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2008:156 CIV

M A S T E R ' S T H E S I S

Design of a Test Facility Aimed for Measurement of Gas Turbine Vane

Film Cooling Effectiveness

Daniel Edebro

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ABSTRACT

A test facility to examine the beneficial effects of film cooling has been designed and built. The test facility test section is made to resemble a modern first stage guide vane.

The rig was design to make use of a transient infrared thermography test were the time history of the object under the assumption of a semi-infinite body is assumed.

This allows the simultaneous determination of both the heat transfer coefficient and

the adiabatic wall effectiveness from a single experiment.

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ACKNOWLEDGEMENT

This thesis work was carried out during 2007 at Siemens Industrial Turbomachinery AB in Finspång. It is a part of the education to receive a degree in Master of science in Engineering physics from Luleå university of technology (LTU).

I would like to thank everyone who has helped me during my work. Especially my

supervisor at Siemens Dr Esa Utriainen, my laboratory supervisor at Siemens, Jonas

Hylén and my supervisor at LTU, Senior lecturer Roger Hermansson. I also would

like to thank all the nice people at Siemens who helped me with this and that.

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NOMENCLATURE... 1

1 INTRODUCTION ... 2

1.1 BACKGROUND... 2

1.2 AIM AND OBJECTIVE... 5

1.3 OUTLINE OF THIS THESIS... 5

2 BASIC HEAT TRANSFER AND FILM COOLING THEORY... 6

2.1 SIMPLE CONVECTION... 6

2.2 BASIC FLOW THEORY... 6

2.3 HIGH SPEED FLOWS... 8

2.4 FILM COOLING... 8

3 MEASURING FILM COOLING PERFORMANCE ... 11

3.1 THE IMPORTANCE OF FLUID TEMPERATURES... 11

3.2 MEASURING TEMPERATURE AND HEAT FLUX... 12

3.2.1 Thermocouples ... 12

3.2.2 Infrared thermography... 12

3.2.3 Thermochromatic Liquid crystals ... 14

3.3 EVALUATION METHODS AVAILABLE... 14

3.3.1 Adiabatic wall method ... 14

3.3.2 Tracer gas technique... 15

3.3.3 Naphthalene sublimation technique ... 15

3.3.4 Superposition method of film cooling... 15

3.3.5 Thin conductive model ... 16

3.3.6 Semi infinite model... 17

4 DESIGN OF TEST RIG AND EXPERIMENTAL SETUP... 20

4.1 THE TEST FACILITY... 20

4.2 DETAILED DESCRIPTION OF TEST RIG PARTS... 21

4.2.1 Inlet shut off valve ... 21

4.2.2 Inlet diffuser ... 21

4.2.3 Settling chamber with honeycomb and transition duct ... 21

4.2.4 Turbulence grid... 21

4.2.5 Contraction ... 22

4.2.6 Quick bypass valve... 22

4.2.7 Outlet diffusor ... 23

4.2.8 Secondary air supply unit ... 24

4.3 TEST SECTION DESIGN... 24

4.3.1 Step 1. Vane geometry extraction... 25

4.3.2 Step 2. Vane scaling ... 25

4.3.3 Step 3. Flow channel design (to meet engine profile pressure distribution) ... 25

4.3.4 Step 4. Manufacturing of testsection ... 30

4.4 INSTRUMENTATION... 33

4.4.1 Vane instrumentation ... 33

4.4.2 V-cone mass flow meter ... 34

4.4.3 Test section inlet and outlet pressure ... 34

4.5 INFRARED SYSTEM... 34

5 TEST METHOD ... 35

5.1 PROPOSED TEST PROCEDURE... 35

5.1.1 Pre-test preparations ... 35

5.1.2 Test... 35

5.1.3 Post processing ... 36

5.2 EXPECTED UNCERTAINTIES... 36

6 SUMMARY AND DISCUSSION... 39

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7 LITTERATURE... 40

APPENDIX 1. VANE SCALING PROCEDURE ... 1

APPENDIX 2. TEST FACILITY FLOW CHART... 3

APPENDIX 3. PICTURES... 4

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Nomenclature

a Absorbed ratio of radiation α Thermal diffusivity [ α = k/( ρ c

p

)]

BR Blowing ratio

C Concentration

c

p

Specific heat at constant pressure Cp Static pressure coefficient

DR Density ratio

ε Emitted ratio of radiation erfc Complementary error function η Adiabatic effectiveness

h Heat transfer coefficient

I Momentum flux ratio

k Thermal conductivity L Characteristic length

λ Wave-length

m Emitted radiation

µ Dynamic viscosity

Pr Prandtl number

r Reflected ratio of radiation

ρ Density

s/s

max

Distance from trailing edge

t Time

τ Transmitted ratio of radiation U Electric potential

u Velocity in x-direction

Subscripts

0 Properties without film cooling, properties at t=0 aw Adiabatic wall

c Coolant

e Emitted

e

λ

Emitted at specific wave length

Free stream

iw Impermeable

measured Measured

r Recovery

w Wall

amb Ambient

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1 Introduction 1.1 Background

A gas turbine is a device that produces work. This can be done through torque delivered from a shaft as in industrial gas turbines or it can be done by ejecting air through a jet nozzle as in aircraft jet engines. The simplest design consists of three parts: a compressor (a), a combustor (b) and a turbine (c).

Figure 1.1 Gas turbine cycle

Figure 1.2 Modern gas turbine, Siemens SGT-800

The air enters at (1) and is compressed in the compressor (a). After that the

compressed air is mixed with the fuel in the combustor (b) and ignited. This causes the mixture to heat up and expand. The expanded gas is forced through the turbine (c) which produces work.

The turbine itself is composed by a series of fixed vanes and rotating blades mounted

in pairs on an axis. Each pair is called a stage and the number of stages can differ.

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Figure 1.3 Stationary vanes and rotating blades

The simplest gas turbine can be approximated with the ideal Joule-Brayton cycle.

