic suction side isentropic Mach number

interpolating spline together with the distributions of two different approximating

polynomials.

Figure 4.12 Generic Mach number distribution featuring an inflection point in the leading

edge region

It can be observed that even if a reduction of the polynomial order leads to differences in the

location of the zero passages, the oscillations are reduced and a better overall approximation

is ensured. Extensive preliminary investigations were performed using a large database of


different blade geometries in order to assess the best suitable polynomial order. These

investigations indicated that a fourteenth order polynomial order represents a best

compromise solution for the approximation of the second derivates of the profile Mach

number distribution. The figure shows also that the approximating polynomials do not

proceed to the end of the suction side. The approximation takes place in fact between 5%

axial chord length and 5% behind the last maximum on the profile suction side. This

limitation was introduced in order to prevent an undesirable influence of local leading and

trailing edge phenomena onto the form of the approximating polynomial.

Figure 4.13 Schematic representation of the isentropic Mach number evaluation process


A particular treatment of the suction side leading edge region was necessary in order to ensure

that curvature changes, even those starting upstream of 5% axial chord are accurately

predicted. Figure 4.12 illustrates an example of a generic profile Mach number distribution

obtained during the optimisation loop. This distribution features an inflection point in the

suction side leading edge region. In this case a treatment of the second and third derivatives

with the interpolation and approximation capabilities offered by the NAG libraries is quite

difficult because of the strong gradients featured by the profile Mach number in this region.

Therefore, a local search for “absolute” maxima and minima is performed and the inflection

point is located at half distance between these local peaks.

Table 4.1 Nomenclature for the evaluation of the profile velocity distribution

Factor Name Explanation − Calculation method

Mais-MAX-SS/PS Maximum on the suction / pressure side – cubic spline

Mais-MIN-SS/PS Minimum on the suction/pressure side – cubic spline

Mais-MAX-SS-LE Maximum on the suction side leading edge region – absolute search

Mais-MIN-SS-LE Minimum on the suction side leading edge region – absolute search

Mais-MAX-PS-TE Maximum on the pressure side trailing edge region – absolute search

Mais-MIN-PS-TE Minimum on the pressure side trailing edge region – absolute search

Mais-TE Isentropic profile Mach number at the trailing edge

Mais-INFL-SS/PS Inflection point on the suction / pressure side – cubic spline, polynomial

Mais-INFL-SS-LE Inflection point on the suction side leading edge region – local search

AMais-MAX-SS Area between the linear segment and the segment of the Mach number

curve connecting two consecutive suction side maxima– cubic spline

AMais-INFL-SS

Area between the linear segment and the segment of the Mach number

curve connecting two consecutive inflection points – cubic spline,

polynomial

Diff(k) kth diffusion factor – ratio between consecutive maximum and minimum

or definition (4.5)

A schematic representation of the quantities used within the evaluation of the isentropic

profile Mach number distribution is illustrated in Figure 4.13. The nomenclature used for the

whole set of parameters determined within this process is shown in Table 4.1. The right hand

column displays the calculation method and the factors involved in the calculation. The

notation “cubic spline” in the right column, for example, means that the calculation of the

related parameter is obtained evaluating the interpolating spline curve. In the figure, the zone


delimited by the continuous straight line connecting two consecutive Mach number maxima

and the suction surface velocity curve is indicated as AMais-MAX-SS. Such areas are

associated with flow diffusion phenomena between two local consecutive maxima on the

profile suction side. Regions delimited by the dashed straight line connecting two local

inflection points and the velocity curve are indicated as AMais-INFL-SS in the figure. These

regions indicate zones where no continuous acceleration is featured on the profile. Diffusion

regions on the pressure side and in the leading and trailing edge local regions are quantified

using appropriate diffusion factors. Various definitions of the diffusion factors are

implemented within AUSWERT. The definition used within the optimisation process for the

generic kth factor corresponds to the rectangular area indicated in the figure on the pressure

side:

( ) ( ) ( )( ) ( ) ( )( )is is

is is Ma MIN k Ma MAX kDiff k Ma MAX k Ma MIN k x x= − ⋅ − (4.5)

This ensures an optimal treatment of the diffusion regions in particular for zones featuring an

almost constant velocity level along large axial intervals. Thus the distance between two

consecutive maxima and minima is considered as well and the diffusion factors associated

with slightly different maxima and minima are appropriately amplified. The definition of the

back diffusion factor instead is simply expressed by the ratio between the last local Mach

number maximum on the suction side and the exit isentropic Mach number.

4.3 Validation of the flow solver

The assessment of the reliability of the flow solver TRACE for the present application is of

major importance in order to ensure consistency of the optimisation results. Therefore, an

extensive validation process has to be performed. The comparison of the Navier-Stokes

predictions with the measured results, however, can only be carried out if the measured

aerodynamic loading distribution and the boundary layer development on the blade profile are

accurately reproduced. Thus, the first step of the validation process consists of determining

the numerical boundary conditions for which the aerodynamic loading on the profile is well

predicted. A comparison of computed and measured isentropic profile Mach number

distributions at reference conditions (Ma2th=0.75; Re2th=1 200 000; β1=β1,Ref) is shown in

Figure 4.14. The key boundary data for computations and experiments are listed as well. The

computed velocity distributions agree well with the measured ones. The computational results

show that the flow solver predicts total pressure loss coefficients somewhat higher than the

measured ones. This difference, however, remains approximately constant for a wide

operating range. In order to obtain a better insight into the over-prediction of the total pressure

losses, extensive calculations of the datum profile T150 were carried out at reference

operating conditions. Also different formulations of the Spalart-Allmaras turbulence model

were tested. The results are displayed in Figure 4.15. The influence of the inlet turbulence

intensity on the level of the total pressure losses is illustrated as well. The labelling SAL is


used to indicate a low-Reynolds formulation of the Spalart-Allmaras turbulence model. SA2

indicates instead the two-layer version of the model implemented in TRACE (Eulitz, 2000).

Computations (TRACE) T150 T151 T152

Inlet flow angle β1 [°] 133.3 135.9 131.5

Inlet Mach no. Ma1 [-] 0.42 0.34 0.40

Tot. pr. losses ζ/ζT150,Exp [-] 1.09 0.81 1.03

Exit flow angle β2 [°] 30.5 23.4 29.1

Ax. vel. dens. ratio AVDR [-] 1.02 1.04 1.04

Turbulence intensity Tu1 [%] 3.7 5.2 4.9

Experiments T150 T151 T152

Inlet flow angle β1 [°] 133.3 135.9 131.5

Inlet Mach no. Ma1 [-] 0.42 0.34 0.40

Tot. pr. losses ζ/ζT150,Exp [-] 1.00 0.68 0.90

Exit flow angle β2 [°] 32.7 25.0 30.5

Ax. vel. dens. ratio AVDR [-] 1.07 1.04 1.01

Turbulence intensity Tu1 [%] 3.0 1.5 2.0

Figure 4.14 Comparison of experiments and computations at reference operating

conditions (Ma2th=0.75; Re2th=1 200 000; β1=β1,Ref)

The results indicate that if the free stream turbulence intensity correction (FSTI)5 is not active,

the differences between the two-layer and the low-Reynolds formulation of the one equation

turbulence model are limited. The Menter formulation of the turbulence model destruction

term (Menter, 1994) in combination with a two-layer approach is indicated as

5 This correction was introduced by Eulitz to extend the original Spalart-Allmaras model for periodic-unsteady simulations (Eulitz, 2000).


SA2 noFSTI DM. The low Reynolds formulation of the model without FSTI-correction

(SAL noFSTI) features slightly lower losses than the other methods and was used within the

optimisation process.

Figure 4.15 Influence of the inlet turbulence intensity and turbulence model formulation on

the prediction of the total pressure losses

Figure 4.16 Influence of the inlet turbulence intensity on the location of transition for T150


Even if the predicted total pressure losses match the experimental data for an inlet turbulence

level of 1.5%, this value was not used for the computations. The inlet turbulence intensity,

Tu1, used for the computations was instead chosen in such a way that the predicted transition

zone matches as closely as possible the experiments. Whilst for T151 and T152 the location

of the transition can be seen well from the oil flow pictures, for T150 the oil flow pictures

performed at reference conditions do not provide useful information in this context.

Therefore, it was assumed that the transition start on the suction side has to be found at a

location around 20% axial chord, where the gradients of the profile velocity distribution for

T150 are strongly reduced and a velocity plateau appears. By varying the inlet turbulence

intensity, the highest value was determined for which the predicted transition start is located

at about 20% axial chord. Figure 4.16 displays the effect of the variation of the inlet

turbulence intensity onto the transition behaviour of the suction surface of the turbine cascade

T150. Therefore an inlet turbulence value of 3% was chosen for the following investigations.

In a similar fashion, using the information derived from the oil flow pictures (see Table 7.5),

an inlet turbulence value of 1.5% and 2.0% was chosen to match the suction surface transition

zones of T151 and T152 respectively. Recent investigations performed by Schwarze (2005)

on highly loaded low pressure turbine cascade blades using an extended version of the

standard k-ω two-equation model coupled with a modified version of the original Abu-

Ghannam and Shaw model (Abu-Ghannam et al., 1980), as implemented recently in TRACE

(Kožulovic et al., 2004), showed a strong reduction of the total pressure losses gap between

calculations and experiments. Thus, the prediction capabilities of the code implementing this

modelling approach should be investigated in more detail for the present class of profiles.

In order to assess the reliability of the code in predicting the exit flow angles the RANS solver

results were compared with standard correlations from the literature, even in presence of the

observed constant offset. In this context the sinus rule and a compressible correlation by

Traupel (1977) were analysed. The computed exit flow angles better match the values

calculated with the sinus rule than the measured angles. The exit flow angles resulting from

the application of the compressible exit flow angle correlation of Traupel (1977) for turbine

cascade blades, however, correspond better to the measured flow angles. This correlation is

derived from the application of the continuity and momentum law to the control volume

ABCDEFA specified in figure 3.16:

22 22 2 2

21 cos

tan 1 1cos(90 ) 2 cos(90 )

u

e e

e M W ββt β β

⎧ ⎫⎡ ⎤⎛ ⎞⎪ ⎪⎢ ⎥= ⋅ ⋅ − ⋅ −⎨ ⎬⎜ ⎟− −⎢ ⎥⎝ ⎠⎪ ⎪⎣ ⎦⎩ ⎭ (4.6)

where the angle (90 − βe) represents the tangent to the blade suction surface at the cascade

opening (point E). The product (Mu2·W2)2 corresponds to the ratio (w2)

2·ρ2/κ·p2. Figure 4.17

illustrates the behaviour of these different approaches for predicting the cascade deflection.

