EFFECTS OF REALISTIC COMBUSTOR EXIT PROFILES ......EFFECTS OF REALISTIC COMBUSTOR EXIT PROFILES ON A TURBINE VANE ENDWALL William F. Colban IV Thesis submitted to the Faculty of the

EFFECTS OF REALISTIC COMBUSTOR EXIT PROFILES ON A TURBINE VANE ENDWALL

William F. Colban IV

Thesis submitted to the Faculty of the Virginia Polytechnic Institute and State University

in partial fulfillment of the requirements for the degree of

Master of Science

in Mechanical Engineering

Dr. Karen A. Thole, Chair Dr. Thomas Diller

Dr. Brian Vick

January 4, 2002 Blacksburg, Virginia

Keywords: Endwall Heat Transfer, Secondary Flow Field

© 2002, William F. Colban IV

i

Abstract

Engine designers continually push the combustor exit temperature higher to

produce more power from gas turbine engines. These high turbine inlet temperatures,

coupled with high turbulence levels and flow field non-uniformities, make turbine vane

and endwall cooling a very critical issue in engine design. To appropriately cool these

surfaces, knowledge of the passage flow field and endwall temperature distribution at

representative engine conditions is necessary.

A combustor test section was used to simulate realistic turbine inlet profiles of

turbulence, normalized temperature, normalized total pressure, and normalized

streamwise velocity to study the flow field in a turbine vane passage and the adiabatic

temperature distribution on the endwall. The combustor liner film-cooling and exit slot

flows were varied independently to determine their relative effect on endwall cooling in

the downstream turbine vane.

Flow field measurements revealed the presence of a previously unmeasured third

vortex in the vane passage. The tertiary vortex was located above the passage vortex and

had rotation opposite to the passage vortex. Increasing the amount of slot flow reduced

the size and strength of the nearwall vortices, while increasing the size and strength of the

tertiary vortex. Adiabatic endwall temperature measurements revealed higher

temperatures surrounding the base of the vane. The endwall measurements also showed

that the exit slot flow was effective at cooling only a region of the endwall near the vane

leading edge on the suction side. Increasing slot flow was found to have a larger thermal

benefit to the endwall relative to increasing combustor liner film-cooling.

ii

Acknowledgements

First and foremost I would like to thank my Lord and Savior, Jesus Christ. I owe

all things, great and small, to Him. I would also like to thank my family for all their love

and support. Mom, Ellis, and EJ, thanks for always being there. I love you all very

much. I would especially like to thank my advisor, Dr. Karen Thole for giving me the

opportunity to learn a great deal and pushing me to achieve. I would also like to thank

her for always giving of her time freely, even when she probably didn’t have any to

spare.

I would sincerely like to thank the sponsors of my research, United Technologies

and Pratt & Whitney. I greatly appreciated the advice and comments concerning my

research that I received from Joel Wagner and John Wiedemer. During my stay at

VTExCCL, I have had the opportunity to work with some great people, all of whom I

would like to mention: Mike, Ryan, Joe, Andy, (and the new people) Severin, Chris, Sac,

Dan, and Evan. You guys made it fun. I would also like to thank all of my professors for

teaching me, I appreciate it much more than I may have shown.

Finally, I would like to thank the people who helped me forget about my research

in the rare moments when I had spare time.

iii

Table of Contents

Abstract ................................................................................................................................. i

Acknowledgments ................................................................................................................. ii

Nomenclature ........................................................................................................................ v

List of Tables......................................................................................................................... ix

List of Figures ....................................................................................................................... x

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

2. Review of Literature.......................................................................................................... 6

2.1 Flow Field Studies with Uniform Inlet Conditions and a Turbulent Boundary

Layer Approaching the Vane..................................................................................... 6

2.2 Combustor Exit Profile Studies................................................................................. 7

2.3 Flow Field, Thermal Field, and Endwall Heat Transfer Studies with Realistic

Turbine Inlet Conditions ........................................................................................... 8

2.4 Objectives and Uniqueness of Research ................................................................... 14

3. Experimental Facilities and Instrumentation..................................................................... 27

3.1 Experimental Facilities.............................................................................................. 27

3.2 Measurements and Instrumentation........................................................................... 35

3.3 Uncertainty Analysis ................................................................................................. 44

4. Test Matrix ........................................................................................................................ 66

4.1 Combustor Exit Profile Sensitivity ........................................................................... 66

4.2 Design of Test Matrix ............................................................................................... 69

5. Thermal Field and Flow Field Results .............................................................................. 83

5.1 Effects of Liner Coolant on the Stagnation Plane Thermal Field ............................. 83

5.2 Effects of Slot Flow on Secondary Flows ................................................................. 86

5.3 Analysis of High Order Statistics .............................................................................. 96

iv

6. Endwall Adiabatic Effectiveness Results.......................................................................... 127

6.1 Effects of Liner Cooling............................................................................................ 128

6.2 Effects of Slot Flow Cooling..................................................................................... 132

6.3 Comparison of Liner Cooling to Slot Flow Cooling................................................. 133

7. Conclusions and Recommendations for Future Work ...................................................... 151

7.1 Measurements of Thermal and Flow Field ............................................................... 152

7.2 Measurements of Adiabatic Effectiveness ............................................................... 153

7.3 Recommendations for Future Work.......................................................................... 154

References ............................................................................................................................. 155

Appendix A: Programs for Surface Temperature Analysis.................................................. 160

Appendix B: Calculations for Uncertainty Analysis ............................................................ 167

Appendix C: Flow Case Conditions..................................................................................... 177

Vita ........................................................................................................................................ 187

v

Nomenclature

a = represents the instantaneous fluctuation of a particular velocity component

Ahole = area of film-cooling of dilution hole

BFR = slot bleed flow ratio

C = true chord of stator vane

Cd = discharge coefficient

D = film-cooling hole diameter or slot feed hole diameter

h = exit slot height

J = momentum flux ratio, 2

2jetjet

U

VJ

∞∞ρ

ρ=

J1 = momentum flux ratio of the first row of dilution holes

J2 = momentum flux ratio of the second row of dilution holes

K = non-dimensional acceleration parameter, dx

dUU

K 2

∞

∞

ν=

Kt = kurtosis, ( )22

4

ta

aK =

kcond = thermal conductivity

L = length of the combustor

M = dimensionless blowing parameter, ee

cc

UUM

ρρ=

.m = mass flow rate

cool.

m = mass flow rate exiting the liner panels, dilution jets, and exit slots

h.

m = core mass flow rate entering the simulator

total.

m = total mass flow rate exiting the combustor

MFR = slot mass flow rate

Nhole = number of film-cooling or dilution holes

P = vane pitch or slot feed hole spacing

Pd = dilution jet dynamic pressure

vi

Po = total pressure

Poc = total pressure measured in the plenum

Pocl = total pressure at the centerline (midspan)

ocl

_P = average total pressure at the midspan

Ps = static pressure

P∞ = freestream static pressure

R = gas constant

Reinlet = inlet Reynolds number, ν

=CU

Re inletinlet

s = distance along the vane surface as defined in Figure 3.6

S = vane span or surface that defines a vortex

Sk = skewness, ( ) 2/32

3

ka

aS =

Sp = film-cooling hole spacing in the pitchwise direction

Ss = film-cooling hole spacing in the streamwise direction

t = liner panel thickness

T = temperature

T1 = temperature entering the compressor

T2 = temperature entering the combustor

T3 = temperature entering the turbine

T4 = temperature exiting the turbine

Taw = adiabatic wall temperature

Tcool = average coolant temperature

Th = freestream temperature entering the combustor

T∞ = mass averaged freestream velocity, total

hhcoolcool

m

TmTmT ⋅

⋅⋅

∞⋅+⋅=

Tu = turbulence intensity, inlet

rmsrmsrms

U3)wvu(

Tu⋅

++=

U, V, W = global mean velocities as defined in Figure 3.6

Uc = coolant velocity

vii

Ue = freestream velocity upstream of the vane leading edge

Uinlet = area-averaged turbine inlet velocity in the streamwise direction

U∞ = freestream velocity

u, v, w = local mean velocities as defined in Figure 3.6

ums = streamwise velocity at the midspan

urms = root-mean-square of local mean velocity u

utrue = true streamwise velocity

Vjet = dilution jet velocity, jet

djet

P2Vρ

=

Vn = normal mean flow velocity, msmsn cosvsinuV ψ⋅+ψ⋅−=

Vs = streamwise mean flow velocity, msmss sinvcosuV ψ⋅+ψ⋅=

Vz = spanwise mean flow velocity, wVz =

vmeas = measured pitchwise velocity

vms = pitchwise velocity at the midspan

vrms = root-mean-square of local mean velocity v

vtrue = true pitchwise velocity

wmeas = measured spanwise velocity

wrms = root-mean-square of local mean velocity w

wtrue = true spanwise velocity

X, Y, Z = global coordinates as defined in Figure 3.6

x, y, z = local coordinates as defined in Figure 3.6

Greek

α = probe head tilt angle

δ = boundary layer thickness

∆P = normalized total pressure, 2

inlet

oclo

U21

PPPρ

−=∆

ε = surface emissivity

φ = yaw or pitch angle,

=φ −

uwtan 1

viii

Γ = circulation, ∫Ω=ΓS

sdS

η = adiabatic effectiveness, ∞

∞

−−=η

TTTT

cool

aw

_η = pitch-averaged adiabatic effectiveness

=η = area-averaged adiabatic effectiveness

ηGT = gas turbine efficiency, 23

14GT TT

TT1

−−

−=ηηηη

ν = kinematic viscosity

θ = non-dimensional temperature, ∞

∞

−−

=θTT

TT

cool

, probe head rotation angle

ρ = density

ρc = coolant density

ρe = freestream density upstream of the vane leading edge

ρjet = density of dilution jet flow

ρ∞ = mainstream density

ψ = yaw angle, )uv(tan 1−=ψ

ψms = flow-turning angle at the midspan, )uv

(tanms

ms1ms

−=ψ

Ωs = streamwise vorticity, z

Vn

V nzs ∂

∂−∂

∂=Ω

ix

List of Tables Table 3.1. Film-cooling hole spacing for each panel in the pitchwise and streamwise

directions (t = 1.27 cm, D = 0.7) ................................................................... 46 Table 3.2. Feed hole parameters for the three slot flow cases........................................ 46 Table 3.3. Location of vane static pressure taps measured from the vane stagnation

point............................................................................................................... 46 Table 3.4. Global location of endwall thermocouples.................................................... 47 Table 3.5. Global location of endwall markers .............................................................. 48 Table 3.6. Summary of uncertainty analysis .................................................................. 49 Table 4.1. Percentage of coolant based on exit mass flow (jet momentum flux ratios

are in parentheses) ......................................................................................... 74 Table 5.1. Circulation, Γ, for each vortex given for cases 2 and 5 and for a turbulent

boundary layer ............................................................................................... 99

x

List of Figures Figure 1.1 The Heinkel He-178 airplane, the first aircraft to fly powered by a gas

turbine engine (http://www.soton.ac.uk)................................................. 4 Figure 1.2 The Brayton cycle (Çengel and Boles, 1998).......................................... 4 Figure 1.3 A Pratt and Whitney JT9D PW4000 combustor design containing inlet

swirlers, dilution holes, and film-cooling holes and slots (P&W, 1988) 5 Figure 2.1 Secondary flow model proposed by Langston (1980)............................. 17 Figure 2.2 Temperature profile normal to the flow exiting a Conway engine

combustor (Halls, 1970).......................................................................... 17 Figure 2.3 Temperature profile normal to the flow exiting a combustor (Suo,

1985)........................................................................................................ 18 Figure 2.4 Freestream velocity field at the combustor exit showing spanwise and

pitchwise variation (Barringer et al., 2001)............................................. 18 Figure 2.5 Turbulence levels at the combustor exit showing spanwise and

pitchwise variation (Barringer et al., 2001)............................................. 19 Figure 2.6 Thermal field exiting the combustor showing variation in the spanwise

direction (Barringer et al., 2001) ............................................................. 19 Figure 2.7 Total pressure contour exiting the combustor showing variation in the

spanwise direction (Barringer et al., 2001) ............................................. 20 Figure 2.8 Spatially averaged total pressure profiles exiting the combustor for

cases with and without combustor dilution flow (Barringer et al., 2001). Also shown is the total pressure profile for a turbulent inlet boundary layer (Zess and Thole, 2001) ................................................... 20

Figure 2.9 Exit slot flow visualization streamlines showing the flow directed

towards the suction side of the vane (Shih et al., 2000).......................... 21 Figure 2.10 Thermal field measured at 25% of axial chord downstream of the vane

leading edge for a bleed flow rate =1.5% (Oke et al., 2000)................... 21 Figure 2.11 Thermal field measured at 25% of axial chord downstream of the vane

leading edge for a bleed flow rate =3.0% (Oke et al., 2000)................... 22

xi

Figure 2.12 Thermal field measured at x/C = 0.9 with a slot mass flow rate of 4.0%, showing slot coolant remaining near the vane pressure side (Oke et al., 2001).............................................................................................. 22

Figure 2.13a-c Stanton number contours for (a) high inlet freestream turbulence levels

near 19.5% and (b) low freestream turbulence levels of 0.6%. Stanton number augmentation (c) from the case with low turbulence to the case with high turbulence is also shown (Radomsky and Thole, 2000).......... 23

Figure 2.14 Measured endwall effectiveness contours for slot coolant with

dimensionless blowing parameter M = 0.75 (Blair, 1974)...................... 24 Figure 2.15 Computational endwall effectiveness levels showing slot coolant

effective in region near vane leading edge on the suction side (Shih et al., 2000).................................................................................................. 24

Figure 2.16 Pitch-averaged endwall effectiveness levels showing a sharp decline in

effectiveness near the vane leading edge (Shih et al., 2000)................... 25 Figure 2.17 Measured endwall effectiveness levels showing the slot coolant to be

beneficial only in a region near the leading edge by the vane suction side (Nicklas, 2001)................................................................................. 25

Figure 2.18 Computational endwall effectiveness levels with a combustor modeled

upstream of the vane cascade (Stitzel, 2001). Also included is a coolant slot in a backward-facing step configuration. The contour shows that the slot coolant is only beneficial in a region in the leading edge region near the suction side ............................................................ 26

Figure 3.1 Schematic of closed-loop wind tunnel facility ........................................ 50 Figure 3.2 Cut-away of combustor simulator test section, showing individual

plenum supply chambers ......................................................................... 50 Figure 3.3 Film-cooling hole and dilution jet orientation (dimensions are in cm)... 51 Figure 3.4 Film-cooling hole spacing in the pitchwise and spanwise directions ..... 51 Figure 3.5 Schematic of exit slot showing feedholes and staggered array of pin

fins........................................................................................................... 52 Figure 3.6 Global and local coordinate systems ....................................................... 52 Figure 3.7 Location of measurement planes; inlet, stagnation (SP), and suction

side 2 (SS2) ............................................................................................. 53

xii

Figure 3.8 Total pressure profiles exiting the combustor for heated flow and isothermal flow, illustrating the effect of density on the total pressure profile ...................................................................................................... 54

Figure 3.9a, b Thermocouple rake (a) diagram and (b) orientation in the stagnation

measurement plane.................................................................................. 55 Figure 3.10a, b Kiel probe rake (a) diagram showing enlarged picture of probe head

and (b) orientation of rake in the inlet measurement plane..................... 56 Figure 3.11 LDV system setup for spanwise (w) velocity measurements.................. 57 Figure 3.12 Illustration of probe head rotation angle (θ) for spanwise velocity

measurements .......................................................................................... 58 Figure 3.13 Total pressure profiles showing passage symmetry ................................ 59 Figure 3.14 Illustration of probe head tilt angle (α) for spanwise and pitchwise

velocity measurements ............................................................................ 60 Figure 3.15 LDV system setup for streamwise (u) and pitchwise (v) velocity

measurements .......................................................................................... 61 Figure 3.16 Illustration of probe head rotation angle (θ) for pitchwise velocity

measurements .......................................................................................... 61 Figure 3.17 Flow turning angle at the midspan for the two slot flow cases for

which flow field measurements were taken. Also shown are computational predictions (Lethander, 2001) for the same geometry and flow conditions ................................................................................. 62

Figure 3.18 Infrared camera viewing port location (Radomsky, 2000)...................... 63 Figure 3.19 Infrared camera positioning for the surface temperature measurements. 63 Figure 3.20a Endwall adiabatic effectiveness contours for case 3 measured during

two separate experiments showing repeatability..................................... 64 Figure 3.20b Endwall adiabatic effectiveness contours for case 3 measured during

two separate experiments showing repeatability..................................... 65 Figure 4.1 Exit total pressure profile sensitivity to panel 1 mass flow..................... 75 Figure 4.2 Flow visualization for panel 1................................................................. 75

xiii

Figure 4.3 Combustor liner adiabatic effectiveness. From a computational study performed by Stitzel (2001) .................................................................... 76

Figure 4.4 Exit total pressure profile sensitivity to panel 4 mass flow..................... 76 Figure 4.5 Exit total pressure profile sensitivity to dilution flow............................. 77 Figure 4.6a, b Dilution flow visualization for (a) nominal dilution flow conditions

and (b) top dilution only with higher momentum flux ratios .................. 78 Figure 4.7 Combustor exit total pressure profiles at the midpitch for all five flow

cases ........................................................................................................ 79 Figure 4.8a-c Inlet plane total pressure contours for (a) case 1, (b) case 2, and (c)

case 3 ....................................................................................................... 80 Figure 4.9a-c Slot total pressure contours for (a) case 1, (b) case 2, and (c) case 3...... 81 Figure 4.10a-c Slot total pressure contours for (a) half slot flow (case 4), (b) nominal

slot flow (case 2), and (c) double slot flow (case 5)................................ 82 Figure 5.1a, b Measured stagnation plane thermal fields (Walter, 2001) for case (a) 1

(flat inlet total pressure profile) and (b) 2 (inlet total pressure profile with a peak of ∆P = 0.7).......................................................................... 100

Figure 5.1c Measured stagnation plane thermal fields (Walter, 2001) for case (c) 3

(inlet total pressure profile with a peak of ∆P = 2.2) .............................. 101 Figure 5.2a, b Flow field in the stagnation plane (a) measured for case 2 (Lethander,

2001) and predicted for case 1 (Stitzel, 2001). Note that figures are not the same scale.................................................................................... 102

Figure 5.3 SS2 plane showing mean velocities in the flow direction and the flow

turning angle, ψ ....................................................................................... 103 Figure 5.4a The measured and computational (Lethander, 2001) values for (a) the

flow turning angle at the midspan (ψms).................................................. 104 Figure 5.4b The measured and computational (Lethander, 2001) values for (b) the

streamwise velocity (Vs) at the midspan. Also shown for (a) and (b) are the values published by Kang and Thole (2000) for a study using the same vane geometry and a turbulent boundary layer entering approaching the turbine ........................................................................... 105

Figure 5.5a, b For case 2 (design slot flow) in the SS2 plane; (a) the secondary flow

field and (b) the measured total pressure profile at y/P = 0.1. Note that

xiv

the peak in total pressure corresponds to the same spanwise location as the flow split between the passage vortex and the tertiary vortex........... 106

Figure 5.6a, b For the SS2 plane; (a) the measured secondary flow field (Kang and

Thole, 2000) for a study using the same vane geometry and a turbulent boundary layer approaching the turbine vane cascade and (b) the predicted secondary flow field (Lethander, 2001) for case 2 conditions 107

Figure 5.7 Measured secondary flow field in the SS2 plane for case 5 (double slot

flow) ........................................................................................................ 108 Figure 5.8a, b Measured pitch angle contours in the SS2 plane for (a) case 2 (design

slot flow) and (b) case 5 (double slot flow)............................................. 109 Figure 5.9a, b Measured yaw angle contours in the SS2 plane for (a) case 2 (design

slot flow) and (b) case 5 (double slot flow)............................................. 110 Figure 5.10a, b Streamwise vorticity contours for (a) case 2 (nominal slot flow) and

(b) case 5 (double slot flow).................................................................... 111 Figure 5.10c Streamwise vorticity contours for (c) a turbulent boundary layer (Kang

and Thole, 2000). The surfaces of streamwise vorticity that were used to calculate vortex circulation are outlined in red ................................... 112

Figure 5.11a-c Turbulence intensity contours in the SS2 plane for (a) case 2 (design

slot flow), (b) case 5 (double slot flow), and (c) a turbulent inlet boundary layer (Kang and Thole, 2000).................................................. 113

Figure 5.12a, b Contours of Vs/Uinlet in the SS2 plane for (a) case 2 (design slot flow)

and (b) case 5 (double slot flow) ............................................................. 114 Figure 5.12c Contours of Vs/Uinlet in the SS2 plane for (c) a turbulent inlet boundary

layer (Kang and Thole, 2000).................................................................. 115 Figure 5.13a, b Contours of urms/Uinlet in the SS2 plane for (a) case 2 (design slot flow)

and (b) case 5 (double slot flow) ............................................................. 116 Figure 5.14a, b Contours of Vn/Uinlet in the SS2 plane for (a) case 2 (design slot flow)

and (b) case 5 (double slot flow) ............................................................. 117 Figure 5.15a, b Contours of vrms/Uinlet in the SS2 plane for (a) case 2 (design slot flow)

and (b) case 5 (double slot flow) ............................................................. 118 Figure 5.16a, b Contours of Vz/Uinlet in the SS2 plane for (a) case 2 (design slot flow)

and (b) case 5 (double slot flow) ............................................................. 119

xv

Figure 5.17a, b Contours of wrms/Uinlet in the SS2 plane for (a) case 2 (design slot flow) and (b) case 5 (double slot flow) ............................................................. 120

Figure 5.18 A distribution with positive skewness (Tennekes and Lumley, 1983).... 121 Figure 5.19a, b Distributions with (a) small and (b) large kurtosis (Tennekes and

Lumley, 1983) ......................................................................................... 122 Figure 5.20a, b Contours of skewness in the SS2 plane for case 2 for the u (a) and v

(b) components of velocity...................................................................... 123 Figure 5.20c Contours of skewness in the SS2 plane for case 2 for the w component

of velocity. Note, the scale in Figure 5.20a is different than the one for Figures 5.20b and 5.20c .......................................................................... 124

Figure 5.21a, b Contours of kurtosis in the SS2 plane for case 2 for the u (a) and v (b)

components of velocity ........................................................................... 125 Figure 5.21c Contours of kurtosis in the SS2 plane for case 2 for the w component

of velocity. Note, the scale in Figure 5.21a is different than the one for Figures 5.21b and 5.21c .......................................................................... 126

Figure 6.1 Measured vane pressure distribution for cases 1 through 5. Also

shown is the two-dimensional, inviscid prediction for periodic vanes at low-speed conditions (Radomsky and Thole, 1998) ............................... 136

Figure 6.2 Comparison of thermocouple readings to infrared (IR) camera

measurements at the same endwall location for case 1 ........................... 137 Figure 6.3 Endwall thermocouple locations ............................................................. 138 Figure 6.4 Endwall adiabatic effectiveness contour for case 1 (design slot flow

and a flat inlet total pressure profile)....................................................... 139 Figure 6.5 Endwall adiabatic effectiveness contour for case 2 (design slot flow

and an inlet total pressure profile with a peak value of ∆P = 0.7)........... 140 Figure 6.6 Endwall adiabatic effectiveness contour for case 3 (design slot flow

and an inlet total pressure profile with a peak value of ∆P = 2.2)........... 141 Figure 6.7 Pitch-averaged endwall effectiveness values for case 1. The values

were calculated for each passage and then averaged............................... 142 Figure 6.8 Pitch-averaged endwall effectiveness values for case 2. The values

were calculated for each passage and then average................................. 142

xvi

Figure 6.9 Pitch-averaged endwall effectiveness values for case 3. The values were calculated for each passage and then averaged............................... 143

Figure 6.10 Pitch-averaged endwall effectiveness values for cases 1, 2, and 3.......... 143 Figure 6.11 Augmentation plot of pitch-averaged adiabatic effectiveness for case 1

and case 3 ................................................................................................ 144 Figure 6.12 Endwall adiabatic effectiveness contour for case 4 (half slot flow and

an inlet total pressure profile with a peak value of ∆P = 0.7) ................. 145 Figure 6.13 Endwall adiabatic effectiveness contour for case 5 (double slot flow

and an inlet total pressure profile with a peak value of ∆P = 0.7)........... 146 Figure 6.14 Pitch-averaged endwall effectiveness values for case 4. The values

were calculated for each passage and then averaged............................... 147 Figure 6.15 Pitch-averaged endwall effectiveness values for case 5. The values

were calculated for each passage and then averaged............................... 147 Figure 6.16 Pitch-averaged endwall effectiveness values for cases 4, 2, and 5......... 148 Figure 6.17 Augmentation plot of pitch-averaged adiabatic effectiveness for case 4

(half-slot flow) and case 5 (double slot flow) ......................................... 148 Figure 6.18 Area-averaged endwall effectiveness values for an increase in panel

flow (case 1, 2, and 3) and an increase in slot flow (case 4, 2, and 5) .... 149 Figure 6.19 Pitch-averaged endwall effectiveness values for case 1 compared to

values reported by Barringer, et al. (2001) for case 1 flow conditions and no vane both with and without dilution flow.................................... 149

Figure 6.20 Computationally predicted endwall effectiveness values for case 2

flow conditions (Lethander, 2001) .......................................................... 150

1

Chapter 1

Introduction

The storied history of gas turbines includes people such as Hero of Alexandria

and Leonardo da Vinci. John Barber obtained the first patent for a gas turbine design in

1791. Unfortunately, in the late 18th century, the means to build his design were not

available. Sir Frank Whittle and Dr. Hans Joachim Pabst von Ohain, working

independently of one another, built the first gas turbine engines in the 1930’s (Brun and

Kurz, 2000). Dr. von Ohain put his engine on a Heinkel He-178 (shown in Figure 1.1),

which became the first airplane powered by a gas turbine engine.

Gas turbines today are used primarily in two applications, aircraft and power

generation. Gas turbines have been powering airplanes, both commercial and military,

since 1939 when Dr. von Ohain used a gas turbine for propulsion on the Heinkel He-178

airplane. Gas turbine power plants are common today as an efficient means of power

generation. Gas turbines are also used in a large number of industrial applications to

drive compressors, pumps, and generators.

There are three main components in every gas turbine engine, the compressor,

combustor, and turbine. An ideal gas turbine engine is described by the Brayton cycle

(illustrated in Figure 1.2). The cycle efficiency of the gas turbine engine is just the work

output divided by the work input. This relationship is shown in equation 1.1:

23

14GT TT

TT1

−−

−=ηηηη (1.1)

where T1 is the temperature of the gas entering the compressor, T2 is the temperature of

the gas entering the combustor, T3 is the temperature of the gas entering the turbine, and

T4 is the temperature of the gas exiting the turbine. Equation 1.1 shows that by

increasing the turbine inlet temperature (T3), the gas turbine efficiency is increased. The

power produced by the gas turbine engine is also directly related to the turbine inlet

2

temperature. This fact has led to engine designers pushing the turbine inlet temperature

higher and higher. Typical turbine inlet temperatures in today’s gas turbine engines

range from 2000°F to 3000°F, well above the melting temperatures of the metals that the

turbine is made from.

The increase in turbine inlet temperatures, coupled with high turbulence levels

necessary for the combustion process, has placed tremendous thermal loads on the

turbine vane and endwall surfaces. Complex film-cooling schemes have been

implemented on the vane and endwall surfaces to avoid thermal failure. Relatively

cooler, compressed air (near 1500°R) is bled from the compressor and used to keep the

vane and endwall from failing by way of impingement cooling, convective cooling, and

film-cooling. The task of cooling the vane and endwall surfaces is further complicated

by the presence of complex secondary flows that develop as the flow approaches the vane

and travels through the vane passage. The secondary flow field in the turbine vane

passage is affected by a number of things, including vane geometry and turbine inlet

conditions.

Turbulence inside an engine combustor is generated in a number of ways. Figure

1.3 shows a PW4000 engine combustor containing inlet swirlers, dilution holes, and film-

cooling holes and slots. These mixing and cooling flows generate a large amount of

turbulence. These flows also cause variations in temperature, velocity, total pressure, and

density entering the combustor. These non-uniform turbine inlet conditions place a

further burden on cooling the vane and endwall surfaces. To design a satisfactory

cooling scheme, it is first necessary to understand the effects of the turbine inlet

conditions on the secondary flow field and endwall heat transfer in the turbine passage.

My research focused on the combustor-turbine interaction by modeling representative

turbine inlet conditions for turbulence, total pressure, temperature distribution, and

velocity distribution. This was done by using a combustor simulator (Barringer, et al.,

2001) upstream of the turbine vane cascade to simulate the combustor exit conditions.