This cycle consists of two isotrops and two isobars (figure 1.4 (a)). However in reality there are losses in every process.

Figure 1.4 Idealized gas turbine cycle (a). Gas turbine cycle with losses (b).

The thermal efficiency for the ideal cycle has an analytic solution that can be expressed in the following way:

κ κ

η

1

2

1

1

 

 

− 

= p

p

thermal

(1.1)

Equation (1-1) states that the efficiency only depends on the pressure ratio p

1

p

2

and does not depend on the turbine inlet temperature, T . However, taking into account

3

the losses, the efficiency increases with higher turbine inlet temperature. A turbine with no heat added would produce no work thus an increased heat addition is required and beneficial for the efficiency of the cycle. Turbine designer therefore strive for increased temperature. Nowadays the turbine inlet temperature can exceed 2000 °C.

With these temperatures the components in the turbine need to be extensively cooled (b)

(a)

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in order to avoid failure and increase life span. The components in the flow path, the vanes and blades, are subjected to the highest heat load in the turbine and is therefore cooled with sophisticated methods. The cooling can be sorted into two main groups - internal cooling and film cooling.

Internal cooling is when the surface is cooled from the inside (cold side) of the surface. To augment the heat transfer the internal flow is disturbed in various ways.

The goal is to augment the heat transfer as much as possible with the least amount of cooling air. Internal cooling techniques often used in turbomachinery include Rib turbulated cooling, Impingement cooling, Pin-fin cooling, matrix cooling and dimple cooling to mention a few.

Film cooling is when the cooling air is ejected through small holes drilled in the surface and it differs fundamentally from internal cooling methods. The ejected cooling air should attach to the surface and create an insulating layer of cool air.

Contrary to internal, cooling film cooling protects the surface directly instead of transferring the heat from the inside. Nowadays the trend is to increase the number of film cooling holes to achieve better cooling. The following terminology is also used when referring to film cooling: Effusion cooling is full coverage film cooling;

showerhead cooling is film cooling applied to the stagnation region of a vane or a blade.

Because the cooling air is drawn after the compressor it is detrimental for the cycle efficiency. An effective cooling scheme must cool the surface with the least amount of cooling air. A way of expressing the cooling performance is with the cooling effectiveness, θ.

= − T T

T T

c

θ

w

(1.2)

This parameter is a measure how well the coolant temperature is used to reduce the

wall temperature in respect to the hot gas temperature. θ = 1 means perfect cooling,

that is the wall temperature is equal to the coolant temperature. Fig 1.5 shows

approximate values of cooling effectiveness for different cooling schemes.

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From fig 1.5 it can be seen that film cooling and effusion cooling (full coverage film cooling) outperforms internal cooling schemes.

In order to fully profit from the film cooling the cooling engineer must be able to accurately predict the heat transfer. Despite advances in numerical predictions convective heat transfer is still a tricky business and experimental results are needed.

1.2 Aim and objective

The purpose of this work is to design a test facility aimed to investigate and improve the knowledge of film cooling. The objectives of this project is to

• Carry out a literature study with the aim to learn what methods are available for film cooling experiments

• Choose a suitable test method.

• Design a generic test rig with a replaceable test section.

• Design a test section that gives results that are relevant in a real gas turbine.

• Supervise manufacturing of the test rig.

1.3 Outline of this thesis

First of all a short description of the basics of heat transfer is presented and then,

different test methods of film cooling will be explained. After that, a description of

the design of the test rig will be given. Finally the design of the test rig is discussed.

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2 Basic heat transfer and film cooling theory

In problems involving heat transfer the heat can be transported in three different ways Heat transfer by conduction

Heat transfer by convection Heat transfer by radiation

This chapter will focus only on heat transferred by convection. For information about radiation and conduction the reader is referred to books such as Çengel et al (1997) or Incropera et al (2002).

2.1 Simple convection

Heat transfer by convection is comprised of two mechanisms. Near the wall where the velocity of the fluid is low, random molecular motion or diffusion is of importance.

Off the wall where the fluid flow and velocity is more unpredictable (or even turbulent) the macroscopic motion of the fluid is dominating. Together these two mechanisms govern how fast the heat transfer occurs. The heat transfer rate can be determined by solving the momentum equation and the energy equation. However in everyday engineering situations the knowledge of the complete flow and temperature field is often not needed. Newton’s law of cooling states that,

( −

)

= h T T

q &

w

(2.1)

Thus the surface heat flux is proportional to the temperature difference between the wall and the fluid. A theoretical assumption that sometimes can be made is the assumption of constant property flows. Constant property flow means that material parameters do not change with temperature. For these kinds of flows the heat transfer coefficient is independent of the temperature and only depends on the flow condition provided that the reference temperature has been chosen correctly. The heat transfer coefficient is often presented in a dimensionless form as the Nusselt number,

Nu hL

= k (2.2)

The Nusselt number is based on a characteristic length that can be some length scale

corresponding to the problem. For flows round an airfoil it is often chosen to be the

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coefficient. A turbulent boundary layer will increase mixing of the fluid and thus increase the heat transfer. The thickness of the boundary layer is also of consequence.

A thick boundary will reduce the heat transfer coefficient

Figure 2.1 Forced convection

It is therefore often desirable to keep the boundary layer laminar as long as possible.

The point of transition is often hard to predict and film cooling holes will trigger the transition. The following picture shows the heat transfer rate around a turbine blade.

Figure 2.2 Heat load on blade

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2.3 High speed flows

The reference temperature T

in (2-1) was said to be the static temperature of the main flow. However in turbomachinery flows the velocities are high and viscous dissipation close to the surface will increase the temperature locally. The temperature sensed by the surface is greater than the static temperature (but less than the total temperature). To account for that the heat transfer coefficient is more accurately defined with the so called recovery temperature.

p s

r

C

f u T

T (Pr) 2

2

= + (2.3)

The factor (Pr) f will depend on the state of the boundary layer and according to Schlicting (1968) the following values of (Pr) f should be used:

layer boundary laminar

a

5

for

.