The results correspond to calculations at reference Reynolds number Re2th=1 200 000 and

reference incidence. They show the influence of the Mach number on the reliability of the


prediction method. The abscissa is the angle difference [(90 − βe) − βmet] and quantifies the

geometrical blade suction surface uncovered turning. The ordinates represent the angle

difference between the measured angle and the predicted exit flow angle. The triangles

correspond to the sinus rule, the squares to the Traupel correlation and the circles to the

TRACE calculations. Three exit Mach number were analysed. The symbols at the lowest

Mach number Ma2th=0.65 are grey, the symbols at the reference Mach number Ma2th=0.75 are

white and the symbols for the highest Mach number Ma2th=0.85 are black. The shift of the

symbols in the uncovered turning region of each cascade was introduced only for better

readability of the figure. First of all it can be observed that the Traupel correlation works well

at lower Mach number as long as the geometrical uncovered turning does not exceed a

particular value. The same applies thus for T150 and T152. In order to better interpret the

results for T151, it must be kept in mind that a major assumption of the Traupel correlation is

that the geometric deflection is limited in the rear part of the suction surface (see figure 3.16).

Moreover the exit flow angle predicted for T151 using the Traupel-correlation is the only one

to exceed the measured values, thus not being in line with the tendency featured by the other

two cascades. From these observations one would conclude that the Traupel correlation is no

longer applicable at the aerodynamic loading featured by T151. This is confirmed by

additional results obtained on the highly loaded high pressure turbine blade T120, which was

tested at the High Speed Cascade Wind Tunnel of the University of the German Armed

Forces as well. This turbine cascade features a somewhat higher aerodynamic loading than

T151 and about the same blade uncovered turning. The difference between the measured

angle for T120 and the angle predicted by the sinus rule is 2.5° and the difference obtained

using the Traupel correlation is 2.3° (Homeier, 2005). The fact that the sinus rule and the

Traupel correlation predict almost the same exit flow angle for this case, indicates that no

compressibility effect is introduced by the correlation, opposite to any physical expectation.

This points out the applicability limits of the Traupel approach. By increasing the Mach

number the accuracy of the correlation decreases, as to be expected, since the correlation is

designed for subsonic regimes. The distributions of the sinus-rule results are similar at

different Mach numbers, because this method does not account for compressibility effects.

Furthermore, it can be observed that by increasing the Mach number the sinus rule matches

the experimental results better. This is in line with the observations of chapter 3 (see

figure 3.17). However, the major result displayed in the figure is that for each Mach number

the scattering in y-direction of the exit flow angles predicted from the Navier-Stokes approach

(circles) is the smallest among the three prediction methods. Although an almost constant

offset between predictions and experiments exists. This lets one conclude that for this

application the RANS-approach is more reliable than the sinus rule or the Traupel correlation

and is therefore the most suitable method for the use as a prediction tool within the

optimisation process.


Figure 4.17 Behaviour of different prediction criteria for the cascade deflection at reference

Reynolds number and for different Mach numbers

4.4 Optimisation techniques

Exploratory techniques were coupled to the present aerodynamic design method as a driver

for the automatic search. This ensured the evaluation of designs in a wide design space in

search of the “global” optimum. The attention was focused on two exploratory techniques

implemented within iSIGHT: Multi-Island Genetic Algorithm (MIGA) and Adaptive

Simulated Annealing (ASA). The MIGA technique corresponds to an advanced version of

traditional genetic algorithm (GA) approaches while the ASA algorithm instead belongs to the

family of the simulated annealing techniques which are generic probabilistic heuristic

approaches to the global optimisation problem. The main advantage of both approaches is the

possibility to start an optimisation loop with a high chance of success avoiding extensive

preliminary sensitivity analysis associated with gradient based methods. Furthermore, both

MIGA and ASA techniques are well suited for solving highly non linear problems, like the

present one. This section gives a description of the major features of both techniques. The

reader is referred to the specific literature for a more detailed description of the optimisation

algorithms used.


4.4.1. Multi-Island-Genetic algorithm

The Multi-Island Genetic Algorithm is a modified version of traditional genetic algorithms.

GAs are a particular class of evolutionary algorithms and were first developed and applied by

Holland in the seventies (Holland, 1975). Today, various adaptations of the original

formulation are successfully applied for different classes of optimisation problems. A

description of the major features of standard GAs is found in De Falco (1997).

GAs are optimisation algorithms based on Darwinian models of natural selection and

evolution. The process starts from an initial population containing n randomly chosen

individuals. Each individual is described by a set of variables, which are each treated as a

vector of bits. This means a discretisation of the search domain for each variable

(De Falco, 1997). From the initial population a set of elite individuals is then chosen using an

appropriate selection procedure, based on the quality or fitness of the individuals. In fact each

design point is perceived as an individual with a specified fitness value. In this work, since the

objective function consists of a single value accounting also for the specified aerodynamic

constraints (e.g. cascade deflection), the fitness value is directly associated with the value of

the objective function. The selection procedure probabilistically selects an individual i

(featuring a fitness value fi) to remain in the population and reproduce with the probability

pi = fi/Σjn fj. In this way individuals featuring above average fitness values reproduce,

replacing poorly performing individuals. This reproduction scheme, however, does not forbid

any individual, even the worst in the current population, to be chosen, though this element

features a very low probability. Once the parents for the new generation are chosen, there are

different ways how to recombine the genes of these individuals to generate the offspring

individuals. A traditional recombination operator is represented by the one-point crossover

operator. In this case two parents are chosen randomly among the elite individuals selected

before. Indicating with l the number of bits contained in the generic individual, a crossover

position i between 1 and l is chosen randomly. Afterwards the parents exchange portions of

their binary representations. In this way the first child contains bits 1 through i from the first

parent and bits i+1 to l from the second parent. The second child, instead, contains bits 1

through i from the second parent and bits i+1 to l from the first parent. The process continues

until enough children are produced to replace the parent population. However, some parent

can be maintained in the offspring population. A further operator, called mutation operator, is

applied in order to maintain diversity and avoid that the process leads to stagnation. The

mutation operator changes randomly a bit in the bit’s string representation of an individual.

The described cycle (selection, reproduction and mutation) continues until the average

population fitness (defined as f* = Σjn fj / n) converges to a fixed stable point or until a

specified number of generations has been produced.

The major feature distinguishing a MIGA approach from a traditional GA is the fact that each

population of individuals is divided into sub-populations called islands. The usual genetic


operations (selection, reproduction and mutation) are performed separately on each island. A

further operation called “migration” is used to transfer some individuals from an island to

another one. The migration process is controlled by two major parameters which are the rate

of migration and the interval of migration. The rate of migration corresponds to the

percentage of individuals of each island which will be migrated to another island. The default

value of the iSIGHT version of the MIGA method 0.5 was maintained, corresponding to 50%

of the individuals contained in a sub-population. The interval of migration indicates the

number of generations between each migration process. The iSIGHT default value

corresponds to 5 generations and remained unchanged for the present investigations. Three

other major parameters control the optimisation process. These are the size of sub-populations

(fixed to a default value of 10), the number of islands (also fixed to a default value of 10) and

the number of generations. This parameter was increased to 50, so that 5000 evaluations of

the objective function are ensured. For the further tuning parameters of the present algorithm,

the default values specified within iSIGHT (Engineous Software, 2002) were used.

4.4.2. Adaptive Simulated Annealing

Adaptive Simulated Annealing algorithms (ASA) represent a probabilistic heuristic approach

to the global optimisation problem (Ingber, 1995). This technique is a modified version of the

Simulated Annealing (SA) algorithm, which was invented by Kirckpatrick et al. (1983).

Kirckpatrick generalised the Metropolis Monte Carlo integration algorithm

(Metropolis et al., 1953) in order to handle non-convex cost functions arising in a variety of

problems, e.g. finding the optimal wiring for a densely wired computer chip. One of the major

features of SA algorithms is represented by the possibility to investigate large parameter

search spaces, locating a good approximation of the global optimum of a given function.

The name and inspiration of this class of optimisation techniques derives from the analogy

with the metallurgical process of annealing. This procedure involves heating and controlled

cooling of a part in order to increase the size of its crystals and reduce their defects. The

process of heating causes the atoms to become unstuck from their initial positions (which

represent a local minimum of the internal energy) and randomly wander through states of

higher energy. The slow cooling process gives the material the possibility to find

configurations with lower internal energy than the initial one.

The principles used within the corresponding optimisation technique are similar. Each design

point has an internal energy, which corresponds to the value of the objective function. Thus

finding the global optimum means searching for points in the design space featuring minimal

values of the objective function. The algorithm starts from an arbitrary position within the

specified search space and chooses a certain number of neighbours of this start point. The

quality of each parameter dataset (design point) is determined evaluating the related value of

the objective function. During the search process the algorithm moves from a parameter


dataset to another with a certain probability. The transition probability depends on the energy

gap between the two points (difference of the related values of the objective function) and on

a further parameter, indicated as temperature T. The value of this parameter varies according a

specified rule during the optimisation process. This rule is indicated as the annealing schedule

and specifies the distribution of the temperature T in time. By time is meant the number of

iterations k.

A generic SA method consists of three functional relationships. Indicating the generic design

point as X=(x1, x2, …, xn), the first of these relationships g(X) represents the probability

density of state-space of the n parameters, also called the generating function. A major

property of any simulated annealing algorithm is represented by the statistical condition that

any point of the search space can be sampled infinitely often in the annealing time. This can

be achieved using only generating functions which respect following condition:

0

kk

g∞

= ∞∑ (4.7)

where k0 is a generic state in the annealing time (or generic iteration). The second relationship

identifying a simulated annealing method is represented by the probability density for

acceptance of a new state given a previous value. This function is indicated as h(X). A

possible form for the acceptance function h(X) can be as follows. If the energy difference

between two states ∆E assumes negative values, then the probability h(∆E) to move to the

new design point is 1. If ∆E is positive, the transition probability is e-∆E/T. This rule

corresponds to the Maxwell-Boltzmann distribution governing the distribution of molecular

energy. The third functional specifying the simulated annealing algorithm is the schedule of

annealing the temperature T in annealing-time steps k, indicated by the rule T(k). In fact, the

behaviour of the algorithm depends strongly on the parameter temperature T. High values of

this parameter correspond to a low sensitivity of the algorithm to energy differences, while

low temperatures allow a fine search to be performed. In fact, using the Maxwell-Boltzmann

form of the function h(X), it can be noted that in the extreme case of T = 0 the algorithm

enables only transitions to design points featuring lower energy than the actual one. If T is

infinitely, instead, the algorithm moves around in the search space randomly. The probability

that an SA algorithm finds the global optimum approaches unity as the velocity of the

algorithm cooling rate decreases. Faster cooling processes instead allow reduced code running

times.