Turbine inlet conditions that were not modeled were Mach number, chemical

composition of the gas, and density variation.

This study describes in detail the effects of combustor exit conditions on the

thermal field approaching the vane leading edge, the vane passage secondary flow field,

3

and the endwall heat transfer. The effects of both combustor liner film-cooling and exit

slot flow are examined. Chapter 2 discusses the literature relevant to this study.

Secondary flow field models are discussed, followed by a discussion of realistic

combustor exit conditions. Results from previous studies involving representative

combustor exit conditions are then reviewed, along with results from previous studies

involving combustor-turbine interface slots. Chapter 2 is concluded by listing the

objectives of this research and describing why this research is unique. Chapter 3

describes in detail the experimental facilities, as well as the measurement procedures and

instrumentation. Also included in Chapter 3 is a discussion of experimental uncertainties

for each of the reported values. Chapter 4 discusses the development of the test matrix

that was used for this study. Combustor exit profile sensitivity studies are discussed, as

well as combustor flow visualization. Chapter 4 also describes in detail the five test cases

that were used for this study. Chapter 5 presents the results of the thermal field and flow

field measurements, while Chapter 6 reports the results of the endwall adiabatic

temperature measurements. The final chapter of this report summarizes major findings

and offers recommendations for future research in this area.

4

Figure 1.1. The Heinkel He-178 airplane, the first aircraft to fly powered by a gas

turbine engine (http://www.soton.ac.uk).

Figure 1.2. The Brayton cycle (Çengel and Boles, 1998).

5

Figure 1.3. A Pratt and Whitney JT9D PW4000 combustor design containing inlet

swirlers, dilution holes, and film-cooling holes and slots (Aircraft, 1988).

Inlet Swirlers

Dilution Holes

Film-Cooling Holes and Slots

6

Chapter 2

Review of Literature

A large number of studies exist for turbine vane secondary flows and endwall heat

transfer. These two topics are coupled because the secondary flows, to a large extent,

dictate the endwall heat transfer in the nozzle guide vanes. For the most part, the past

research has been done using uniform turbine inlet conditions and assuming a turbulent

boundary layer for the velocity approaching the vane platform. This chapter will show

that neither assumption is accurate. Non-uniformities at the combustor exit result from

both dilution jet flow and liner film-cooling inside the combustor. Also, a number of gas

turbine engines currently have a slot between the combustor-turbine interface. The flow

exiting this slot, which is typically cooler leakage flow, has a significant effect on the

temperature and total pressure profiles approaching the vane. Although a fair amount of

research involves flush slots, none of these studies have been done using the combined

effects of dilution jets, liner cooling jets, and a protruding slot on the turbine inlet flow

field.

This review of literature focuses on three areas: studies that use uniform inlet

conditions and an assumed turbulent boundary layer approaching the vane along the

upstream platform; studies of the flow and thermal fields exiting the combustor to clarify

realistic turbine inlet conditions; and studies that model realistic turbine inlet conditions.

2.1 Flow Field Studies with Uniform Inlet Conditions and a

Turbulent Boundary Layer Approaching the Vane

Many studies have been done in the past to develop a secondary flow model for

turbine inlet guide vanes. Langston (1980) proposed an accurate secondary flow model

for a low aspect ratio linear vane cascade – this model is illustrated in Figure 2.1. He

7

assumed a turbulent inlet boundary layer for velocity, a uniform inlet temperature profile,

and low freestream turbulence. As the flow stagnates at the vane leading edge, the total

pressure gradient in the boundary layer becomes a static pressure gradient along the vane

leading edge causing a down turning of the flow toward the endwall surface. A

horseshoe vortex is formed that splits into a pressure side leg and a suction side leg.

Strengthened by the cross passage flow, the pressure side leg of the horseshoe vortex

becomes part of the passage vortex. On the suction side of the vane, the horseshoe vortex

wraps around the vane and exits the passage as the counter vortex. Typically much

smaller, the counter vortex rotates in the opposite direction of the passage vortex. Similar

secondary flow models have also been proposed by Marchal and Sieverding (1977),

Sharma and Butler (1987), Goldstein and Spores (1988), and Wang et al. (1997).

Flow field measurements by Kang and Thole (1999) confirmed the secondary

flow model presented by Langston (1980). Kang and Thole used a laser doppler

velocimeter (LDV) to measure six flow field planes around the vane and verified the

formation of the leading edge horseshoe vortex and the passage vortex. The turbine vane

used in my research has the same geometry as the one used in Kang and Thole’s study.

2.2 Combustor Exit Profile Studies

The flow exiting a combustor is highly non-uniform in both the radial and

circumferential directions. Many factors contribute to combustor exit flow non-

uniformity. These factors include, but are not limited to, combustor geometry, the

combustion process, dilution jet flow used for mixing, combustor-liner film-cooling, exit

slot flow, and swirlers placed at the combustor inlet. Studies done by Halls (1970) and

Suo (1985) characterized the temperature field exiting the combustor. While the

temperature fields shown by both Halls (Figure 2.2) and Suo (Figure 2.3) indicate

temperature variation exiting the combustor, the profiles are not similar. This

dissimilarity can be attributed to different combustor geometries, illustrating the strong

dependence of the combustor exit flow field on the combustor geometry.

8

The flow exiting an actual combustor is highly turbulent and varies in

temperature, total pressure, turbulence, and velocity. Barringer et al. (2001) designed a

combustor simulator in order to determine the exit profiles for those properties. Modeled

in the combustor simulator were dilution flow, liner film-cooling, and an exit slot in a

backward-facing step configuration, that injected coolant onto the endwall surface. There

was no vane cascade downstream of the combustor simulator because these experiments

were intended to act as a baseline for future studies such as mine. Shown in Figure 2.4

and Figure 2.5, the streamwise velocity and freestream turbulence fields at the combustor

exit varied in both the pitchwise and spanwise directions. These exit profiles were

affected by both the dilution flow and the liner film-cooling. High turbulence levels

exiting the combustor result from the dilution flow. The normalized temperature and

total pressure fields (Figure 2.6 and Figure 2.7) varied mainly in the spanwise direction.

Primarily, these properties were affected by the liner film-cooling and slot cooling flow.

Pitchwise-averaged total pressure profiles in the spanwise direction are shown in

Figure 2.8 for cases with and without dilution flow. The peak in total pressure is caused

by the liner film-cooling flow. Near the wall, there is a minimum in total pressure

resulting from the slot flow. Also shown in Figure 2.8 is the total pressure profile for a

flat plate, turbulent boundary layer along the approaching endwall (Zess and Thole,

1999). It is clear that both total pressure profiles are significantly different from that of a

turbulent boundary layer. The disparity is important because nearly all of the past

endwall studies have assumed a turbulent inlet boundary layer, which is not the case.

2.3 Flow Field, Thermal Field, and Endwall Heat Transfer Studies

with Realistic Turbine Inlet Conditions

The studies done by Halls (1970), Suo (1985), and Barringer et al. (2001) have

shown that there are large gradients in the temperature profile exiting a combustor

because of the dilution flow, liner film-cooling, and slot cooling. Lakshminarayana

(1975) theoretically examined the effect of a parabolic inlet temperature profile on the

passage vorticity. He showed that the rotation of the passage vortex resulting from a

9

parabolic inlet temperature profile and a uniform velocity profile was opposite to the

rotation of the passage vortex caused by a uniform temperature profile with an inlet

velocity boundary layer. Because of the strong effect of the velocity and temperature

profiles on the total pressure profile, Lakshminarayana’s research showed the importance

of considering the inlet total pressure profile when studying the flow field near the inlet

guide vanes.

Hermanson and Thole (2000) further emphasized the importance of the inlet total

pressure profile on passage secondary flows. They computationally studied the effects of

inlet temperature and velocity profiles on the secondary flow field in a linear stator

cascade. They found that increasing the temperature gradient between the wall and the

freestream tended to change the rotation of the passage vortex. Hermanson and Thole

concluded that the rotation of the passage vortex started to change direction when there

was a point of inflection in the inlet total pressure profile. This computational work

confirmed the earlier theoretical analysis of Lakshminarayana (1975).

Inlet total pressure and temperature profiles are greatly affected by the dilution

jets, combustor-liner film-cooling, and interface slot flow. It is extremely important to

know how these cooling methods influence the secondary flow field in the vane passage

since the endwall heat transfer in the passage is dictated by the secondary flows. Shih et

al. (2000) computationally studied the effect of slot flow on the secondary flow field for a

linear cascade with a contoured endwall. Their slot was located a distance of X/C =

-0.226 upstream of the vane leading edge. Also, the slot was flush with the endwall

surface and angled 35 degrees from the streamwise direction. Shih et al. noted that the

velocity exiting the slot was not uniform and depended on the endwall static pressure

distribution. Regions of lower endwall static pressure resulted in higher slot flow exit

velocity near the turbine midpitch. Flow visualization streamlines shown in Figure 2.9

indicate that the slot flow is directed away from the vane pressure side and towards the

suction side along the endwall.

Burd and Simon (2000) studied the effect of slot flow on the flow field in a linear

cascade with a contoured endwall. The slot was discontinuous in the pitchwise direction,

with a break at Y/P = 0.5 (midpitch) between the vanes. Other features of the slot were

as follows: flush with the surface; angled at 45 degrees into the main flow path; and

10

located at an axial position of XC = -0.1. The velocities exiting the slot were non-

uniform because of the static pressure distribution on the endwall. As the slot bleed flow

ratio (BFR) was increased, the slot exit velocity profile became more uniform. The

lowest slot exit velocities were directly upstream of the leading edge where the endwall

static pressure was the highest. Burd and Simon suggested that increasing the slot BFR

thins the boundary layer inside the passage and reduces the cross passage flow that is

responsible for the development of the passage vortex. These researchers verified a

reduction in passage secondary flows near the trailing edge with velocity measurements.

Experiments reported by Oke et al. (2000) documented the effect of upstream

discrete film cooling jets on the thermal and flow fields in a linear cascade with a

contoured endwall. There were two rows of staggered film-cooling holes with the second

row located a distance of X/C = -0.1 upstream of the vane leading edge. Also, the

cooling holes were oriented at a 45-degree angle with the surface. This cooling

configuration is representative of the combustor-liner film-cooling upstream of the nozzle

guide vanes. Oke et al. found that for low BFRs (1.5% of the core mass flow) the film-

cooling migrated towards the suction side of the vane and into the mainstream (Figure

2.10). BFRs used in this study were between 0.63% and 2.59% of the combustor core

flow. Higher BFRs (3.0% of the core mass flow) provided the film-cooling jets with

sufficient momentum to stay near the pressure side (Figure 2.11). Oke et al. suggested

that at higher BFRs the film-cooling weakened the cross passage secondary flow, thus

allowing the coolant to stay closer to the pressure side.

Oke et al. (2001) studied the effect of a double slot injection on the thermal and

flow fields with a contoured endwall. The locations of the slot injection were at distances

of X/C = -0.23 and X/C = -0.11 as compared with Burd and Simon (2000) who used a

single slot. The slots were not continuous in the pitchwise direction, having a break at

Y/P = 0.5 (mid-pitch) between the vanes. Thermal field measurements showed that the

film cooling exiting the slot was non-uniform because of the discontinuity in the slot at

midpitch. Breaking the slots was thought to provide better cooling near the vane leading

edge. Low mass flow rates (MFRs) resulted in the coolant being swept towards the

suction side of the vane. As slot MFR was increased, the coolant possessed enough

momentum to weaken the leading edge vorticity and passage secondary flow. This

11

weakening of the secondary flows allowed the coolant to remain near the pressure side of

the vane for higher MFRs (Figure 2.12).

Using a transonic wind tunnel, Kost and Nicklas (2001) performed flow field

measurements in a linear vane cascade with a flush slot located at X/C = -0.2 upstream of

the vane leading edge. They determined that slot injection reduced endwall crossflow in

the passage, thus weakening the passage vortex. The horseshoe vortex, however, was

intensified by the slot injection. Kost and Nicklas suggested that the axial location of the

slot in relation to the saddle point (the region near the vane leading edge where the flow

splits) was crucial in determining whether slot injection intensified the horseshoe vortex.

If the slot were placed in the saddle point region, it would strengthen the horseshoe

vortex because of the interaction with the inlet boundary layer. However, if the slot were

placed upstream of the saddle point, it would not have a great effect on the horseshoe

vortex. A previous flow field study done by Kang and Thole (1999) using the same vane

geometry as my research with a turbulent boundary layer approaching the vane showed

the saddle point to be approximately a distance of X/C = -0.2 upstream of the vane

leading edge.

One of the most important issues in the gas turbine industry is that of endwall

surface cooling. Because of the presence of strong secondary flows and high turbulence

levels, the endwall surface is subjected to thermal hot spots. It is necessary to understand

the heat transfer patterns on the endwall in order to design cooling schemes that provide

adequate thermal protection. To completely characterize the heat transfer on the endwall

surface, two measurements are needed: adiabatic effectiveness, which is a normalized

measurement of endwall surface temperature with an adiabatic endwall; and the endwall

heat transfer coefficients, which involve either measuring the endwall surface

temperature with a constant surface heat flux or measuring the endwall heat flux with a

constant surface temperature.

Endwall heat transfer patterns are strongly influenced by the secondary flow field.

Heat transfer is also increased by high turbulence levels, which are present in the

combustor because of the dilution flow (Barringer, et al., 2001). In order to better

understand endwall heat transfer, it is necessary to study endwall heat transfer using

representative turbulence levels entering the turbine. Radomsky and Thole (2000)

12

measured the endwall heat transfer coefficients with high inlet freestream turbulence and

an approaching flat plate, turbulent boundary layer along the upstream wall. They used

an active turbulence grid to generate 19.5% turbulence. This turbulence level is

representative of actual combustor exit levels, as shown by Barringer et al. (2001).

Figures 2.13a and 2.13b show the Stanton number contours for the low (0.6%) and high

(19.5%) freestream turbulence cases. In both cases, a region of high heat transfer

occurred at the vane leading edge. This region of high heat transfer is caused by the

horseshoe vortex bringing hot freestream fluid down to the endwall surface. Figure 2.13c

shows the Stanton number augmentation along with the path of the horseshoe and

passage vortices. This figure indicates that the highest augmentation due to freestream

turbulence occurs in regions where the heat transfer is not dictated by the secondary

flows. These results emphasize the importance of the secondary flows on endwall heat

transfer.

Blair (1974) was the first to examine endwall effectiveness with a flush slot

injection upstream of curved walls representing nozzle guide vanes. His test section was

a single passage that was instrumented with 96 thermocouples on the endwall. Leading

edge effects were not evident because of the nature of the test section. Figure 2.14 shows

the endwall effectiveness contours measured for slot coolant with a dimensionless

blowing parameter of M = 0.75. These contours show a large effectiveness gradient

between the blade suction side and pressure side. This effectiveness gradient is attributed

to endwall secondary flow, which sweeps the injected coolant from the pressure side to

the suction side of the vane. Three coolant mass flows were studied, with small benefits

in endwall effectiveness noted as the dimensionless blowing parameter M was increased

from M = 0.5 to M = 1.0.

Granser and Schulenberg (1990) studied film-cooling effectiveness both

experimentally and computationally with a flush slot upstream of the vane leading edge.

Their experiments showed that increasing the mass flux ratio of the slot injection raised

endwall effectiveness levels. Their computational analysis revealed that the passage

vortex was responsible for lowering effectiveness levels near the vane pressure side. The

computations also showed that the passage vortex caused the slot coolant to migrate

13

towards the suction side of the vane, and eventually to become swept up the vane surface

near the end of the passage.

Shih et al. (2000) computationally predicted endwall effectiveness with slot

injection upstream of the vane leading edge (slot geometry and orientation has been

stated previously). Endwall effectiveness values were computed and are shown in Figure

2.15. It is clear from this contour plot that the slot cooling flow is effective only in the

leading edge region near the vane suction side. As the slot coolant approaches the vane,

it forms a wedge shaped region near the vane suction side. This effect is caused by the

secondary flows lifting the slot coolant off the endwall and into the mainstream. Pitch-

averaged endwall effectiveness values, plotted in Figure 2.16, show a sharp decline in

effectiveness near the leading edge. This decline in effectiveness was attributed to the

cooling flow being swept towards the suction side and then into the mainstream by the

passage vortex.

With a cooling slot upstream of the vane leading edge, Roy et al. (2000) examined

endwall heat transfer both experimentally and computationally. The slot that was used

was not continuous in the pitchwise direction. Near the vane leading edge, slot injection

caused a significant reduction in Stanton number. Stanton numbers were also reduced

near the vane pressure side because of slot injection. Conversely, studies performed with

a continuous upstream cooling slot showed an increase in endwall effectiveness primarily

on the suction side. The computational results of Roy et al. agreed reasonably well with

their experimental findings.

Nicklas (2001) used an infrared camera to measure endwall effectiveness in a

transonic turbine cascade with a continuous cooling slot located at a position of X/C =

-0.2 upstream of the vane leading edge. His results are the thermal complement to the

flow-field work done by Kost and Nicklas (2001). Figure 2.17 shows the endwall

effectiveness measured for a slot blowing ratio of M = 1.3. High effectiveness levels

occur near the beginning of the passage on the suction side. As the flow progresses

through the passage, effectiveness levels near the vane pressure side decrease drastically

because of secondary flow.

Stitzel’s (2001) research was intended to be a computational comparision to my

research and future work. She performed a computational analysis of thermal and flow

14

fields in a combustor simulator and turbine vane cascade. Her computational model

included combustor liner film-cooling flow, combustor dilution flow, and the exit slot

flow. Figure 2.18 shows the adiabatic endwall effectiveness contour for a flow model

with a relatively flat combustor exit total pressure profile. It is interesting to note the

effect of the dilution hole flow on the effectiveness levels above the step. The regions of

high effectiveness on the step correspond to the pitchwise location of the second row of

dilution holes in the combustor simulator. The figure clearly shows that the slot coolant

is only effective in a wedge shaped region near the suction side of the vane leading edge.

The wedge shaped region of slot-affected area has been shown by many of the previous

studies. There is a large effectiveness gradient from the pressure side to the suction side

of the vane because of the cross passage flow. Also, a region of low effectiveness exists

near the vane leading edge resulting from the formation of the horseshoe vortex.

2.4 Objectives and Uniqueness of Research

The objectives of this research were as follows:

• Measure the secondary flow field in a plane in the vane passage and

compare to results that assume a turbulent inlet boundary layer entering

the vane cascade

• Determine the effect of increasing the mass flow exiting the slot on the

secondary flow field in the vane passage

• Measure the endwall adiabatic effectiveness and compare to results that

assume a turbulent boundary layer entering the vane cascade

• Determine the effect of increasing the liner film-cooling on the endwall

adiabatic effectiveness

• Determine the effect of increasing the mass flow exiting the slot on the

endwall adiabatic effectiveness

15

• Compare the benefit in endwall effectiveness obtained from increasing the

liner film-cooling to the benifit in endwall effectiveness obtained from

increasing the mass flow exiting the slot

Prior to performing the experiments that were necessary to accomplish the

research objectives, a number of other experiments (including combustor exit profile

sensitivity studies, flow visualization, and thermal field measurements) were done. It is

necessary to explain the results of these studies in order to fully define the scope of the

research presented in this paper. The results of these prior experiments will be presented

in this paper because they have not previously been published. Joe Walter, a former

student, performed a series of sensitivity studies at the combustor exit by varying the

mass flow exiting the combustor liner panels and dilution jets. Joe also measured the

thermal field approaching the vane stagnation for three of the test cases explained in

chapter 4. Owen Richard, also a former student, did flow visualization experiments for

both the liner panels and dilution jets.

Many turbine vane flow field studies in the past have assumed a turbulent inlet

velocity boundary layer as well as uniform inlet conditions in the freestream. Indications

previously discussed put into question these assumptions and subsequently put the results

of these studies into question. The literature shows that combustor exit flows are non-

uniform in velocity, turbulence, total pressure, and temperature. These properties

independently have a large effect on turbine cascade secondary flows as well as endwall

heat transfer. The lack of experimental research that studies the effect of non-uniform

combustor exit profiles on secondary flow and endwall heat transfer is evident from the

literature. It is also clear that combustor cooling flows such as liner film-cooling and slot

injection greatly affect both the secondary flow field and endwall heat transfer. There

has been a lack of study concerning the effects of upstream film cooling and slot flow on

endwall heat transfer. Almost all of the slot geometries that have been studied have been

flush with the endwall, injecting coolant at an angle into the flow. Only one

computational study (Stitzel, 2001) has been done using a backward-facing step

configuration, which was the geometry used in my research, to inject coolant onto the

16

endwall surface. No experimental research has been published that uses the backward-

facing step configuration.

17

Figure 2.1. Secondary flow model proposed by Langston (1980). Figure 2.2. Temperature profile normal to the flow exiting a Conway engine

combustor (Halls, 1970).

Passage Vortex

Counter Vortex

Endwall Crossflow

Endwall

Inlet Boundary Layer

Saddle Point

18

Figure 2.3. Temperature profile normal to the flow exiting a combustor (Suo, 1985).

Figure 2.4. Freestream velocity field at the combustor exit showing spanwise and

pitchwise variation (Barringer et al., 2001).

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0 0.1 0.2 0.3 0.4 0.5

z / H

y / W

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

U Uinlet

19

Figure 2.5. Turbulence levels at the combustor exit showing spanwise and pitchwise

variation (Barringer et al., 2001).

Figure 2.6. Thermal field exiting the combustor showing variation in the spanwise

direction (Barringer et al., 2001).

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0.0 0.1 0.2 0.3 0.4 0.5Y/W

11

12

13

14

15

16

17

18

Dilution OnTu(%)

ZS

0.00

0.05

0.10

0.15

0.20

0.25

0.0 0.1 0.2 0.3 0.4 0.5

Z/S

Y/ W

-0.100.10.20.30.40.50.60.70.80.91

Dilution On

θθθθ

20

Figure 2.7. Total pressure contour exiting the combustor showing variation in the

spanwise direction (Barringer et al., 2001).

Figure 2.8. Spatially averaged total pressure profiles exiting the combustor for cases with and without combustor dilution flow (Barringer et al., 2001). Also shown is the total pressure profile for a flat plate, turbulent boundary layer along the approaching endwall (Zess and Thole, 2001).

Po – Po ms-ave0.5ρρρρUinlet

2

Po - Poms-ave

0.5 ρρρρ Uave

2

0.0

0.1

0.2

0.3

0.4

0.5

-1.0 -0.5 0.0 0.5 1.0

Dilution On

Dilution Off

Turb. BoundaryLayer δδδδ/S = 0.09(Zess and Thole, 2001)

zS

0.00

0.05

0.10

0.15

0.20

0.25

0.0 0.1 0.2 0.3 0.4 0.5

Z/S

Y/ W

-1.2-1.0-0.8-0.6-0.4-0.20.00.20.40.60.81.01.2

Dilution On

21

Figure 2.9. Exit slot flow visualization streamlines showing the flow directed towards

the suction side of the vane (Shih et al., 2000).

Figure 2.10. Thermal field measured at 25% of axial chord downstream of the vane

leading edge for a bleed flow rate =1.5% (Oke et al., 2000)

22

Figure 2.11. Thermal field measured at 25% of axial chord downstream of the vane

leading edge for a bleed flow rate =3.0% (Oke et al., 2000).

Figure 2.12. Thermal field measured at X/C = 0.9 with a slot mass flow rate of 4.0%,

showing slot coolant remaining near the vane pressure side (Oke et al., 2001).

23

a) b) c) Figure 2.13. Stanton number contours for (a) high inlet freestream turbulence levels

near 19.5% and (b) low freestream turbulence levels of 0.6%. Stanton number augmentation (c) from the case with low turbulence to the case with high turbulence is also shown (Radomsky and Thole, 2000)

24

Figure 2.14. Measured endwall effectiveness contours for slot coolant with dimensionless blowing parameter M = 0.75 (Blair, 1974).

Figure 2.15. Computational endwall effectiveness levels showing slot coolant effective

in region near vane leading edge on the suction side (Shih et al., 2000).

25

Figure 2.16. Pitch-averaged endwall effectiveness levels showing a sharp decline in effectiveness near the vane leading edge (Shih et al., 2000).

Figure 2.17. Measured endwall effectiveness levels showing the slot coolant to be beneficial only in a region near the leading edge by the vane suction side (Nicklas, 2001).

26

Figure 2.18. Computational endwall effectiveness levels with a combustor modeled

upstream of the vane cascade (Stitzel, 2001). Also included is a coolant slot in a backward-facing step configuration. The contour shows that the slot coolant is only beneficial in a region in the leading edge region near the suction side.

1.0 0.9 0.8 0.7 0.6 0.5 0.4

Slot exit

η

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

27

Chapter 3

Experimental Facilities and Instrumentation

As shown in the literature, a greater understanding is necessary of the combustor-

turbine interaction to get an accurate depiction of the heat transfer and fluid mechanics in

the turbine nozzle guide vane. Experiments that study the combustor-turbine interaction

need to have good measurement resolution in order to obtain representative data. One

way to achieve good measurement resolution is to use a large experimental facility. The

experiments presented in this paper were done in a large-scale wind tunnel, which is

described in detail in this chapter.

The first section of this chapter gives an overview of the experimental facilities

and includes two subsections that describe the combustor simulator and the turbine vane

cascade. The second section of the chapter describes the flow field, thermal field, and

adiabatic effectiveness measurements that were performed and the instrumentation that

was used. The final section of this chapter discusses the uncertainty analysis for the

reported values.

3.1 Experimental Facilities

All of the experiments were performed in the large-scale, low-speed, closed-loop

wind tunnel facility shown in Figure 3.1. The flow was driven by a variable speed, 55 hp

fan. First, the air flowed through the main heat exchanger, which lowered the

temperature. After leaving the main heat exchanger, the air was split into three flow

paths in the transition section: a center flow path and two outer flow paths. A perforated

plate provided the required pressure drop to split the flow between the center and outer

flow paths.

28

In the original design, up to 55 kW of heat could be added to the air in the center

flow channel, which represented the combustor core flow, as it passed through a vertical

bank of heaters. However, because the heating elements were initially wired incorrectly,

only 18.3 kW was available for the experiments presented in this paper. The bank of

heaters consisted of eighteen individual fin-strip Watlow heating elements. The heating

elements were mounted horizontally across the channel and perpendicular to the flow

path. In order to control the heater output, the heating elements were arranged in three

groups of six heaters each: an upper section, a middle section, and a lower section. The

amount of power delivered to each group of heating elements was manually controlled by

specifying the desired percentage of maximum available power. Each heating element

could individually receive a maximum of 1.02 kW. A wall-mounted digital display unit

showed the percentage of total power (out of 6.11 kW) that went to each group of heaters.

This heater configuration allowed radial temperature variation entering the combustor

simulator. Radial temperature variation, however, was not used in this study. Following

the heaters, the core flow passed through a series of screens and honeycomb that

straightened the flow and reduced freestream turbulence levels.

Air in each of the two outer flow paths, which represented the combustor cooling

flow, traveled through secondary heat exchangers, and then exited into the combustor test

section through the liner panels, dilution holes, or exit slots. The liquid used in the

secondary heat exchangers to lower the air temperature was tap water. The tap water

temperature varied greatly from winter to summer (being 18°C in the winter and 24°C in

the summer). The thermal properties of the turbine vane Styrofoam limited the maximum

temperature exiting the combustor to 65°C. Because the upper bound for the temperature

difference between the core flow and cooling flow was set, the temperature difference,

and ultimately the temperature measurement resolution, was solely dependent on the

minimum attainable coolant temperature. For this reason, better thermal measurement

resolution was possible in the winter because a larger temperature difference was possible

with the colder tap water. The stagnation plane thermal field measurements presented in

Chapter 5 were done in the winter, while the endwall adiabatic effectiveness

measurements were taken in the summer. The air temperature in the coolant flow

channels was reduced to provide a larger temperature difference between the cooling

29

flow and the combustor core flow. The cooling flow was then mixed with the combustor

core flow and exited into the linear vane test section downstream of the combustor

simulator.

The combustor simulator and the turbine vane cascade were of particular

importance for this study. They are described in greater detail in the following two

subsections.

Combustor Simulator

The design and benchmarking of the combustor simulator test section used in this

study was described in detail by Barringer et al. (2001). Due to the complex nature of the

flow inside the combustor, it was necessary to match relevant flow parameters to ensure

that the simulator accurately modeled the flow field exiting the combustor. Although the

simulator was initially designed to meet specific flow conditions, the final design allowed

much flexibility in generating different combustor exit profiles.