Pr

0

(Pr) = f

layer boundary turbulent

a

33

for

.

Pr

0

(Pr) = f

It is also possible to obtain the recovery temperature experimentally. If the object is made out of a low conducting material the temperature measured at the surface at steady conditions will correspond to the recovery temperature.

2.4 Film cooling

When ejecting coolant onto the surface a third temperature is introduced. The ejected coolant will inevitably mix with the main stream and this new unknown temperature will form. This temperature ranges from the main stream temperature to the coolant temperature and is called the adiabatic wall temperature, T

aw

, or the film temperature.

The surface heat flux in a film cooling situation is defined as,

( T

w

T

aw

)

h

q & = − (2.4)

And without film cooling,

( −

)

= h T T

q &

0 0 w

(2.5)

The ejected cold fluid will decrease the temperature difference that governs the heat

transfer and the heat load on the surface will decrease.

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Figure 2.3 Principle of film cooling

The unknown T

aw

can be determined when film cooling is applied on an adiabatic surface ( q& = 0 ). The measured wall temperature will be equal to T

aw

according to equation (2.6). The adiabatic wall temperature can be rendered dimensionless with the adiabatic effectiveness or film effectiveness,

= −

T T

T T

c

η

aw

(2.6)

However in order to fully estimate the favorable effect of film cooling it is not enough to determine the adiabatic effectiveness. The injection of cooling air will disturb the flow and augment the heat transfer coefficient. That is,

1

0

h

h (2.7)

This is especially true in the region just behind the hole where the flow is subject to disturbance from the ejected coolant.

There are several parameters that affect film cooling performance (h and η):

Momentum flux ratio Blowing ratio

Density ratio

Turbulence intensity and length scale Pressure gradient

Radial pressure gradient Boundary layer state Cooling hole geometry

Mainstream Reynolds number Mach number

Surface roughness Etc….

The first three are defined in the following way:

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Blowing ratio

c c

u BR u

ρ ρ

= (2.8)

Density ratio

c

DR ρ ρ

= (2.9)

Momentum flux ratio

2 2 2

c c

u

u DR

I BR

ρ ρ

=

= (2.10)

They are a measure how much air and with what energy the coolant is ejected. The turbulence intensity and length scale of the mainstream will also affect the cooling performance. It is not hard to imagine that increased turbulence intensity will dilute the coolant much faster and reduce the adiabatic effectiveness. The pressure gradient of the mainstream in the both radial and stream wise direction will also affect cooling performance. Geometrical effects like cooling hole geometry and surface roughness have been intensively studied by many researcher.

The mainstream Reynolds number and Mach number will also have effect on the

cooling performance. When doing aerodynamic tests it is often suggested to match

both the Reynolds- and the Mach number. In the present study only the Re number

was preserved due to limitations described in chapter 4.

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3 Measuring film cooling performance

Film cooling has been studied for many years and there are many ways to determine film cooling performance. This chapter describes how to measure film performance. It also describes the present evaluation method.

3.1 The importance of fluid temperatures

The main feature of film cooling is to protect the surface by a cool layer of air. The inevitable mixing of the coolant and the mainstream will create a gas/coolant mix film with unknown temperature. To determine this temperature the simultaneous

determination of the coolant, the main stream and the wall temperature is required.

This can be done either by thermocouples or some other method. No matter what method chosen to measure these temperatures it will be associated with uncertainties.

To keep the uncertainties to a minimum the difference between the coolant and the mainstream need to be as high as possible. An important film cooling performance parameter often used is the so called adiabatic effectiveness. The adiabatic

effectiveness relates the temperature of the gas/coolant mixture with the mainstream and coolant temperature. The following table shows the relative error for the adiabatic effectiveness for a given coolant temperature T

c

, measured wall temperature T

aw

, mainstream temperature T

and estimated uncertainties in measured wall temperature and fluid temperatures. The calculated values are approximated by a root-sum-square error propagation formula applied to the equation for the film effectiveness (equation 2.6). If f = f(x

1

,x

2

,x

3

) describes the quantity that is to be calculated the following expression estimates the error for f that stems from error in input values.

2

3 3 2

2 2 2

1

1



 

∂ + ∂

 

 

∂ + ∂

 

 

= ∂ dx

x dx f

x dx f

x df f

Table 3. 1. Uncertainty in determination of adiabatic effectiveness depending on temperatures.

Taw Tc T η % error

30 ± 0.5ºC 20 ± 0.5ºC 60 ± 0.5ºC 0.75 ± 0.025 2.1%

45 ± 0.5ºC 20 ± 0.5ºC 60 ± 0.5ºC 0.375 ± 0.025 4.1%

55 ± 0.5ºC 20 ± 0.5ºC 60 ± 0.5ºC 0.125 ± 0.025 13.3%

24 ± 1.0ºC 20 ± 1.0ºC 40 ± 1.0ºC 0.80 ± 0.065 8.1%

30 ± 1.0ºC 20 ± 1.0ºC 40 ± 1.0ºC 0.50 ± 0.061 12.2%

38 ± 1.0ºC 20 ± 1.0ºC 40 ± 1.0ºC 0.10 ± 0.067 67.5%

35 ± 2.0ºC 20 ± 2.0ºC 80 ± 2.0ºC 0.75 ± 0.066 5.7%

50 ± 2.0ºC 20 ± 2.0ºC 80 ± 2.0ºC 0.50 ± 0.066 8.2%

70 ± 2.0ºC 20 ± 2.0ºC 80 ± 2.0ºC 0.167 ± 0.066 26.2%

The uncertainty decreases with increased temperature difference between the coolant and the main flow. The secondary air (coolant) can either be hotter or colder than the mainstream. Ligrani et al. (1994) used heated air as coolant with the mainstream temperature at ambient to evaluate film performance on a flat plate. Ekkad et al.