One of the main features distinguishing an Adaptive Simulated Annealing algorithm from any

other SA method is represented by the possibility to consider differences in each parameter-

dimension, e.g. handle with different sensitivities of the parameters. In fact, different design

parameters have different finite ranges, fixed by physical considerations, and different

annealing-time-dependent sensitivities, quantified by the curvature of the objective function at

local minima. This feature is achieved by appropriately formulating the annealing schedule


Ti(k) of the single design parameters, as specified by Ingber (1995). Furthermore, another

adaptive property of the ASA method is represented by the re-annealing process. In fact,

every multi-dimensional search for a non-linear physical problem has inevitably to take into

account different changing sensitivities of the parameters during the search process. For the

ASA method at any annealing-time it is possible to enlarge the range over which the

relatively insensitive parameters are being searched, in dependence of the more sensitive

parameters. This is done by periodically rescaling the annealing time k, at some user-defined

number of accepted or generated states. This means re-annealing the various design

parameters, after increasing the temperature in an appropriate way. Particularly advantageous

is that both features do not imply any operational interaction of the user.

The present investigations were performed using the standard iSIGHT configuration of the

ASA algorithm (Engineous Software, 2002). Only the initial value of the parameter

temperature T0 and the relative rate of parameter annealing were changed. Preliminary

investigations showed, that a more exhaustive search for the present application is ensured by

increasing the initial value of the parameter temperature T to 10 and halving the parameter

which describes the velocity of the cooling process (relative rate of parameter annealing).

This operations, however, are associated with an increase of the execution time of the

algorithm.

4.5 Set up of the objective function and constraints

The design of the objective function F is a major task for the successful application of the

optimisation method. In order to reduce the computational efforts, a single-value objective

function approach was chosen (see section 2.4). This reduces greatly the code running time

but requires a higher knowledge of the significant variation gradients of the aerodynamic

parameters in order to tailor the related terms of the objective function and balance in this way

the weighting of the various goals. In extensive preliminary investigations different

mathematical formulations of the terms of F have been tested in order to determine the most

suitable form for this scope. One of the major challenges in tailoring the objective function

was represented by the strong diversities in the scales of the different aerodynamic

parameters. Nevertheless, an objective function structure was developed, which makes use of

a limited set of terms featuring similar characteristics and which can be easily represented in a

compact form.

The targets of the present aerodynamic optimisation can fundamentally be divided into two

categories. On the one hand, blade geometries are searched which feature low total pressure

losses at a fixed cascade deflection. On the other hand, the profile velocity distribution of

these blades has to satisfy the discussed aerodynamic requirements for an efficient cooling of

the blade. Transforming these aerodynamic requirements into objective function components

to be minimised (e.g. the fixed cascade deflection can be expressed as the difference between


the actual exit flow angle and the datum exit flow angle), a single-value minimisation

problem can be formulated. The objectives considered within the present work lead to an

objective function F featuring the following terms:

{ }{ }

is is is

ζ β

Ma MAX SS AMa MAX SS BD Diff DS LE Diff SS LE AMa INFL SS

F F F

F F F F F F− − − − − − − − − −

= + +

+ + + + + + (4.7)

The first two terms Fζ and Fβ consider respectively the total pressure losses and the cascade

deflection. The second bracket contains the terms associated with the evaluation of the profile

Mach number distribution. Thus the term FMais-MAX-SS limits the Mach number level on the

profile suction surface. It quantifies the difference between the peak Mach number on the

suction side and the reference Mach number, expressed as a function of the aerodynamic

loading. The term FAMais-MAX-SS quantifies the diffusion phenomena between consecutive local

maxima on the suction surface. This aspect is not necessarily evaluated as detrimental within

the optimisation process, as long as the diffusion zone does not alter the predicted boundary

layer development so much that the integral cascade aerodynamic performances are

significantly modified. This is confirmed by the results obtained by deactivating this term.

The results are illustrated in section 5.1.1 of the next chapter. In Figure 5.7 the local peak

Mach number featured in the front part of the suction side does not influence significantly the

boundary layer development and transition occurs relatively far downstream on the suction

surface. The objective function component FBD quantifies the adverse pressure gradient of the

back diffusion region on the suction surface. The terms FDiff-DS-LE and FDiff-SS-LE are associated

with local diffusion regions occurring in the front part of the profile pressure and suction

surface respectively (see equation 4.5 for the definition of the diffusion factors). The

component FAMais-INFL-SS has the role to quantify the smoothness of the acceleration on the

suction surface identifying eventual inflection points of the profile Mach number distribution.

This term has to be directly considered within the optimisation in analogy to FAMais-MAX-SS in

order to ensure a uniform acceleration on the entire profile suction surface.

The objective function F can be written in a more detailed form, developing the various

components:

( ){ }( ) ( )( ){

( ) ( ) ( )( ) ( )( )max - - ( ) - /

β2

Ma3

k Diff2

C

ζ β1 2 2,T150

C

Ma1 is is Ma2

f Diff k C kDiff1 Diff3

k

F C ζ C β β

C Ma MAX SS j Ma REF t l C

C k C k

⎡ ⎤= ⋅ + ⋅ − +⎣ ⎦

⎡ ⎤+ ⋅ − − +⎣ ⎦

⎫+ − ⎬

⎭∑

(4.8)

The whole set of constants C was tailored in such a way that the related terms of the objective

function F are negligible with respect to the total pressure losses as long as the respective

calculated parameter is within a specified tolerance region. Extensive first analyses showed


that a combination of polynomial and exponential functions is suited best to treat different

aerodynamic parameters in an appropriate fashion.

The weighting factor Cζ was introduced in order to compare the various terms of F with a

value accounting for the cascade losses which is well above zero. For the present

investigations the constant Cζ was set to 50.

In order to permit a tolerance region of ± 0.1° for the cascade deflection the constant Cβ1 was

set to 5 and a polynomial of 4th order was chosen for this term (Cβ2=4).

The reference Mach number Mais-REF was used to estimate the maximum Mach number

allowed on the profile suction side at a particular aerodynamic loading (pitch to chord

ratio t/l). The values of Mais-REF were obtained by interpolating the values of the reference

cascades T150 and T151 with a 3rd order polynomial. The value of the constant Mais-REF at

t/l = 0.732 was derived from T150 and set to 0.925. At t/l = 0.9572 Mais-REF assumed the

value 0.988, according to the peak suction side Mach number of turbine cascade T151. At

t/l = 0.89 and at t/l = 1.15 the values 0.953 and 1.17 were respectively used. The constant

CMa1 was set to 8, while the translation factor CMa2 was set to 0.08. The present term of the

objective function corresponds to a polynomial of 6th order (CMa3=6).

The last term of F contains the diffusion terms regarding the front part of the profile velocity

distribution on the pressure and the suction side (Diff-DS-LE and Diff-SS-LE). Furthermore,

this term contains the contributions associated with the area between the linear segments

connecting consecutive local maxima and isentropic Mach number curves (AMais-MAX-SS) as

well as the contribution related to the inflection points of the velocity distribution on the

suction side (AMais-INFL-SS). Preliminary investigations revealed that exponential functions

are best suited for taking into account both the diffusion terms and the mentioned areas within

the objective function. The index k distinguishes the various terms. The auxiliary function fk

used within the exponent of the first constant CDiff1(k) was introduced in order to control better

the behaviour of the related curve. The values of the constants CDiff,k and auxiliary functions fk

are listed in Table 4.2. Thereby the product Diff(k)·CDiff2,k is indicated as Exp(k). Using the

values of this table the term of the objective function related to the area between two local

consecutive maxima on the suction surface FAmais-MAX-SS assumes the following form:

( )- -

- - 1000 1000AMa MAX SSis

is

eAMa MAX SSF = − (4.9)

Such an exponential representation of this factor was introduced because the values of the

areas AMais-MAX-SS and AMais-INFL-SS become significant already at values which are an

order of magnitude lower than the values of the local diffusion factors Diff-DS-LE and Diff-

SS-LE.

Figure 4.18 shows a comparison of different exponential formulations used for the various

components of F. It can be observed that the function ( ) 1000 1000xeF x = − is particularly


appropriate for these terms since it assumes higher values than the other exponential functions

already at lower abscissa values. Furthermore the increase of the right branch of the curve

takes place under more moderate gradients than for the other functions. In fact, increasing the

exponent basis to 100, without introducing a control function fk (like for the function

F(x) = 10010·x), leads to strong gradients in a very restricted region. Thus the introduction of

an exponential formulation for fk makes sure that the associated function is still comparable

with the other terms of F, even at higher values of the contributions AMais-MAX-SS and

AMais-INFL-SS. This circumstance avoids an excessive increase of the objective function F,

when the related factor rises. This is of major importance considering that during the

optimisation process different zones of the definition space are scanned by the algorithm.

Therefore strong changes of the objective function occurring in a small zone of the parameter

space have to be avoided. This could in fact lead the algorithm to misleading interpretations

of the results, because geometries located very closely together in the search space assume

quite different values of F.

Table 4.2 Constants for the diffusion terms of the objective function

Diff(k) CDiff1,k CDiff2,k CDiff3,k fk

FDiff-SS-LE 10 10 1 −

FDiff-DS-LE 10 5 1 −

FAMais-MAX-SS 1000 1 1000 eExp(k)

FAMais-INFL-SS 1000 1 1000 eExp(k)

FBD 10 0.1 1 −

An example quantifying the different parameters used for building the objective function F

testifies the suitability of the proposed functions. Figure 4.19 illustrates the isentropic Mach

number distributions on the datum profile T150 and on the optimised profile ASAT151. The

zones of curvature change on the suction surface, individuated during the evaluation process,

are represented by thicker curve segments. The sum of the areas between the linear segments

connecting the inflection points and the profile Mach number distribution corresponds to the

parameter AMais-INFL-SS. The various aerodynamic parameters and the related values of the

single objective function components are listed in Table 4.3. The integral total pressure losses

are related to the integral experimental data of T150. During the optimisation process,

however, the absolute value of the total pressure losses is used. This example underlines the

potential of the proposed functions for suppressing the diffusion factor in the front part of the

pressure surface and the area between consecutive inflection points during the optimisation

process. The design method is able to reduce the component FAMais-INFL-SS by an order of

magnitude leading to values comparable to the integral total pressure losses. The local

diffusion phenomena in the front part of the profile Mach number distribution are completely

suppressed.