The simulator was designed to fit into an existing wind tunnel that contained a

linear vane cascade that was scaled up by a factor of nine. This constraint resulted in a

linear simulator with geometry that was also scaled up by a factor of nine. Also matched

was the actual turbine inlet Reynolds number of Reinlet = 2.2x105. To design the

simulator entrance height and the contraction region, a non-dimensional acceleration

parameter, K (given in equation 3.1), was matched to that of a Pratt & Whitney engine

combustor:

dxdU

UK 2

∞

∞

ν= (3.1)

where ν is the kinetic viscosity, U∞ is the free stream velocity, and dx

dU∞ is the free

stream velocity gradient in the axial direction. The final two liner panels in the

combustor simulator form a 17.1° contraction, which reduced the entrance height of 99.1

cm to an exit height of 49.8 cm. The combustor simulator contracted only in the

30

spanwise direction. The area ratio of combustor inlet area to combustor exit area was

0.64.

A detailed rendering of the combustor simulator is shown in Figure 3.2. The

simulator included a series of four liner panels, two rows of in-line dilution holes, and an

exit slot at the combustor-turbine interface. In an engine, the liner panels supply film-

cooling to the combustor wall, while the dilution jets provide the mixing necessary for

combustion. In the simulator, each of the liner panels, rows of dilution holes, and exit

slots received coolant air from plenum supply chambers in the outer flow paths. The air

flow rate exiting each of the liner panels and rows of dilution holes was controlled using

shutters placed at the entrance to each plenum. Equation 3.2 was used to determine the

mass flow rate, .

m , exiting the liner panels:

)PP(2ANCm ocholeholed

.

∞−ρ⋅⋅= (3.2)

where Cd is the film-cooling hole discharge coefficient, Nhole is the number of holes in

each panel, Ahole is the area of each film-cooling hole, ρ is the coolant air density, and Poc

and P∞ are the coolant supply pressure and the freestream static pressure, respectively.

The relevant discharge coefficient data was taken from the study reported by Barringer et

al. (2001). The freestream static pressure at each panel was measured using a static

pressure tap that was placed at the end of each panel and made flush with the surface. To

measure Poc, a total pressure tap was placed inside each plenum. The total pressure taps

were connected to the same Model W0602/1P-24T Scanivalve, while all the static

pressure taps were connected to a separate Model W0602/1P-24T Scanivalve. This

configuration allowed quick measurement of the pressure difference for each liner panel

using an Omega Model PX653-02D5V 2-inch pressure transducer. Over 10 seconds,

10000 samples were averaged to determine the pressure difference term in equation 3.2,

and accurately set the mass flow rates exiting each panel.

Because of the high amount of mass flow exiting the dilution holes, the dilution

supply chambers were not large enough to be plenums. For this reason, it was not

possible to set the mass flow rate exiting the dilution holes using equation 3.2. A pitot-

31

static probe was used to measure the dynamic pressure (Pd) of the dilution jet stream.

Measurements were taken across each dilution jet, converted to velocities (Vjet) using

equation 3.3, and then area-averaged to calculate the average dilution jet velocity.

jet

djet

P2V

ρ= (3.3)

Equation 3.4 was then used to determine the mass flow rate, ⋅

m , exiting the dilution jets:

holeholejet ANVm ⋅⋅⋅ρ=⋅

(3.4)

where Nhole is the number of dilution holes in each row, and Ahole is the area of each of

the dilution holes. Each plenum chamber was also instrumented with a type E

thermocouple, which monitored the air temperature in that plenum. Prior to each of the

experiments a bias reading was taken for the plenum thermocouples, which revealed only

a 0.15°C temperature variation. Even though each of the plenums received coolant air

from the same source, the measured temperature variation during the experiments was as

high as 1.8°C. The variation was such that the warmest temperature was measured in the

first plenum, and the coolest temperature was measured in the exit slot. The coolant

temperature decreased axially throughout the combustor simulator, which suggested a

vertical temperature distribution in the coolant flow channel. A possible reason for the

temperature variation is inadequate insulation between the heated center flow path and

the adjacent outer coolant flow paths.

The placement of the liner film-cooling holes and dilution holes is shown in

Figure 3.3. The location of the first row of dilution holes corresponded to the same

pitchwise location as the vane leading edge, while the second row lined up with the

midpitch location. The first row of dilution holes was located a distance of X/L = -0.56

(X/C = -1.52) upstream of the vane leading edge, where L is the length of the combustor

(C is the true vane chord). The second row of dilution holes was located a distance of

X/L = -0.44 (X/C = -1.19) upstream of the vane leading edge. The diameter of the

32

dilution holes was 14.7 cm for the first row and 17.1 cm for the second row. The film-

cooling holes each had a diameter of 0.7 cm and were arranged in a staggered array

shown in Figure 3.4. The film-cooling hole spacings for each panel in the pitchwise and

streamwise directions are given in Table 3.1. The film-cooling holes on the second and

third liner panels were more densely spaced than the film-cooling holes on the first and

fourth liner panels in order to match engine mass flow rates. Each liner panel was 1.27

cm thick and made from General Plastics polyurethane foam, Model FR-6708, with a low

thermal conductivity (kcond = 0.037 W/m-K) so that an adiabatic assumption could be

made.

The combustor simulator was 1.22 turbine sectors in width. As a result, some

rows of film-cooling holes near the sides of the combustor simulator were not located

directly upstream of the turbine sector in which the measurements in this study were

performed. Prior to the surface temperature measurements on the endwall, the outer two

rows of film-cooling holes on both sides of panel 4 were plugged in order to match

desired momentum flux ratios for the engine. Each of the rows of film-cooling holes that

were plugged was located at a pitchwise direction outside of the turbine sector

(determined by the pitchwise location of the stagnation point on the outer two vanes).

While the adiabatic effectiveness measurements were being performed, it was discovered

that the effectiveness levels were not periodic between the two passages. The levels near

the pressure side on the outer passage were much higher than those near the pressure side

on the inner passage. Likewise, the effectiveness levels near the inner passage suction

side were higher than those near the suction surface on the outer passage. It was

determined that the plugged film-cooling holes in panel 4 were creating a cooling deficit

near the outer passage pressure side and the inner passage suction side. The plugs were

removed, since the momentum flux ratio requirement for the combustor design conditions

was no longer a constraint, and the problem was eliminated.

Both sides of the simulator were made from plexiglass. The inner side of the

simulator was made from a series of removable 1.27 cm thick plexiglass panels, which

allowed quick access to the inside of the simulator. The coupling between each panel

could be removed and replaced with brush seals, which would allow measurement access

to the interior of the simulator. Also located on the inner side of the test section was a

33

Velmex model VP 9000 traverse system. This system allowed controlled movement of

instrumentation inside the test section, with 76 cm of travel capability in both the span

and pitch directions. The outer side of the simulator was made from one solid sheet of

1.27 cm thick plexiglass. This plexiglass window allowed optical access for laser-

Doppler velocimetry (LDV) measurements.

A detailed rendering of the exit slot is shown in Figure 3.5. The exit slot was that

of a backward-facing step configuration. Cooling flow entered through the feedholes,

which metered the flow. Then, the flow traveled through a staggered array of pin fins. In

an actual engine, the pin fins are designed to conduct heat away from the top of the step.

The heat was then transferred from the pin fins, via convection, to the coolant airflow.

However, the pin fins did not serve that purpose in this test section since the top of the

step was considered adiabatic for measurement purposes. To achieve different slot mass

flows for the three slot flow cases that were studied (as will be described in Chapter 4),

the feedhole diameter, D, and spacing, P, were varied. These dimensions are given in

Table 3.2 along with the hole area per sector and hole area per slot area per sector. These

values are important because they show that the feedholes, not the exit slot area, were

what metered the slot flow. Also shown in Figure 3.5 is the last row of film-cooling

holes in panel 4. The last row of film-cooling holes was located 24.3 film-cooling hole

diameters (X/C = -0.31) upstream of the vane stagnation. The mass flow exiting the slot

was determined using equation 3.2, where Cd = 0.7 is the feed hole discharge coefficient,

Nhole is the number of feed holes in each slot, Ahole is the feed hole area, and Poc and P∞

are the coolant supply pressure in the slot plenum and the freestream static pressure

above the slot, respectively.

Turbine Vane Cascade

The turbine vane test section was a two-dimensional linear vane cascade.

Previously reported studies performed with this vane test section include Radomsky and

Thole (1998), Kang and Thole (2000), and Zess and Thole (2001). The vane test section

modeled a single sector of a Pratt & Whitney 6000 turbine vane scaled up by a factor of

nine. The vane was constructed from rigid Styrofoam, so that an adiabatic assumption

can be applied to the vane. The vane was then coated with fiberglass to ensure a uniform

34

smooth surface. By using bleed slots and tailboards located on the two sides of the test

section, periodic flow between the two passages was maintained. Figure 3.6 shows the

global and local coordinates used for this study as defined from the center vane in the

vane test section. The origin of the global coordinate system was located at the vane

stagnation point on the lower endwall, while the origin of the local coordinate system was

located on the lower endwall at any specified distance along the vane surface, s. These

coordinate systems were useful to designate the location of the measurements in the vane

test section.

The center vane was instrumented with static pressure taps that were placed flush

with the vane surface at midspan at several locations along the suction and pressure

surfaces (see Table 3.3 for exact locations). The pressure taps were installed to ensure

that the stagnation location was in the correct place, and that the pressure distribution on

the vane surface matched the two-dimensional, inviscid prediction for periodic vanes at

low-speed conditions (Radomsky and Thole, 1998). The inner and outer vanes were also

instrumented with static pressure taps to ensure that the stagnation point was in the

correct location. The vane pressure side on the outer passage was constructed using a

flexible wall, which is described in detail by Bangert (1996). The flexible wall was made

from 6.4 mm thick plexiglass, which allowed optical access for LDV measurements from

the side of the vane passage. The wall exactly matched the vane geometry up to the

location of the vane trailing edge. Following the trailing edge, the flexible wall was

adjusted to match the predicted pressure distribution for the center vane.

The lower endwall was made from General Plastics polyurethane foam, Model

FR-6708, with a low thermal conductivity (kcond = 0.037 W/m-K), so that an adiabatic

assumption could be made for the endwall surface. Several type E thermocouples were

embedded flush with the endwall surface so that the infrared camera could be calibrated

properly (see Table 3.4 for exact location of thermocouples). The thermocouples were

inserted from below the lower endwall surface through the polyurethane foam and coated

with a highly conductive thermal paste (OmegaTherm 201) to ensure that the endwall

surface remained flat. Small thumbtacks were also embedded flush with the endwall

surface and used as spatial reference points for the infrared camera images (see Table 3.5

for exact location of thumbtacks). The endwall was painted black to raise the surface

35

emissivity (ε) as close as possible to a value of 1, and provide good radiation

characteristics.

3.2 Measurements and Instrumentation

The following subsections describe the measurements that were performed in this

study and the instruments used to take the measurements. The first subsection describes

the thermal field measurements that were taken in the stagnation plane and the flow field

measurements that were taken in the vane passage. The thermocouple rake used to

perform the thermal field measurements is described in detail, as well as the laser-

Doppler velocimetry (LDV) system used to take the flow field measurements. Also

discussed are the angle sensitivities of the LDV probe head associated with measurement

orientation. The second subsection describes the endwall surface temperature

measurements. The procedure to calibrate the infrared camera is described in this

subsection, as well as the method used to analyze surface temperature data.

Thermal Field and Flow Field Measurements

The thermal field and flow field measurement planes are shown in Figure 3.7.

Thermal field measurements were taken in the stagnation plane. Total pressure field

measurements will also be presented that were taken in the inlet plane (Walter, 2000).

Flow field measurements were taken in the SS2 plane. The SS2 measurement plane was

normal to the vane surface and located a distance of s/C = 0.35 along the vane suction

side from the vane stagnation location. Isothermal conditions were used for the flow

field measurements, because heating was used only for the thermal field measurements.

To insure the same flow field characteristics were present with and without heating, an

analysis was done to determine the effect of heating on the total pressure profile exiting

the combustor. This analysis was done because the literature showed that the secondary

flow field in the vane passage is primarily dictated by the turbine inlet total pressure

profile (Hermanson and Thole, 2000).

36

The following analysis was done to compare the effects of variable density due to

heating on the total pressure profile exiting the combustor. The total pressure was

normalized using equation 3.5:

2inlet

oclo

U21

PPP

ρ

−=∆ (3.5)

where Po is the measured total pressure, Pocl is the total pressure at the midspan, and Uinlet

is the mass-averaged inlet velocity (6.25 m/s). The measured total pressure, Po, is given

by equation 3.6,

2so u

21PP ρ+= (3.6)

where Ps is the static pressure at the measurement location and u is the local streamwise

velocity at the measurement location. To compare the isothermal flow condition to the

heated flow condition, the assumption that the static pressure distribution was the same

for both conditions was made. The local streamwise velocity, u, was known from LDV

measurements in the stagnation plane (Lethander, 2001). The density as a function of

temperature could be determined using the Ideal Gas Law (equation 3.7),

TRPs

⋅=ρρρρ (3.7)

where Ps is the static pressure and was approximately equal to atmospheric pressure, T is

the local measured temperature for the heated condition (Walter, 2001), and R is the gas

constant (286.9 J/kg-K for air). Using equations 3.5, 3.6, and 3.7 along with measured

total pressures, temperatures, and velocities, the total pressure profile for the isothermal

flow condition was transformed to the total pressure profile for the heated flow condition.

The density analysis was done for the flow case with a peak value of total

pressure of ∆P = 1 (see Chapter 4), because temperature and velocity data was available

37

for these conditions. The temperatures ranged from 21.88°C at 7% span to 26.68°C at

46% span. The total pressure profiles entering the turbine at the stagnation plane for

heated and isothermal conditions are shown in Figure 3.8. There is very little difference

between the two profiles, with the largest difference occurring at the peak level in total

pressure. The peak total pressure, ∆P, for the heated condition was 2.2% higher than the

peak total pressure for the isothermal condition. As a result, the heaters and heat

exchangers were not operating during the total pressure and velocity measurements

because the effect of density variation on those measurements was considered to be

negligible.

The thermal field in the stagnation plane was measured with a single type E

thermocouple rake shown in Figure 3.8a. The thermocouple wire diameter was 0.3 mm

and the bead diameter was approximately 0.7 mm. By removing the thermocouple a

distance of 7.6 cm from the base of the rake using a 3.2 mm diameter aluminum tube,

unobtrusive thermal field measurements were possible. The thermocouple was located

approximately 6 mm from the end of the aluminum rod to minimize conduction effects

from the rod to the thermocouple. The orientation of the thermocouple in the stagnation

plane is shown in Figure 3.8b.

The pressure field measurements were taken with a rake of four small Kiel probes

(shown in Figure 3.9a) spaced 1 cm apart, each having an inner diameter of 1.6 mm for

the probe and an outer diameter of 3.2 mm for the shroud. Because of the shroud, the

Kiel probe was not as sensitive to the flow angle as other pressure measuring instruments.

The Kiel probe’s sensitivity to yaw angle, φ, was ± 52° and the probe’s sensitivity to

pitch angle, Ψ, was ± 45°. Figure 3.9b shows the orientation of the Kiel probe rake in the

inlet measurement plane above the slot. The diameter of the Kiel probe head was ten

times smaller than the height of the exit slot, which allowed acceptable measurement

resolution for the total pressure measurements. The total pressure field measurements

and the total pressure profiles were taken at an axial location of X/C = -0.1. The total

pressure profiles were measured directly upstream of the vane stagnation.

Flow field measurements were taken with a two-component, back-scatter, fiber

optic, LDV system. A TSI model 9201 Colorburst separator was used together with a 5

W laser. A TSI model IFA 755 Digital Burst Correlator, which was controlled by TSI’s

38

FIND software for Windows, was used to process the data. A 350 mm focusing lens was

used to measure all three components of velocity in the SS2 plane. The probe volume for

the 350 mm lens was 1.3 mm in length and 90 microns in diameter. At every

measurement location, 20,000 data points were taken for each velocity component.

Measurements were taken in a 1 cm x 1 cm grid for the entire SS2 plane starting 1 cm off

the suction surface and 1 cm off the endwall all the way until midspan and the pressure

surface. The velocity data was corrected for bias effects by applying residence time

weighting in the analysis.

The streamwise (u) and pitchwise (v) components of velocity were measured

from above the test section, while the spanwise (w) component of velocity was measured

from the side through the flexible wall. Positioning of the LDV system for the spanwise

velocity measurements is shown in Figure 3.11. The spanwise velocity measurements

were extremely sensitive to the probe rotation angle (θ) for this LDV setup. Figure 3.12

illustrates the rotation angle for the spanwise velocity measurements. The measured

spanwise velocity, wmeas, for a given rotation angle, θ, is given by equation 3.8

)sin(u)cos(ww truetruemeas θ⋅+θ⋅= (3.8)

where wtrue is the true spanwise velocity and utrue is the true streamwise velocity. The

true streamwise velocity (utrue) was between 19 m/s and 30 m/s for the SS2 measurement

plane. For a rotation angle of θ = 2°, and a true spanwise velocity of wtrue = 1m/s (wtrue

ranged between –3.6 m/s and 8.4 m/s in the SS2 measurement plane, with the average

value being 0.2 m/s), the measured spanwise velocity was between 1.66 m/s and 2.05

m/s. This small rotation angle of θ = 2° resulted in spanwise velocity uncertainties

between 66% and 105%, with increasing uncertainties for smaller magnitudes of

spanwise velocities.

Ideally, the flow through the vane passage should be symmetric. This situation

would result in a zero spanwise velocity at the midspan. The following procedure was

used to ensure that the probe head rotation angle was 0°. First, the spanwise velocity was

measured at the midspan. The rotation angle was then calculated using equation 3.8,

where wtrue = 0 m/s and utrue was between 19 m/s and 30 m/s (depending on pitch

39

location). Then, the probe head was rotated by the calculated rotation angle and the

spanwise velocity at the midspan was measured again. Using this procedure, the

spanwise velocity profile at the midspan was minimized. Also, the probe head rotation

from the initial setup was not more than 2°.

To make the assumption of zero spanwise velocity at the midspan, it was first

necessary to verify symmetric flow conditions throughout the vane passage. Total

pressure profiles were taken at two locations across the entire span; at a location of Y/P =

0.5 and X/C = 0 (midpitch at the stagnation point), and at a location of y/P = 0.1 in the

SS2 measurement plane. The total pressure profiles (shown in Figure 3.13) indicate

symmetric flow conditions between 10% and 90% span entering the vane passage and in

the SS2 measurement plane. The total pressure gradient at the midspan was zero, which

means that there was no force driving the flow either up or down. The total pressure

profiles shown in Figure 3.13 confirm the assumption of zero spanwise velocity at the

midspan.

Because of the size of the LDV probe head and the overhang of the top endwall, it

was not possible to measure the spanwise velocities for the entire SS2 plane without

tilting the probe head along its axis. Figure 3.14 shows a vector representation of the

measurement of the spanwise velocity component. The true spanwise velocity

component, wtrue, was determined using equation 3.9:

)sin(v)cos(ww truemeastrue α⋅−α⋅= (3.9)

where α is the probe tilt angle and vtrue is the true pitchwise velocity component. The

true pitchwise velocity component was measured from above, which minimized the

uncertainty in this transformation. A constant tilt of α = 5.5 ° was applied to all the

spanwise velocity measurements.

The LDV system was positioned atop the vane test section, as shown in Figure

3.15, to measure the streamwise (u) and pitchwise (v) components of velocity. Just as the

spanwise velocity measurements were extremely sensitive to the probe rotation angle, the

pitchwise velocity measurements were as well. Figure 3.16 illustrates the rotation angle

40

for the pitchwise velocity measurements. The measured pitchwise velocity, vmeas, for a

given rotation angle, θ, is given by equation 3.10

)sin(u)cos(vv truetruemeas θ⋅+θ⋅= (3.10)

where vtrue is the true pitchwise velocity and utrue is the true streamwise velocity. The true

streamwise velocity (utrue) was between 19 m/s and 30 m/s for the SS2 measurement

plane. For a rotation angle of θ = 2°, and a true pitchwise velocity of vtrue = 1m/s (vtrue

ranged between –8.3 m/s and 1.9 m/s in the SS2 measurement plane, with the average

value being –3.2 m/s), the measured pitchwise velocity was between 1.66 m/s and 2.05

m/s. This small rotation angle of θ = 2° resulted in pitchwise velocity uncertainties

between 66% and 105%, with increasing uncertainties for smaller magnitudes of

pitchwise velocities.

The following procedure was followed to obtain a rotation angle of zero. First,

the flow turning angle at the midspan (ψms) was measured and compared to

computational predictions (Lethander, 2001) for the same geometry and flow conditions.

Then, the probe head was rotated until the values for ψms agreed with the predictions.

Using this procedure, the probe head rotation from the initial setup was not more than 2°,

which was consistent with the spanwise rotational corrections. Figure 3.17 shows the

measured flow turning angle for the two flow field cases (one case was design slot flow,

and the other case was double slot flow, as seen in Chapter 4), along with the

computational predictions. There is very good agreement between the measured and

predicted flow turning angles.

A tilt along the probe axis was needed to measure the pitchwise velocity

component near the suction surface and pressure surface (see Figure 3.14). The tilt did

not affect the streamwise velocity measurements. Using the equation 3.11, the true

pitchwise velocities were obtained.

)sin(w)cos(vv measmeastrue α⋅+α⋅= (3.11)

41

A tilt of α = 5.5° was made so that the measured pitchwise velocity component would be

orthogonal to the measured spanwise velocity component and equation 3.11 would be

correct.

Adiabatic Effectiveness Measurements

For the endwall surface temperature measurements, the mass flow rate through

the primary heat exchanger was 20 GPM of tap water, which was 100% of full operating

conditions. The mass flow rate of tap water through each of the secondary heat

exchangers was 8 GPM, which was also 100% of full operating conditions. The heaters

were designed to supply up to 55 kW of heat to the air; however, they were initially wired

incorrectly. The heaters were wired to provide a maximum of only 18.3 kW of heat for

these experiments. Because of natural convective effects, the lower section of heaters

were set to full power, but the middle and upper heater sections were operated at reduced

power in order to maintain a uniform radial temperature distribution entering the

combustor. For the endwall surface temperature measurements, the lower heater section

was set to 100% power (6.11 kW), the middle heater section was set to 72% power (4.4

kW), and the upper heater section was set to 55% power (3.36 kW). Using these heater

settings, the temperature rise across the bank of heaters ranged from 14°C to 17°C for the

five endwall surface temperature experiments. This temperature rise across the heaters

was determined from the temperature measured downstream of the heaters, the

temperature exiting the turbine vane test section, and the temperature drop across the

main heat exchanger (determined in a separate set of experiments).

The endwall surface temperature experiments typically took between 2 ½ hours

and 4 ½ hours to reach steady state. Steady state was determined by monitoring the

endwall thermocouples. When the temperature difference for each endwall thermocouple

became less than 0.1°C over a time period of 30 minutes, the experiment was assumed to

have come to steady state. The data taking portion of the experiment typically took

between 1 ½ hours to 2 hours, during which time the endwall, freestream, and coolant

temperature would change by no more than 0.2°C, or else all the data would be repeated.

Endwall surface temperature measurements were taken with an Inframetrics

model 760 infrared camera. The camera was calibrated using the thermocouples

42

embedded in the endwall surface. Typically, the maximum and minimum thermocouple

temperatures would be used to calibrate the camera so that it accurately measured the

surface temperature over the entire temperature range. To calibrate the camera, the

surface emissivity and background temperature variables were adjusted. Ideally, surface

emissivity (ε) should be 1 for a black surface. However, surface imperfections on the

endwall were such that ε = 0.89 for these experiments. The background temperature

corresponded to the ambient laboratory temperature at the time of each picture. This

temperature changed slightly over the course of an experiment, so it was monitored

closely.

Thirteen different viewing locations were necessary to completely map the

endwall surface. The top endwall was made from plexiglass and contained thirteen

removable lexan inserts, 11.43 cm in diameter (see Figure 3.18 for port locations). The

insert was removed while a picture was being taken in that viewing portal, and the

camera was positioned above the portal as seen in Figure 3.19. A plexiglass cover was

placed over the port when the lexan insert was removed so that air could not flow into or

out of the vane passage. The cover had a 5.5 cm diameter hole in the center which the

camera lens fit into. The camera was supported from below with a plexiglass frame and

from the side with another piece of plexiglass. These rigid supports ensured that the

camera was completely vertical and stable while the pictures where being taken.

The pictures were taken from a distance of one span (54.86 cm) away from the

endwall surface. At this distance, the picture covered an area that was 19.4 cm x 15.7

cm. Each picture was divided into 255 x 206 pixel locations, which caused each pixel to

represent an area of 0.076 cm x 0.076 cm. The infrared camera performed a spatial

integration over 0.37 cm to determine the temperature designation for each pixel. A total

of 16 images were averaged for each picture, and 5 pictures were taken at each viewing

location, which provided 80 surface temperature measurements at each pixel location.

At each viewing location, the five pictures were averaged using a Matlab program

(see Appendix A). The pictures were then transformed into the global coordinate system

using an in-house Fortran program (Kholi, 1998, as shown in Appendix A). To do this, it

was necessary to have two location markers in each picture. Knowing the global location

of each marker, the correct global coordinate position could then be assigned to each

43

pixel location. The thirteen averaged pictures were then meshed together using another

in-house Fortran program (Kholi, 1998, as shown in Appendix A). Overlapping points

were averaged again to form a complete representation of endwall surface temperature.

The endwall surface temperature data is presented in terms of adiabatic

effectiveness using equation 3.12:

∞

∞

−−

=ηTTTT

cool

aw (3.12)

where Taw is the measured adiabatic wall temperature, T∞ is the mass-averaged

freestream temperature entering the turbine test section (T∞ ranged between 30.5°C and

32.9°C for the endwall surface temperature measurements), and Tcool is the average

coolant temperature (Tcool ranged between 24.1°C and 25.6°C for the endwall surface

temperature measurements). The average coolant temperature was supposed to be

calculated from the temperatures measured in each of the liner panel, dilution jet, and exit

slot plenums. However, because of the temperature variation in the plenum

thermocouples of up to 1.8°C during the endwall surface temperature measurements, an

alternative method was used to determine the coolant temperature. The coolant

temperature was determined by using the lowest temperature that was measured on the

endwall with the infrared camera. This method was valid because the lowest endwall

temperature occured at the midpitch location immediately after the exit slot. At this

location, the endwall surface temperature reached an equilibrium with the coolant

temperature before the high turbulence levels in the passage were able to mix out the

coolant. The mass averaged freestream temperature was determined using equation 3.13:

total

hhcoolcool

m

TmTmT ⋅

⋅⋅

∞⋅+⋅

= (3.13)

where coolm⋅

is the total mass flow exiting the liner panels, dilution jets, and slots, hm⋅

is

the core mass flow entering the simulator, and Th is the freestream temperature entering

44

the simulator (measured using a thermal rake of 5 type E thermocouples, spaced 2.54 cm

apart, similar to the rake shown in Figure 3.8a). Th ranged between 39.3°C and 44.5°C

for the endwall surface temperature measurements. For each case, the thermal rake used

to measure the freestream temperature was biased to the endwall thermocouples, which

were used to calibrate the IR camera. In this way the freestream temperature was biased

to the coolant temperature, which was determined using the IR camera, with bias values

being close to 0.15°C for each case.

To demonstrate the repeatability of the endwall adiabatic effectiveness

measurements, the measurements were performed twice for case 3 (described in chapter

4). Figure 3.20 shows the results from both of these experiments. Clearly, these contours

are similar. The effectiveness levels are similar above the slot, at the vane leading edge,

in the vane passage, and at the vane trailing edge. Also, the region of the endwall that

was effectively cooled by the exit slot flow is nearly the same size and shape in Figures

5.20a and 5.20b.

3.3 Uncertainty Analysis

An uncertainty analysis was performed on each of the values presented in this

study. The partial derivative method, described in detail by Moffat (1988), was used for

the uncertainty analysis. The total uncertainty for each measured value was defined as

the square root of the sum of the squares of the precision uncertainty and the bias

uncertainty.

The precision uncertainty for each value was determined by taking the standard

deviation of a number of measurements at the same location. To determine the precision

uncertainty for the adiabatic wall temperatures, ten infrared camera pictures were taken

of the endwall in a region with a large temperature gradient, with each picture being an

average of 16 measurements. For the pressure measurements, the precision uncertainty

was taken from the study done by Barringer (2001). This was assumed to be valid

because the pressure measurements reported in Barringer’s study were made with same

instruments and data acquisition system in a relatively similar flow field. The precision

45

uncertainties that occurred for the thermal fields were similar to those reported by

Barringer (2001) given the similarity in the flow field and measurement devices. For

each velocity component, 25000 data points were taken over a period of 20 to 40

seconds. Repeated measurements were not taken at each location, so to determine the

precision uncertainty in velocity measurements, a set of 25000 data points was split into 5

groups of 5000 data points. This allowed for the precision uncertainty to be calculated,

although it is an overestimate of the actual precision uncertainty.