(1998) used a heated mainstream. Baldauf heated the mainstream air with a

270 kW-heater to study film cooling performance on a flat plate. Mouzon et al. (2005)

used a liquid nitrogen heat exchanger and ejected air with a coolant temperature of

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about -110 °C and a mainstream temperature of 25 °C in their closed wind tunnel.

However in order to avoid condensation the test section must be very dry (closed wind tunnel) and the cooling air has to be dried.

3.2 Measuring temperature and heat flux

Most methods for evaluation of film cooling performance require that you accurately can predict the temperature of an object. This can be done with discrete measurement point or by some method with good spatial resolution such as infrared thermography or liquid crystals. In the following sub-chapters the most common ways of measuring temperatures are described. A longer description of infrared thermography is also given.

3.2.1 Thermocouples

With thermocouples the temperature at discrete locations can be measured.

Thermocouples rely on the thermoelectric Seebeck effect (Bengtsson, 2001). Two electrical leads made of different metals are joined in one end. When exposing the junction to a temperature an electrical voltage can be detected between the leads.

There are different types of thermocouples depending on the temperature range.

Type Material Interval (°C)

J Iron – Constantan -200…+900

K Chromel – Alumel -250…+900

S Platinum – Platinum/Rhodium -50…+1800

T Copper – Constantan -200…+400

In the present rig type K thermocouples have been used mounted in the coolant plenums and on the airfoil surface.

Thermocouples are small and thus have quick response time. Abuaf et al (1997) used 40 thermocouples mounted on the test surface to evaluate adiabatic effectiveness and heat transfer coefficients.

3.2.2 Infrared thermography

Infrared thermography is a measuring technique that is frequently used by thermal

researchers. The method is based on measuring the thermal radiation that is emitted

by every object and converting it to temperature. Decreasing prices of cameras and

increased resolution makes this technique attractive as it is relatively simple, gives

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 

 

 −

=

1 )

, (

2

5 1 T e c

e T c

m

λ λ

λ

λ (3.1)

The intensity peaks for each temperature is given by Wien’s displacement law, mK

T

3

max

= 2 . 898 ⋅ 10

λ (3.2)

From this it can be seen that the higher temperature shift the intensity maximum towards shorter wavelengths. This is why a red glow can be seen when heating a piece of metal. The increased temperature shifts the emitted radiation towards the visible spectrum. When the temperature is further increased, more and more of the emitted radiation is in the visible spectrum (300-600 nm) and when it is real hot it appears as white (all colors equals white).

In reality there are very few completely “black” surfaces. Instead the surface emits less energy and distribution differs from that of a black body. The term spectral emissivity is defined as the ratio of the radiation intensity of the surface at a specified wavelength to that of a black body,

λ

ε

λ e

e

m

= m (3.3)

In general the spectral emissivity varies depending on wavelength and the distribution don’t resemble that of a black body. A surface that is almost black in the visible spectrum can have a completely different spectral emissivity in the infrared region. A gray surface is a surface that has constant spectral emissivity. Many surfaces can be approximated with this behavior in a confined spectral interval.

When using an infrared camera there is lots of things to keep in mind. The radiation from the object will not only depend on its temperature but also on its surrounding and path. The following expression applies for an object

= 1 + +

λ λ

λ

τ r

a (3.4)

According to Kirchoff’s law the radiation absorbed must be equal to the radiation emitted ( a

λ

= ε

λ

) and for opaque objects 3.4 reduces to,

= 1 +

λ

ε

λ

r (3.5)

This means that for materials with low emissivity the reflection is high. If the

reflection part is high the radiation observed will not represent the temperature of the

object but some mixture of the objects temperature and intensity reflected of the

object. Furthermore the radiation will be attenuated in the atmosphere and camera

aperture before hitting the detector. The amount of radiation that actually reaches the

detector can be written as,

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atm ambient

object

measured

I I I

I = ετ + ( 1 − ε ) τ + ( 1 − τ ) (3.6)

Equation 3.6 tells us that care need to be taken when determining the object parameters. First of all the emissivity of the body should be as close to one as possible. This is usually done by painting the surface with a matt black paint.

Secondly the transmission, τ, need to be determined. If the medium between the object and the camera is air the transmission can be calculated with an empirical formula provided that air temperature and humidity is specified. However if, as in the present case, a viewing glass is used the transmission needs to be calculated. This can be done by calibrating with thermocouples. Sapphire glasses have a transmission of about 60%.

3.2.3 Thermochromatic Liquid crystals

Liquid crystals are substances that in certain phases have mechanical properties of a liquid, but the optical properties of a crystal (Drost 1997). Their optical properties can depend on such things as mechanical stress, electrical fields and temperature. Liquid crystals can be divided into three groups: smectic, nematic and cholesteric depending on its molecular structure (Gao 2002). Thermochromatic liquid crystals (TLC) fall under the category cholesteric. TLC reflect incident light selectively depending on temperature and view angle.

The TLC is only active in a specific temperature range. This range is called

bandwidth and outside this temperature range the crystals are completely transparent.

Bandwidths can range from 0.5 °C up to 30 °C.

Their relatively low price and good spatial resolution have made TLC very popular in heat transfer research. The color is usually captured by a CCD-camera and interpreted in a computer. However the viewing angle dependency requires that special care is taken when lighting the object. Usually cold light is used with fixed camera positions.

A calibration for each camera view is needed.

3.3 Evaluation methods available

A literature study was done in order to investigate available methods and thereby decide how to design the present model. In the subsequent chapters these methods have been described.

3.3.1 Adiabatic wall method

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heater foils on the surface and setting the coolant and main stream temperature equal.