The results presented in this work were obtained using a reduced set of 15 parameters to

describe the blade profile. More level of detail was use in the representation of the suction

surface, where 8 parameters were employed (k1, ρ1v, σ1v, w2, k2, ρ2r, σ2r and γH). On the

pressure side instead only 4 parameters (w3, k3, r3v and r4r) plus one additional common

parameter γH were used. A set of 3 parameters (αN, αH and βSG) completes the profile

description. Extensive investigations showed that the only way to suppress the separation

bubble in the front part of the pressure surface realizing at the same time a uniform

acceleration over the front suction side is an asymmetrical representation of the leading edge,

using the angles w2, and w3 (see chapter 5). In contrast, the profile trailing edge remained

symmetrical. For each parameter an initial variation range was fixed with respect to the

parameters of the datum profile T150. Then the parameter range was adjusted according to the

distribution of each parameter within the prescribed limits. In fact, if the parameter

distribution resulting from preliminary tests became denser around a border of the prescribed

parameter range this range was appropriately enlarged. Further preliminary studies using 3

additional parameters (σ3v, k4 and σ4r) for the complete description of the pressure side spline

did not show any kind of improvement with respect to the results presented in the next

section. However, the increase of the number of parameters to 18 was associated with a

noticeable rise of the computational efforts (about 1.5 days to convergence instead of 1 day).

In order to restrict the search to a sub domain of realistic geometries within the parameter

definition range some geometrical and mechanical constraints were specified. An admissible

range between –10 and +20% of the datum profile T150 was fixed for the blade sectional

area. Variations of the moments of inertia between –10 and +40% of the reference values for

cascade T150 were allowed.


Figure 4.18 Comparison of different exponential functions used for the objective function F

Figure 4.19 Zones of change of curvature on the suction surface of the reference profile

T150 and the optimised profile ASAT151


Table 4.3 Aerodynamic parameters and relative components of the objective function F

for turbine cascade blades T150 and ASAT151

Turbine Cascade Blade T150

ζAdim β2 Mais-MAX-SS Diff-SS-LE Diff-DS-LE AMais-MAX-SS AMais-INFL-SS BD

1.09 30.45 0.925 0.01 0.26 0.0 0.002 0.24

Fζ Fβ2 FMais-MAX-SS FDiff-SS-LE FDiff-DS-LE FAMais-MAX-SS FAMais-INFL-SS FBD

<2.0 0.0 0.0 0.26 18.95 0.0 13.91 0.06

Turbine Cascade Blade ASAT151

ζAdim β2 Mais-MAX-SS Diff-SS-LE Diff-DS-LE AMais-MAX-SS AMais-INFL-SS BD

0.84 30.41 0.998 0.0 0.0 0.0 0.0002 0.33

Fζ Fβ2 FMais-MAX-SS FDiff-SS-LE FDiff-DS-LE FAMais-MAX-SS FAMais-INFL-SS FBD

<2.0 0.02 0.14 0.0 0.0 0.0 1.38 0.08

5. Results and discussion 93

5. Results and discussion

The present section contains the results obtained applying the automatic design procedure at

different aerodynamic loadings. The investigations were run fixing the cascade deflection to

the value of the datum profile T150 and optimising the profile shape for various blade

spacings. The main target of the optimisation process was the reduction of the cascade total

pressure losses considering the discussed requirements on the profile velocity distribution for

an efficient cooling of the blade. The search space was restricted constraining the profile area

and section modulus according to the indications given at the end of the previous section. The

present investigations were performed using a set of 15 parameters for the description of the

blade geometry within the geometry generator PROGEN. The form of the objective function

F and the parameters used are described in the previous chapter as well. The trailing edge

thickness to pitch ratio and the axial chord were fixed at the values of the datum profile T150.

The influence of the trailing edge thickness on the cascade aerodynamic behaviour was

quantified by performing additional investigations presented at the end of this chapter.

Figure 5.1 shows typical convergence behaviour obtained during an optimisation run carried

out using an adaptive simulated annealing algorithm (ASA). The diagram shows that the

optimisation process converges after about 600 evaluations of the objective function F. This

corresponds to a reduction of the objective function of about 98% with respect to the

reference starting value and to a real computational time of about 24 hours on two SGI MIPS-

RISC 14000 processors of the SGI Origin 3800 system6. Preliminary investigations indicated

that an increase of the parameter temperature T and a reduction of the parameter describing

the cooling time with respect to the standard iSIGHT settings of ASA leads to improved

performance of the algorithm for the present application. The diagram refers to investigations

performed with a temperature parameter value of 10 and a halved cooling time parameter with

respect to the iSIGHT standard settings for the algorithm. The diagram shows that the

modified settings ensure that the algorithm still has sufficient energy to explore completely

different regions of the search space even after convergence has been reached. This is

expressed by the high values assumed by the objective function F even after convergence.

The convergence behaviour obtained using a multi island genetic algorithm (MIGA) is

illustrated in Figure 5.2. The investigations were performed using the iSIGHT standard

settings of the algorithm. A comparison with the convergence behaviour of ASA shows the

superiority of a simulated annealing approach for the present application.

6 The reference value of the objective function corresponds to the value assumed by F for the reference geometry used at the particular blade spacing at which the procedure is run (e.g. at the blade spacing of T151, the reference geometry corresponds to T150B−see section 5.1.1)

94 5. Results and discussion

Figure 5.1 Typical convergence behaviour for the design procedure in combination with

an adaptive simulated annealing algorithm

Figure 5.2 Typical convergence behaviour for the design procedure in combination with a

multi island genetic algorithm


In fact, at about 5000 evaluations the MIGA results feature a significantly reduced but still

high value of the objective function F, indicating that the optimisation process has not yet

converged. Furthermore the distribution of the individuals in Figure 5.2 reveals the formation

of subpopulation clusters presenting similar values of the objective function.

5.1 Validation of the procedure at different aerodynamic loadings

The reliability of the method is demonstrated at variable aerodynamic loading, comparing the

optimisation results with the experimental and computational data of the reference cascades.

The results obtained from these investigations are illustrated in Figure 5.3. This diagram

shows the computed and measured integral total pressure losses versus the aerodynamic lift

coefficient. Thereby the results of the design method are compared with the reference data

obtained on cascade T150 and T151. Since the aerodynamic loading level of the profile T152

is about the same as for the datum blade T150, the data of T152 are not shown here for

clarity. The integral total pressure losses are referred to the experimental results obtained on

the datum profile T150 at reference operating conditions (Re2th=1 200 000, Ma2th=0.75,

β1=β1,T150). The triangles represent the TRACE computations, while the squares correspond to

the experimental results.

Figure 5.3 Predicted total pressure losses and comparison with the values of the reference

cascades T150 and T151

The results of the optimisation method are represented by circles. The aerodynamic loading

was modified by changing the pitch to chord ratio. The operating conditions were fixed at the


reference conditions of the datum profile, maintaining the cascade deflection featured by

T150 at the reference operating point. The trailing edge thickness and the axial chord were

fixed at the values of the datum profile T150. The optimisation data presented in the figure

were obtained by running the design method at an inlet turbulence intensity Tu1 of 3%. The

results shown in the diagram are summarised in Table 7.6 (see Appendix).

The comparison of the experimental and the numerical results of the reference profiles reveals

the discrepancies already discussed in chapter 4. While the difference in vertical direction can

be directly attributed to the over-prediction of the total pressure losses, the discrepancy in the

horizontal direction can be mainly associated with the difference between the predicted and

the measured exit flow angle, since this is directly used for the determination of the lift

coefficient CL (equation 3.1). Nevertheless both the discrepancies in the total pressure losses

and exit flow angles remain nearly constant for all the reference profiles T150, T151 and

T152, independent of the aerodynamic loading, as observed in the previous chapter.

Furthermore this difference remains approximately constant over a wide operating range for

each reference blade geometry. This leads to the conclusion that the computational results on

the three reference turbine cascades represent a reliable reference for the assessment of the

capabilities of the design method.

The optimisation results indicate the high potential of the method in reducing the total

pressure losses at increased aerodynamic loading. Furthermore, it can be observed that at the

examined reference Reynolds number Re2th=1 200 000, the expected increase of the right

branch of the curve could not be detected. This indicates that even at very high lift

coefficients (point 4 in the plot), the method locates blade geometries, which avoid separation

phenomena. The direct comparison of the optimisation results and the reference data shows a

slight reduction of the total pressure losses at the spacing of the datum profile T150 (point 1

in the diagram, further on indicated as ASAT150). The results obtained at the pitch ratio of

turbine blade T151 (point 3, ASAT151) feature slightly higher losses than T151. In this case,

however, a comparison can only be performed considering that the optimised blade geometry

ASAT151 features the same trailing edge ratio as T150, which is higher than the one of T151.

In order to quantify the influence of the trailing edge thickness on the cascade total pressure

losses, additional investigations were performed. These were carried out on an auxiliary blade

geometry obtained from T150 by reducing the trailing edge thickness to the value of T151.

The resulting blade geometry, called T150HK, was re-staggered in order to perform the

comparison at an unchanged cascade deflection. These investigations showed that the

reduction of the total pressure losses between cascade T150 and T151 (indicated by the

segment AC in the diagram) is attributable by 50% to the reduced trailing edge thickness

featured by T151 (segment AB), while the remaining 50% originates from the reduced wetted

surface (segment BC). The results of these investigations are discussed in more detail at the


end of this chapter. These considerations point out clearly the high potential of the developed

method for the reduction of the total pressure losses at high aerodynamic loading.

5.1.1. Results at the spacing of turbine cascade blade T151

Firstly the results of the automatic procedure for the re-design of cascade T150 at the blade

spacing of T151 are presented. The profile Mach number distribution obtained in this case is

compared with the reference distributions in Figure 5.4. The velocity distribution on ASAT151

is represented by the continuous line, the Mach number distribution on the turbine cascade

blade T151 is represented by the dashed line and the dash-dotted line corresponds to the

datum profile T150. The results on an additional reference profile called T150B correspond to

the dash-dotted-dotted line. This profile was obtained from T150 by reducing the blade

stagger angle and the exit blade metal angle in order to ensure the same deflection as T150 at

the pitch ratio of T151. Turbine cascade T151 features ten degrees higher deflection than

cascade T150B, but somewhat lower mass flow capacity. Nevertheless its profile velocity

distribution features smooth acceleration both on the suction and on the pressure surface and a

comparison with the optimisation results is useful to assess the efficiency of the present

method. The comparison shown in Figure 5.4 indicates that the optimisation procedure is able

to locate blade geometries featuring smooth profile Mach number distributions and at the

same time reduced total pressure losses. The optimised geometries respect the specified

geometric and mechanic requirements and ensure the required cascade deflection.