The bias uncertainty for the pressure measurements was 0.5% of the pressure

transducer range. The bias uncertainty for the thermocouple temperature measurements

was 0.15°C, which was the thermocouple variation recorded during a bias reading taken

prior to running the experiments. The bias uncertainty for all velocity measurements

using the LDV was 1.0% of the measured mean quantity.

Table 3.6 summarizes the results from the uncertainty calculations. Detailed

uncertainty calculations for this study are given in Appendix B. In general, the

uncertainty increased as the magnitude of the measured quantity decreased. A fairly high

uncertainty of 17.59% was calculated for a value of η = 0.2. It should be pointed out

however, that most of the measured endwall adiabatic effectiveness levels were above η

= 0.2. Overall, there were low uncertainties for each of the mean and fluctuating flow

quantities. A high percent uncertainty of 25.53% in pitch angle for a value of φ = 3.40°

was calculated. The actual uncertainty in the angle was 0.87°, which was the same

amount of uncertainty that was calculated for the larger pitch angle of φ = 19.22°. The

reason for the high percent uncertainty is because of the small φ value.

46

Table 3.1. Film-cooling hole spacing for each panel in the pitchwise and streamwise directions (t = 1.27 cm, D = 0.7).

Liner Geometry Sp/D Ss/D

Panel 1 10.1 5.8 Panel 2 6.1 3.5 Panel 3 6.1 3.5 Panel 4 10.1 5.8

Table 3.2. Feed hole parameters for the three slot flow cases.

D (cm)

P (cm)

Hole Area/Sector (cm2)

Hole Area/Slot Area/Sector

Half Slot Flow 0.47 3.81 4.16 0.028 Design Slot Flow 0.94 7.62 8.33 0.057 Double Slot Flow 0.94 3.81 16.66 0.114 Table 3.3. Location of vane static pressure taps measured from the vane stagnation

point. Pressure Side Suction Side

s/C s/C -0.022 0.035 -0.04 0.075 -0.067 0.135 -0.107 0.195 -0.205 0.281 -0.287 0.342 -0.366 0.424 -0.524 0.505 -0.617 0.648 -0.708 0.714 -0.795 0.81

0.934 1.03 1.101

47

Table 3.4. Global location of endwall thermocouples.

X/C Y/C -0.0043 -0.4661 0.1657 -0.5195 0.23572 -0.573 0.29131 -0.6435 0.33728 -0.7173 0.39287 -0.7761 0.46235 -0.8456 0.47839 -0.9044 -0.0011 0.26191 0.57085 -0.9129

48

Table 3.5. Global location of endwall markers.

X/C Y/C -0.0321 0.02138 -0.0321 0.02673 -0.0321 0.03207 -0.0053 0.21915 -0.0053 0.42226 -0.0053 0.55856 0.12026 0.21915 0.1216 0.41959 0.28062 0.21648 0.35278 0.0588 0.40623 0.05612 0.41025 -0.0989 0.41424 -0.2098 0.51045 -0.2138 0.48373 -0.4623 0.56925 -0.4623 0.62003 -0.7162 0.53451 -0.7136 -0.0267 -0.1737 0.08018 -0.2673 0.08018 -0.3955 0.1951 -0.3929 0.08018 -0.4627 0.08018 -0.5853 -0.0214 -0.5853 -0.0187 -0.4436 0.24988 -0.628 0.33674 -0.628 0.47838 -0.8686 0.49602 -0.7868

49

Table 3.6. Summary of uncertainty analysis.

Variable Percent Uncertainty ∆P = 1.827 3.05 ∆P = 0.210 12.17 θ = 0.609 5.42 θ = 0.211 13.49 η = 0.9 4.10 η = 0.2 17.59

Vz/Uinlet = 1.39 1.05 Vz/Uinlet = 0.19 3.02 Vn/Uinlet = -0.73 2.70 Vn/Uinlet = 0.19 7.26 Vs/Uinlet = 4.64 1.01 Vs/Uinlet = 3.31 0.94

wrms/Uinlet = 0.612 1.41 wrms/Uinlet = 0.152 1.32 vrms/Uinlet = 0.536 1.44 vrms/Uinlet = 0.300 2.57 urms/Uinlet = 0.427 1.93 urms/Uinlet = 0.186 5.27

ψ = 16.22° 1.57 ψ = 1.30° 7.57 φ = 19.22° 4.98 φ = 3.40° 25.53 Tu = 0.52 1.64 Tu = 0.17 2.83

50

Figure 3.1. Schematic of closed-loop wind tunnel facility

Figure 3.2. Cut-away of combustor simulator test section, showing individual plenum

supply chambers.

DilutionHoles

Film Cooling

51

Figure 3.3. Film-cooling hole and dilution jet orientation (dimensions are in cm).

Figure 3.4. Film-cooling hole spacing in the pitchwise and spanwise directions.

Turbine Sector

40.6 37.9 45.740.6

111.8

91.4

10.2

10.2

70.9 94.8

X

Y

52

Figure 3.5. Schematic of exit slot showing feedholes and staggered array of pin fins. Figure 3.6. Global and local coordinate systems.

s

Y, V

Z, W X, U

x, u

y, vz, w

53

Figure 3.7. Location of measurement planes: inlet, stagnation (SP), and suction side 2

(SS2).

SS2

SPInlet

54

Figure 3.8. Total pressure profiles exiting the combustor for heated flow and isothermal flow, illustrating the effect of density on the total pressure profile.

0.0 0.2 0.4 0.6 0.8 1.00

0.1

0.2

0.3

0.4

0.5

Isothermal Flow

Heated Flow

Z/S

(Po - P

o,CL) / 0.5 ρ U

inlet

2

55

a) b) Figure 3.9. Thermocouple rake (a) diagram and (b) orientation in the stagnation

measurement plane.

Thermocouple Rake

2.9 h

h Z0.6 cm

7.6 cm Aluminum Tube

Thermocouple Bead (D = 0.7 mm)

Thermocouple Wire (D = 0.3 mm)

56

a) b) Figure 3.10. Kiel probe rake (a) diagram showing enlarged picture of probe head and

(b) orientation of rake in the inlet measurement plane.

Keil Probe Rake

2.9 h

h Z

Inner Probe (D = 1.6 mm)

Outer Shroud (D = 3.2 mm)

57

Figure 3.11. LDV system setup for spanwise (w) velocity measurements.

58

Figure 3.12. Illustration of probe head rotation angle (θ) for spanwise velocity

measurements.

wtrue

wmeas

θ

utrue

Vane

Endwall

Endwall

SS2 Plane

Probe Head

Laser Beams

59

-5 -4 -3 -2 -1 0 10

0.2

0.4

0.6

0.8

1

Mid-pitch, Inlet Plane

SS2 Plane at y/P = 0.1Z/S

(Po - P

o,ms) / 0.5 ρ U

in2

Figure 3.13. Total pressure profiles showing passage symmetry.

60

Figure 3.14. Illustration of probe head tilt angle (α) for spanwise and pitchwise

velocity measurements.

wmeas

α

vmeas

wtrue

vtrue

α

Vane

Flexible Wall

Lower Endwall

Top Endwall Overhang

Probe Head for Spanwise Measurements

Laser Beams

Probe Head for Pitchwise Measurements

Laser Beams

61

Figure 3.15. LDV system setup for streamwise (u) and pitchwise (v) velocity

measurements. Figure 3.16. Illustration of probe head rotation angle (θ) for pitchwise velocity

measurements.

vtrue

vmeas

utrue

θ

Flexible Wall

VaneSS2 Plane

Probe Head

Laser Beams

62

0

5

10

15

20

0 0.05 0.1 0.15 0.2 0.25

CFD ResultsDouble SlotDesign Slot

ψψψψ

y/P

ms

Figure 3.17. Flow turning angle at the midspan for the two slot flow cases for which

flow field measurements were taken. Also shown are computational predictions (Lethander, 2001) for the same geometry and flow conditions.

63

Figure 3.18. Infrared camera viewing port location (Radomsky, 2000). Figure 3.19. Infrared camera positioning for the surface temperature measurements.

-1.00

-0.75

-0.50

-0.25

0.00

0.25

0.50

0.75

1.00

1.25

-0.50 -0.25 0.00 0.25 0.50 0.75

Y/P

X/C

IR Camera

Plexiglass Supports

Top Endwall

Lens

Port

Plexiglass Port Cover

64

a)

1.00

0.75

0.50

0.25

0.00

-0.25

-0.50

-0.75

-1.00

-0.25 0.00 0.25 0.50 0.75

Y/C

X/C

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

∞

∞

−−=η

TTTT

cool

aw

65

b) Figure 3.20. Endwall adiabatic effectiveness contours for case 3 measured during two

separate experiments showing repeatability.

1.00

0.75

0.50

0.25

0.00

-0.25

-0.50

-0.75

-1.00

-0.25 0.00 0.25 0.50 0.75

Y/C

X/C

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

∞

∞

−−=η

TTTT

cool

aw

66

Chapter 4

Test Matrix

To accomplish the research objectives (see section 2.4), it was necessary to design

a test matrix. Changes in combustor liner coolant and slot flow were quantified in terms

of their effect on the total pressure profile exiting the combustor. In order to accurately

design a test matrix, it was first necessary to determine how the panel flows and dilution

jets individually affected the combustor exit profile.

This chapter describes the development of the test matrix. The first section

discusses the combustor exit profile sensitivity studies. It also discusses the flow

visualization done for the liner panels and dilution jets. The second section in this

chapter describes the five test cases that were designed. Three of the cases were intended

to study the effect of liner coolant on the downstream turbine sector. The other two

cases, along with one of the first three, were intended to study the effect of slot flow on

the downstream turbine sector.

4.1 Combustor Exit Profile Sensitivity

Before the measurements described in the following chapters were done, a series

of sensitivity studies were performed to determine the effect of panel flow and dilution jet

flow on the total pressure profile exiting the combustor simulator (Walter 2000).

Barringer et al. (2001) found that the total pressure field exiting the combustor simulator

was non-uniform in the pitchwise direction, with a peak in total pressure in the near wall

region. There were two theories as to the cause of the peak in the total pressure profile.

The first theory was that the peak was caused by the film-cooling flow exiting the

combustor liner panels. The second theory was that it was caused by dilution jet

impingement on the opposite combustor wall. To determine which hypothesis was

67

correct, the flow exiting the liner panels and dilution jets were varied independently,

noting the effect on the exit total pressure profile.

The first sensitivity study was done on the first liner panel. This panel is located

122 cm upstream of the combustor exit. To determine the effect of the first panel on the

total pressure field exiting the combustor, the flow rate through that panel was varied,

while the flow rates through the other panels and the dilution jets remained constant.

Three different percentages of the total exit mass flow were studied; 1.5%, 2.2%, and

3.6%. The total pressure profile was measured at a pitch location of Y/P = 0 and

normalized using equation 4.1:

2inlet

oclo

U5.0PPP

ρ−=∆ (4.1)

where Po is the measured total pressure, Pocl is the total pressure at the midspan, and Uinlet

is the mass-averaged inlet velocity (6.25 m/s). Figure 4.1 shows the results from the

sensitivity study for panel 1. No noticeable changes occurred in the total pressure profile

exiting the combustor for any of the three flow rates that were studied.

Exit profile insensitivity to panel 1 can be better understood from the results of

flow visualization studies (Richard, 2000). To perform these tests, the plenum supply

chambers for either the panels or the dilution jets were filled with fog. Pictures were

taken as the fog exited the plenum into the combustor simulator. Figure 4.2 shows the

flow visualization for the first liner panel. Film-cooling flow exiting the first panel

completely covered the wall until it reached the first row of dilution jets. As the film-

cooling flow approached the first row of dilution jets, it was entrained into the free

stream. This entrainment helps to explain why the amount of flow rate exiting the first

panel does not affect the total pressure profile exiting the combustor. The first row of

dilution jets mixed out the film-cooling flow exiting the first panel, so it essentially had

no effect beyond panel 1. Another important consequence of film-cooling entrainment is

that a thermal hot spot was formed just downstream of the dilution holes. The thermal

hot spots downstream of the dilution jets can be seen in Figure 4.3 (from a computational

study by Stitzel, 2000).

68

The second sensitivity study was done on the third and fourth liner panels. Just as

with the first panel, the mass flow rate through the last two panels was varied while the

flow rate exiting the other panels and the dilutions jets remained constant. The total

pressure profile exiting the combustor was measured at a pitch location of Y/P = 0 for

three different mass flow rates; 1.5%, 2.2%, and 3.5%. Shown in Figure 4.4 are the

results from the sensitivity study for panels 3 and 4. Clearly, the amount of mass flow

exiting the last two panels has a significant effect on the total pressure profile exiting the

combustor. Increasing the mass flow exiting panels 3 and 4 increases the peak in total

pressure in the near wall region. The total pressure levels in the free stream above 20%

span remain relatively constant for each of the three trials, indicating that the only effect

of increasing the flow rate through the last two panels is to increase the peak in total

pressure in the near wall region.

To verify that the panel flow exiting the third and fourth liner panels was solely

responsible for the peak in total pressure, the effect of dilution jet flow on the total

pressure profile exiting the combustor was examined. In theory, if the peak in total

pressure was being caused by dilution jet impingement on the opposite combustor wall,

then increasing the momentum flux ratios of the dilution jets would increase the peak in

total pressure. To test this theory, the total pressure profile exiting the combustor for

nominal dilution jet conditions (J1 = 105 and J2 = 28, where J1 and J2 are the momentum

flux ratios for the first and second row of dilution holes) was compared to the profile for

a case with only top dilution flow and increased dilution jet momentum flux ratios (J1 =

174, J2 = 42). The total pressure profile was measured at a pitch location of Y/P = 0.

Figure 4.5 shows the measured total pressure profiles exiting the combustor for each

dilution case. The peak value is higher in Figure 4.5 than in Figure 4.4 because the panel

flow exiting the last two panels was increased slightly. The peak in the total pressure

profile in Figure 4.5 was essentially unaffected by the increase in dilution jet momentum

flux ratio. This result suggested that the dilution flow was not responsible for the peak in

total pressure exiting the combustor in the near wall region.

For the case with both top and bottom dilution on, the profile in Figure 4.5 is flat

above 25% span. However, for the case without bottom dilution, the profile is not as flat

69

in that same region. The reason is that the bottom dilution jets provided a great deal of

mixing when they were on, flattening out the profile in the freestream.

The flow visualization done for the first row of dilution jets helped explain why

the dilution flow did not affect the peak in total pressure. Figure 4.6a shows the flow

visualization for the nominal dilution jet case. Penetrating only to near midspan, the

dilution flow did not even reach the opposite combustor wall. The dilution jets in the

combustor simulator were in-line, meaning that the top and bottom dilution jets were

located in the same pitchwise direction. This explained why the jet only penetrated to

midspan, because it was impinging on the opposite dilution jet. Some engines, however,

have staggered dilution jets. To see if a staggered jet would reach the opposite wall, the

bottom dilution jets were plugged, and the momentum flux ratio of the top dilution jets

was increased as much as possible. The flow visualization for this case is shown in

Figure 4.6b. Even without the bottom dilution flow, the top dilution jets only penetrated

slightly past midspan. This result suggested that the combustor core flow was sufficient

to mix out the dilution jets before they reached the opposite wall.

4.2 Design of Test Matrix

In order to independently study the effects of both liner coolant and slot flow, five

test cases of turbine inlet conditions were developed. Three test cases kept the slot flow

and dilution flow constant and varied only the film-cooling exiting the third and fourth

combustor liner panels. These three cases were intended to have a nominal, reduced, and

increased amount of liner coolant. Two other cases were then developed to study the

effect of slot flow on the downstream turbine. These cases had the same combustor flow

conditions as the nominal liner coolant case, with either a reduced or increased amount of

slot flow.

Using the results of the sensitivity studies, five flow cases were chosen to

independently study the effects of increasing the film-cooling flow out of the last two

panels and increasing the exit slot flow. Table 4.1 shows the flow rates and momentum

flux ratios for each of the five test cases (a detailed description of each case is given in

70

Appendix C), while Figure 4.7 shows the total pressure profile exiting the combustor for

each flow case. These total pressure measurements were taken at a pitch location of Y/P

= 0.5. Case 1 had a relatively flat exit profile and a reduced amount of liner coolant from

the nominal case (Case 2). The flow conditions for Case 1 were the same as those for

which the combustor simulator was designed. Case 2 was intended to be the nominal

case for both liner coolant flow and slot flow and had a peak value in total pressure of ∆P

= 0.7. The peak was formed by increasing the total amount of film-cooling exiting the

third and fourth panels from 10% of the total exit mass flow for case 1 to 14.4% for case

2. Case 3 was obtained by further increasing the amount of mass flow exiting the third

and fourth liner panels to 18.2% of the total exit mass flow. This additional increase

resulted in a peak in total pressure of ∆P = 2.2.

The total pressure was also measured in the exit slot. Because the pressure

exiting the slot was non-uniform in both the pitchwise and spanwise directions,

measurements were taken at five different span locations (Z/S = 0.001, 0.007, 0.014,

0.021, and 0.028) and pitch-averaged. The pitch-averaged slot measurements for each

case were normalized using equation 4.1, and added to Figure 4.7. The pitchwise total

pressure variation results from the non-uniformity in exit slot flow due to the presence of

the pin fins (Barringer et al., 2001) and the static pressure distribution on the endwall

(Shih et al., 2000). The range in pitch location for the total pressure measurements was

determined by examining the adiabatic effectiveness contours to see where coolant flow

was exiting the slot. As expected, the pitch-averaged total pressure profiles below the

step were the same for each of the first three cases (as seen in Figure 4.7). The exit slot

flow was kept constant at 1.26% of the combustor exit mass flow for each of the first

three cases.

Total pressure contours were taken in the inlet plane for case 1, case 2, and case 3

(Walter 2000). Equation 4.2 was used to normalize the total pressure measurements:

2inlet

ocl

__

o

U5.0PPP

ρρρρ−=∆ (4.2)

71

where ocl__

P is the pitch-averaged value of total pressure at the midspan. Figure 4.8 shows

the total pressure contours in the inlet plane for cases 1, 2, and 3. These contours reflect

the profiles shown in Figure 4.7 for each of the first three cases. The contour for case 1

was uniform in the pitchwise direction and flat above 10% span, with only a small rise in

total pressure near the wall. Case 2 shows pitchwise uniformity, with a flat contour

above 15% span. The peak in total pressure of ∆P = 1.0 occured at a pitch location of

Y/P = 0, which corresponded to the vane stagnation location. At a pitch location of Y/P

= 0.5, the peak total pressure was ∆P = 0.7, which corresponded to the peak value shown

in Figure 4.7 for the total pressure profile at the same pitch location.

Case 3 was not entirely uniform in the pitchwise direction, showing slightly

higher total pressure levels between Y/P = -0.3 and Y/P = 0.3. The reason for the lower

total pressure values near midpitch (Y/P = 0.5) was because of the location and

orientation of the second row of dilution holes. The second row of dilution holes was

located at midpitch and angled into the direction of the flow. The dilution holes created a

flow blockage in the midpitch region resulting in lower velocities near Y/P = 0.5

(Barringer et al., 2001). The effect of lower streamwise velocities near midpitch was

seen as a reduction in total pressure levels at that location. The peak in total pressure of

∆P = 2.0 occured at a pitch location of Y/P = 0, corresponding to the vane stagnation

location. At the midpitch location (Y/P = 0.5), the peak total pressure was slightly lower

and approximately ∆P = 1.5. The peak value at the midpitch location did not correspond

to the peak level shown in the total pressure profile in Figure 4.7 of ∆P = 2.2 for case 3.

The reason for this discrepancy was in the way the two pressures were normalized. The

profile in Figure 4.7 was normalized using equation 4.1, which used the difference

between the measured total pressure and the total pressure at the midspan. The total

pressure contour in Figure 4.8c was normalized using the pitch-averaged total pressure at

the midspan, which was not constant for case 3. The total pressure at the midspan was

lower at midpitch than at the stagnation point. The reason that the peak total pressure at

the midpitch location for case 2 agreed for the contour and profile was because there was

only a slight pitchwise total pressure variation above 15% span.

The total pressure contours measured below the step for cases 1, 2, and 3 are

shown in Figure 4.9. These pressure measurements were normalized using equation 4.1,

72

where Pocl was measured at the midspan location of Y/P = -0.5. The total pressure

contours for the first three cases show very good agreement with each other. Clearly,

total pressure variation exists in both the spanwise and pitchwise direction for the exit

slot flow. The total pressure levels in the slot ranged from ∆P = 0.0 to ∆P = -3.5. The

total pressure gradient between the liner flow above the step and the slot flow below the

step increased for each case. For each case, the average total pressure below the step was

∆P = -2.5, while the total pressure peak just above the slot was approximately ∆P = 0.0

for case 1, ∆P = 0.7 for case 2, and ∆P = 2.2 for case 3. The pressure gradient between

the flow above and below the step gave an indication of the amount of liner flow that was

being driven towards the endwall as it entered the turbine section. The steeper the

pressure gradient, the more liner flow would be forced towards the endwall.

Cases 4 and 5 were developed in order to study the effect of slot flow on the

downstream turbine. Case 4 was obtained by reducing the slot mass flow rate from

1.26% of the total exit mass flow to 0.63% and keeping all other conditions the same as

case 2. The 0.63% of additional flow that was used in the slot for case 2 was added back

into the main stream for case 4. Figure 4.7 shows that the total pressure measurements

below the step for case 4 were lower than those for case 2, which was expected because

of the reduced mass flow exiting the slot in case 4. Case 5 was obtained by doubling the

amount of slot flow from 1.26% of the total exit mass flow to 2.52%, and keeping all

other flow conditions the same as case 2. The total pressure measurements below the

step were much higher for case 5 than for case 2, which was expected because of the

increased mass flow exiting the slot in case 5. As described in section 3.1 (Combustor

Simulator), the slot flow was varied by changing the diameter and spacing of the

feedholes (see Figure 3.5 and Table 3.2).

The total pressure contours measured below the step for cases 2, 4, and 5 are

shown in Figure 4.10. These pressure measurements were normalized using equation 4.1,

where Pocl was measured at the midspan location of Y/P = -0.5. Generally, the total

pressure levels in the slot were lower for case 4 than for case 2, indicating reduced mass

flow exiting the slot. There was a large pressure gradient between the liner flow above

the step (which had a total pressure level near ∆P = 0.7) to the slot flow below the step

(which had an average total pressure level of ∆P = -2.79) for case 4. The total pressure

73

levels in the slot for case 5 were much higher than for case 2. The total pressure gradient

between the liner flow above the step (which had a total pressure level near ∆P = 1.0) and

the slot flow below the step (which had an average total pressure level of ∆P = -1.25) was

less for case 5 than for any of the previous cases.

Endwall adiabatic effectiveness measurements were taken for all five test cases.

Thermal field measurements were only taken for the first three cases because of the large

total pressure gradient between the liner flow and the slot flow. This large total pressure

gradient keeps the slot flow near the endwall, which would indicate that changing the slot

flow has little effect on the stagnation plane thermal field. Flow field measurements in

the SS2 plane were taken for case 2 and case 5. The flow field is altered by changing the

driving pressure gradient between the liner coolant and the slot flow. Based on the

literature review (see Chapter 2), the secondary flow field in a turbine vane passage is

affected by increasing the amount of slot flow, which also reduces the driving pressure

gradient between the liner flow and slot flow. To verify this stipulation, the secondary

flow field was mapped out in the SS2 measurement plane for the nominal slot flow case

(case 2) and the double slot flow case (case 5).

74

Table 4.1. Percentage of coolant based on exit mass flow (jet momentum flux ratios are in parentheses).

Case 1 2 3 4 5

Panel 1 1.5 (15.6) 1.5 (17.3) 1.5 (19.7) 1.5 (16.8) 1.5 (18.4) Panel 2 3.5 (12.3) 3.5 (13.7) 3.4 (15.1) 3.5 (13.3) 3.5 (14.5) Panel 3 3.4 (7.7) 4.5 (13.9) 5.4 (21.6) 4.5 (13.6) 4.5 (14.4) Panel 4 1.6 (2) 2.7 (5.5) 3.7 (10.3) 2.7 (5.4) 2.7 (5.6)

Dilution 1 8.8 (130) 8.3 (128) 7.9 (128) 8.3 (125) 8.3 (136) Dilution 2 8.8 (33) 8.5 (33) 8.2 (33) 8.5 (32) 8.5 (34)

Slot 0.63 0.63 0.63 0.315 1.26

75

Figure 4.1. Exit total pressure profile sensitivity to panel 1 mass flow.

Figure 4.2. Flow visualization for panel 1.

-0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.00.0

0.1

0.2

0.3

0.4

0.5Panel 1 Flow = 1.5%

Panel 1 Flow = 2.2%

Panel 1 Flow = 3.6%

(Po - P

ocl) / 0.5 ρ U

inlet

2

Z/S

Design Conditions

Top of Slot

Panels 2-4 and Dilution Flowsat Case 1 Conditions

76

Figure 4.3. Combustor liner adiabatic effectiveness. From a computational study

performed by Stitzel (2000).

Figure 4.4. Exit total pressure profile sensitivity to panel 4 mass flow.

-0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0

Panel 4 Flow = 1.5%

Panel 4 Flow = 2.2%Panel 4 Flow = 3.5%

0.0

0.1

0.2

0.3

0.4

0.5

(Po - P

ocl) / 0.5 ρ U

inlet

2

Z/S

Design Conditions

Top of Slot

Panels 1-3 and Dilution Flowsat Case 1 Conditions

Panel 1 Panel 2

77

Figure 4.5. Exit total pressure profile sensitivity to dilution flow.

-0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.00.0

0.1

0.2

0.3

0.4

0.5Top Dilution OnlyJ

1 = 174, J

2 = 42

Top and Bottom DilutionJ

1= 105, J

2 = 28

Z/S

(Po - P

ocl) / 0.5 ρ U

inlet

2

Panel Flows at Case 3 Conditions

78

(a)

(b) Figure 4.6. Dilution flow visualization for (a) nominal dilution flow conditions and

(b) top dilution only with higher momentum flux ratios.

79

Figure 4.7. Combustor exit total pressure profiles at the midpitch for all five flow

cases.

-3.0 -2.0 -1.0 0.0 1.0 2.0 3.00.0

0.1

0.2

0.3

0.4

0.5Case 1 (Design)

Case 2Case 3Case 4,(Case 2, half-slot flow)Case 5,(Case 2, double-slot flow)

Repeat Case 1

Z/S

(Po - P

ocl) / 0.5 ρ U

inlet

2

80

(a)

(b)

(c) Figure 4.8. Inlet plane total pressure contours for (a) case 1, (b) case 2, and (c) case 3.

0.0

0.1

0.2

0.3

0.4

0.5

-0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5

Z/S

Y/P

0.0

0.1

0.2

0.3

0.4

0.5

-0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5

Z/S

Y/P

-0.5

0

0.5

1

1.5

2

0.0

0.1

0.2

0.3

0.4

0.5

-0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5

Z/S

Y/P

Po - Pocl

0.5ρρρρUinlet2

81

(a)

(b)

(c) Figure 4.9. Slot total pressure contours for (a) case 1, (b) case 2, and (c) case 3.

Po - Pocl

0.5ρρρρUinlet2

0.00

0.01

0.02

0.03

-0.75 -0.70 -0.65 -0.60 -0.55 -0.50 -0.45 -0.40 -0.35 -0.30 -0.25

Z/S

Y/P

0.00

0.01

0.02

0.03

-0.75 -0.70 -0.65 -0.60 -0.55 -0.50 -0.45 -0.40 -0.35 -0.30 -0.25

Z/S

Y/P-4-3.5-3-2.5-2-1.5-1-0.500.51

0.00

0.01

0.02

0.03

-0.75 -0.70 -0.65 -0.60 -0.55 -0.50 -0.45 -0.40 -0.35 -0.30 -0.25

Z/S

Y/P

82

(a)

(b)

(c) Figure 4.10. Slot total pressure contours for (a) half slot flow (case 4), (b) nominal slot

flow (case 2), and (c) double slot flow (case 5).