These heater foils give a constant heat flux when they are run through by an electrical current. By knowing the current and the voltage drop over the heater foil the power dissipated can be calculated. The wall temperature is then measured. The heat transfer coefficient is given by the following equation,

(

) ( =

)

= T T

UI T

T h q

w w

foil heater

(3.7)

3.3.2 Tracer gas technique

With this method the adiabatic effectiveness measurements can be done without heating or cooling the fluids. Instead a foreign gas is injected and the concentration is measured at discrete locations downstream of the hole. The adiabatic effectiveness is given by the following expression,

iw coolant p

p coolant

p p

iw

C C C

C η

η η

 

 

 − +

=

, ,

1

(3.8)

Where the local impermeable wall effectiveness, η

iw

is given by,

= −

C C

C C

coolant iw

η

iw

(3.9)

This technique can only be used when the molecular Schmidt and Prandtl numbers are equal (Drost, 1998).

3.3.3 Naphthalene sublimation technique

In this technique the surface is coated with a naphthalene layer. A mass-heat-transfer analogy allows the determinations of both adiabatic effectiveness and heat transfer coefficient. For further information about this method the reader is referred to Gas Turbine heat transfer and cooling technology (2000).

3.3.4 Superposition method of film cooling

Instead of using the adiabatic wall temperature as the reference temperature the superposition method of film cooling uses the mainstream temperature, T

, to define the heat transfer coefficient.

( T T

w

)

h

q & = ′

− (3.10)

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Because this heat transfer coefficient is defined with the mainstream temperature as the reference temperature it must be dependant on temperature. Equalizing equation (3.10) with (2.1), gives rise to the following expression.

( )

w c

T T

T h T

h

= −

′ =

θ

ηθ ,

1 (3.11)

This expression contains two unknowns. The adiabatic effectiveness and the heat transfer coefficient. By knowing h′ for at least two values of θ the effectiveness and film heat transfer coefficient can be solved for. In this way both film performance parameters can be obtained in a single test. Equation 3.11 is valid for constant

property flows but when altering the parameter θ the flow is altered. It is thought that altering the wall temperature is the best way to insure that the flow stays as

undisturbed as possible.

Several researchers have used this method. Martiny et al (1995) applied a thin heater foil on a film cooled flat plate and varied the power through it. By knowing the heat produced in the heater foil the heat transfer coefficient h′ could be calculated. They used five power levels corresponding to five different values of the wall temperature

T

w

and thus different values of θ . Baldauf et al (2001) also used the superposition method but with a different approach. Instead of a heater foil on the surface the backside of the film cooled surface was cooled and heated with a cooling circuit with hot/cold oil in it. The heat flux was calculated with a FE solver with the measured wall temperature as upper boundary condition on the film cooled side and a convective boundary condition on the other side.

3.3.5 Thin conductive model

With this transient method a thin walled model with high thermal conductivity is used. It uses the lumped parameter equation which can be used when the convection is small compared to the conduction. The biot number is the ratio of the internal resistance of a solid to the boundary layer thermal resistance (Incropera 2001). The thin conductive model method is valid for small values of Bi (Bi<1) which means that the conduction inside the body is much faster than the rate of convection. By exposing the film cooled surface to a steady flow and monitoring the temperature over time both the heat transfer coefficient and adiabatic effectiveness can be calculated by curve fitting the measured data to the following expression:

LC t h w

state steady

w

T t

T

ρ

− ( ) =

,

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3.3.6 Semi infinite model

Another way of doing film cooling experiments is to use the semi-infinite model. In the semi-infinite approach an object, initially at a uniform temperature T

0

, is suddenly exposed to a steady flow. By evaluating the temperature of the object the heat transfer coefficient and the adiabatic effectiveness can be determined. The following

approximations are made when using a semi-infinite model:

1) The surface temperature is initially uniformly T

0

. 2) The test object has infinite depth.

3) There is a constant heat load on the surface.

4) The surface is flat.

From 3) and 4) one can draw the conclusion that the heat flux is only in the “depth”

direction. The heat equation then becomes:

2 2

y T t

T

= ∂

∂ α (3.13)

The hot side of the surface (the film cooled side) is imposed with a convective boundary condition.

(

aw w

)

y

T T y h

T = −

− ∂

=0

λ (3.14)

Further boundary conditions are

0

0

, ( , 0 )

) ,

( y t T T y t T

T → ∞ = = = (3.15)

This can be solved analytically. The following statement describes the wall temperature in the semi-infinite solid:

( )

 

 

 +

 −

 

= 

+

k t h t e y

t y T

T

T t y

T

hky hk t

aw

α α

α

α

2 erfc 2

, erfc

2

2

0

0

(3.16)

Evaluating equation at the surface (y = 0) we obtain

( ) ( )

k t e h

T T

T t T

aw

w

α

β β

β

=

− =

− 1

2

erfc ,

0

0

(3.17)

Equation 3.17 can be rewritten with the adiabatic effectiveness in the following way:

( ) ( ( ) ) [ ( ) ]

k t e h

T T T T

T t

T

w c

α

β β

η − − −

β

=

− +

=

0 0

1

2

erfc , (3.18)

Equation 3.18 contains the two unknowns η and h. Thus knowing the wall

temperature for at least two points in time the adiabatic effectiveness and the heat

transfer coefficient can be determined. More points give an over determined system of

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equations and decreases uncertainty. Figure 3.1 shows the rise in temperature at a specific point during the test.

Figure 3. 1. Wall temperature rise in specific point. For this specific case the temperature rises from 273 K to 300. Plotting the measured wall temperature rise a curve like equation 3.18 can be fitted to

get the heat transfer coefficient and adiabatic wall temperature.

The wall temperature can be determined by either liquid crystals or infrared

thermography. However the limited bandwidth and complex calibration needed for the liquid crystals technique makes infrared thermography a simpler alternative.