The profile Mach number distribution on turbine cascade ASAT151 fulfils the specified

aerodynamic requirements for an optimal cooling of the blade profile. This demonstrates the

capabilities of the method and the successful design of the objective function for this

application. The flow accelerates smoothly under quite high gradients in the front part of the

blade suction side. This region is followed by a second acceleration area with moderate

gradients which terminates at the suction side peak Mach number. The maximal suction side

Mach number is located slightly below 1.0, as prescribed in appropriate form within the

objective function. Geometries featuring supersonic flow regions on the suction surface, like

the reference profile T150B, are excluded during the optimisation process. The flow on the

pressure side accelerates smoothly over the entire profile featuring stronger gradients in the

rear part of the blade, where a relaminarisation region is predicted. The short separation

bubble featured by the datum profile T150 in the leading edge region on the pressure surface

is no longer present on ASAT151, indicating that the method is able to identify and suppress

this feature. The results of preliminary investigations, performed at the present blade spacing

and presented in this section as well, indicate that the separation bubble in this area and the

local diffusion phenomena in the front part of the suction surface can be suppressed only

using an asymmetric representation of the blade leading edge.


Figure 5.4 Optimisation results at the blade spacing of turbine cascade T150

Figure 5.5 Comparison of the optimised blade ASAT151 with the profiles T150 and T151


Figure 5.5 shows a comparison of the optimised blade geometry ASAT151 and of the datum

profile T150. The geometry T151 is shown for comparison as well, even though the

geometrical and mechanical constraints in this case differ strongly from the conditions of

T150, used as a reference for the optimisation. The optimised blade ASAT151 is represented by

a continuous line, while the datum profile T150 corresponds to the dash-dotted line. The

zoom of the leading edge region reveals the asymmetry of the optimised blade shape in this

region. Moreover, the detail of the rear part of the blade shows that the new design features an

area distribution fulfilling the requirements for the placement of the necessary internal cooling

air channels. This is associated with large wedge angles at the trailing edge (higher than 4

degrees). A further increase of the aerodynamic loading leads to blade geometries, whose

curvature in the rear part of the suction surface can not be further increased because of

undesired flow over-expansions. This produces the generation of blade geometries with low

profile wedge angles at the trailing edge (see section 5.1.3). Using the tangent angles, wi, at

the blade control points 2 and 3 (see section 4.1) instead of a single wedge angle, γ, at the

leading edge ensures that the form of the suction side spline is decoupled from the form on

the pressure surface. A comparison of the present results with the results obtained using a

symmetric leading edge (presented at the end of this section) indicates that the asymmetric

leading edge approach provides better conditions for an optimal distribution of the blade

curvature over the entire suction surface. In addition the suppression of local diffusion zones

in the front part of the suction and the pressure surface becomes possible. In order to obtain a

smooth acceleration in the front part of the suction surface the related spline segment features

high values of the tangent angle, w2. The suppression of local diffusion zones in the front part

of the pressure surface is achieved in combination with nearly horizontal tangents at the blade

control point 3 (corresponding to w3 values of almost 90 degrees). The increase of the overall

thickness of the profile has to be carefully limited. In fact, an increase of the blade thickness

is associated with higher internal cooling air mass flow and complexity of the internal cooling

channels with a consequent increase of the casting costs.

In the following the calculated boundary layer development on the optimised blade ASAT151

is compared with the reference data on T150 and T150B. The upper diagram in Figure 5.6

illustrates the calculated distribution of the wall shear stress Cf. The distribution of the form

factor H12 on the suction and the pressure surface of the optimised blade geometry ASAT151

and of the reference blades T150 and T150B is shown in the central and the lower diagram of

the same figure. The bars shown in the form factor diagrams indicate the extension of the

transition zones. The results show that, in spite of the increased aerodynamic loading, the

transition location on the suction side of ASAT151 is placed approximately at the same position

as for the datum profile T150. The distribution of the wall shear stress in the front part on the

suction side of ASAT151 is somewhat higher than for the two other cascades. This is in

accordance with the increased loading of the front part of the suction side of the optimised

profile ASAT151.


Figure 5.6 Boundary layer development on the optimised and the reference blade profiles

(the bars indicate the transition regions)


In the rear part of the suction side, where a full turbulent boundary layer exists, ASAT151

features lower wall shear stress values than T150 or T150B. For the cascade blade T150B the

wall shear stress increase in the rear suction side region is related to the shock occurring in

this region. For all the examined profiles the code predicts a relaminarisation in the rear part

of the pressure side. This is associated with the high acceleration gradients featured by the

profile Mach number distributions in this region and is indicated by the strong increase of the

form factor. For cascade T150, the short separation bubble featured in the front part of the

pressure side causes the turbulent boundary layer to develop further upstream than for the

other two cascades, as shown by the bars in the diagram at the bottom of Figure 5.6.

Extensive preliminary investigations were performed at this blade to pitch ratio in order to test

different formulations of the objective function F. These calculations were performed at a

lower inlet turbulence intensity Tu1 = 1.5%. The weighting coefficient for the total pressure

losses in the objective function was reduced from 50 to 1 in order to limit the weight of the

total pressure losses on the optimisation results. This gave the possibility to investigate in

more detail the behaviour of the other terms related to cascade deflection and profile Mach

number distribution.

Figure 5.7 presents the geometries and the related velocity distributions resulting from the

application of different formulations of the objective function, F. The blade geometries

ASAT151-A, ASAT151-B and ASAT151-C are obtained from preliminary investigations carried out

at reduced inlet turbulence level (Tu1 = 1.5%), while the geometry ASAT151 is the optimised

blade, whose features have already been presented in the first part of this section. While for

the description of the blade nose of the profile ASAT151 an asymmetrical approach was used,

the other cascades feature symmetrical leading edges. The relative total pressure losses and

exit flow angles for these blade geometries are shown in the figure as well. The bars represent

the extension of the computed transition zones on the blade suction surface. The total pressure

losses for profile ASAT151-A are slightly lower than for ASAT151-B and ASAT151-C. The increase

of the inlet turbulence level for ASAT151 moves the transition zone towards the leading edge,

with a related increase of the total pressure losses. The optimised blade ASAT151 is the result

of investigations performed using an objective function like in equation 4.7 and repeated here:

{ }{ }

is is is

ζ β

Ma MAX SS AMa MAX SS BD Diff DS LE Diff SS LE AMa INFL SS

F F F

F F F F F F− − − − − − − − − −

= + +

+ + + + + + (5.1)

where the structure and significance of the single components is described in detail in

section 4.5. Instead, the geometry ASAT151-A is the result of an optimisation carried out using

a simplified form of the objective function, which takes into account only the integral total

pressure losses, the cascade deflection and the maximal Mach number on the suction surface.

This is expressed in the form:

- -isβ Ma MAX SSF ζ F F= + + (5.2)


where, as already mentioned, the component accounting for the total pressure losses is

expressed as the integral value of the total pressure losses and FMais-MAX-SS is the linear

function (Mais-MAX-SS − 1.0) / 10.0. This term is activated only if on the suction surface the

maximal Mach number is greater than 1.0. Furthermore the term Fβ remains unchanged with

respect to the form used for ASAT151 (see section 4.5).

Figure 5.7 Optimisation results for different formulations of the objective function F

The objective function used for the investigations relative to the optimised blade geometry

ASAT151-B has the form:

- - - -is isβ Ma MAX SS AMa MAX SS BDF ζ F F F F= + + + + (5.3)


Thus no information about local diffusion phenomena in the front part of the pressure and the

suction surface is considered in this case. Furthermore, the component accounting for the area

among inflection points on the profile velocity distribution FAMais-INFL-SS is excluded as well.

The objective function used for cascade ASAT151-C features all the terms contained in the

objective function of ASAT151 with the exception of FDiff-SS-LE and FAMais-INFL-SS. Moreover, the

total pressure losses are expressed without using any weighting factor:

- - - - - -is isβ Ma MAX SS AMa MAX SS BD Diff DS LEF ζ F F F F F= + + + + + (5.4)

The profile Mach number distribution featured by ASAT151-A reveals clearly that a linear form

for the term taking into account the Mach number level in the objective function is not a

suitable approach to avoid supersonic regions on the blade profile. For this term a polynomial

of higher order was therefore proposed (see section 4.5) and applied for generating the other

cascades presented in this section. Moreover, as long as the suction peak in the front part of

the suction side is not strong enough to generate turbulent boundary layers or the following

acceleration region leads to a process of boundary layer relaminarisation, the local region is

not negatively rated within the optimisation loop. This circumstance is clearly shown from the

results on cascades ASAT151-A, ASAT151-B and ASAT151-C, where the solver predicts a

relaminarisation in the acceleration region following the local suction peak on the front part of

the suction surface. Therefore, the objective function F used to obtain ASAT151 was provided

with a supplementary term for the quantification of local diffusion phenomena in the front

part of the suction surface, since these phenomena are not advantageous for an efficient action

of the shower head cooling in this area.

Even if the presence of local diffusion zones leads to earlier transition of the boundary layer,

the influence of the pressure side boundary layer on the integral value of the total pressure

losses is moderate. Therefore the introduction of an additional term in the objective function

F accounting for the diffusion in the front part of the pressure surface is necessary to control

the formation of suction peaks in this area. This is confirmed by a comparison of the forms of

the profile velocity distribution of ASAT151-C and ASAT151 (both featuring the objective

function term FDiff-DS-LE) with those of turbine cascade blades ASAT151-A and ASAT151-B.

Furthermore an accurate analysis of the velocity distribution on ASAT151-C in the front part of

the pressure side reveals that the flow does not accelerate as smoothly as at the same location

on ASAT151. This leads to the conclusion that only the combination of an asymmetrical

representation of the leading edge with this additional term of the objective function ensures

optimal conditions for finding profiles like ASAT151 featuring smooth acceleration in the front

part of the pressure surface.

Another additional feature of the objective function applied for cascade ASAT151 is

represented by the term FAMais-INFL-SS. This term ensures a smoother acceleration on the suction

surface by penalising the regions between local inflection points in an appropriate way. The


successful realisation of the scope of this additional term is demonstrated by the acceleration

behaviour in the front part of the suction surface on ASAT151.

The present results show that at convergence, independent of the specific form of the profile

Mach number distribution, the method is able to produce geometries featuring an almost

constant level of losses and quite similar cascade deflections. The total pressure losses are

considerably reduced if compared with the reference geometries, both using relatively simple

objective functions like for ASAT151-A and more complex formulations of F like for ASAT151-C

or ASAT151. In particular a comparison of the integral aerodynamic performance parameters

for the cascades ASAT151-A, ASAT151-B and ASAT151-C shows that the modifications of the

objective function concerning the requirements on the profile velocity distribution for an

efficient cooling do not influence the optimisation in terms of overall aerodynamic cascade

performance.