Po - Pocl

0.5ρρρρUinlet2

0.00

0.01

0.02

0.03

-0.75 -0.70 -0.65 -0.60 -0.55 -0.50 -0.45 -0.40 -0.35 -0.30 -0.25

Z/S

Y/P

0.00

0.01

0.02

0.03

-0.75 -0.70 -0.65 -0.60 -0.55 -0.50 -0.45 -0.40 -0.35 -0.30 -0.25

Z/S

Y/P-4-3.5-3-2.5-2-1.5-1-0.500.51

0.00

0.01

0.02

0.03

-0.75 -0.70 -0.65 -0.60 -0.55 -0.50 -0.45 -0.40 -0.35 -0.30 -0.25

Z/S

Y/P

83

Chapter 5

Thermal Field and Flow Field Results

After developing the test matrix discussed in Chapter 4, thermal field

measurements were performed to study the effect of liner coolant on the stagnation plane

thermal field. Flow field measurements were also performed to study the effect of slot

flow on the secondary flow field in the vane passage. The first section of this chapter

discusses in detail the thermal field measurements that were done in the stagnation plane.

Measured and predicted stagnation plane flow field results will supplement the thermal

field measurements. The second section of this chapter discusses the flow field

measurements that were performed in a suction side measurement plane. Prior to

discussing the results, the velocity transformation used to examine the secondary flow

field is explained. The flow field results are presented in the form of secondary velocity

vectors, and contours of turbulence intensity, flow angles, velocities, and vorticity.

Comparisons to a previous experimental flow field study performed by Kang and Thole

(2000) will be made to distinguish these results from studies performed with a turbulent

boundary layer as the turbine inlet profile.

5.1 Effects of Liner Coolant on the Stagnation Plane Thermal Field

Thermal field measurements were performed for case 1, case 2, and case 3 to

study the effects of increasing the combustor liner coolant on the thermal field

approaching the vane. A former student, Joe Walter, took these measurements in the

winter of 2001, before leaving school to become a pilot. Case 1 had the least amount of

liner film-cooling exiting the third and fourth liner panels (10% of the total exit mass

flow). The amount of film coolant was increased for case 2 (14.4% of the total exit mass

flow), and again for case 3 (18.2% of the total exit mass flow). The thermal field

84

measurements are presented in terms of a non-dimensional temperature, θ, as defined in

equation 5.1:

∞

∞

−−

=θTT

TT

cool

(5.1)

where T∞ is the mass averaged freestream temperature (given in equation 3.13), and Tcool

is the average coolant temperature determined by averaging the thermocouple

temperatures in each of the liner panel, dilution hole, and exit slot plenums.

Figure 5.1 shows the thermal fields for cases 1, 2, and 3. It is clear from these

thermal fields that the temperature of the air above the step was reduced as the amount of

film coolant increased. The maximum θ value above the step was θ = 0.4 for case 1, θ =

0.5 for case 2, and θ = 0.6 for case 3. Higher θ values indicate lower air temperatures.

Negative values of θ were measured above approximately 15% span for each case. The

reason for the negative θ values was that the temperature above 15% span was warmer

than T∞, which resulted in a negative θ value using equation 5.1. Large amounts of

cooling flow through the liner panels, dilution holes, and exit slots reduced the value of

T∞ such that it was cooler than the heated air temperature in the freestream.

One trend that is clear from the thermal fields shown in Figure 5.1 is that as the

amount of film coolant was increased, more coolant was being driven up the vane surface

in the spanwise direction. For example, the θ = 0.1 contour touched the vane surface at

approximately 8% span for case 1, 19% span for case 2, and 28% span for case 3. The

transport of coolant up the vane surface as the film-cooling was increased indicates that

increasing the combustor liner film-cooling does not directly translate to better endwall

cooling. Engine designers believed that increasing liner coolant would help cool the

endwall in the downstream turbine. However, the stagnation plane thermal fields in

Figure 5.1 indicate that a large amount of the additional film-cooling was being

transported along the vane away from the endwall thereby having no benefit on the

endwall.

Another important trend that can be seen from the stagnation plane thermal fields

shown in Figure 5.1 is that as the combustor liner film-cooling was increased, cooler air

85

was being ingested into the exit slot. For example, the θ = 0.1 contour was being pulled

into the slot in case 1, the θ = 0.4 contour was drawn into the slot in case 2, and the θ =

0.5 contour was pulled into the slot in case 3. Figure 5.2a shows velocity measurements

taken with the LDV in the stagnation plane for case 2 (Lethander, 2001). These

measurements revealed that the film coolant above the step was being pulled down

towards the endwall. Stitzel (2001) used the CFD software Fluent to predict the flow

field in the stagnation plane for case 1 flow conditions. Her prediction, shown in Figure

5.2b, shows the formation of a leading edge vortex as the film coolant is forced down

towards the endwall and into the slot. The velocity measurements in Figure 5.2a were

not sufficient to verify the formation of the leading edge vortex, but they show the

beginning of what could possibly be a leading edge vortex as the film coolant approached

the vane leading edge and turned down towards the endwall. The thermal field

measurements indicate that this downward flow pulled liner coolant into the slot under

the step. Because more coolant was ingested into the slot as the film-cooling was

increased, it is reasonable to believe that the downward flow was stronger for larger

amounts of film-cooling flow.

The two previous trends, coolant transport up the vane span and coolant ingestion

into the slot, can be explained by the total pressure profiles exiting the combustor for the

three cases that were studied. Figure 4.7 shows the total pressure profiles for each flow

case. As the amount of liner film-cooling was increased from case 1 to case 2, and

further increased from case 2 to case 3, the pressure difference between the peak total

pressure and the midspan total pressure was increased. The pressure difference between

the peak total pressure and the exit slot total pressure was also increased. Because the

flow stagnates at the vane stagnation location, these total pressure gradients become static

pressure gradients as the flow approached the vane. The resulting static pressure

gradients cause the coolant to go either up the vane surface, or into the exit slot.

As the liner film-cooling was ingested into the slot, it mixed with the cooler slot

flow, and raised the temperature of the air exiting onto the endwall surface. Although the

liner coolant was much cooler than the combustor core flow, it was still warm relative to

the slot flow. For case 1, with the warmest of slot ingestion, the θ value exiting the slot

in the stagnation plane was near θ = 0.6 (shown in Figure 5.1a). For case 2, which had

86

more slot ingestion, the maximum θ value exiting the slot in the stagnation plane was

near θ = 0.5 (shown in Figure 5.1b). Similar θ values were measured for case 3 in the

stagnation plane (Figure 5.1c). This result shows that increasing the liner film-cooling

has the detrimental effect of raising the air temperature exiting the slot.

The thermal field results indicate that increasing the amount of liner film-cooling

was not beneficial to endwall cooling in the downstream turbine vane passage near the

vane stagnation plane. First, as film-cooling was increased, more coolant was transported

along the vane span because of the increased static pressure gradient between the liner

flow and the midspan flow. Although this coolant provided no thermal benefit to the

endwall, it did provide a thermal benefit to the vane surface, which is another critical

surface in terms of thermal failure. Second, as liner film-cooling was increased, more

liner coolant was ingested into the exit slot. The liner coolant mixed with the cooler slot

flow, resulting in higher air temperatures exiting the slot. The increased slot ingestion

resulted from the strengthening of the static pressure gradient between the film coolant

and the slot flow.

5.2 Effects of Slot Flow on Secondary Flows

Velocity measurements were taken in the SS2 measurement plane with a two-

component LDV system. The SS2 plane was located a distance of s/C = 0.35 from the

vane stagnation point along the vane suction side (see Figure 5.3). All three components

of velocity were measured for case 2 (design slot flow) and case 5 (double slot flow).

Chapter 3 describes in detail the measurement procedure and the velocity corrections that

were necessary to capture the spanwise (w) and pitchwise (v) velocity components.

Chapter 4 describes in detail the two flow cases that were studied for the flow field

measurements.

The measured local mean velocities (u, v, and w) were transformed into mean

velocities in the flow direction (Vs, Vn, and Vz, as shown in Figure 5.3). The direction of

the flow streamline was determined by measuring the flow turning angle at the midspan,

ψms, which is given in equation 5.2:

87

)uv

(tanms

ms1ms

−=ψψψψ (5.2)

where vms and ums were the local measured pitchwise and streamwise velocities at the

midspan. The flow turning angle is illustrated in Figure 5.3. Equations 5.3, 5.4, and 5.5

were used to transform the measured local mean velocities into mean velocities in the

streamwise direction (Vs) and mean velocities normal to the flow streamlines (Vn and

Vz).

msmss sinvcosuV ψψψψψψψψ ⋅+⋅= (5.3)

msmsn cosvsinuV ψψψψψψψψ ⋅+⋅−= (5.4)

wVz = (5.5)

By transforming the measured local velocities, a clear picture of the secondary flow field

was obtained. By definition, secondary flows are the velocity vectors normal to the local

streamwise direction (which is determined by ψms), so it was appropriate to view the

secondary flow field using the transformation given by equations 5.2 through 5.5. In

contrast, many of the flow field studies in the literature are presented in axial

measurement planes that are perpendicular to the turbine inlet flow streamlines. These

axial measurement planes skew the secondary flows and do not give an accurate

representation of the vortices that develop in the passage.

Before the velocity transformations were made, the flow turning angles at the

midspan, ψms, and the measured streamwise velocities, Vs, at the midspan were compared

to a three-dimensional, periodic, and viscous CFD prediction for the same flow

conditions as case 2 and the same geometry as the experiments (Lethander, 2001).

Measured values of ψms and Vs were also compared to those reported by Kang and Thole

(2000) in a study using the same vane geometry and a turbulent boundary layer as the

turbine inlet condition. Figure 5.4a shows the measured and computational values for the

flow turning angle at the midspan. Near the suction side of the vane, the flow turning

88

angle approached ψms = 0° for case 2 and 5, as well as the CFD prediction, which is

expected if the flow was following the streamline defined by the vane surface. The flow

turning angles at the midspan measured by Kang and Thole did not agree with the

measured and predicted values for this study. The flow turning angle increased linearly

across the SS2 measurement plane, with values near 17° at the pressure side of the

neighboring vane. The streamwise velocities at the midspan were normalized using the

turbine inlet velocity, Uinlet, and are shown in Figure 5.4b. The streamwise velocities are

highest near the vane suction side, with values of Vs/Uinlet near 4.8. The streamwise

velocity decreases in a linear fashion across the SS2 measurement plane, with the lowest

values at the pressure side of the vane near Vs/Uinlet = 3.2. The values of streamwise

velocity measured by Kang and Thole agreed well with those presented in this study.

Overall, there was good agreement between the predicted and measured values for both

ψms and Vs for the design slot flow case (case 2) and the double slot flow case (case 5).

The secondary flow field in the SS2 plane for case 2 is shown in Figure 5.5a. The

secondary velocities were normalized using the turbine inlet velocity, Uinlet. Three

distinct vortices were present in the SS2 plane; the suction side corner vortex, the passage

vortex, and a third vortex located above the passage vortex with rotation opposite to the

passage vortex. The suction side corner vortex and the passage vortex are both included

in the secondary flow models discussed in chapter 2, such as the one shown in Figure 2.1

(proposed by Langston, 1980). The third vortex has been predicted computationally by

Hermanson and Thole (2000) and verified in a computational study by Lethander (2000),

but has not been shown experimentally in any of the published literature.

The passage vortex is caused from the interaction between two pressure gradients;

the pressure gradient between the film-cooling flow and slot flow and the cross-passage

pressure gradient. These pressure gradients cause the flow to rotate in a clockwise

direction. The passage vortex brings warmer freestream fluid down to the endwall along

the pressure side corner, and lifts the cooler exit slot flow off of the endwall. The center

of the passage vortex in the SS2 plane was located at a pitch location of y/P = 0.10 and a

span location of Z/S = 0.05. When a vortex is bounded on two sides by a wall, such as

the passage vortex in the vane passage, a smaller vortex with opposite rotation forms in

the corner. The suction side corner vortex develops as a result of the corner effects

89

associated with the larger passage vortex. This vortex wraps around the suction side of

the vane, bringing warmer freestream fluid down to the suction side corner and sweeping

cooler vane film-cooling and exit slot flow off of the vane and endwall surfaces. The

center of the suction side corner vortex was located at a pitch location of y/P = 0.02 and a

span location of Z/S = 0.02 in the SS2 plane.

The formation of the tertiary vortex can be understood from the measured total

pressure profile in the SS2 plane. Figure 5.5b shows the total pressure profile measured

at a pitch location of y/P = 0.1 in the SS2 plane for case 2. The flow split between the

tertiary vortex and the passage vortex at a pitch location of y/P = 0.1 occurs at a span

location of Z/S = 0.11, which corresponds to the span location of the peak in the total

pressure profile. The local peak in total pressure results from the film-cooling flow

exiting the combustor, and causes the flow to either go up towards the midspan or down

towards the endwall. The pressure gradient between the film-cooling flow and the mid-

span flow, coupled with the cross passage pressure gradient, causes the tertiary vortex.

The rotation of the tertiary vortex is opposite to the rotation of the passage vortex because

of the opposite direction of the spanwise pressure gradient.

The flow split between the tertiary vortex and the passage vortex occurs at 17%

span near the vane suction side, and at 5% span near the vane pressure side. The tertiary

vortex drives the flow down the vane suction side towards the endwall and up the vane

pressure side towards the midspan. This counterclockwise rotation would tend to lift

critical film-cooling off of the vane surface. Because secondary flows introduce

aerodynamic penalties in the turbine passage, the presence of the tertiary vortex has

aerodynamic as well as thermal consequences to the turbine stator vanes.

The literature review in section 2.2 concerning combustor exit conditions shows

that assuming a turbulent boundary layer as the inlet profile to the turbine cascade is not

valid. Kang and Thole (2000) used a turbulent boundary layer with a boundary layer

thickness of δ/S = 0.1 as the turbine inlet condition. The flow field that they measured in

the SS2 plane is shown in Figure 5.6a. The importance of correctly modeling the

combustor exit flow when studying the flow field in the downstream turbine vane

passage is illustrated by the differences in Figure 5.5a and Figure 5.6a. Figure 5.6a

shows the presence of the suction side corner vortex and the passage vortex. However,

90

the tertiary vortex is not present in the flow field measured by Kang and Thole. The

passage vortex is present because the total pressure gradient between the near wall and

the endwall still exits for the turbulent boundary layer. The tertiary vortex was not

measured by Kang and Thole because there was no pressure gradient between the near

wall and the midspan flow, as there was for case 2.

Figure 5.6b shows the secondary flow field in the SS2 plane that was predicted by

Lethander (2001) for case 2. The three-dimensional, periodic, and viscous CFD

prediction shows the presence of all three vortices that were measured in this study. The

predicted tertiary vortex was closer to the endwall and the pressure side of the vane than

the measured tertiary vortex. The center of the tertiary vortex was at a span location of

Z/S = 0.16 for the predictions compared to a span location of Z/S = 0.23 for the

measurements. Also, the center of the tertiary vortex was at a pitch location of y/P = 0.18

for the predictions compared to a pitch location of y/P = 0.12 for the measurements. The

predicted tertiary vortex shown in Figure 5.6b was also smaller in size than the measured

tertiary vortex shown in Figure 5.5a. For the predicted flow field, there was no spanwise

flow above 30% span, while a small amount of spanwise flow occurred up to 50% span

for the measured flow field.

Figure 5.7 shows the effect of doubling the slot flow on the secondary flow field

in the SS2 plane. The size of the passage vortex in the spanwise direction was reduced

from case 2 (design slot flow). The reason for this reduction in size was because the

additional slot flow in case 5 increased the total pressure exiting the slot. As a result, the

total pressure gradient between the film coolant and slot flow decreased. This total

pressure gradient was partially responsible for the formation of the passage vortex. The

decrease in driving pressure ultimately reduced the size of the passage vortex in the

spanwise direction. On the other hand, the tertiary vortex increased in size slightly with

the additional slot flow. The higher total pressure in the slot caused less flow to be driven

down towards the endwall, which in turn caused more flow to be turned up towards the

midspan, resulting in a larger tertiary vortex. The center of the passage vortex moved

from y/P = 0.10 in case 2 to y/P = 0.12 in case 5, slightly closer to the pressure side of the

vane.

91

The reduction in size of the passage vortex as slot flow was increased is better

understood by examining the pitch angle contours. The pitch angle, φ, is defined in

equation 5.6:

= −

uwtan 1φφφφ (5.6)

where w and u are the local mean velocities in the spanwise and streamwise directions.

Contours of pitch angle, which illustrate the upward turning angle of the secondary flow

vectors, are shown in Figure 5.8 for cases 2 and 5. Near the upward leg of the passage

vortex, the pitch angles for the design slot flow are higher than those for the double slot

flow, with a maximum of φ = 18.7° at a span location of Z/S = 0.04 and a pitch location

of y/P = 0.07. In contrast, the maximum pitch angle for the double slot flow case near the

upward leg of the passage vortex was φ = 12.3° at a span location of Z/S = 0.04 and a

pitch location of y/P = 0.09. Likewise, the minimum pitch angle near the downward leg

of the passage vortex for case 2 was larger in magnitude than case 5. The minimum pitch

angle for case 2 was φ = -8.6° at a span location of Z/S = 0.05 and a pitch location of y/P

= 0.15, while for case 5, the minimum pitch angle was φ = -5.0° at a span location of Z/S

= 0.05 and a pitch location of y/P = 0.17. The smaller pitch angles present in case 5

suggest that the additional slot flow tends to reduce the strength of the spanwise flow.

Yaw angle contours for case 2 and case 5 are shown in Figure 5.9. The yaw angle

is given by equation 5.7:

= −

uvtan 1ψψψψ (5.7)

where v and u are the local measured velocities in the pitchwise and streamwise

directions. The yaw angle contours in Figure 5.9 are shown as the difference between the

local yaw angle and the flow turning angle at the midspan. The contours for both cases

are similar, indicating that yaw angle was not dependent on changes in slot flow. This

92

seems reasonable since the yaw angles are controlled more by the cross-passage pressure

gradient, which is the same in both cases.

Although vector diagrams of secondary flow can show changes in vortex size,

conclusions about the changes in vortex strength cannot be made from vector diagrams.

To determine whether or not the strength of the vortices in the SS2 plane had changed

from case 2 to case 5, it was necessary to examine the streamwise vorticity levels.

Streamwise vorticity, Ωs, is given by equation 5.8,

zV

nV nz

s ∂∂

−∂

∂=Ω (5.8)

where n

Vz

∂∂ is the spanwise velocity gradient in the pitchwise direction, and

zVn

∂∂ is the

pitchwise velocity gradient in the spanwise direction. Figure 5.10 shows contours of

streamwise vorticity for case 2 (Figure 5.10a) and case 5 (Figure 5.10b). The vorticity

contours show that the strength of both the passage and suction side corner vortices was

reduced with additional slot coolant. It is not immediately clear from the streamwise

vorticity contours whether the tertiary vortex increased or decreased in strength since this

vortex was much weaker in strength.

Figure 5.10c shows the streamwise vorticity calculated for the case with a

turbulent boundary layer. The strength of the passage vortex is stronger for this case than

either case 2 or case 5, with a maximum streamwise vorticity of ΩsC/Uinlet = 90.6 at the

center of the passage vortex. There was essentially no streamwise vorticity above 10%

span because all the secondary flow occurred below this position.

To quantify the strength reduction of the vortices, it is necessary to calculate the

circulation of each vortex. The circulation, Γ, is given by equation 5.9:

∫Ω=ΓS

sdS (5.9)

93

where Ωs is the streamwise vorticity given by equation 5.8 and S is the surface that

contained the vortex. Positive circulation values indicate clockwise rotation, while

negative circulation values indicate counterclockwise rotation. Values of circulation

were calculated for the passage vortex, suction side corner vortex, and tertiary vortex for

cases 2 and 5. Contours of Ωs = 0 in Figures 5.10a and 5.10b defined the surface

boundaries for each vortex. Circulation values for each vortex are shown in Table 5.1 for

case 2, case 5, and a turbulent boundary layer. The strength of the passage vortex was

reduced slightly from that with the turbulent boundary layer. The strength of the passage

vortex was nearly the same for the turbulent boundary layer case. The circulation

magnitude of the suction side corner vortex and the passage vortex were reduced slightly

from case 2 to case 5, while a large increase in circulation magnitude occurred for the

tertiary vortex as slot flow increased.

Turbulence levels were examined in terms of turbulence intensity, Tu, which is

defined in equation 5.10:

inlet

rmsrmsrms

U3)wvu(

Tu⋅

++= (5.10)

where urms, vrms, and wrms are the local measured fluctuating velocities in the streamwise,

pitchwise, and spanwise directions. Figures 5.11a and 5.11b show the turbulence

intensity contours in the SS2 plane for case 2 and case 5. The location of the maximum

turbulence intensity corresponds to the location where the passage vortex and the suction

side corner vortex interacted with one another (see Figure 5.5a for case 2 and Figure 5.7

for case 5). The location of maximum turbulence intensity shifted from y/P = 0.04 in

case 2 to y/P = 0.07 in case 5. This shift agrees with the reduction in passage vortex size.

Maximum turbulence intensity levels of Tu = 50 % for the design slot case were slightly

higher than for the double slot flow case, which had a maximum level of Tu = 40%. The

turbulence was greater for case 2 because the passage vortex was stronger for this case.

The turbulence intensity contour measured by Kang and Thole (2000) in the SS2

plane is shown in Figure 5.11c. The turbulence levels are significantly lower than those

shown for case 2 (Figure 5.11a) and case 5 (Figure 5.11b). Once again, the peak

94

turbulence level is located where the suction side corner vortex and passage vortex

interact (see Figure 5.6a). The maximum turbulence level reported by Kang and Thole

was 35%, while the maximum turbulence level seen in this study in the SS2 plane was

50% for the design slot flow case. Two peaks in turbulence were measured by Kang and

Thole. The second peak, located at y/P = 0.13 and Z/S = 0.04 was located at the center of

the passage vortex and due to the unsteady nature of that vortex. The center of the

passage vortex in Figure 5.11c was further from the point of interaction between the

suction side corner vortex and the passage vortex than for cases 2 or 5. The absence of

the second distinctive turbulent peak in Figures 5.11a and 5.11b suggests that turbulence

levels were too high to cause another local maxima for cases 2 and 5.

Turbulence levels in the freestream were relatively high for cases 2 and 5, near

25%, as compared to levels below 1% measured by Kang and Thole (2000). Cases 2 and

5 were done with relatively high levels of freestream turbulence entering the turbine vane

cascade due to the dilution flow in the combustor simulator (between 12% and 17%, see

Barringer, et al, 2001). On the other hand, Kang and Thole’s measurements were

performed with 0.6% inlet freestream turbulence. Radomsky and Thole (2001) studied

the boundary layer development along the vane surface for high levels of inlet freestream

turbulence (19.5%). At distances of s/C = 0.21 and s/C = 0.50 along the vane suction

side, which border the SS2 plane, they reported turbulence levels at the edge of the

boundary layer to be 13.99 % and 19.09%, respectively. These values are close to the

freestream turbulence levels for cases 2 and 5 in the SS2 plane, but there is still a

difference on the order of 5-10%. The additional freestream turbulence above 10% span

for cases 2 and 5 can be attributed to the presence of the tertiary vortex.

Contours of streamwise velocity (Vs/Uinlet) for case 2 and case 5 are shown in

Figures 5.12a and 5.12b. Above 10% span, the contours are similar for each case, which

indicates that the tertiary vortex had no effect on the streamwise velocity profile. There

was a non-uniformity in the streamwise velocity gradient below 10% span for cases 2 and

5 near a pitch location of y/P = 0.10, as seen by the distortion in the Vs/Uinlet = 4.0

contours in Figures 5.12a and 5.12b. Turbine rotor blades are designed for a specific

velocity field exiting the stator vanes. Any distortion in the streamwise velocity profile

entering the rotor blades causes the rotors to be less efficient. The distortion in the

95

streamwise velocity profiles shown in Figures 5.12a and 5.12b directly translates to a loss

in engine power. Figure 5.12c shows the streamwise velocity contours presented by

Kang and Thole (2000). Little distortion occurs in the streamwise velocity contours, and

maximum and minimum levels of Vs/Uinlet are similar to those measured for cases 2 and

5.

For reference reasons, each component of velocity and turbulence will be

presented next. Although this data has been shown previously in terms of vectors and

turbulence intensity, it is instructive to examine each component separately. The

turbulence contours for the streamwise velocity are shown in Figure 5.13. Streamwise

turbulence levels above 10% span were similar for both cases. However, below 10%

span, streamwise turbulence levels for case 2 were higher than those for case 5. The

larger streamwise turbulence levels for case 2 can be attributed to the fact that the suction

side corner vortex and the passage vortex were stronger with less slot flow.

Contours of normal velocity (Vn/Uinlet) for both cases in the SS2 plane are shown

in Figure 5.14. The normal velocity field for each case was very similar, with only a

slightly higher maximum value of Vn/Uinlet = 0.6 for case 2, as compared to a maximum

value of Vn/Uinlet = 0.4 for case 5. The normalized pitchwise turbulence fields for case 2

and case 5 are shown in Figure 5.15. Above 10% span, the two contours are essentially

the same. Below 10% span, higher values of vrms/Uinlet were present for the design slot

case than for the double slot case. Once again, the higher turbulence levels below 10%

span for case 2 were a result of the increased intensity of the two endwall vortices.

Spanwise velocity (Vz/Uinlet) contours for both slot flow cases are shown in Figure

5.16. Above 20% span, the spanwise velocity fields were very similar for each case.

Below 20% span, smaller magnitudes of spanwise velocity can be seen in Figure 5.16b

for case 5, further showing the reduction in passage vortex intensity as slot flow was

increased. Figure 5.17 shows the spanwise turbulence contours for both slot flow cases.

As seen in the streamwise and pitchwise turbulence contours, the spanwise turbulence

contours for each slot flow case are very similar above 10% span. Again, lower

turbulence levels were seen for the double slot flow case below 10% span due to the

reduction in strength of the endwall vortices.

96

By examining Figures 5.13, 5.15, and 5.17, it is clear that the turbulence in the

SS2 plane was not isotropic or homogeneous. While the spanwise and pitchwise

turbulence contours and levels were somewhat similar, the streamwise turbulence contour

was much different than either the spanwise or pitchwise turbulence contours. Levels of

streamwise turbulence were also less than either the spanwise or pitchwise levels.

5.3 Analysis of High Order Statistics

It is interesting to perform a higher order statistical analysis on the velocity data in

the SS2 measurement plane. Skewness, defined in equation 5.11, is a measure of how

centered a data set is around the mean.

( ) 2/32

3

ka

aS = (5.11)

The value ‘a’ represents the instantaneous fluctuation of a particular velocity component.

For a data set in which the instantaneous fluctuations are perfectly centered on the mean,

such as a Gaussian distribution, Sk = 0. A positive skewness occurs when large negative

values of a3 are not as common as large positive values of a3 (see Figure 5.18). Kurtosis,

defined in equation 5.12, is a measure of how spread out a data set is over the measured

range.

( )22

4

ta

aK = (5.12)

For a Gaussian distribution, Kt = 3. If a data set is more widely spread out over the range

it is described as platykurtic (see Figure 5.19a), and kurtosis values are lower than 3.

Data sets that are centered very tightly around the mean, but have a large range are

termed leptokurtic (see Figure 5.19b), and have kurtosis values greater than 3. In order to

97

get an accurate result for these statistics, a large number of data points are needed. For

each measurement location in the flow field, 25,000 data points were taken for each

velocity component.

The skewness contours for each component of velocity in the SS2 plane for case 2

are shown in Figures 5.18a, 5.18b, and 5.18c. Skewness levels for the streamwise

velocity component show low levels near the vane suction side, and extremely high levels

near the vane pressure side, especially near the endwall and the midspan (see Figure

5.18a). High levels of skewness occur near the vane suction side above 10% span, and

on the endwall above y/P = 0.7 for the pitchwise component of velocity (see Figure

5.18b). The minimum skewness for the pitchwise velocity component occurs near the

suction side/endwall corner. The maximum skewness levels for spanwise velocity occur

in the suction side/endwall corner (see Figure 5.18c). A band of high skewness begins in

the suction side/endwall corner, goes up to approximately 10% span, and then goes

towards the vane pressure side and towards the endwall, touching the endwall at y/P =

0.15. This band of high skewness values corresponds to a region within the passage

vortex core and indicates more positive values of w3.

Figures 5.19a, 5.19b, and 5.19c show the kurtosis contours in the SS2 plane for

case 2 for the streamwise, pitchwise, and spanwise components of velocity respectively.

As for the third order statistic of skewness, the fourth order statistic of kurtosis for the

streamwise component of velocity is lower near the vane suction side and much higher

near the vane pressure side (see Figure 5.19a). Kurtosis levels are two orders of

magnitude larger for the streamwise velocity component than for either the spanwise or

pitchwise velocity components. These high kurtosis values for the streamwise velocity

component indicate the wide range of the velocity distribution. Due to the high

streamwise acceleration of the flow, it is quite plausible that the range of instantaneous

streamwise velocity components is relatively wide. Aside from a few local maximums,

the majority of the kurtosis levels are Gaussian for the pitchwise velocity component in

the SS2 plane (see Figure 5.19b). Besides a maximum of Kt = 9 near the suction

side/endwall corner, levels of kurtosis for the spanwise component of velocity are nearly

Gaussian for the majority of the flow field (see Figure 5.19c).