However several researchers have used liquid crystals to determine the film

performance. Drost et al 1998 used liquid crystals with a small bandwidth and tracked a specific color change. By slightly altering the coolant temperature an over

determined system of equations was created. Another approach was taken by Ekkad et

al 2004. He used an infrared camera to track how the wall temperature changes with

time. The heated main flow was suddenly diverted into the test section and the

temperature was recorded. A similar approach has been utilized in the current work.

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( ) ( ( ) ) [ ( ) ]

( )

( ) [ ( ) ]

=

+

∆ +

=

N

i

i t

i c i i

c w

t e

T T

T

e T T T

T T

t T

i

2

) ( ,

, ,

0 1 , 1 , 1

, 0

) ( erfc 1

erfc 1

2

2

τ β η

β η

τ β

β

K

(3.19)

This means that the heat transfer coefficient and adiabatic effectiveness can be solved for if the temperature-history is also known. This method was used by among others Ekkad et al (2005).

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4 Design of test rig and experimental setup

Based on the study of the different test methods described above the semi-infinite model was chosen. The advantage of this model is that the effectiveness and the heat transfer coefficient can be determined at the same time. The same setup can also be used in the adiabatic wall test method to determine the effectiveness. The test rig was designed for this test method. A brief description of the test rig is first presented below followed by a more detailed description of important parts.

4.1 The test facility

The test facility as built is shown in figure 4.1. It consists of the following parts - (1) Inlet valve

- (2) Inlet diffuser

- (3) Settling chamber with honeycomb - (4) Transition duct

- (5) Contraction

- (6) Bypass quick valve - (7) Test section

- (8) Outlet diffuser

- (9) Secondary air supply unit

Figure 4.1. Newly built film cooling test rig

(1)

(2) (3)

(4) (5) (6)

(7) (8)

(9)

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valve the test section is located followed by an outlet diffuser that decreases the speed of the air

To supply film cooling air to the test section a secondary air supply unit was developed. The mainstream air supply unit was basically a 100 mm tube with four ball valves mounted on them, one for each cooling chamber. With the valves the pressure in the cooling chamber and hence the mass flow could be regulated.

4.2 Detailed description of test rig parts

4.2.1 Inlet shut off valve

After the inlet of the rig there is a big butterfly valve. This valve makes it possible to completely shut of the air to the test rig. It also serves another purpose. Running the compressor at full speed and throttling the inlet valve will raise the temperature of the main stream thus decreasing the uncertainties in the experiment.

Ideally a heater can be used to raise the temperature thus making the experiment less noisy. To raise the temperature of 3.5 kg/s of air with say 20 ºC would require a heater with a power output of approximate 80 kW. It is also important that the heating coils does not get to hot and that the pressure drop is manageable. This will potentially require a big heater. However, the limited time for this work did not allow to buy a heater.

4.2.2 Inlet diffuser

Downstream of the inlet valve there is an inlet diffuser. The inlet diffuser increases the dimensions from an inlet diameter of 340 mm to 500 mm. The diffuser is 1200 mm long.

4.2.3 Settling chamber with honeycomb and transition duct

To decrease turbulence and to make the flow calmer and more uniform there is a 600 mm long settling chamber with a honey comb attached inside. The honeycomb is basically a series of straws closely spaced together that calms the flow. After the settling chamber there is a 1000 mm long transition duct which smoothly converts the flow path from round (Diameter 500 mm) to rectangular (436 x 574 mm).

4.2.4 Turbulence grid

After the transition duct there is a turbulence grid. A turbulence grid is basically a device that increases turbulence in the test section to some level.

Turbulence is thought to have a big influence on film cooling performance.

Turbulence is usually described as a percentage that relates the fluctuations of the flow to the average velocity. Depending how the metal grid is designed different levels of turbulence can be achieved.

The current turbulence grid was recovered from an old test rig and has 21 mm square

openings and 6 mm bars.

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4.2.5 Contraction

In the contraction the air is accelerated as the dimensions are reduced from the transition duct to the inlet of the test section.

The shape of the contraction was taken from Hjärne et al (2003). The following function describes the profile of the contraction (equation 4.1).

( )

( )

 



− ≤

 

 

  −

− =

1 1 1

/ 0 1

1 3

3 1 3

3

2 1

2

L X x X

L x

L X x X

L x

H H

H

H (4.1)

Figure 4.2. Profile of the contraction.

The values of H

1

and H

2

are dictated by the size of the connecting rig. However, both the length and the inflection point (X) was chosen so that the outlet flow profile was as uniform as possible. To determine this a parameter study was made using CFD.

Several 2D models with varying L and X was tested. The L and X that produced the most uniform outlet velocity profile was X=0.5 and L=1000 mm and was chosen.

4.2.6 Quick bypass valve

To create the quick and distinct raise in temperature that is needed for the semi-

infinite method a custom quick valve was designed. It was constructed as a three-way

valve that allows the air to be bypassed around the test section. The bypass valve is

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Figure 4.3. Principle of bypass valve. Prior to the test the air is bypassed as shown in (a). Just before the test is started the air is led into the test section (b).

To redirect the air back into the test section a lever is pulled. To ensure safe handling the lever is pulled by a double acting pneumatic cylinder. The force required to close the valve is the greatest at the beginning of the closure then decreases and the flap slams shut.

Figure 4.4. Bypass valve with pneumatic cylinder.

4.2.7 Outlet diffusor

After the test section there is an outlet diffusor that increases the dimensions of the flow path to the outlet piping. A correctly designed diffuser increases the dimensions

(a)

(b)

Airfoil leading edge

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without risking separation of the flow. The diffuser design was made using tables from Miller (1990).

4.2.8 Secondary air supply unit

To dispense the film cooling air to the four plenums in the guide vane an air supply unit was built. The film cooling air stems from the high pressure air system. The air first passes through a pressure reducing valve that decreases the pressure. It is transported in a rubber tube to the air supply unit which is basically a pipe with a diameter of 100 mm. On this pipe four small ball valves are welded on. The air goes through rubber tubing to the plenums where the air is dispensed through the film cooling holes on the airfoil. No individual flow measurements can be done to measure how much air is coming through each tube. However, the mass flow through each tube can be determined by measuring both the pressure in the air supply unit and outside of the vane.