5.1.2. Results at the spacing of turbine cascade blade T150

Further investigations were carried out at the blade spacing of the datum turbine cascade

blade T150. Thereby the structure of the objective function and the blade parameters were

derived from the investigations performed at the pitch to chord ratio of turbine blade cascade

T151. Using the results obtained at increased aerodynamic loading, an asymmetrical leading

edge representation was used. Furthermore, the objective function was provided with an

additional term accounting for the axial position of the maximal Mach number on the suction

surface with respect to the location of the throat of the turbine cascade passage:

- - - - - - - -

- -

is is

is

ζ β Ma MAX SS AMa MAX SS BD Diff DS LE Diff SS LE

AMa INFL SS Xe

F F F F F F F F

F F

= + + + + + + +

+ + (5.5)

The importance of this additional term in fulfilling of the requirements regarding the form of

the profile Mach number distribution is discussed in the present section. The results obtained

using this additional term in F are compared with the results derived from an objective

function without this additional component. The profile Mach number distribution of the

optimised profile ASAT150 is compared with the velocity distribution of the reference cascades

T150 and T152 in Figure 5.8. This figure shows that the present design method ensures

smooth acceleration on the suction side and is able to suppress the short separation bubble

featured at the front part of the pressure surface by T150 even at reduced aerodynamic

loading. Furthermore, the maximal Mach number featured by ASAT150 on the suction side is

lower than the suction side peak Mach number on the reference cascades. The deceleration

taking place in the rear part of the suction surface of ASAT150 occurs under moderate

gradients, as well. The reduction of the maximal Mach number on the suction surface depends

greatly on the formulation of the related term of the objective function FMais-MAX-SS. In fact,

preliminary investigations performed using a more aggressive formulation of the term

limiting the peak Mach number on the suction surface showed that a further reduction of the


Mach number level is possible. The figure illustrates that the Mach number distribution on the

pressure surface of profile T152 is smoother than for the other two cascades. Since the present

investigations were carried out using a set of only three parameters for the description of the

pressure side spline segment, the necessary parameters for the representation of this part of

the blade should be investigated in more detail in order to produce smoother velocity

distributions on the pressure surface.

Figure 5.8 Optimisation results at the blade spacing of turbine cascade T150

Figure 5.9 Comparison of the optimised blade ASAT150 with the profiles T150 and T152


A comparison of the optimised profile geometry ASAT150 and of the reference geometries

T150 and T152 is shown in Figure 5.9. The turbine cascade blade T152 features a lower

stagger angle than T150 or ASAT150. This is necessary in order to ensure the prescribed

deflection (almost the same as for T150) in spite of the increased throat opening associated

with the reduced trailing edge thickness of T152. The enlargement of the leading edge region

shown on the left hand side of the figure illustrates the asymmetrical form of the blade nose of

ASAT150. This ensures the suppression of local diffusion phenomena in this area. The area

distribution in the rear part of the blade ensures the placement of the necessary cooling ducts.

Figure 5.10 Optimisation results for different formulations of the objective function F


Figure 5.10 displays the results obtained applying the optimisation method at the pitch to

chord ratio of turbine cascade blade T150. Different formulations of the objective function, F,

were used. The results indicate that the introduction of ad hoc tailored terms in the objective

function ensures a successful control of the lift distribution over the blade surface. The bars

represent the extension of the transition zones on the suction side. The blade geometry

MIGAT150 is the result of the investigations carried out with a multi island genetic algorithm

at the given aerodynamic loading. In this case, even if F is reduced significantly, no full

convergence was reached after about 5000 evaluations, corresponding to a real time of more

than 8 days. This is a quite large time compared with a usual running time (about 24 hours)

for the investigations carried out with an adaptive simulated annealing algorithm. The

comparison of the profile velocity distributions confirms that the ASA approach presents the

most advantageous characteristics for this kind of application. The integral results show that

also at this aerodynamic loading the method is able to reduce the cascade total pressure losses

maintaining the prescribed deflection.

The effects of different formulations of the components of the objective function related to the

Mach number distribution are presented in the following. The turbine cascade ASAT150-A is

obtained using an objective function with the same structure as the one used for cascade

ASAT151 (equation 5.1). However, the term related to the peak Mach number on the suction

side, FMais-MAX-SS, is modified, as described in section 4.5, in order to take into account the

reduced aerodynamic loading and consequently reduced peak Mach numbers. The profile

Mach number distribution on ASAT150-A is more front loaded than the other configurations

and the peak Mach number is located upstream of the cascade passage throat. Even if the lift

distribution on ASAT150-A is more in front loaded than the others, the transition zone is placed

further axially downstream compared to the other configurations. This can be explained

considering that at the present free stream turbulence level (Tu1 = 3.0%) the transition region

is located in the front part of the profile, at a position where visible changes of the

acceleration gradients occur. The flow follows the profile in this zone smoothly to a slightly

greater extent on ASAT150-A than on the other blades. Furthermore, it has to be considered that

an eventual further acceleration taking place on ASAT150-A downstream of 40% axial chord is

limited by the term of the objective function controlling the peak Mach number on the suction

surface. The maximum admissible Mach number is already achieved at 40% axial chord.

Even if for ASAT150-A the acceleration in the front part of the profile suction side and on the

whole profile pressure side is smooth, it has to be considered that due to the limited

knowledge of the efficiency of film cooling on rotor blades in presence of such profile

distributions (see section 2.2), it is common for these applications to place the maximal

suction side Mach number in the vicinity of the passage throat. Considering this aspect and

since one of the major drivers of the present method is its applicability as a reliable tool

within industrial blade design procedures, an additional term for generating aft-loaded profiles

was integrated within the objective function. This term limits the movement of the suction


side peak Mach number upstream of the blade throat. After extensive preliminary tests the

following polynomial formulation could lead to the most suitable performance:

( ){ } 3

1 2( - - ) ( )XeC

Xe is Xe XeF x Ma MAX SS x Throat C C= ⎡ − − ⎤ ⋅⎣ ⎦ (5.6)

An appropriate choice of the coefficients ensures that if the position of the velocity maximum

on the suction surface is located downstream of the passage throat, the term FXe becomes

negligible. The blade geometry ASAT150 results from the application of the same objective

function as ASAT150-A but with the additional term FXe as specified in equation 5.6. The

turbine blade ASAT150-B is obtained using the same objective function as for ASAT150 but with

modified coefficients for FXe in order to enlarge the tolerated zone downstream of the cascade

passage throat. The coefficients used for ASAT150 are CXe1=0.12, CXe2=6.0 and CXe3=14.

Instead for ASAT150-B the admissible range was enlarged by reducing CXe1 to 0.08. The

resulting velocity distributions on cascade ASAT150 and ASAT150-B show that this approach

permits the integration of further lift distribution rules within the optimisation process.

5.1.3. Optimisation results at varied blade spacing

The results obtained at the pitch to chord ratio of turbine cascade blades T150 and T151

indicate that the aerodynamic design method generates blade geometries featuring reduced

total pressure losses by respecting the prescribed cascade deflection. The additional terms of

the objective function, introduced for controlling the velocity distribution on the blade profile,

do not alter significantly the minimal level of losses obtainable using the optimisation

method. The present section illustrates the additional results of the optimisation method at two

further blade loadings, indicated in Figure 5.3 as turbine cascade blades 2 and 4. The present

investigations were carried out in order to ascertain the minimal level of losses obtainable

applying the present aerodynamic design method at different lift coefficients.

Figure 5.11 illustrates the velocity distributions and integral cascade performances for the

profiles obtained from the optimisation process. The results obtained at t/l = 0.89 and at

t/l = 1.15 are illustrated respectively on the left and on the right hand side of the figure. Whilst

the investigations performed at t/l = 0.89 were carried out using the same structure of the

objective function and the same parametrical description of the blade as for ASAT151, the

results at t/l = 1.15 were obtained using the same structure of the objective function, F, and

the same parametrical description of the blade (symmetrical leading edge) used for ASAT151-C.

The term of the objective function, FMais-MAX-SS, introduced for controlling the maximal Mach

number on the suction surface is modified according to the different loading levels (see

section 4.5). As shown in Figure 5.11, the blade geometry ASA2 features an asymmetrical

blade nose while ASA4 presents a symmetrical leading edge. The considerations outlined in

section 5.1.1 about the advantages of an asymmetrical description of the blade leading edge

are underlined again comparing the velocity distributions on the present profiles.


Figure 5.11 Optimisation results at further blade spacing (left: t/l = 0.89; right: t/l = 1.15)

5.1.4. Modification of the geometrical and mechanical constraints

Additional investigations were carried out at the pitch to chord ratio of the datum profile T150

modifying the geometrical and mechanical constraints which the blade profiles have to

respect. In fact, as already mentioned in the previous sections, the introduction of an

asymmetrical representation of the blade leading edge decouples the suction side from the

pressure side, leading to a class of optimised profiles with high blade section areas.

Figure 5.12 shows a typical distribution of the section area resulting from an optimisation run

performed using an asymmetrical description of the blade leading edge. The diagram shows

that after a limited number of evaluations, the optimisation procedure generates geometries

which all feature high blade section areas, being located on the upper limit for the relative

area (20% higher than the area for T150). The increase of the blade section area is associated

with an increased demand of internal cooling air mass flow and eventually with a new and

more complex design of the internal cooling channels, which may have important

consequences regarding the blade casting costs. In particular the results presented in the figure

refer to an optimisation carried out at the pitch to chord ratio of the datum profile T150. It is

indeed at low pitch ratio where the present circumstance assumes particular relevance. In fact,

at high blade spacing the increase of the necessary cooling air per pitch is associated with

higher blade section areas. At the same time however, high blade spacing means an overall

reduction of the number of blades with a related reduction of the manufacturing costs.

Therefore if the optimisation method leads to high blade section areas already at a low blade

spacing (where no counterbalancing advantage deriving from a reduced number of parts is


present) it is necessary to assess the capability of the design procedure by searching for

optimised blade profiles in a new range of reduced section areas at a lower blade spacing.

Figure 5.12 Relative profile area distribution for asymmetrical leading edge description

With this in mind, investigations were carried out using the same settings used for ASAT150

and reducing the range of admissible blade section areas from 0.90 ≤ Area/AreaT150 ≤ 1.20 to

0.70 ≤ Area/AreaT150 ≤ 0.90. The constraints on the section modula were adjusted

accordingly. In order to reduce the blade section area in such a way, the blade nose thickness

was reduced by one third. Thus within the present investigations blade geometries are

obtained, which no longer feature thick blade noses typical of high pressure turbine profiles.

However, the aim of the present investigations is the assessment of the behaviour and

reliability of the numerical design method at changed geometrical and mechanical conditions

and this aspect is thus not irrelevant in this context.