98

The flow field results presented in this section demonstrate the importance of

modeling the combustor exit flow field when studying the secondary flows in the turbine

vane. The presence of a previously unmeasured third vortex was revealed, confirming

the predictions of Hermanson and Thole (2000) and Lethander (2001). This third vortex

introduces aerodynamic, as well as thermal penalties to the turbine stator vanes. A

distortion in the streamwise velocity profile was also observed near the endwall (see

Figures 5.12a and 5.12b), which would lead to a reduction in engine power. Increasing

the amount of slot flow was seen to reduce the size and strength of the passage vortex.

The distortion in the streamwise velocity profile was also somewhat reduced with the

increase in exit slot flow.

99

Table 5.1. Circulation, Γ, for each vortex given for cases 2 and 5 and for a turbulent boundary layer.

Vortex inletUC ⋅Γ

(Case 2) inletUC ⋅

Γ

(Case 5) inletUC ⋅

Γ

(Kang and Thole)

Suction Side Corner -0.32 -0.25 -0.29 Passage 5.99 5.54 6.24 Tertiary -14.14 -23.81 N/A

100

a) b)

∞

∞

−−

=θTT

TT

cool

0.0

0.1

0.30.4

-0.1

0.50.0

0.1

0.2

0.3

0.4

0.5

-0.30 -0.25 -0.20 -0.15 -0.10 -0.05 0.00

Z/S

X/C

0.20.6

-0.1

-0.1

00.10.2

0.4

0.0

0.1

0.2

0.3

0.4

0.5

-0.30 -0.25 -0.20 -0.15 -0.10 -0.05 0.00

Z/S

X/C

0.3

0.5

101

c) Figure 5.1. Measured stagnation plane thermal fields (Walter, 2001) for case (a) 1

(flat inlet total pressure profile), (b) 2 (inlet total pressure profile with a peak of ∆P = 0.7), and (c) 3 (inlet total pressure profile with a peak of ∆P = 2.2.

-0.1

0

0.40.5

0.5

0.0

0.1

0.2

0.3

0.4

0.5

-0.30 -0.25 -0.20 -0.15 -0.10 -0.05 0.00

Z/S

X/C

0.10.20.3

0.6

102

a) b) Figure 5.2. Flow field in the stagnation plane (a) measured for case 2 (Lethander,

2001) and predicted for case 1 (Stitzel, 2001). Note that figures are not the same scale.

0.0

0.1

0.2

0.3

0.4

0.5

0.3 0.2 0.1 0.0

Z/S

X/C

U/Uinlet = 1

0.00

0.05

0.10

0.15

-0.15 -0.10 -0.05 0.00

Z/S

X/C

U/Uinlet = 1

103

Figure 5.3. SS2 plane showing mean velocities in the flow direction and the flow

turning angle, ψ.

SP ψ

Vz, w(z)

v (y)

u (x)

Vs (s)

X/C

Y/P

-1.2

-0.8

-0.4

0.0

0.4

0.8

1.2

-0.8 -0.4 0.0 0.4 0.8 1.2

SS2

Vn (n)

104

a)

-5

0

5

10

15

20

0.00 0.05 0.10 0.15 0.20 0.25

Viscous CFD Prediction(Lethander, 2001)

Case 5 (Double Slot)Case 2 (Nominal Slot)

Turbulent Boundary Layer(Kang and Thole, 2000)

ψψψψ

y/P

ms

105

b) Figure 5.4. The measured and computational (Lethander, 2001) values for (a) the flow

turning angle at the midspan (ψms) and (b) the streamwise velocity (Vs) at the midspan. Also shown for (a) and (b) are the values published by Kang and Thole (2000) for a study using the same vane geometry and a turbulent boundary layer entering approaching the turbine.

0

1

2

3

4

5

0.00 0.05 0.10 0.15 0.20 0.25

Case 2 (Nominal Slot)Case 5 (Double Slot)

Viscous CFD Prediction(Lethander, 2001)

Turbulent Boundary Layer(Kang and Thole, 2000)

y/P

Vs

Uinlet

106

a) b) Figure 5.5. For case 2 (design slot flow) in the SS2 plane; (a) the secondary flow field

and (b) the measured total pressure profile at y/P = 0.1. Note that the peak in total pressure corresponds to the same spanwise location as the flow split between the passage vortex and the tertiary Vortex

0.0

0.1

0.2

0.3

0.4

0.5

0.00 0.05 0.10 0.15 0.20 0.25

Z/S

y/P

U/Uin = 1

Tertiary Vortex

Passage Vortex

Suction Side Corner Vortex -1.5 -1.0 -0.5 0.0 0.5

0.0

0.1

0.2

0.3

0.4

0.5

(Po - P

ocl) / 0.5 ρρρρ U

in

2

Z/S

107

a) b) Figure 5.6. For the SS2 plane; (a) the measured secondary flow field (Kang and

Thole, 2000) for a study using the same vane geometry and a turbulent boundary layer approaching the turbine vane cascade and (b) the predicted secondary flow field (Lethander, 2001) for case 2 conditions.

0.0

0.1

0.2

0.3

0.4

0.5

0.00 0.05 0.10 0.15 0.20 0.25

Z/S

y/P

U/Uin = 1

0.0

0.1

0.2

0.3

0.4

0.5

0.00 0.05 0.10 0.15 0.20 0.25

Z/S

y/P

U/Uin = 1

108

Figure 5.7. Measured secondary flow field in the SS2 plane for case 5 (double slot flow).

0.0

0.1

0.2

0.3

0.4

0.5

0.00 0.05 0.10 0.15 0.20 0.25

Z/S

y/P

U/Uin = 1

109

= −

uwtan 1φφφφ

a) b) Figure 5.8. Measured pitch angle contours in the SS2 plane for (a) case 2 (design slot

flow) and (b) case 5 (double slot flow).

0

0

0

0

510

15

-5

0.0

0.1

0.2

0.3

0.4

0.5

0.00 0.05 0.10 0.15 0.20 0.25

Z/S

y/P

0

0

0

0

0

5

5

10

0.0

0.1

0.2

0.3

0.4

0.5

0.00 0.05 0.10 0.15 0.20 0.25

Z/S

y/P

110

msψψψψψψψψ −

a) b) Figure 5.9. Measured yaw angle contours in the SS2 plane for (a) case 2 (design slot

flow) and (b) case 5 (double slot flow).

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0.00 0.05 0.10 0.15 0.20 0.25

Z/S

y/P

05

0

-5

10

0

0

0 05

5

-5

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0.00 0.05 0.10 0.15 0.20 0.25

Z/S

y/P

111

inlet

s

UC⋅Ω

a) b)

0.0

0.1

0.2

0.3

0.4

0.5

0.00 0.05 0.10 0.15 0.20 0.25

Z/S

y/P

0

0

2040

0

-40

0.0

0.1

0.2

0.3

0.4

0.5

0.00 0.05 0.10 0.15 0.20 0.25

Z/S

y/P

0

0

00

2040

-20

-60 80

112

c) Figure 5.10. Streamwise vorticity contours for (a) case 2 (nominal slot flow), (b) case 5

(double slot flow), and (c) a turbulent boundary layer (Kang and Thole, 2000). The surfaces of streamwise vorticity that were used to calculate vortex circulation are outlined in red.

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0.00 0.05 0.10 0.15 0.20 0.25

Z/S

y/P

0

200

60

100

-40

113

( )inlet

rmsrmsrms

U3wvu

Tu⋅

++=

a) b)

c) Figure 5.11. Turbulence intensity contours in the SS2 plane for (a) case 2 (design slot

flow), (b) case 5 (double slot flow), and (c) a turbulent inlet boundary layer (Kang and Thole, 2000).

0.0

0.1

0.2

0.3

0.4

0.5

0.00 0.05 0.10 0.15 0.20 0.25

Z/S

y/P

0.45

0.35

0.25

0.20

0.25

0.25

0.2

0.25

0.25

0.25

0.25

0.3

0.4

0.3

0.0

0.1

0.2

0.3

0.4

0.5

0.00 0.05 0.10 0.15 0.20 0.25

Z/S

y/P

0.00

0.05

0.10

0.15

0.20

0.00 0.05 0.10 0.15 0.20 0.25

Z/S

y/P

0.050.15

0.35

0.25

114

inlet

s

UV

a) b)

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0.00 0.05 0.10 0.15 0.20 0.25

Z/S

y/P

3.43.6

3.84.0

4.2

4.4

4.6

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0.00 0.05 0.10 0.15 0.20 0.25

Z/S

y/P

3.43.6

3.84.0

4.2

4.4

4.6

4.8

115

c) Figure 5.12. Contours of Vs/Uinlet in the SS2 plane for (a) case 2 (design slot flow), (b)

case 5 (double slot flow), and (c) a turbulent inlet boundary layer (Kang and Thole, 2000).

3.43.63.844.24.44.6

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0.00 0.05 0.10 0.15 0.20 0.25

Z/S

y/P

116

inlet

rms

Uu

a) b) Figure 5.13. Contours of urms/Uinlet in the SS2 plane for (a) case 2 (design slot flow) and

(b) case 5 (double slot flow).

15

15

202530

15

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0.00 0.05 0.10 0.15 0.20 0.25

Z/S

y/P

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0.00 0.05 0.10 0.15 0.20 0.25

Z/S

y/P

15

20

15

30

40

20

117

inlet

n

UV

a) b) Figure 5.14. Contours of Vn/Uinlet in the SS2 plane for (a) case 2 (design slot flow) and

(b) case 5 (double slot flow).

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0.00 0.05 0.10 0.15 0.20 0.25

Z/S

y/P

0.0

0.2

0.6

0.2

-0.2

-0.6

-0.2

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0.00 0.05 0.10 0.15 0.20 0.25

Z/S

y/P

-0.2

0.0

0.20.4-0.2

-0.2

0.0

0.4 -0.6

0.0

118

inlet

rms

Uv

a) b) Figure 5.15. Contours of vrms/Uinlet in the SS2 plane for (a) case 2 (design slot flow) and

(b) case 5 (double slot flow).

20

20

25

25

30

30

30

30 35

3540

4550

40

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0.00 0.05 0.10 0.15 0.20 0.25

Z/S

y/P

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0.00 0.05 0.10 0.15 0.20 0.25

Z/S

y/P

30 25

20

3530

354555

119

inlet

z

UV

a) b) Figure 5.16. Contours of Vz/Uinlet in the SS2 plane for (a) case 2 (design slot flow) and

(b) case 5 (double slot flow).

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0.00 0.05 0.10 0.15 0.20 0.25

Z/S

y/P

0.00.00.2

-0.2

-0.4

0.20.6

1.0

1.20.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0.00 0.05 0.10 0.15 0.20 0.25

Z/S

y/P

0.4

0.0

0.2

0.2

0.40.8

0.0

0.0

-0.4

-0.2

120

inlet

rms

Uw

a) b) Figure 5.17. Contours of wrms/Uinlet in the SS2 plane for (a) case 2 (design slot flow)

and (b) case 5 (double slot flow).

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0.00 0.05 0.10 0.15 0.20 0.25

Z/S

y/P

30

3035

25

20

30

30

35

25

4050

600.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0.00 0.05 0.10 0.15 0.20 0.25

Z/S

y/P

30

40

25 20

3530

35

30

4050

121

Figure 5.18 A distribution with positive skewness (Tennekes and Lumley, 1983).

122

a)

b) Figure 5.19 Distributions with (a) small and (b) large kurtosis (Tennekes and Lumley,

1983).

123

a) b)

0

0.1

0.2

0.3

0.4

0.5

0 0.05 0.1 0.15 0.2 0.25

Z/S

y/P

-10123456789

0

0.1

0.2

0.3

0.4

0.5

0 0.05 0.1 0.15 0.2 0.25

Z/S

y/P

-1.0-0.8-0.6-0.4-0.20.00.20.40.60.81.0

124

c) Figure 5.20. Contours of skewness in the SS2 plane for case 2 for the u (a), v (b), and

w (c) components of velocity. Note, the scale in Figure 5.18a is different than the one for Figures 5.18b and 5.18c.

0.0

0.1

0.2

0.3

0.4

0.5

0.00 0.05 0.10 0.15 0.20 0.25

Z/S

y/P

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

125

a) b)

0

0.1

0.2

0.3

0.4

0.5

0 0.05 0.1 0.15 0.2 0.25

Z/S

y/P

0

50

100

150

200

250

0

0.1

0.2

0.3

0.4

0.5

0 0.05 0.1 0.15 0.2 0.25

Z/S

y/P

2

3

4

5

6

7

8

9

10

126

c) Figure 5.21. Contours of kurtosis in the SS2 plane for case 2 for the u (a), v (b), and w

(c) components of velocity. Note, the scale in Figure 5.19a is different than the one for Figures 5.19b and 5.19c.

0.0

0.1

0.2

0.3

0.4

0.5

0.00 0.05 0.10 0.15 0.20 0.25

Z/S

y/P

2

3

4

5

6

7

8

9

10

127

Chapter 6

Endwall Adiabatic Effectiveness Results

The adiabatic surface temperatures were measured on the endwall for each of the

five cases discussed in chapter 4 to study the effects of both liner film-cooling and slot

flow on the endwall adiabatic effectiveness levels. Cases 1, 2, and 3 were studied to

show how increasing the combustor liner film-cooling flow affected the endwall

adiabatic effectiveness levels in the downstream turbine vane passage. Cases 4, 2, and 5

show the effects of increasing the exit slot mass flow on the endwall adiabatic

effectiveness levels in the downstream turbine vane passage.

For each case, measurements were made prior to measuring the endwall surface

temperature to verify the flow field in the passage and to verify the accuracy of the

infrared (IR) camera measurements. The static pressure distribution along the vane

surface was measured prior to each experiment and compared to the two-dimensional,

inviscid prediction for periodic vanes at low-speed conditions (Radomsky and Thole,

1998). Figure 6.1 shows the static pressure measurements for all five cases plotted

against the computationally predicted static pressure distribution. There was good

agreement between the measured static pressure distribution and the predicted static

pressure distribution for all five cases. These measurements verified periodic flow

between the two passages for each case.

To be certain that the IR camera was calibrated correctly, temperatures measured

by thermocouples embedded in the endwall were compared to those measured by the IR

camera at the same locations on the endwall. Figure 6.2 shows the comparison for case

1. This comparison was made in terms of the non-dimensional temperature, η (see

section 3.3 for definition, also redefined in section 6.1). A difference in η values of η =

0.1 corresponds to a difference in temperature of 0.6 °C for each of the flow cases. There

was reasonable agreement between the IR camera and endwall thermocouple

temperatures for case 1. The largest disagreement between the IR camera measurements

and the endwall thermocouples for each case occurred for the thermocouples located in

128

the passage. Figure 6.3 shows the location of the endwall thermocouples. The

thermocouples from X/C = 0.15 to X/C = 0.4 were in a region where a high temperature

gradient existed. Because of the large temperature gradient in this region, the

temperature measured by the IR camera was extremely sensitive to local pitchwise

direction. Minor errors in the coordinate transformation of the IR camera pictures

resulted in noticeable disagreements between temperatures measured by the endwall

thermocouples and temperatures measured using the IR camera.

The results of the endwall adiabatic effectiveness studies are discussed in this

chapter in three sections. The first section discusses the effect that increasing the amount

of combustor liner film-cooling has on the endwall adiabatic effectiveness. The second

section examines the results of increasing the mass flow exiting the slot on the endwall

adiabatic effectiveness. The final section of this chapter compares the thermal benefits

gained from increasing panel flow to the thermal benefits gained from increasing slot

flow.

6.1 Effects of Liner Cooling

The endwall adiabatic surface temperature results in this chapter are presented in

terms of an adiabatic effectiveness, η, which was defined earlier in chapter 3 and again

here as shown in equation 6.1:

∞

∞

−−=η

TTTT

cool

aw (6.1)

where Taw is the measured adiabatic wall temperature, T∞ is the mass-averaged

freestream temperature entering the turbine test section, and Tcool is the temperature of the

exit slot flow. Figures 6.4, 6.5, and 6.6 show the endwall adiabatic effectiveness contours

for case 1 (design slot flow and a flat inlet total pressure profile), case 2 (design slot flow

and an inlet total pressure profile with a peak value of ∆P = 0.7), and case 3 (design slot

flow and an inlet total pressure profile with a peak value of ∆P = 2.2).

129

A few general adiabatic effectiveness patterns were present on the endwall for all

three cases. First, the slot coolant exited onto the endwall in a region near the suction

side of the vane leading edge. As the cooling flow continued through the passage, it was

swept off of the endwall, forming a distinct wedge-shaped pattern of higher effectiveness.

At an axial location of X/C = 0.25 there was almost no slot coolant left on the endwall

surface in each case. The endwall region near the pressure side of the vane saw no

thermal benefit from the slot flow, because all of the slot coolant exited near the vane

suction side and was then swept off of the endwall. The secondary flow field presented

in chapter 5 shows the passage vortex and a suction side corner vortex. The passage

vortex swept the slot coolant towards the vane suction side and off of the endwall, while

the suction side corner vortex swept the slot coolant away from the vane suction side and

off the endwall. The effects of these two vortices on the endwall cooling can be seen in

the endwall effectiveness contours by the narrowing of the coolant-affected region as it

progressed through the passage.

Another trend that is present in each of the endwall effectiveness contours is that

the slot flow was ineffective near the vane leading edge. There was a warm ring around

the vane leading edge, indicated by lower effectiveness values, which continued around

the pressure and suction sides of the vane. The stagnation plane thermal field results

presented in chapter 5 indicate that low effectiveness near the leading edge was caused by

warmer air being brought down to the endwall near the vane stagnation point (shown in

Figure 5.2). The flow field results discussed in chapter 5 show that the suction side

corner vortex and the passage vortex continue to bring hotter freestream fluid down

towards the endwall, which results in the ring of low adiabatic effectiveness around the

vane suction side and pressure side.

To determine the effect of increasing the combustor liner film-cooling on the

endwall effectiveness, a comparison between Figures 6.4, 6.5, and 6.6 is necessary. A

slight increase in effectiveness can be seen above the step from case 1 to case 2, and

again from case 2 to case 3. This result is expected from the fact that the film cooling

exiting the last two combustor liner panels was increased from 10% of the total exit mass

flow for case 1, to 14.4 % for case 2, and 18.2% for case 3. The increase in effectiveness

above the slot is also verified by the stagnation plane thermal field results presented in

130

chapter 5, which indicate the θ levels increased above the slot as liner coolant was

increased (see Figure 5.1). The θ values above the step for the stagnation plane thermal

field measurements presented in Figure 5.1 are consistent with the η values above the

step in the stagnation plane shown in Figures 6.4, 6.5, and 6.6 for the endwall adiabatic

effectiveness measurements.

In comparing Figure 6.5 to 6.4, the region just upstream of the vane leading edge

and downstream of the step was at a higher η value for case 2 than case 1. The trend of

increased effectiveness near the vane leading edge was seen again as liner coolant was

further increased from case 2 to case 3. As previously discussed in chapter 5, the peak in

the total pressure profile exiting the combustor increased as liner coolant was increased,

which caused the static pressure gradient between the liner coolant and the slot to

increase near the vane stagnation point. As the driving pressure increased, more liner

coolant was forced down towards the endwall. Because the liner coolant was at a low

temperature, effectiveness values measured upstream of the vane leading edge increased

as more coolant was forced down towards the endwall.

The slot flow in general was affected by increasing the liner coolant. As liner

coolant increased, more of it was ingested into the slot (see section 5.1). Although the

liner flow was much cooler than the core flow, it was warmer than the slot flow. As more

liner coolant was ingested into the slot, the area on the endwall where the slot flow was

effective (indicated by the wedge-shaped region of higher adiabatic effectiveness)

decreased, as shown from case 1 (Figure 6.4) to case 3 (Figure 6.6). This phenomena

shows that increasing the liner coolant can actually have a detrimental affect on the

endwall heat transfer near the entrance of the vane passage.

To quantify the thermal benefit, or lack thereof, that the endwall received from

increased liner coolant, adiabatic effectiveness levels were pitch-averaged at different

axial locations upstream of the vane and in the vane passage. For each case, the pitch-

averaged effectiveness levels were calculated for both the inner and outer passages, and

then an average of the two values was taken for comparison with other cases. Figures

6.7, 6.8, and 6.9 show the pitch-averaged effectiveness values for cases 1, 2, and 3,

respectively. The agreement between the values for the inner and outer passages was

131

good for case 2 and case 3, with slight variations seen in case 1. Again, a difference of _η

= 0.1 was equivalent to a difference in temperature of 0.6 °C for each case. Agreement

of pitch-averaged effectiveness values between the inner and outer passages indicated

periodicity between the two passages.

In each case, the first point that was calculated was above the step, and the second

was just downstream of the step, which is why there was a sharp increase in effectiveness

initially. For each case, the pitch-averaged effectiveness levels on the endwall were high

initially, followed by a sharp decline at an axial location just before X/C = 0.0. The

pitch-averaged effectiveness decreased gradually following X/C = 0.0, with only a slight

reduction throughout the remainder of the passage.

Figure 6.10 compares the pitch-averaged effectiveness values for cases 1, 2, and

3. As previously discussed, small increases in effectiveness above the step can be seen as

the liner coolant was increased. Also, the effect of the increasing the liner coolant on the

reduction in slot coverage can be seen by the low value of effectiveness at an axial

location of X/C = -0.05 for case 3 of _η = 0.7 (compared to

_η = 0.81 for cases 1 and 2).

The effectiveness levels for case 1 were on average _η = 0.1 below those for cases 2 and 3

following an axial position of X/C = 0.15. There was no additional increase in endwall

effectiveness seen in the passage from case 2 to case 3 by further increasing the liner

coolant. This result suggests that there is an optimum amount of liner film-cooling from

which the endwall heat transfer will benefit. One reason for this is because the adiabatic

effectiveness levels in the vane passage are primarily dictated by the secondary flow

field. Another reason follows from the results of the stagnation plane thermal fields

presented in chapter 5. As the amount of film-cooling was increased, more coolant was

transported up the vane surface in the spanwise direction (see Figure 5.1), providing

additional thermal benefit to the vane leading edge. Although more liner coolant was

being added to the flow, more was also being driven away from the endwall.

The trends seen in Figure 6.10 are more clearly shown in an augmentation plot.

Augmentation values are presented in terms of percent increase or decrease in adiabatic

effectiveness relative to case 2. Pitch-averaged augmentation values for case 1 and case

3 are shown in Figure 6.11. Near the leading edge, there is a negative augmentation for

132

case 3, indicating the detrimental effect of increasing the liner coolant to the leading edge

region. In the passage, there was little augmentation from case 2 to case 3. On the

contrary, case 1 augmentation was much lower in the passage (near -20%), which

indicates the negative effect of decreasing the liner coolant on the passage endwall

adiabatic effectiveness.

6.1 Effects of Slot Flow Cooling

The effect of slot flow on the endwall adiabatic effectiveness levels was studied

by both reducing (case 4) and increasing (case 5) the slot mass flow from the design case

(case 2). Both case 4 and case 5 were at the same combustor liner film-cooling

conditions as case 2 with the only difference being that case 4 had half the design slot

flow and case 5 had double the design slot flow. Contours of endwall effectiveness are

shown in Figures 6.12 and 6.13 for cases 4 and 5. For cases 4, 2, and 5 (in order on

increasing slot flow) the effectiveness levels above the step were the same. This was

expected, since the combustor flow conditions were the same for each case.

Near the vane leading edge on the suction side, the effectiveness levels were

similar for case 4 and case 2. The region on the endwall effectively cooled by the slot

flow was the same size for these two cases. The reduction in slot flow from the design

case is evident from the lower effectiveness levels in the passage and near the vane

pressure side. The adiabatic effectiveness levels were similar upstream of the vane

leading edge for case 4 and case 2, indicating that this region is not very sensitive to

small changes in slot flow.

As the amount of slot flow was increased from case 2 (design slot flow, Figure

6.5) to case 5 (double slot flow, Figure 6.13), the region of the endwall effectively cooled

by the slot flow was clearly enlarged. However, the adiabatic effectiveness levels near

the vane pressure side and in the passage were similar for these two cases. The

stagnation region effectiveness levels were slightly higher for case 5, which suggests that

if the slot flow is large enough, it can start to counter the effect of liner coolant ingestion.

Again, pitch-averaged effectiveness levels were calculated for each case, both in

the inner and outer passages. Figure 6.14 and 6.15 show the pitch-averaged effectiveness

133

levels for cases 4 and 5. Good passage periodicity is shown by the fact that the

effectiveness levels for the inner and outer passages were very similar for case 4 and case

5. The same general patterns can be seen in these plots as those shown for cases 1, 2, and

3; a high initial endwall adiabatic effectiveness, which decreases sharply just before X/C

= 0.0, and then gradually throughout the rest of the passage.

Figure 6.16 shows the pitch-averaged effectiveness levels for cases 4, 2, and 5 (in

order of increasing slot flow). As stated previously, the effectiveness levels above the

step were similar for each of these three cases. This can be seen from the _

η values at

X/C = -0.1, which were all approximately 0.5. The enlargement of the slot coverage in

case 5 near the entrance to the passage was reflected in the pitch-averaged effectiveness

levels. The pitch-averaged effectiveness levels were approximately _

η = 0.15 higher for

case 5 than for cases 4 and 2 over the range X/C = 0.0 to X/C = 0.125. After an axial

location of X/C = 0.25, the effectiveness levels for case 2 and case 5 were essentially the

same, and remained approximately _

η = 0.05 higher than case 4 (half slot flow)

throughout the remainder of the vane passage.

Pitch-averaged augmentation values for cases 4 and 5 are shown in Figure 6.17.

Once again, augmentation values are presented in terms of percent increase or decrease in

adiabatic effectiveness relative to case 2. The increase in effectiveness near the leading

edge for case 5 is shown by high augmentation values (near 20%) from X/C = 0.0 to X/C

= 0.15. Augmentation for case 5 in the passage was minimal. On the contrary, there

were low augmentation values (between –15% and –20%) in the passage for case 4.

6.3 Comparison of Liner Cooling to Slot Flow Cooling

To compare the effect of increasing the combustor liner film-cooling on endwall

adiabatic effectiveness levels to the effect of increasing the exit slot mass flow on the

endwall adiabatic effectiveness levels, the area-averaged effectiveness (=η ) was calculated

for each case. The area-averaged effectiveness was an axial average of the calculated

134

pitch-averaged effectiveness values from X/C = 0.0 to X/C = 0.5. Figure 6.18 shows the

area-averaged effectiveness for each case plotted versus the mass flow exiting the four

combustor liner panels and the exit slot. The trade-off between increases in panel flow

and increases in slot flow can be seen in Figure 6.18.

Increasing the liner coolant gave only a slight increase in area-averaged

effectiveness, and only until the amount of coolant was 12.5% of the total exit mass flow.

After that point, the area-averaged effectiveness level remained constant, at a value of

approximately 0.45. Alternatively, Figure 6.18 shows that increasing the slot flow

resulted in a greater increase in area-averaged effectiveness for a smaller increase in total

mass flow. Also, over the investigated range, the area-averaged effectiveness did not

plateau for increases in slot flow. One possible reason for this has to do with ingestion of

liner coolant into the slot. As slot coolant was increased, less liner coolant was ingested

into the slot. The main differences in the endwall adiabatic effectiveness between the

two forms of cooling were found in the near slot region.

A previous experimental investigation was done by Barringer, et al.(2001) to

measure the endwall adiabatic effectiveness downstream of the combustor simulator

without a vane test section. Their experiments were performed with a flat plate test

section downstream of the combustor simulator. Endwall effectiveness was measured

downstream of the same combustor simulator used in the present study both with and

without dilution flow. Their measurements were done using combustor flow conditions

that were the same as case 1 (described in chapter 4). Figure 6.19 shows the pitch-

averaged effectiveness downstream of the combustor simulator as reported by Barringer,

et al. as well as the pitch-averaged effectiveness for case 1 (also shown in Figure 6.11).

Figure 6.19 shows that the addition of dilution flow drastically reduced endwall adiabatic

effectiveness. Furthermore, the presence of the vane test section, which gives rise to

secondary flows, reduced endwall effectiveness even more. This figure indicates that

reducing or eliminating the secondary flows in the turbine cascade would have a

significant thermal benefit for the endwall.

A computational study was performed by Lethander (2001) using the same flow

conditions as case 2 (described in chapter 4) and the same vane geometry as my

experimental study. The only geometrical features of the combustor-turbine interface

135

that were not modeled by Lethander were the slot feed holes and pin fins. Lethander

used 10% turbulence intensity in the freestream as the turbine inlet condition (compared

to levels between 12% and 17% for combustor simulator, measured by Barringer, et al.,

2001). The predicted endwall adiabatic effectiveness contour is shown in Figure 6.20.