Figure 4.5. Secondary air supply unit.

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The following sub-chapters describe the work done to design the test section.

4.3.1 Step 1. Vane geometry extraction

The guide vane geometry was extracted from the midspan of a real guide vane. Also the vane pitch at this position was used.

4.3.2 Step 2. Vane scaling

When performing fluid experiments it is important to preserve the dynamic similarity of the flow. Different dimensionless numbers, such as the Reynolds number, the Froude number and the Mach number, classify the flow. Depending on the type of flow some of these numbers can be of greater importance than the others. For instance, incompressible air flow usually only requires that the Reynolds number is kept constant in the scale model as to the real geometry. High speed gas flows as found in turbomachinery are compressible and both the Reynolds number and the Mach number should be preserved. However, the experimental facilities that were available did not allow for this. Also, in large parts of the flow around the guide vane the velocities are not that high and compressible effects are therefore not that large.

Therefore it was decided that the test section should at least have the same Reynolds number as you would find in a real gas turbine.

As the size of the vane is increased the Reynolds number also increases. However as the size of the vane increases the size of the flow path also increases and a larger mass flow is required. The mass flow is however limited by the capacity of the compressor.

More details on the scaling is described in Appendix 1, the result of the scaling was that the vane chord length should be 3.5 times that of the original geometry. This gives a vane with a chord length of approximately 44 cm.

4.3.3 Step 3. Flow channel design (to meet engine profile pressure distribution)

The linear cascade test section is made up by three airfoils and two flow passages.

The side walls of the test section were specially designed to get the correct flow around the airfoil despite the limited flow passages. The ideal design of a linear cascade is several airfoils placed side by side. This makes the flow around each the same as the other ones. When fewer airfoils is used there can be a flow imbalance i.e.

more of the flow want to go through one flow passage then the other as shown in

figure 1.5. This unwelcome effect was cured by custom shaping the side walls.

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Figure 4.6. Perfect periodicity (a). Bad periodicity(b).

The shaping of the side walls also had another purpose. When doing low speed experiments the effects of compressibility are lost. These effects have the greatest influence in regions were air velocities are high like near the throat on the suction side of an airfoil. These effects makes the airfoil profile pressure distribution to differ. The pressure distribution can be quantified non-dimensionally with the static pressure coefficient. This coefficient is defined in the following way.

inlet inlet

p

U

P C P

ρ 5 . 0

= − (4.1)

Figure 4.6 shows a plot of the static pressure coefficient (at midspan) taken from a

real engine simulation done by Anders Jönsson at Siemens.

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Figure 4.7. Vane pressure distribution taken from engine simulation

The high speed region at the suction side is especially hard to mimic. This is where the design of the side walls comes in to play. By adjusting the sides the test section the pressure distribution can be altered (Figure 4.8). This was done numerically with CFD.

Figure 4.8.The part of the side walls that was changed to meet engine profile pressure distribution

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4.3.3.1 CFD-calulations

All the simulations was made using Ansys CFX. The mesh and geometry was created and altered in ICEM CFD. Figure 4.9 describes the iteration procedure to meet the engine profile pressure distribution.

Figure 4.9.Iteration procedure to meet engine profile pressure distribution.

The simulations were first done with a rough tetrahedral mesh with a pressure total Change

geometry

Mesh geometry (rough mesh)

Perform simulation

Pressure distribution OK?

No

Refine Mesh Perform

simulation

Yes

Pressure distribution OK?

No

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Figure 4.10. Refined mesh

The final result is shown in figure 4.11. The static pressure was successfully

reproduced by altering the side walls. The periodicity can be shown in the contour

plot in figure 4.12.

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Figure 4.11. Static pressure coefficient

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piece of polycarbonate it was decided that thinner sheets was to be glued together forming a big sheet. This proved to be a mistake as the glue did not stick everywhere.

The piece of polycarbonate was then placed in a cutter which cut out the airfoil profile from a computer model of the vane. Then, the plenums and film cooling holes was manually drilled. Finally the vane was coated with a diffuse black paint which increased its emissivity.

Figure 4.13. Painted guide vane

4.3.4.2 Side vanes

The side vanes were made by cutting a thick metal sheet with a laser cutter. The geometry was extracted from the I-DEAS geometry and exported to an .iges format that could be read by the cutter.

Figure 4.14. Sidewalls of the test section prior to assembly.

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4.3.4.3 Top and side plates

The top plates and all the side plates were cut out with a laser cutter. Rectangular holes were placed were the view port was located.

Figure 4.15. Top (cover) plate of test section

4.3.4.4 Optical access

Infrared thermography method requires expensive special glass windows. For the

present a short-wave camera is used which requires sapphire glass. To gain optical

access and to reduce production cost a solution with one exchangeable window was

chosen. When not in use the frame was fitted with a dummy window made of steel.

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4.4 Instrumentation

4.4.1 Vane instrumentation

The center vane is instrumented with 9 thermocouples and with 16 static pressure taps located on the surface of the vane. The nine thermocouples is used to calibrate the infra red camera. The pressure taps is used to determine the pressure distribution around the vane to be able to determine flow velocity. Furthermore total pressure and temperature can be measured in the cooling hole plenum inside the vane. This is to control how much air is discharged from the cooling holes. The figure below shows a sketch of the vane geometry with instrumentation.

Figure 4.17. Locations of instrumentation

Figure 4.18. Instrumented vane

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4.4.2 V-cone mass flow meter

At the inlet tubing a V-cone mass flow meter is attached. The V-cone is a measuring- device relying on differential pressure. V-cone is shaped as a cone that is placed in the middle of the pipe. This should supposedly produce better result with out the need for a long inlet section. The V-cone requires two pressure gauges and temperature

measurement.