Figure 5.13 shows the optimisation results at the modified geometrical and mechanical

boundary conditions. The resulting geometry is indicated in the figure with ASAT150-C. The

dash-dotted line represents the velocity distribution on the datum profile T150. The results of

the present investigations indicate that even at modified geometrical and mechanical

constraints the method produces blade geometries leading to low losses and presenting the

prescribed aerodynamic features concerning velocity distribution and cascade deflection. The

bar indicates the location of the predicted transition zone on the suction surface of the profile

ASAT150-C. This zone is shifted slightly downstream with respect to ASAT150 and is associated

with a reduction of the level of the total pressure losses.


Figure 5.13 Optimisation results at modified boundary conditions

5.2 Influence of the trailing edge on the aerodynamic behaviour

The trailing edge thickness represents a major factor for the assessment of the optimised

turbine profiles. The reference cascade blades T151 and T152 feature a reduced trailing edge

thickness with respect to the datum profile. In order to quantify the influence of this

geometrical parameter on the aerodynamic performances of the examined profiles additional

investigations were carried out. Preliminary studies took place on the auxiliary turbine

cascade blade T150HK. This geometry was obtained by reducing the trailing edge thickness to

the throat ratio of the datum profile T150 to the value of T151 and re-staggering the profile in

order to maintain the same deflection of T150.

The modifications of the profile were performed within the parametrical geometry generator

PROGEN. In this way, the form of the pressure and suction surface is modified according to

the reduced profile thickness at the trailing edge and the continuity of the profile derivatives

up to the second order at the blade control points is preserved. The resulting blade geometry

T150HK is compared with the datum profile T150 in Figure 5.14.


Figure 5.14 Comparison of the geometries of the turbine cascades T150HK and T150

Figure 5.15 Calculated wall shear stress on the turbine cascade blades T150 and T150HK


The boundary layer development predicted on the suction and the pressure surface of the two

profiles does not reveal significant differences as shown from the skin friction distribution on

the blade profile in Figure 5.15. Therefore a comparison between T150 and T150HK allows a

direct assessment of the effects of the trailing edge thickness on the cascade total pressure

losses. The evaluation of the predicted losses leads to the conclusion that half of the

difference between the total pressure losses featured by cascade T150 and T151 is attributable

to the reduced trailing edge thickness. Using the present approach the difference between the

predicted exit flow angles for the cascades T150 and T150HK is limited to one tenth of degree.

Cecchi (2003) quantified the influence of the trailing edge thickness in separate

investigations. The trailing edge thickness to throat ratio of the datum profile was reduced to

the value of T151 but the profile was closed by rotating the pressure side curve with respect to

the conjunction point between the leading edge and the pressure side curve. The resulting

blade geometry is indicated as T150HK1 in the following. This approach leads to a

discontinuity of the profile both in the leading and in the trailing edge region. However, since

both discontinuities take place on the pressure surface in zones featuring strong acceleration

gradients, their influence on the boundary layer development is not relevant. Calculations

performed by Martinstetter (2004b) with the RANS solver TRACE on the same blade

geometries attest the negligible influence of these geometric discontinuities on the

development of the boundary layer. The numerical simulations by Cecchi (2003) were carried

out using the viscous-inviscid cascade analysis code MISES (Drela et al., 1998). The

beginning of transition was forced at xax/lax = 0.2 on the suction surface both for T150 and for

T150HK1. This corresponds to the position of abrupt change of the velocity gradients in the

accelerating region of the suction surface. The calculations with MISES performed on T151

fixed the beginning of the transition on the suction surface at a location xax/lax = 0.6. Using the

present approach the cascade exit flow angle was not forced. The 40% of the total pressure

loss reduction between T150 and T151 can be attributed to the reduced trailing edge

thickness. The residual 60% is attributable to the reduced wetted surface featured by T151.

This result is similar to those obtained from the calculations performed with TRACE on the

profile T150HK, where the exit flow angle was forced by modifying the profile suction side.

Since the results regarding T150HK1 obtained from calculations performed with TRACE again

indicate that 50% of the integral total pressure losses difference between T150 and T151

depends on the trailing edge thickness, the slight difference between the two approaches is to

be ascribed to the different simulation methods.

In order to assess the sensitivity of the cascades to the trailing edge thickness at different

Mach number regimes, additional investigations were performed. Starting from the datum

profile T150 and modifying the trailing edge to throat ratio, various blade profiles were

obtained. Only the pressure side of these profiles was modified accordingly and the exit flow

angle was not forced. Figure 5.16 shows the integral total pressure losses resulting from the


calculations with TRACE. Each curve in the diagram corresponds to a defined trailing edge to

throat ratio. The abscissa corresponds to the operating Mach number and the ordinates

represent the integral total pressure losses. The circles correspond to the experimental (white)

and numerical (grey) results obtained on the baseline T150. At subsonic flow regimes the

sensitivity of the profiles to Mach number variations is quite limited and a higher trailing edge

thickness corresponds to higher losses. At an increased Mach number, where supersonic flow

regions appear on the profile suction surface, the profiles presenting reduced trailing edge

thickness react more sensitively to Mach number changes. This is illustrated by the increased

gradients featured by the curves for a lower trailing edge ratio in the right part of the diagram.

This evidence is associated with a decrease of the shock wave strength for increased trailing

edge blockage. In fact, a higher trailing edge thickness is associated with higher velocities at

the cascade exit plane and thus reduced velocity differences between peak suction surface

Mach number and exit Mach number. These considerations are illustrated in Figure 5.17 by

the stronger shock wave featured by the profile with reduced trailing edge thickness at

transonic flow regimes (Ma2th = 0.90) with respect to the baseline profile T150.

Figure 5.16 Trailing edge effects on the total pressure losses at different Mach number

regimes (TRACE calculations)


Figure 5.17 Profile Mach number at Ma2th = 0.90 at changed trailing edge thickness

Figure 5.18 Trailing edge effects on the total pressure losses at different Mach number

regimes (MISES calculations)


The distribution of the total pressure losses over the Mach number at a changed trailing edge

thickness predicted with the MISES code (Cecchi 2003) shows a stronger sensitivity for the

trailing edge ratio at higher Mach number regimes. This depends fundamentally on the

stronger shock waves predicted at transonic conditions by MISES with respect to TRACE

(Martinstetter, 2004b). The results obtained by Cecchi are represented in Figure 5.18. In this

case the predicted sensitivity of the turbine cascades to the trailing edge thickness for

transonic flow regimes is so high that the total pressure losses featured by the blades with

reduced profile thickness at the trailing edge exceed the values of the blades with higher

trailing edge blockage.

6. Summary and conclusions 117

6. Summary and conclusions

The design of turbine cascade blades for heavy duty gas turbines has to take into account

various often counteracting aspects deriving from the interaction of different disciplines. A

major aim pursued in the development of modern turbine bladings is a reduced number of

blades. In fact, even if the maximal temperature in heavy duty gas turbines is somewhat lower

than in aero engines, life expectations and maintenance intervals are expressed here in

thousand of hours instead of hours (Madfeld et al., 2004). This corresponds to a demanding

challenge for the materials applied in the high pressure components, which can be met only

making use of advanced materials (e.g. Nickel based super alloys or ceramic composite

matrix) in combination with expensive casting techniques for obtaining single crystal

structures, advanced thermal protection coatings and extensive cooling procedures. All these

aspects contribute to increased manufacturing costs. Thus, the reduction of the number of

blades represent a possible way for limiting costs. Furthermore, this design strategy is

associated with beneficial effects under an aerodynamic point of view like reduced wetted

surface and reduced quantities of cooling air mass flow per stage. Nevertheless, the resulting

increase of the aerodynamic lift coefficients produces unfavourable effects like increased

secondary flow losses, highly convex profile curvatures and undesired supersonic flow

regions over the blade suction surface. Moreover, the increased profile aerodynamic loading

makes the cooling efforts per unit pitch higher as well and the beneficial effects of a reduced

number of parts could be even suppressed.

In this context the development of reliable and fast automatic tools assume major importance

for the designer, facilitating a rapid reaction to continuously changing boundary conditions

specified during an iterative process in which different goals from different disciplines have

to be accounted for. In the present work an automatic design method for the aerodynamic

optimisation of two-dimensional turbine blade profiles for the application in the front stages

of heavy duty gas turbines was developed and validated. The design process consists mainly

of three major components: a flow simulation procedure (TRACE, DLR Cologne), a

parametric geometry generator (PROGEN) and an optimisation algorithm. The whole

procedure was set up within the commercial software package iSIGHT. Since both the

operating and the geometric conditions of turbine blade for these applications can

significantly differ from the conditions at which the flow solver was validated, an extensive

experimental database was set up in a preliminary phase of this work and used for calibrating

the flow solver and validating the design method.

Extensive measurements were performed at the High Speed Cascade Wind Tunnel of the

University of the German Armed Forces Munich at Mach- and Reynolds numbers typical for

turbomachinery applications on three different reference high pressure turbine profiles

designed by ALSTOM (T150, T151 and T152). Three different designs were investigated.

118 6. Summary and conclusions

The datum profile T150 is compared with a highly loaded design (T151) and a further design

(T152) featuring moderate aerodynamic loading but smooth profile velocity distribution for

an efficient cooling of the blade.

Extensive computations were performed with a two-dimensional version of the RANS solver

TRACE implementing an adaptation of the one-equation turbulence model by Spalart and

Allmaras (Eulitz, 2000) coupled with the transition correlation by Drela (1995). The choice of

a one-equation turbulence model approach derived from the necessity to simulate thin

boundary layers, typical for the present high Reynolds number range, avoiding an excessive

number of nodes near the blade solid wall, as required by two-equation models. Furthermore,

a too high mesh resolution could slow down the flow simulation process and the whole

optimisation loop. The comparison of computations and experiments indicate some defined

discrepancies in pressure loss coefficient and exit flow angle. However, these differences

remain almost constant for different blade designs over a wide operating range. The results

obtained on the reference cascades indicate an over-prediction of the integral total pressure

losses coefficient of about 10%, while the computed cascade deflection exceeds the measured

values of a value between 1.5° and 2.0°. Further studies performed with standard exit flow

angle correlations from the literature showed that even if a gap is present, the RANS method

is more reliable than the sinus rule and a correlation by Traupel (1977) since the difference

between measurements and calculations remains almost uninfluenced by significant changes

of the blade design.

The automatic flow simulation procedure used within the developed design method is set up

coupling the flow solver with an ad hoc developed automatic mesh generation procedure

(GRIDMOD) and evaluation method (AUSWERT). The grid generation method operates

maintaining a fixed mesh topology and adapting the mesh mainly in the boundary layer region

where mesh lines orthogonal to the wall surface are required in order to ensure an accurate

reproduction of the boundary layer development. The evaluation procedure determines the

cascade integral aerodynamic coefficients by homogenising the wake flow using the

procedure by Amecke (1967). The treatment of the profile velocity distribution with

interpolating splines and approximating polynomials ensures the recognition of maxima,

minima and inflection points.