Lethander’s predictions show that the slot flow exits onto the endwall near the vane

suction side and is then swept into the freestream by the passage and suction side

vortices. The region of influence of the slot flow shown by Lethander is smaller than that

reported experimentally in this study (see Figure 6.5). The low adiabatic effectiveness

levels beneath the slot in Figure 6.20 show how far the liner coolant would be ingested

under the slot if the pin fins were not present. Effectiveness levels in the passage shown

in Figure 6.20 are between η = 0.4 and η = 0.3, which is comparable to those measured in

case 2 (see Figure 6.8). Also, the computational prediction in Figure 6.20 shows the

warm ring (indicated by lower effectiveness levels) around the vane leading edge, which

was documented in this study. Overall, there is fairly good agreement between the

computational prediction and the experimental results for case 2.

Increasing liner coolant was only beneficial to endwall cooling up to a certain

amount of liner coolant (defined by Figure 6.18). After that point, additional liner

coolant had no benefit to endwall cooling. However, increasing the amount of slot flow

continued to raise endwall adiabatic effectiveness levels (also shown in Figure 6.18).

The results of this study would be very beneficial to an engine designer. If there were

only a limited amount of cooling air available for endwall cooling, where it should be

used would be an important issue. Examining Figure 6.18 shows that the optimal

operating point for liner flow would be at case 2 conditions. Any additional coolant flow

that is available should be used as slot flow.

136

-30

-25

-20

-15

-10

-5

0

5

-1.0 -0.5 0.0 0.5 1.0 1.5

Inviscid Prediction(Radomsky and Thole, 1998)Design CaseCase 2Case 3Case 4Case 5

s/C

(Po - P

ocl)

1/2ρ Uinlet

2

Figure 6.1. Measured vane pressure distribution for cases 1 through 5. Also shown is

the two-dimensional, inviscid prediction for periodic vanes at low-speed conditions (Radomsky and Thole, 1998).

137

Figure 6.2. Comparison of thermocouple readings to infrared (IR) camera measurements at the same endwall location for case 1.

0.0

0.2

0.4

0.6

0.8

1.0

-0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6

ThermocoupleIR Camera

η

X/C

stagnation trailingedge

138

Figure 6.3. Endwall thermocouple locations.

1.00

0.75

0.50

0.25

0.00

-0.25

-0.50

-0.75

-1.00

-0.25 0.00 0.25 0.50 0.75

Y/C

X/C

139

Figure 6.4. Endwall adiabatic effectiveness contour for case 1 (design slot flow and a flat inlet total pressure profile).

1.00

0.75

0.50

0.25

0.00

-0.25

-0.50

-0.75

-1.00

-0.25 0.00 0.25 0.50 0.75

Y/C

X/C

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

∞

∞

−−=η

TTTT

cool

aw

140

Figure 6.5. Endwall adiabatic effectiveness contour for case 2 (design slot flow and an inlet total pressure profile with a peak value of ∆P = 0.7).

1.00

0.75

0.50

0.25

0.00

-0.25

-0.50

-0.75

-1.00

-0.25 0.00 0.25 0.50 0.75

Y/C

X/C

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

∞

∞

−−=η

TTTT

cool

aw

141

Figure 6.6. Endwall adiabatic effectiveness contour for case 3 (design slot flow and an inlet total pressure profile with a peak value of ∆P = 2.2).

1.00

0.75

0.50

0.25

0.00

-0.25

-0.50

-0.75

-1.00

-0.25 0.00 0.25 0.50 0.75

Y/C

X/C

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

∞

∞

−−=η

TTTT

cool

aw

142

Figure 6.7. Pitch-averaged endwall effectiveness values for case 1. The values were calculated for each passage and then averaged.

Figure 6.8. Pitch-averaged endwall effectiveness values for case 2. The values were calculated for each passage and then averaged.

0.0

0.2

0.4

0.6

0.8

1.0

-0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6

Inner PassageOuter PassageAverage

η

X/C

stagnation trailingedge

0.0

0.2

0.4

0.6

0.8

1.0

-0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6

Inner PassageOuter PassageAverage

η

X/C

stagnation trailingedge

143

Figure 6.9. Pitch-averaged endwall effectiveness values for case 3. The values were calculated for each passage and then averaged.

Figure 6.10. Pitch-averaged endwall effectiveness values for cases 1, 2, and 3.

0.0

0.2

0.4

0.6

0.8

1.0

-0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6

Inner PassageOuter PassageAverage

η

X/C

stagnation trailingedge

0.0

0.2

0.4

0.6

0.8

1.0

-0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6

Case 1Case 2Case 3

η

X/C

stagnation trailingedge

144

Figure 6.11. Augmentation plot of pitch-averaged adiabatic effectiveness for case 1 and case 3.

-20.0

-10.0

0.0

10.0

20.0

-0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6

Case 1 AugmentationCase 3 Augmentation

η − ηCase 2

ηCase 2

X/C

145

Figure 6.12. Endwall adiabatic effectiveness contour for case 4 (half slot flow and an inlet total pressure profile with a peak value of ∆P = 0.7).

1.00

0.75

0.50

0.25

0.00

-0.25

-0.50

-0.75

-1.00

-0.25 0.00 0.25 0.50 0.75

Y/C

X/C

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

∞

∞

−−=η

TTTT

cool

aw

146

Figure 6.13. Endwall adiabatic effectiveness contour for case 5 (double slot flow and an inlet total pressure profile with a peak value of ∆P = 0.7).

1.00

0.75

0.50

0.25

0.00

-0.25

-0.50

-0.75

-1.00

-0.25 0.00 0.25 0.50 0.75

Y/C

X/C

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

∞

∞

−−=η

TTTT

cool

aw

147

Figure 6.14. Pitch-averaged endwall effectiveness values for case 4. The values were calculated for each passage and then averaged.

Figure 6.15. Pitch-averaged endwall effectiveness values for case 5. The values were calculated for each passage and then averaged.

0.0

0.2

0.4

0.6

0.8

1.0

-0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6

Inner PassageOuter PassageAverage

η

X/C

stagnation trailingedge

0.0

0.2

0.4

0.6

0.8

1.0

-0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6

Inner PassageOuter PassageAverage

η

X/C

stagnation trailingedge

148

Figure 6.16. Pitch-averaged endwall effectiveness values for cases 4, 2, and 5.

Figure 6.17. Augmentation plot of pitch-averaged adiabatic effectiveness for case 4

(half-slot flow) and case 5 (double slot flow).

0.0

0.2

0.4

0.6

0.8

1.0

-0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6

Case 2Case 5

Case 4

η

X/C

stagnation trailingedge

-20.0

-10.0

0.0

10.0

20.0

-0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6

Case 4 AugmentationCase 5 Augmentation

X/C

η − ηCase 2

ηCase 2

149

Figure 6.18. Area-averaged endwall effectiveness values for an increase in panel flow (case 1, 2, and 3) and an increase in slot flow (case 4, 2, and 5).

Figure 6.19. Pitch-averaged endwall effectiveness values for case 1 compared to values

reported by Barringer, et al. (2001) for case 1 flow conditions and no vane both with and without dilution flow.

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.5 1.0 1.5 2.0

With Vane

No Vane, Dilution, TCNo Vane, Dilution, IRNo Vane, No Dilution, TCNo Vane, No Dilution, IR

η

X/C

Case 1 Conditions

Barringer, et al (2001)

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.10 0.11 0.12 0.13 0.14 0.15

Panel Flow IncreaseSlot Flow Increase

η

Coolant Flow from Liner and Slot

150

Figure 6.20. Computationally predicted endwall effectiveness values for case 2 flow

conditions (Lethander, 2001).

minmax

max

TTTT

−−=ηηηη

151

Chapter 7

Conclusions and Recommendations for Future Work

Thermal field, flow field, and endwall adiabatic effectiveness measurements were

taken for a turbine vane in the endwall region for realistic combustor exit conditions. A

combustor simulator was used to model the turbine inlet conditions. Realistic conditions

for turbulence levels, normalized temperature distribution, normalized total pressure

distribution, and normalized velocity distribution were simulated. Particular attention

was paid to the effects of varying the amount of combustor liner flow and exit slot flow.

A test matrix was developed to study the effects of these coolant flows on the flow and

thermal fields, as well as the endwall surface temperature distribution.

The thermal field measurements showed that the liner flow was transported up the

vane surface and also down towards the endwall as the liner mass flow was increased.

Neither of these trends is beneficial to endwall cooling. The flow field measurements

showed the presence of a third vortex that has been previously predicted computationally,

but not been measured previously. This vortex presents both thermal and aerodynamic

penalties to the turbine vanes. The adiabatic effectiveness measurements generated an

operating curve for cooling flow distribution for the maximum obtainable thermal benefit

to the endwall for a given amount of cooling flow.

This chapter summarizes the main results of this research. The first section

discusses the thermal field measurements taken in the stagnation plane as well as the flow

field measurements taken in the SS2 plane. The second section of this chapter discusses

the endwall adiabatic effectiveness measurements. The final section of this chapter offers

some suggestions for future work that might be performed in this area of research.

152

7.1 Measurements of Thermal and Flow Field

Thermal field measurements were taken in the stagnation plane for three cases

with increasing amounts of combustor liner mass flow. Two important trends were

observed as the amount of coolant exiting the panels was increased. First, as the amount

of film-coolant increased, more film-coolant was transported along the vane surface

towards midspan. Second, as the amount of film-coolant was increased, more film-

coolant was ingested into the slot. Both of these trends were explained by examining the

total pressure exiting the combustor in the stagnation plane. As film-coolant was

increased, a peak in total pressure was created in the near-wall region above the step.

This peak increased with additional film-coolant, creating a large pressure gradient

between the lower pressure midspan flow, and also between the lower pressure slot flow.

As the flow approached the vane stagnation, these total pressure gradients became static

pressure gradients, forcing the flow either up the vane span or into the slot. Neither of

these effects was beneficial to endwall cooling in the downstream turbine vane cascade.

The film-coolant ingested into the slot actually raised the temperature of the cooler slot

flow, making it less effective as endwall coolant. The film-coolant transported up the

vane span had no effect on endwall cooling, although it may have provided some thermal

benefit to the vane surface.

Detailed flow field measurements were taken in the vane passage in a plane

perpendicular to the vane suction side. These measurements were taken for two amounts

of slot flow and compared to existing data in the same measurement plane where a

turbulent boundary layer was used as the turbine inlet profile. Three vortices were

evident in the secondary flow field; a suction side corner vortex, a passage vortex, and a

vortex located above the passage vortex with opposite rotation. The presence of this

tertiary vortex had not been reported previously in any experimental studies. The reason

for the existence of this tertiary vortex is because of the presence of an additional

pressure gradient in the vane passage. The film-cooling flow exiting the combustor

forms a pressure gradient between the near-wall region and the endwall, and also between

the near-wall region and the midspan. The first pressure gradient exists for the case with

a turbulent boundary layer, while the second does not. Coupled with the cross-passage

153

pressure gradient, the passage and tertiary vortices are formed, with their rotation being

determined by the direction of the driving pressure gradients.

In comparing the sizes and strengths of the suction side corner and passage

vortices between the turbulent boundary layer case and the results obtained in this study,

little change was found. A slight reduction in the size and strength of the passage vortex

was observed as the amount of slot flow was increased. On the contrary, an increase in

both size and strength was observed in the tertiary vortex as slot flow was increased. A

large deflection in the streamwise velocity profile was measured in the SS2 plane, which

has implications on the power output of the turbine.

7.2 Measurements of Adiabatic Effectiveness

Endwall adiabatic effectiveness measurements were performed with an infrared

camera for increasing amounts of both liner film-coolant and exit slot flow. Three

general trends were observed for each case that was measured. First, low levels of

effectiveness existed at the vane leading edge. This was a result of the warmer flow

being forced down towards the endwall by the static pressure gradient at the vane surface.

Second, low coolant levels were indicated at the vane leading edge that wrapped around

the pressure and suction sides of the vane, forming a warm ring around the vane on the

endwall. This warm ring occurs in a region of high mechanical vane stress and makes the

vane more susceptible to forms of thermal and mechanical failure. The warm ring around

the vane is caused by the secondary flows that develop in the vane passage. Third, the

slot flow was only effective at cooling a small region of the endwall near the suction side

of the leading edge. This was because as the slot flow progressed through the passage, it

was quickly lifted off the endwall by the secondary flows and replaced by warmer air.

The effects of varying the film-coolant and slot flow were quantified in terms of

area-averaged adiabatic effectiveness. By examining the results of the endwall

effectiveness measurements in this way, it was apparent that there was an optimum

amount of film-coolant past which no additional thermal benefit was seen on the endwall.

Conversely, this effect was not seen from increasing the amount of exit slot flow. The

154

results of this study would be very beneficial to an engine designer. If there were only a

limited amount of cooling air available for endwall cooling, where it should be used

would be an important issue. The ideal operating point would be to use the optimum

amount of liner-coolant, and then use all additional available coolant in the exit slot.

7.3 Recommendations for Future Work

Based on the results of this study, the following recommendations are made for

areas of future research. First, to determine the thermal effect of the tertiary vortex on the

vane surface, detailed thermal measurements should be made on the surface of the vane.

It would also be interesting to study the vane temperature distribution in the presence of

the tertiary vortex both with and without vane film-cooling. The endwall effectiveness

measurements presented in this study showed the presence of a warm ring around the

vane on the endwall. Another suggestion is to investigate cooling methods at the vane

stagnation and along the vane surface near the endwall to try and eliminate the warm ring

around the vane

155

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Barringer, M. D., 2001, “Design and Benchmarking of a Combustor Simulator Relevant

to Gas Turbine Engines,” Master’s Thesis, Virginia Polytechnic and State University.

Barringer, M. D., Richard, O. T., Walter, J. P., Stitzel, S. M., and Thole, K. A., 2001,

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0170.

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Çengel, Y. A., and Boles, M. A., 1998, Thermodynamics: An Engineering Approach,

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156

Goldstein, R. J. and Spores, R. A., 1988, “Turbulent Transport on the Endwall in the

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Granser, D. and Schulenberg, T., 1990, “Prediction and Measurement of Film Cooling

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157

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Turbine Cascade Over a Contoured Endwall: Discrete Hole Injection of Bleed Flow,”

ASME Paper No. 2000-GT-214.

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158

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159

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160

Appendix A: Programs for Surface Temperature Analysis

This appendix documents the computer programs that were used to analyze the

endwall surface temperature measurements.

• MATLAB program used to average the five infrared images taken at each viewing

location % % Read in and average local data files % clear; data1=load('c:\File Folder\filename_1.txt'); data2=load('c:\File Folder\filename_2.txt'); data3=load('c:\File Folder\filename_3.txt'); data4=load('c:\File Folder\filename_4.txt'); data5=load('c:\File Folder\filename_5.txt'); for j=1:255; for i=1:196; averageddata(i,j)=(data1(i,j)+data2(i,j)+data3(i,j)+data4(i,j)+data5(i,j))/5.0; end end save 'c:\Destination Folder\filename_avg.txt' averageddata -ascii; % % Plot Contour of Averaged Data % figure(1);contourf(averageddata);caxis([18 28]);colorbar;

• Fortran program used to transform the averaged picture into the global coordinate

system (Kholi, 1998) *********************************************************************** This program reads data from the Inframterics program and converts pixel-temperature data to x,y-temperature data output masks reference points, blind spot and three additional points *********************************************************************** PROGRAM CAMERA IMPLICIT REAL *8 (A-H,O-Z) DIMENSION XCOORD(300,300), YCOORD(300,300) DIMENSION TEMP(300,300), GLOBALX(300,300), GLOBALY(300,300) INTEGER NUMX, NUMY PI=3.1415927 *********************** CONTROL NUMBER OF POINTS TO BE SKIPPED

161

*********************** NSKIP=7 NPBLIND=10 NPREF=3 ***************************************** OPEN DATA FILE AND READ PIXEL DATA ***************************************** DO 5 I=1,300 DO 4 J=1,300 XCOORD(I,J)=0.0 YCOORD(I,J)=0.0 GLOBALX(I,J)=0.0 GLOBALY(I,J)=0.0 TEMP(I,J)=0.0 4 CONTINUE 5 CONTINUE OPEN(UNIT=10, FILE="data.txt", STATUS="OLD") OPEN(UNIT=11, FILE="camera_data.dat", STATUS="UNKNOWN") OPEN(UNIT=12, FILE="camera_test.dat", STATUS="UNKNOWN") OPEN(UNIT=13, FILE="ref_pixel_data.txt", STATUS="OLD") OPEN(UNIT=14, FILE="avg_input.dat",STATUS="UNKNOWN") NUMY=255 NUMX=195 READ(13,*) DUMMY READ(13,*) NPY1, NPX1 WRITE(6,*) 'LOCATION OF FIRST REFERENCE PIXEL =',NPX1,NPY1 READ(13,*) DUMMY READ(13,*) X1, Y1 WRITE(6,*) 'X AND Y COORDINATES FOR THIS PIXEL =',X1,Y1 READ(13,*) DUMMY READ(13,*) NPY2, NPX2 WRITE(6,*) 'LOCATION OF SECOND REFERENCE PIXEL =',NPX2,NPY2 READ(13,*) DUMMY READ(13,*) X2, Y2 WRITE(6,*) 'X AND Y COORDINATES FOR THIS PIXEL =',X2,Y2 READ(13,*) DUMMY READ(13,*) BETA READ(13,*) DUMMY READ(13,*) NYBLIND, NXBLIND NYBLIND=NYBLIND+1 NXBLIND=NXBLIND+1 READ(13,*) DUMMY READ(13,*) NUMBER IF(NUMBER.EQ.1) THEN READ(13,*) NYMASK1,NXMASK1 NYMASK1=NYMASK1+1 NXMASK1=NXMASK1+1 ELSEIF(NUMBER.EQ.2) THEN

162

READ(13,*) NYMASK1,NXMASK1 READ(13,*) NYMASK2,NXMASK2 NYMASK1=NYMASK1+1 NXMASK1=NXMASK1+1 NYMASK2=NYMASK2+1 NXMASK2=NXMASK2+1 ELSEIF(NUMBER.EQ.3) THEN READ(13,*) NYMASK1,NXMASK1 READ(13,*) NYMASK2,NXMASK2 READ(13,*) NYMASK3,NXMASK3 NYMASK1=NYMASK1+1 NXMASK1=NXMASK1+1 NYMASK2=NYMASK2+1 NXMASK2=NXMASK2+1 NYMASK3=NYMASK3+1 NXMASK3=NXMASK3+1 ENDIF WRITE(6,*) '********************************' WRITE(6,*) 'PLEASE WAIT, READING DATA FILES!' WRITE(6,*) '********************************' NPX1=NPX1+1 NPY1=NPY1+1 NPX2=NPX2+1 NPY2=NPY2+1 WRITE(6,*)NUMX,NUMY DO 13 I=1,NUMX WRITE(6,*) I READ(10,*) (TEMP(I,J),J=1,NUMY) 13 CONTINUE WRITE(6,*) TEMP(1,1), TEMP(2,2) DO 15 I=1,NUMX DO 14 J=1,NUMY WRITE(12,*) I,J,TEMP(I,J) 14 CONTINUE 15 CONTINUE ************************************************ CONVERT TO X,Y COORDINATES ************************************************ REFPIX=(FLOAT((NPX1-NPX2)**2+(NPY1-NPY2)**2))**0.5 REFDIS=((X1-X2)**2+(Y1-Y2)**2)**0.5 SCALE=REFDIS/REFPIX WRITE(6,*) 'SCALE IN INCHES/PIXEL :' WRITE(6,2) SCALE DO 20 I=1,NUMX DO 19 J=1,NUMY XCOORD(I,J)=-(I-1)*SCALE YCOORD(I,J)=(J-1)*SCALE 19 CONTINUE 20 CONTINUE DO 25 I=1,NUMX DO 24 J=1,NUMY

163

WRITE(12,8) I,J,XCOORD(I,J),YCOORD(I,J),TEMP(I,J) 24 CONTINUE 25 CONTINUE 8 FORMAT(F7.3,2X,F7.3,2X,F4.1) **************************************************** NOW TRANSFORM AXES TO GLOBAL COORDINATE SYSTEM **************************************************** ALPHA=ATAN(ABS((FLOAT(NPX2-NPX1))/(FLOAT(NPY2-NPY1)))) WRITE(6,*) 'MISALIGNMENT OF FRAME (IN DEG) :' WRITE(6,2) 180.*ALPHA/PI WRITE(6,*) 'ROTATION WITH RESPECT TO GLOBAL X-Y :' WRITE(6,2) BETA ALPHA=ALPHA+BETA*PI/180. WRITE(6,*) 'TOTAL ROTATION =' WRITE(6,2) 180.*ALPHA/PI 2 FORMAT(F9.3) DO 35 I=1,NUMX DO 34 J=1,NUMY GLOBALX(I,J)=XCOORD(I,J)*COS(ALPHA)+YCOORD(I,J)*SIN(ALPHA) GLOBALY(I,J)=-XCOORD(I,J)*SIN(ALPHA)+YCOORD(I,J)*COS(ALPHA) WRITE(12,8) I,J,GLOBALX(I,J),GLOBALY(I,J),TEMP(I,J) 34 CONTINUE 35 CONTINUE WRITE(6,*) 'X1 =', X1 WRITE(6,*) 'X1LOCAL =', GLOBALX(NPX1,NPY1) WRITE(6,*) 'Y1 =', Y1 WRITE(6,*) 'Y1LOCAL =', GLOBALY(NPX1,NPY1) XOFFSET=X1-GLOBALX(NPX1,NPY1) YOFFSET=Y1-GLOBALY(NPX1,NPY1) DO 45 I=1,NUMX DO 44 J=1,NUMY GLOBALX(I,J)=GLOBALX(I,J)+XOFFSET GLOBALY(I,J)=GLOBALY(I,J)+YOFFSET WRITE(12,8) GLOBALX(I,J),GLOBALY(I,J),TEMP(I,J) 44 CONTINUE 45 CONTINUE ****************************************** FINAL OUTPUT IS WRITTEN HERE ****************************************** NCOUNT=0 DO 55 I=1,NUMX,NSKIP DO 54 J=1,NUMY,NSKIP NSWITCH=0 NRAD1=((I-NXBLIND)**2+(J-NYBLIND)**2)**0.5 NRAD2=((I-NPX1)**2+(J-NPY1)**2)**0.5 NRAD3=((I-NPX2)**2+(J-NPY2)**2)**0.5 IF((NRAD1.LE.NPBLIND).OR.(NRAD2.LE.NPREF).OR.(NRAD3.LE.NPREF)) / THEN

164

NSWITCH=1 ENDIF IF((NUMBER.EQ.1).AND.(NSWITCH.EQ.0)) THEN NRAD4=((I-NXMASK1)**2+(J-NYMASK1)**2)**0.5 IF(NRAD4.LE.NPREF) NSWITCH=1 ELSEIF((NUMBER.EQ.2).AND.(NSWITCH.EQ.0)) THEN NRAD4=((I-NXMASK1)**2+(J-NYMASK1)**2)**0.5 NRAD5=((I-NXMASK2)**2+(J-NYMASK2)**2)**0.5 IF((NRAD4.LE.NPREF).OR.(NRAD5.LE.NPREF)) NSWITCH=1 ELSEIF((NUMBER.EQ.3).AND.(NSWITCH.EQ.0)) THEN NRAD4=((I-NXMASK1)**2+(J-NYMASK1)**2)**0.5 NRAD5=((I-NXMASK2)**2+(J-NYMASK2)**2)**0.5 NRAD6=((I-NXMASK3)**2+(J-NYMASK3)**2)**0.5 IF((NRAD4.LE.NPREF).OR.(NRAD5.LE.NPREF).OR.(NRAD6.LE.NPREF)) / NSWITCH=1 ENDIF IF(NSWITCH.EQ.0) THEN WRITE(11,8) GLOBALX(I,J),GLOBALY(I,J),TEMP(I,J) NCOUNT=NCOUNT+1 ENDIF 54 CONTINUE 55 CONTINUE WRITE(6,*) 'TOTAL NUMBER OF OUTPUT POINTS =', NCOUNT WRITE(14,*) NCOUNT STOP END

• Fortran program used to smooth all of the averaged, transformed infrared camera

images into one picture (Kholi, 1998) *********************************************************************** THIS PROGRAM READS IN CAMERA DATA AND SMOOTHS THE REGIONS WHICH HAVE OVERLAP BETWEEN FRAMES *********************************************************************** PROGRAM SMOOTH IMPLICIT REAL *8 (A-H,O-Z) DIMENSION X(25000), Y(25000), STANTON(25000) DIMENSION MASK(25000), XTEMP(25000), YTEMP(25000), STATEMP(25000) DIMENSION XAVG(25000), YAVG(25000), STANAVG(25000) DO 5 I=1,10000 X(I)=0.0 Y(I)=0.0 STANTON(I)=0.0 MASK(I)=0.0 XTEMP(I)=0.0 YTEMP(I)=0.0 STATEMP(I)=0.0 XAVG(I)=0.0 YAVG(I)=0.0 STANAVG(I)=0.0 5 CONTINUE RAD=0.4

165

NUM=14380 ********************************************** OPEN DATA FILE AND READ X, Y, STANTON ********************************************** OPEN(UNIT=10, FILE="data.txt", STATUS="OLD") OPEN(UNIT=11, FILE="output.dat", STATUS="UNKNOWN") WRITE(6,*) 'NUMBER OF POINTS =', NUM WRITE(6,*) 'READING DATA FILE!' DO 10 I=1,NUM READ(10,*) X(I), Y(I), STANTON(I) 10 CONTINUE WRITE(6,*) 'FINISHED READING DATA FILES!' CLOSE(10) ************************************************ SMOOTH DATA ************************************************ WRITE(6,*) 'NOW SMOOTHING DATA' NTOTAL=0 DO 30 I=1,NUM NSMOOTH=1 DO 29 J=1,NUM RADTEST=SQRT((X(I)-X(J))**2+(Y(I)-Y(J))**2) IF((RADTEST.LT.RAD).AND.(J.NE.I).AND.(MASK(J).NE.1)) THEN MASK(I)=1 MASK(J)=1 NSMOOTH=NSMOOTH+1 XTEMP(NSMOOTH)=X(J) YTEMP(NSMOOTH)=Y(J) STATEMP(NSMOOTH)=STANTON(J) ENDIF 29 CONTINUE IF(NSMOOTH.GT.1) THEN NTOTAL=NTOTAL+1 DO 27 K=1,NSMOOTH XAVG(NTOTAL)=XAVG(NTOTAL)+XTEMP(NSMOOTH) YAVG(NTOTAL)=YAVG(NTOTAL)+YTEMP(NSMOOTH) STANAVG(NTOTAL)=STANAVG(NTOTAL)+STATEMP(NSMOOTH) 27 CONTINUE XAVG(NTOTAL)=XAVG(NTOTAL)/FLOAT(NSMOOTH) YAVG(NTOTAL)=YAVG(NTOTAL)/FLOAT(NSMOOTH) STANAVG(NTOTAL)=STANAVG(NTOTAL)/FLOAT(NSMOOTH) ENDIF 30 CONTINUE WRITE(6,*) 'NUMBER OF SMOOTHED POINTS =', NTOTAL WRITE(6,*) 'WRITING SMOOTHED DATA' DO 35 I=1,NUM IF(MASK(I).NE.1) THEN WRITE(11,8) X(I), Y(I), STANTON(I)

166

ENDIF 35 CONTINUE WRITE(11,*) '***************' 8 FORMAT(F7.3,2X,F7.3,2X,F4.1) DO 36 I=1,NTOTAL WRITE(11,8) XAVG(I), YAVG(I), STANAVG(I) 36 CONTINUE CLOSE(11) STOP END

167

Appendix B: Calculations for Uncertainty Analysis

This appendix shows the uncertainty analysis calculations.