4.4.3 Test section inlet and outlet pressure

At the inlet eight static pressure taps is installed. Downstream of the vane eight more pressure taps are located at equal distance relative to each other and two at the end of the test section where it connects to the outlet diffuser. These measurements are made to get an idea about the flow in the rest of the test section. It could also be used to validate future CFD-calculations.

4.5 Infrared system

For the vane surface temperature distribution measurements an infrared camera is

used. The camera to be used is a Agema Thermovision 900. This camera can detect

infrared radiation in the 3.5-5 µm interval (Agema 1994).

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5 Test method

The test rig was designed to use the Semi-infinite method of determining. This transient method determines both the adiabatic effectiveness and the heat transfer coefficient in a single test. Chapter 5.1 describes how the test method is meant to be implemented in practice.

5.1 Proposed test procedure

5.1.1 Pre-test preparations

First of all the flow is diverted into the test section and the film air is turned on F. The massflow of the main stream is measured using the V-cone flow meter. The massflow of the coolant is also measured. After this is done the main stream is diverted from the test section and it is cooled down to room temperature.

Figure 5. 1. Flow path before test. Test section is bypassed

5.1.2 Test

First of all the infrared camera is turned on. After that the air is redirected back into

the test section and the camera records the heating of the airfoil.

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Figure 5. 2. Flow path during test. The air is let back into the test section and recording is initiated.

This will heat up the test object.

5.1.3 Post processing

After the test the recorded sequence is downloaded to a PC and post processed. Under the semi-infinite assumption the temperature raise of each pixel should follow the following equation.

( ) ( )

k t e h

T T

T t T

aw

w

α

β

β

β =

− =

− 1

2

erfc ,

0

0

(5.1)

The IR sequence contains multiple pairs of T

w

and t. To find the two unknowns a least-squares fitting of the measured data is made. The value of T

aw

and h that corresponds to the smallest sum of the following expression is the result.

( )

=

=

N

i

w i

w

t T

T

1

2 exp

)

,

(

ε min (5.2)

This can be done in for instance Matlab quite quickly.

5.2 Expected uncertainties

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Table 5. 1. Expected uncertainties of measured quantities

Quantity Value Uncertainty

Mainstream temperature, T

40 º C ±1 º C

Coolant temperature, T

c

20 º C ±1 º C

Initial temperature, T

0

20 º C ±1 º C

Measured wall temperature, T

aw

20-40º C ±1 º C

Thermal conductivity, k 0.21 W/mK ±0.005 W/mK

Specific heat at constant pressure, Cp

1170 J/kg K ±5 W/mK

Density, ρ 1200 kg/m

3

±5 kg/m

3

Time, t - ±0.1 s

With these errors the following uncertainties can be expected.

Table 5. 2. Expected uncertainties of results

h = 500 W/m2 K, ηη η η = 0.1, Taw = 38 ° °°°C δ h = ± 67.9 W/m2 K (13.6 %)

δη = ± 0.050 (50.78 %) δ Taw = ± 0.46 °C (0.15 %)

h = 500 W/m2 K, ηη η η = 0.5, Taw = 30 °°°° C δ h = ± 120.8 W/m2 K (24.2 %)

δη = ± 0.042 (8.4 %) δ Taw = ± 0.45 ° C (0.15 %)

h = 500 W/m2 K, ηη η η = 0.8, Taw = 24 °°°° C δ h = ± 300.85 W/m2 K (60.2 %)

δη = ± 0.047 (5.9 %) δ Taw = ± 0.45 ° C (0.15 %)

From table 5.1 it can be seen that well at cooled areas ( η close to 1) the relative uncertainty in the heat transfer coefficient is almost 60%. This is because when the test is initiated both the coolant temperature and the initial temperature of the vane is the same. Also, in regions with low effectiveness the relative uncertainty in the determination of the adiabatic effectiveness is about 50%. However, the same

uncertainty for the steady-state method adiabatic wall method is 67% given the same conditions (see table 3.1).

There are many things that can be done to improve the method. These are - Raise temperature of mainstream

Raising the mainstream temperature to about 60 ºC will decrease the

uncertainties throughout. For instance, the uncertainty of the adiabatic

effectiveness will decrease from approximately 50% to 33 %. This gives

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reasonable result with an effectiveness as low as this.

- Pre cool test section prior to testing

The relative high errors of the test heat transfer coefficient in highly cooled areas stems from the fact that when the test is initiated the vane and the adiabatic wall temperature have almost the same temperature. This fixed by pre-cooling the test section before the test.

- Measure temperature more exactly

Measure the temperature more precise will decrease uncertainty. However, it can be more work than it is worth to measure more accurately.

- Trigger the bypass valve at the same time as the camera - automatically

Uneven and different procedure when the air is let into the test section will

cause a systematic error. This process can be automatically triggered reducing

uncertainty due to user error.

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6 Summary and discussion

A test facility for the investigation of film cooling performance on a scaled vane has been designed and manufactured at Siemens in Finspång. The test section design of the test facility was a scaled up guide vane with a mild curvature. This design was chosen over for instance a flat plate due to better applicability to reality and fewer studies made. The design flow, pressure and scale were chosen to get an engine-like flow in terms of Reynolds number. In addition the test section geometry was modified in order to mimic the pressure distribution around the airfoil.

The semi-infinite film cooling evaluation method was chosen to test film cooling performance. The possibility to obtain both the heat transfer coefficient and the adiabatic effectiveness from a single test makes the current evaluation method very attractive. Assuming uniform conditions and by limiting the test time HTC values and adiabatic effectiveness can thus be obtained without heater foils or lateral conduction associated with steady state methods. The steady-state condition also allows an easy method of finding the adiabatic effectiveness which is considered to be the most important film cooling performance.

Infrared thermography was chosen in order to achieve high spatial resolution and

relatively simple temperature measurement.

References

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