The main optimisation target of the developed procedure is the reduction of the cascade total

pressure losses imposing a fixed operating point. Additional requirements on the profile

pressure distribution for cooling demands were introduced in appropriate fashion in the

objective function as well. This is a fundamental condition for ensuring the generation of

optimised profiles which are relevant for practical applications. A major concern was thereby

the development of a method which does not merely optimise the location of the transition

zone, sacrificing the quality of the velocity distribution on the blade profile. All the objectives

were assembled into a scalar objective function F. The structure of the different terms of this

6. Summary and conclusions 119

function was tailored ad hoc during extensive preliminary investigations in order to ensure a

balanced treatment of the various contributions. A combination of polynomial and

exponential functions was demonstrated to be suited best for the present problem.

The design method was developed for the application in an industrial framework. Therefore

particular attention was given to reduced design time frames. This requirement was met by

combining the two-dimensional simulation approach with a global stochastic optimisation

technique like Adaptive Simulated Annealing. This algorithm showed best capabilities in

coupling with the present highly non linear objective function and ensured a rapid and

exhaustive investigation of large design spaces for locating optimal solutions.

The developed method was validated at various aerodynamic loadings. A comparison of

optimised and reference results underlines the high potential of the present approach for

reducing the cascade total pressure losses. The documented results indicate that the method is

able to generate geometries fulfilling the specified requirements on flow deflection and profile

velocity distribution. A maximal reduction of the total pressure losses coefficient by about

20% is achieved at pitch to chord ratio higher than for T151 with respect to the datum profile

T150 at reference operating conditions. The slight increase of the total pressure losses

coefficient of the optimised blades at the datum pitch to chord ratio is counterbalanced by an

evident improvement of the profile velocity shape. The present results indicate the necessity

to introduce appropriate terms in the objective function F for the control of the profile Mach

number distribution. In fact, even if the presence of these zones does not alter the boundary

layer development on the profile surface and therefore the integral performance coefficients,

they have to be separately considered in order to produce velocity distributions on the profile

which feature optimal aerodynamic characteristics for an efficient cooling of the blade. An

optimal acceleration behaviour on suction and pressure surface was achieved using an

asymmetrical representation of the blade leading edge. Thus, the suction and pressure side

spline segments were decoupled from each other. This led to increased sectional areas of the

optimised blades. Therefore, in order to assess the capabilities of the present method at

changed boundary conditions, the level of the admissible areas and momentum of inertia was

strongly reduced. The results obtained from these additional investigations confirm the

validity of the present automatic design approach at changed boundary conditions.

The trailing edge thickness to chord ratio was fixed to the value of the datum profile during

the optimisation process. Since this value differs from the corresponding values featured by

the further reference profiles, additional investigations were performed to quantify this

difference. The results of the related flow calculations indicate that 50% of the total pressure

loss reduction between the reference profiles T150 and T151 is attributable to the reduced

trailing edge thickness.

The automatic design method developed within the present work represents a useful tool for

application in an industrial framework within the design process of turbomachinery blades.

120 6. Summary and conclusions

However, due to the limited actual computational resources a direct extension of the tool in

the present configuration for three dimensional blade design appears difficult. Nevertheless

the structure of the developed method allows the quasi-three dimensional design of the blade

profiles on different stream surfaces. This could be used in combination with appropriate

interpolation procedures over the blade span. A further step for the extension of the

capabilities of the tool is an extensive validation work taking into account changing operating

conditions. Here particular attention should be given to the reliability of the procedure in

higher Mach number regimes, which is very significant for heavy duty gas turbine

applications.

The general formulation used for the present method facilitates the extension of its application

field to the optimisation of turbine profile blades for gas turbine aero engines. However, some

circumstances have to be considered. In fact, while for heavy duty gas turbines the operation

point is almost fixed, for gas turbine aero engines different operation conditions have to be

taken into account. In this case the efficient operation of the blades at different incidences is

of fundamental importance and has to be appropriately considered within the objective

function. The present investigations indicate that the optimised turbine blade profiles feature

high loading levels in the front part of the suction surface. This has to be accurately limited to

ensure an efficient operation at positive incidences. A proposal for the extension of the

method in this direction could be to integrate the information deriving from the Euler

simulation of the blade at positive incidence within the objective function. In this way the

computational time of the method will not be increased significantly. In a second step a

selection of the best solutions could be analysed in more detail performing viscous

calculations at positive incidences as well.

7. Annex 121

7. Annex

Table 7.1 Measured integral total pressure loss coefficients (values expressed as ratio to

the measured total pressure losses for T150 at reference operating conditions)

Ma2th

Re2th 0.65 0.75 0.85

600 000 1.00 0.69 - 0.94 0.69 0.88 1.10 0.82 -

900 000 1.00 0.67 - 1.00 0.64 0.86 1.06 0.72 -

∆β1=0°

Reference

incidence 1 200 000 1.06 0.75 0.90 1.00 0.68 0.90 1.10 0.76 0.92

Ma2th Re2th

0.65 0.75 0.85

400 000 - - - - - 0.92 - - -

600 000 - - - 0.90 0.68 0.85 - - -

900 000 - - - - 0.63 0.78 - - -

∆β1=−10°

Negative

incidence

1 200 000 - 0.66 0.85 1.00 0.65 0.86 - 0.71 0.85 Ma2th

Re2th 0.65 0.75 0.85

600 000 - - - 1.32 0.86 1.01 1.35 - -

900 000 - - - - 0.87 1.06 - - -

∆β1=+10°

Positive

incidence 1 200 000 - 0.95 1.09 1.32 0.92 1.09 1.23 0.96 1.10

Table 7.2 Measured integral exit flow angles (values in degrees)

Ma2th

Re2th 0.65 0.75 0.85

600 000 32.9 24.7 - 32.6 24.5 30.1 31.6 24.2 -

900 000 33.0 25.0 - 32.7 24.6 30.3 31.7 24.4 -

∆β1=0°

Reference

incidence 1 200 000 33.0 25.2 30.6 32.7 25.0 30.5 31.8 24.6 30.1

Ma2th Re2th

0.65 0.75 0.85

400 000 - - - - - 29.8 - - -

600 000 - - - 31.8 24.6 30.0 - - -

900 000 - - - - 24.7 30.1 - - -

∆β1=−10°

Negative

incidence

1 200 000 - 25.0 30.6 32.1 24.9 30.3 - 24.7 30.0 Ma2th

Re2th 0.65 0.75 0.85

600 000 - - - 32.7 25.7 30.6 31.9 - -

900 000 - - - - 25.8 30.7 - - -

∆β1=+10°

Positive

incidence 1 200 000 - 26.1 31.2 32.7 25.8 30.8 31.9 25.4 30.5

122 7. Annex

Table 7.3 Measured axial velocity density ratios

Ma2th

Re2th 0.65 0.75 0.85

600 000 1.079 1.020 - 1.087 1.021 0.997 1.050 1.021 -

900 000 1.080 1.034 - 1.074 1.031 1.007 1.051 1.033 -

∆β1=0°

Reference

incidence 1 200 000 1.077 1.042 1.014 1.074 1.044 1.011 1.048 1.039 1.007

Ma2th Re2th

0.65 0.75 0.85

400 000 - - - - - 0.974 - - -

600 000 - - - 1.055 1.008 0.983 - - -

900 000 - - - - 1.020 0.998 - - -

∆β1=−10°

Negative

incidence

1 200 000 - 1.025 1.006 1.044 1.026 1.000 - 1.026 0.998 Ma2th

Re2th 0.65 0.75 0.85

600 000 - - - 1.085 1.083 1.026 1.106 - -

900 000 - - - - 1.090 1.034 - - -

∆β1=+10°

Positive

incidence 1 200 000 - 1.091 1.042 1.075 1.090 1.039 1.092 1.084 1.039

Table 7.4 Measured inlet turbulence level (values in percent)

Ma2th

Re2th 0.65 0.75 0.85

600 000 - - - 3.36 4.90 3.90 - - -

∆β1=0°

Reference

incidence 1 200 000 4.06 - - 3.70 5.20 4.90 3.41 - -

Table 7.5 Measured location of the transition zones (xax/lax suction surface) resulting

from the oil flow pictures

Ma2th

Re2th T150 T151 T152

600 000 0.65 − 0.90 0.75 − 0.90 0.65 − 0.80

∆β1=0°

Reference

incidence 1 200 000 - ... − 0.65 0.30 − 0.50 Ma2th

Re2th T150 T151 T152

400 000 - - 0.75 − 0.90

600 000 - - 0.70 − 0.80

∆β1=−10°

Negative

incidence 1 200 000 - 0.80 − 0.85 0.40 − 0.60

Ma2th Re2th

T150 T151 T152 ∆β1=+10°

1 200 000 ... − 0.02 0.05 − 0.20 -

7. Annex 123

Table 7.6 Geometric and aerodynamic results of reference and optimised turbine blades

Blade

geometry t/l [-] rTE/l [-] ζ/ζT150,exp [-] β2 [°] Ma1 [-] CL [-]

T150 (Exp.) 0.7320 0.0205 1.00 32.7 0.42 0.88

T150 (CFD) 0.7320 0.0205 1.09 30.5 0.42 0.86

T150B (CFD) 0.9572 0.0205 0.92 31.3 0.43 1.15

T151 (Exp.) 0.9572 0.0134 0.68 25.0 0.34 1.08

T151 (CFD) 0.9572 0.0134 0.81 23.4 0.34 1.05

T152 (Exp.) 0.7266 0.0116 0.90 30.5 0.40 0.86

T152 (CFD) 0.7266 0.0116 1.03 29.1 0.40 0.83

ASAT150 0.7320 0.0205 1.08 30.4 0.42 0.86

ASA2 0.8900 0.0205 0.87 30.5 0.42 1.06

ASAT151 0.9572 0.0205 0.84 30.4 0.42 1.15

ASA4 1.1500 0.0205 0.81 30.4 0.41 1.40

124 8. References

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Vita

Personal Pasquale Cardamone Born in Catanzaro (Italy) on the 10th of May 1973

Italian nationality

Married, one child

Education

September /1978 – June/1986 Primary and secondary school in Catanzaro

September/1986 – July/1991 Scientific High school in Catanzaro

October/1991 – April 1999 Degree in Mechanical Engineering at the University of

Florence Professional experience April 1999 – January 2000 Research fellow at the institute of energetics of the

University of Florence (Prof. Martelli) February 2000 – June 2005 PhD Student at the Institute of Jet Propulsion of the

German Armed Forces University Since July 2005 Project engineer at E.ON Energy Projects in Munich

Aerodynamic Optimisation of Highly Loaded Turbine Cascade ...

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