• Total Pressure Measurements, ∆P

2

Uinlet

2

Pocl

2

Po

P inletoclou

UPu

PPu

PPU

⋅

∂∆∂+

⋅

∂∆∂+

⋅

∂∆∂=∆

2inleto U

2PP

⋅ρ=

∂∆∂

2inletocl U

2P

P⋅ρ

−=∂∆∂

3inlet

oocl

inlet U)PP(4

UP

⋅ρ−=

∂∆∂

High value of ∆P = 1.827

Variable Value Precision

Uncertainty

Bias

Uncertainty

Total

Uncertainty

∆P 1.827 - - 0.0558 (3.05%)

ρ (kg/m3) 1.09 - - -

Uinlet (m/s) 6.25 - - 0.0848

Po (Pa) 49.818 0.209 0.3113 0.3749

Pocl (Pa) 10.669 0.209 0.3113 0.3749

Low value of ∆P = 0.210

Variable Value Precision

Uncertainty

Bias

Uncertainty

Total

Uncertainty

∆P 0.210 - - 0.0255 (12.17%)

ρ (kg/m3) 1.09 - - -

Uinlet (m/s) 6.25 - - 0.0848

Po (Pa) 15.179 0.209 0.3113 0.3749

Pocl (Pa) 10.713 0.209 0.3113 0.3749

168

• Thermal Field Measurements, θ

2

T

2

Tcool

2

T uT

uT

uT

Ucool

⋅

∂θ∂+

⋅

∂θ∂+

⋅∂θ∂=

∞∞

θ

∞−=

∂θ∂

TT1

T cool

( )2coolcool TT

TTT ∞

∞

−−=

∂θ∂

( ) ∞∞

∞

∞ −−

−−=

∂θ∂

TT1

TTTT

T cool2

cool

High value of θ = 0.609

Variable Value Precision

Uncertainty

Bias

Uncertainty

Total

Uncertainty

θ 0.609 - - 0.0330 (5.42%)

T (°C) 18.24 - - 0.2

Tcool (°C) 15.315 - - 0.2

T∞ (°C) 22.8 - - 0.2

Low value of θ = 0.211

Variable Value Precision

Uncertainty

Bias

Uncertainty

Total

Uncertainty

θ 0.211 - - 0.0285 (13.49%)

T (°C) 23.95 - - 0.2

Tcool (°C) 16.79 - - 0.2

T∞ (°C) 25.864 - - 0.2

169

• Endwall Effectiveness Measurements, η

2

T

2

Tcool

2

Taw

uT

uT

uT

Ucoolaw

⋅

∂η∂+

⋅

∂η∂+

⋅

∂η∂=

∞∞

η

∞−=

∂η∂

TT1

T coolaw

( )2cool

aw

cool TTTT

T ∞

∞

−−=

∂η∂

( ) ∞∞

∞

∞ −−

−−=

∂η∂

TT1

TTTT

T cool2

cool

aw

High value of η = 0.9

Variable Value Precision

Uncertainty

Bias

Uncertainty

Total

Uncertainty

η 0.9 - - 0.0369 (4.10%)

Taw (°C) 26.014 0.083 0.15 0.1714

Tcool (°C) 25.338 - - 0.2

T∞ (°C) 32.1 - - 0.2

Low value of η = 0.2

Variable Value Precision

Uncertainty

Bias

Uncertainty

Total

Uncertainty

η 0.2 - - 0.0352 (17.59%)

Taw (°C) 30.748 0.083 0.15 0.1714

Tcool (°C) 25.338 - - 0.2

T∞ (°C) 32.1 - - 0.2

170

• Flow Field Measurements, urms, vrms, and wrms

High values Variable Value Uncertainty

inlet

rms

Uu

42.7% =

rmsuU 0.0515 m/s

(1.93%)

inlet

rms

Uv

53.6% =

rmsvU 0.0482 m/s

(1.44%)

inlet

rms

Uw

61.2% =

rmswU 0.0540 m/s

(1.41%)

Low values Variable Value Uncertainty

inlet

rms

Uu

18.6% =

rmsuU 0.0612 m/s

(5.27%)

inlet

rms

Uv

30.0% =

rmsvU 0.0481 m/s

(2.57%)

inlet

rms

Uw

15.2% =

rmswU 0.0126 m/s

(1.32%)

171

• Flow Turning Angle, ψ

2

v

2

u uv

uu

U

⋅∂∂+

⋅∂∂= ψψψψψψψψ

ψψψψ

+

−=∂∂

2

22

uv1u

vuψψψψ

+

=∂∂

2

2

uv1u

1vψψψψ

High value of ψ = 16.22°

Low value of ψ = 1.30°

Variable Value Precision

Uncertainty

Bias

Uncertainty

Total

Uncertainty

ψ 16.22° - - 0.2550° (1.57%)

u (m/s) 19.4506 0.0344 0.1945 0.1975

v (m/s) 5.6584 0.0481 0.0566 0.0743

Variable Value Precision

Uncertainty

Bias

Uncertainty

Total

Uncertainty

ψ 1.30° - - 0.0956° (7.35%)

u (m/s) 29.3688 0.0344 0.2937 0.2957

v (m/s) 0.6662 0.0481 0.0067 0.0486

172

• Spanwise Velocity, Vz

2z

2

vz

2

wmeas

zV uVu

vVu

wVU

measz

⋅∂∂+

⋅∂∂+

⋅

∂∂= αααααααα

( )ααααcosw

V

meas

z =∂∂

( )ααααsinv

Vz −=∂∂

( ) ( )αααααααααααα

cosvsinwVmeas

z ⋅−⋅−=∂∂

High value of Vz = 8.69m/s Variable Value Precision

Uncertainty

Bias

Uncertainty

Total

Uncertainty

Vz (m/s) 8.69 - - 0.0911 (1.05%)

wmeas (m/s) 8.4462 0.0334 0.0845 0.0908

v (m/s) -2.9937 0.0704 0.0299 0.0765

α 5° - - 0.2°

Low value of Vz = 1.19 m/s Variable Value Precision

Uncertainty

Bias

Uncertainty

Total

Uncertainty

Vz (m/s) 1.19 - - 0.0359 (3.02%)

wmeas (m/s) 1.2043 0.0334 0.0120 0.0355

v (m/s) 0.0958 0.0704 0.0010 0.0704

α 5° - - 0.2°

173

• Pitchwise Velocity, Vn

2

ms

n2

vn

2

un

V msnuVu

vVu

uVU

⋅

∂∂+

⋅∂

∂+

⋅∂

∂= ψψψψψψψψ

( )msn sin

uV ψψψψ−=∂∂

( )msn cos

vV ψψψψ=∂

∂

( ) ( )msmsms

n sinvcosuV ψψψψψψψψψψψψ

⋅−⋅−=∂∂

High value of Vn = -5.78 m/s Variable Value Precision

Uncertainty

Bias

Uncertainty

Total

Uncertainty

Vn (m/s) -5.78 - - 0.1557 (2.70%)

u (m/s) 23.6894 0.0344 0.2369 0.2394

v (m/s) -8.3344 0.0704 0.0833 0.1091

ψms 6.0843° - - 0.2550°

Low value of Vn = 1.19 m/s Variable Value Precision

Uncertainty

Bias

Uncertainty

Total

Uncertainty

Vn (m/s) 1.19 - - 0.0865 (7.26%)

u (m/s) 28.4382 0.0344 0.2844 0.2865

v (m/s) -0.0382 0.0704 0.0004 0.0704

ψms 3.5175° - - 0.0956°

174

• Streamwise Velocity, Vs

2

ms

s2

vs

2

us

V mssuVu

vVu

uVU

⋅

∂∂+

⋅∂∂+

⋅∂∂= ψψψψψψψψ

( )mss cos

uV ψψψψ=∂∂

( )mss sin

vV ψψψψ=∂∂

( ) ( )msmsms

s cosvsinuV ψψψψψψψψψψψψ

⋅+⋅−=∂∂

High value of Vs = 29.02 m/s Variable Value Precision

Uncertainty

Bias

Uncertainty

Total

Uncertainty

Vs (m/s) 29.02 - - 0.2926 (1.01%)

u (m/s) 29.0658 0.0344 0.2907 0.2927

v (m/s) 1.8607 0.0704 0.0186 0.0728

ψms 1.30° - - 0.0956°

Low value of Vs = 20.70 m/s Variable Value Precision

Uncertainty

Bias

Uncertainty

Total

Uncertainty

Vs (m/s) 20.70 - - 0.1949 (0.94%)

u (m/s) 19.8174 0.0344 0.1982 0.2011

v (m/s) -5.9991 0.0704 0.0600 0.0925

ψms 16.2203° - - 0.2550°

175

• Pitch Angle, φ

2

v

2

u uv

uu

U

⋅∂∂+

⋅∂∂= φφφφφφφφ

φφφφ

+

−=∂∂

2

22

uw1u

wuφφφφ

+

=∂∂

2

2

uw1u

1wφφφφ

High value of φ = 19.22°

Low value of φ = 3.40°

Variable Value Precision

Uncertainty

Bias

Uncertainty

Total

Uncertainty

φ 19.22° - - 0.9567° (4.98%)

u (m/s) 24.9445 0.0344 0.2494 0.2518

w (m/s) 8.6943 0.4505 0.0869 0.4588

Variable Value Precision

Uncertainty

Bias

Uncertainty

Total

Uncertainty

φ 3.40° - - 0.8669° (25.53%)

u (m/s) 29.7148 0.0344 0.2971 0.2991

w (m/s) 1.7635 0.4505 0.0176 0.4508

176

• Turbulence Intensity, Tu

2

Uinlet

2

wrms

2

vrms

2

urms

Tu inletrmsrmsrmsu

UTuu

wTuu

vTuu

uTuU

⋅

∂∂+

⋅

∂∂+

⋅

∂∂+

⋅

∂∂=

inletrms U31

uTu

⋅=

∂∂

inletrms U31

vTu

⋅=

∂∂

inletrms U31

wTu

⋅=

∂∂

2inlet

rmsrmsrms

inlet U3wvu

UTu

⋅++

−=∂∂

High value of Tu = 0.52 Variable Value Uncertainty

Tu 0.52 0.0086 (1.64%)

urms (m/s) 2.6690 =rmsuu 0.0515

vrms (m/s) 3.3473 =rmsvu 0.0482

wrms (m/s) 3.8254 =rmswu 0.0540

Uinlet (m/s) 6.25 =inletUu 0.0848

Low value of Tu = 0.17 Variable Value Uncertainty

Tu 0.17 0.0048 (2.83%)

urms (m/s) 1.1623 =rmsuu 0.0612

vrms (m/s) 1.1401 =rmsvu 0.0481

wrms (m/s) 0.9480 =rmswu 0.0126

Uinlet (m/s) 6.25 =inletUu 0.0848

177

Appendix C: Flow Case Conditions

This appendix gives the exact flow and thermal conditions for each of the five cases for which adiabatic effectiveness was measured. • Case 1 (design slot flow, flat inlet total pressure profile)

Pressure (in H20) Local Velocity (m/s)panel 1 bottom 0.1525 panel 1 bottom 1.56panel 1 top 0.1525 panel 1 top 1.56panel 2 bottom 0.15 panel 2 bottom 1.73panel 2 top 0.15 panel 2 top 1.73panel 3 bottom 0.2 panel 3 bottom 2.54panel 3 top 0.2 panel 3 top 2.54dilution 1 bottom 1.24 dilution 1 bottomdilution 1 top 1.24 dilution 1 topdilution 2 bottom 0.56 dilution 2 bottomdilution 2 top 0.56 dilution 2 toppanel 4 bottom 0.22 panel 4 bottom 5.25panel 4 top 0.22 panel 4 top 5.25slot bottom 2.3 slot bottomslot top 2.3 slot top

Jet Velocity (m/s) Mass Flow Rate (kg/s)panel 1 bottom 6.17 panel 1 bottom 0.06panel 1 top 6.17 panel 1 top 0.06panel 2 bottom 6.07 panel 2 bottom 0.14panel 2 top 6.07 panel 2 top 0.14panel 3 bottom 7.01 panel 3 bottom 0.14panel 3 top 7.01 panel 3 top 0.14dilution 1 bottom 19.72 dilution 1 bottom 0.37dilution 1 top 19.72 dilution 1 top 0.37dilution 2 bottom 14.60 dilution 2 bottom 0.37dilution 2 top 14.60 dilution 2 top 0.37panel 4 bottom 7.41 panel 4 bottom 0.07panel 4 top 7.41 panel 4 top 0.07slot bottom slot bottom 0.03slot top slot top 0.03

total 4.18

178

Mass Flow Rate (%) Momentum Flux Ratiopanel 1 bottom 1.48 panel 1 bottom 15.60panel 1 top 1.48 panel 1 top 15.60panel 2 bottom 3.45 panel 2 bottom 12.29panel 2 top 3.45 panel 2 top 12.29panel 3 bottom 3.44 panel 3 bottom 7.65panel 3 top 3.44 panel 3 top 7.65dilution 1 bottom 8.77 dilution 1 bottom 129.65dilution 1 top 8.77 dilution 1 top 129.65dilution 2 bottom 8.78 dilution 2 bottom 33.15dilution 2 top 8.78 dilution 2 top 33.15panel 4 bottom 1.65 panel 4 bottom 1.99panel 4 top 1.65 panel 4 top 1.99slot bottom 0.63 slot bottomslot top 0.63 slot top

Cd Number of HolesPanel 1 0.738705 Panel 1 202Panel 2 0.733497 Panel 2 478Panel 3 0.733497 Panel 3 413Panel 4 0.738705 Panel 4 187Dilution 1 0.8285 Dilution 1 3Dilution 2 0.9123 Dilution 2 2Exit Slot 0.7 Exit Slot 15

Area per Hole (m^2) Inlet Area (m^2) 1.1071Panel 1 0.0000456 Air Density (kg/m^3) 1.09Panel 2 0.0000456 Fan Speed (Hz) 41.5Panel 3 0.0000456 Inlet Velocity (m/s) 1.51Panel 4 0.0000456 Inlet Mass Flow (kg/m^3) 1.8222Dilution 1 0.0056865 Area at Panel 3 (m^2) 0.9935Dilution 2 0.0115291 Area at Panel 4 (m^2) 0.7097Exit Slot 0.0000713

T freestream (deg C) 39.314T coolant (deg C) 24.1025T infinity (deg C) 30.7332Delta T (deg C) 6.6307

179

• Case 2 (design slot flow, inlet total pressure profile with a peak of ∆P = 0.7)

Pressure (in H20) Local Velocity (m/s)panel 1 bottom 0.15 panel 1 bottom 1.47panel 1 top 0.15 panel 1 top 1.47panel 2 bottom 0.15 panel 2 bottom 1.64panel 2 top 0.15 panel 2 top 1.64panel 3 bottom 0.34 panel 3 bottom 2.45panel 3 top 0.34 panel 3 top 2.45dilution 1 bottom 1.24 dilution 1 bottomdilution 1 top 1.24 dilution 1 topdilution 2 bottom 0.56 dilution 2 bottomdilution 2 top 0.56 dilution 2 toppanel 4 bottom 0.59 panel 4 bottom 5.19panel 4 top 0.59 panel 4 top 5.19slot bottom 2.3 slot bottomslot top 2.3 slot top

Jet Velocity (m/s) Mass Flow Rate (kg/s)panel 1 bottom 6.12 panel 1 bottom 0.06panel 1 top 6.12 panel 1 top 0.06panel 2 bottom 6.07 panel 2 bottom 0.14panel 2 top 6.07 panel 2 top 0.14panel 3 bottom 9.14 panel 3 bottom 0.19panel 3 top 9.14 panel 3 top 0.19dilution 1 bottom 18.60 dilution 1 bottom 0.35dilution 1 top 18.60 dilution 1 top 0.35dilution 2 bottom 14.10 dilution 2 bottom 0.35dilution 2 top 14.10 dilution 2 top 0.35panel 4 bottom 12.13 panel 4 bottom 0.11panel 4 top 12.13 panel 4 top 0.11slot bottom slot bottom 0.03slot top slot top 0.03

total 4.18

180

Mass Flow Rate (%) Momentum Flux Ratiopanel 1 bottom 1.47 panel 1 bottom 17.29panel 1 top 1.47 panel 1 top 17.29panel 2 bottom 3.45 panel 2 bottom 13.69panel 2 top 3.45 panel 2 top 13.69panel 3 bottom 4.49 panel 3 bottom 13.87panel 3 top 4.49 panel 3 top 13.87dilution 1 bottom 8.28 dilution 1 bottom 128.42dilution 1 top 8.28 dilution 1 top 128.42dilution 2 bottom 8.48 dilution 2 bottom 32.99dilution 2 top 8.48 dilution 2 top 32.99panel 4 bottom 2.70 panel 4 bottom 5.47panel 4 top 2.70 panel 4 top 5.47slot bottom 0.63 slot bottomslot top 0.63 slot top

Cd Number of HolesPanel 1 0.738705 Panel 1 202Panel 2 0.733497 Panel 2 478Panel 3 0.733497 Panel 3 413Panel 4 0.738705 Panel 4 187Dilution 1 0.8285 Dilution 1 3Dilution 2 0.9123 Dilution 2 2Exit Slot 0.7 Exit Slot 15

Area per Hole (m^2) Inlet Area (m^2) 1.1071Panel 1 0.0000456 Air Density (kg/m^3) 1.09Panel 2 0.0000456 Fan Speed (Hz) 41.3Panel 3 0.0000456 Inlet Velocity (m/s) 1.42Panel 4 0.0000456 Inlet Mass Flow (kg/m^3) 1.7136Dilution 1 0.0056865 Area at Panel 3 (m^2) 0.9935Dilution 2 0.0115291 Area at Panel 4 (m^2) 0.7097Exit Slot 0.0000713

T freestream (deg C) 39.613T coolant (deg C) 24.1025T infinity (deg C) 30.4621Delta T (deg C) 6.3596

181

• Case 3 (design slot flow, inlet total pressure profile with a peak of ∆P = 2.2)

Pressure (in H20) Local Velocity (m/s)panel 1 bottom 0.153 panel 1 bottom 1.39panel 1 top 0.153 panel 1 top 1.39panel 2 bottom 0.15 panel 2 bottom 1.56panel 2 top 0.15 panel 2 top 1.56panel 3 bottom 0.5 panel 3 bottom 2.39panel 3 top 0.5 panel 3 top 2.39dilution 1 bottom 0.7 dilution 1 bottomdilution 1 top 0.7 dilution 1 topdilution 2 bottom 0.49 dilution 2 bottomdilution 2 top 0.49 dilution 2 toppanel 4 bottom 1.1 panel 4 bottom 5.15panel 4 top 1.1 panel 4 top 5.15slot bottom 2.3 slot bottomslot top 2.3 slot top

Jet Velocity (m/s) Mass Flow Rate (kg/s)panel 1 bottom 6.18 panel 1 bottom 0.06panel 1 top 6.18 panel 1 top 0.06panel 2 bottom 6.07 panel 2 bottom 0.14panel 2 top 6.07 panel 2 top 0.14panel 3 bottom 11.09 panel 3 bottom 0.23panel 3 top 11.09 panel 3 top 0.23dilution 1 bottom 17.70 dilution 1 bottom 0.33dilution 1 top 17.70 dilution 1 top 0.33dilution 2 bottom 13.70 dilution 2 bottom 0.34dilution 2 top 13.70 dilution 2 top 0.34panel 4 bottom 16.56 panel 4 bottom 0.15panel 4 top 16.56 panel 4 top 0.15slot bottom slot bottom 0.03slot top slot top 0.03

total 4.19

182

Mass Flow Rate (%) Momentum Flux Ratiopanel 1 bottom 1.48 panel 1 bottom 19.71panel 1 top 1.48 panel 1 top 19.71panel 2 bottom 3.44 panel 2 bottom 15.11panel 2 top 3.44 panel 2 top 15.11panel 3 bottom 5.43 panel 3 bottom 21.55panel 3 top 5.43 panel 3 top 21.55dilution 1 bottom 7.85 dilution 1 bottom 128.35dilution 1 top 7.85 dilution 1 top 128.35dilution 2 bottom 8.21 dilution 2 bottom 32.90dilution 2 top 8.21 dilution 2 top 32.90panel 4 bottom 3.67 panel 4 bottom 10.33panel 4 top 3.67 panel 4 top 10.33slot bottom 0.63 slot bottomslot top 0.63 slot top

Cd Number of HolesPanel 1 0.738705 Panel 1 202Panel 2 0.733497 Panel 2 478Panel 3 0.733497 Panel 3 413Panel 4 0.738705 Panel 4 187Dilution 1 0.8285 Dilution 1 3Dilution 2 0.9123 Dilution 2 2Exit Slot 0.7 Exit Slot 15

Area per Hole (m^2) Inlet Area (m^2) 1.1071Panel 1 0.0000456 Air Density (kg/m^3) 1.09Panel 2 0.0000456 Fan Speed (Hz) 41.5Panel 3 0.0000456 Inlet Velocity (m/s) 1.34Panel 4 0.0000456 Inlet Mass Flow (kg/m^3) 1.6170Dilution 1 0.0056865 Area at Panel 3 (m^2) 0.9935Dilution 2 0.0115291 Area at Panel 4 (m^2) 0.7097Exit Slot 0.0000713

T freestream (deg C) 44.465T coolant (deg C) 25.6T infinity (deg C) 32.8760Delta T (deg C) 7.2760

183

• Case 4 (half slot flow, inlet total pressure profile with a peak of ∆P = 0.7)

Pressure (in H20) Local Velocity (m/s)panel 1 bottom 0.15 panel 1 bottom 1.49panel 1 top 0.15 panel 1 top 1.49panel 2 bottom 0.15 panel 2 bottom 1.66panel 2 top 0.15 panel 2 top 1.66panel 3 bottom 0.34 panel 3 bottom 2.48panel 3 top 0.34 panel 3 top 2.48dilution 1 bottom 1.24 dilution 1 bottomdilution 1 top 1.24 dilution 1 topdilution 2 bottom 0.56 dilution 2 bottomdilution 2 top 0.56 dilution 2 toppanel 4 bottom 0.59 panel 4 bottom 5.22panel 4 top 0.59 panel 4 top 5.22slot bottom 2.3 slot bottomslot top 2.3 slot top

Jet Velocity (m/s) Mass Flow Rate (kg/s)panel 1 bottom 6.12 panel 1 bottom 0.06panel 1 top 6.12 panel 1 top 0.06panel 2 bottom 6.07 panel 2 bottom 0.14panel 2 top 6.07 panel 2 top 0.14panel 3 bottom 9.14 panel 3 bottom 0.19panel 3 top 9.14 panel 3 top 0.19dilution 1 bottom 18.60 dilution 1 bottom 0.35dilution 1 top 18.60 dilution 1 top 0.35dilution 2 bottom 14.10 dilution 2 bottom 0.35dilution 2 top 14.10 dilution 2 top 0.35panel 4 bottom 12.13 panel 4 bottom 0.11panel 4 top 12.13 panel 4 top 0.11slot bottom slot bottom 0.01slot top slot top 0.01

total 4.18

184

Mass Flow Rate (%) Momentum Flux Ratiopanel 1 bottom 1.47 panel 1 bottom 16.79panel 1 top 1.47 panel 1 top 16.79panel 2 bottom 3.45 panel 2 bottom 13.33panel 2 top 3.45 panel 2 top 13.33panel 3 bottom 4.49 panel 3 bottom 13.60panel 3 top 4.49 panel 3 top 13.60dilution 1 bottom 8.28 dilution 1 bottom 125.06dilution 1 top 8.28 dilution 1 top 125.06dilution 2 bottom 8.48 dilution 2 bottom 32.34dilution 2 top 8.48 dilution 2 top 32.34panel 4 bottom 2.70 panel 4 bottom 5.39panel 4 top 2.70 panel 4 top 5.39slot bottom 0.32 slot bottomslot top 0.32 slot top

Cd Number of HolesPanel 1 0.738705 Panel 1 202Panel 2 0.733497 Panel 2 478Panel 3 0.733497 Panel 3 413Panel 4 0.738705 Panel 4 187Dilution 1 0.8285 Dilution 1 3Dilution 2 0.9123 Dilution 2 2Exit Slot 0.7 Exit Slot 15

Area per Hole (m^2) Inlet Area (m^2) 1.1071Panel 1 0.0000456 Air Density (kg/m^3) 1.09Panel 2 0.0000456 Fan Speed (Hz) 41.3Panel 3 0.0000456 Inlet Velocity (m/s) 1.42Panel 4 0.0000456 Inlet Mass Flow (kg/m^3) 1.7400Dilution 1 0.0056865 Area at Panel 3 (m^2) 0.9935Dilution 2 0.0115291 Area at Panel 4 (m^2) 0.7097Exit Slot 0.0000713

T freestream (deg C) 41.967T coolant (deg C) 25.6267T infinity (deg C) 32.4299Delta T (deg C) 6.8032

185

• Case 5 (double slot flow, inlet total pressure profile with a peak of ∆P = 0.7)

Pressure (in H20) Local Velocity (m/s)panel 1 bottom 0.15 panel 1 bottom 1.43panel 1 top 0.15 panel 1 top 1.43panel 2 bottom 0.15 panel 2 bottom 1.60panel 2 top 0.15 panel 2 top 1.60panel 3 bottom 0.34 panel 3 bottom 2.41panel 3 top 0.34 panel 3 top 2.41dilution 1 bottom 1.24 dilution 1 bottomdilution 1 top 1.24 dilution 1 topdilution 2 bottom 0.56 dilution 2 bottomdilution 2 top 0.56 dilution 2 toppanel 4 bottom 0.59 panel 4 bottom 5.12panel 4 top 0.59 panel 4 top 5.12slot bottom 2.3 slot bottomslot top 2.3 slot top

Jet Velocity (m/s) Mass Flow Rate (kg/s)panel 1 bottom 6.12 panel 1 bottom 0.06panel 1 top 6.12 panel 1 top 0.06panel 2 bottom 6.07 panel 2 bottom 0.14panel 2 top 6.07 panel 2 top 0.14panel 3 bottom 9.14 panel 3 bottom 0.19panel 3 top 9.14 panel 3 top 0.19dilution 1 bottom 18.60 dilution 1 bottom 0.35dilution 1 top 18.60 dilution 1 top 0.35dilution 2 bottom 14.10 dilution 2 bottom 0.35dilution 2 top 14.10 dilution 2 top 0.35panel 4 bottom 12.13 panel 4 bottom 0.11panel 4 top 12.13 panel 4 top 0.11slot bottom slot bottom 0.05slot top slot top 0.05

total 4.18

186

Mass Flow Rate (%) Momentum Flux Ratiopanel 1 bottom 1.47 panel 1 bottom 18.37panel 1 top 1.47 panel 1 top 18.37panel 2 bottom 3.45 panel 2 bottom 14.45panel 2 top 3.45 panel 2 top 14.45panel 3 bottom 4.49 panel 3 bottom 14.44panel 3 top 4.49 panel 3 top 14.44dilution 1 bottom 8.28 dilution 1 bottom 135.56dilution 1 top 8.28 dilution 1 top 135.56dilution 2 bottom 8.48 dilution 2 bottom 34.34dilution 2 top 8.48 dilution 2 top 34.34panel 4 bottom 2.70 panel 4 bottom 5.61panel 4 top 2.70 panel 4 top 5.61slot bottom 1.27 slot bottomslot top 1.27 slot top

Cd Number of HolesPanel 1 0.738705 Panel 1 202Panel 2 0.733497 Panel 2 478Panel 3 0.733497 Panel 3 413Panel 4 0.738705 Panel 4 187Dilution 1 0.8285 Dilution 1 3Dilution 2 0.9123 Dilution 2 2Exit Slot 0.7 Exit Slot 15

Area per Hole (m^2) Inlet Area (m^2) 1.1071Panel 1 0.0000456 Air Density (kg/m^3) 1.09Panel 2 0.0000456 Fan Speed (Hz) 41.3Panel 3 0.0000456 Inlet Velocity (m/s) 1.42Panel 4 0.0000456 Inlet Mass Flow (kg/m^3) 1.6607Dilution 1 0.0056865 Area at Panel 3 (m^2) 0.9935Dilution 2 0.0115291 Area at Panel 4 (m^2) 0.7097Exit Slot 0.0000713

T freestream (deg C) 42.3567T coolant (deg C) 25.3375T infinity (deg C) 32.1004Delta T (deg C) 6.7629

187

Vita

William Frederick Colban IV

William Frederick Colban IV was born in Beaufort, SC to William Frederick

Colban III and Michelle Pauline Colban at 10:16 pm on November 6, 1980. He lived in

many states as a young child including SC, NC, TN, and NJ before finally settling in

Richmond, VA. He attended the Governor’s School in Richmond, VA and graduated

high school in 1997 at the age of 16. He received his Bachelor of Science in Mechanical

Engineering (Physics Minor) at Virginia Tech in May of 2001 at the age of 20, at which

time he was already well on his way to receiving his master’s degree. In December 2001,

Will earned his Master’s of Science in Mechanical Engineering at the age of 21.

Currently, he plans to spend six months working in Switzerland for ALSTOM Ltd.,

before returning to Virginia Tech and pursuing a Ph. D in mechanical engineering.

Will ran his first marathon on November 10, 2001.

Favorite…

Color Navy Blue

Movie Billy Madison

Baseball Team New York Mets

Soda Root Beer

Fast Food Chain Subway

Food Sub

Season Summer

Animal Turtle (because he beat the rabbit)