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The Dissertation Committee for Kyle Feliciano Chavez certifies that this is the approved version of the following dissertation:

Variable Incidence Angle Film Cooling Experiments on a Scaled Up Turbine Airfoil Model

Committee:

David G. Bogard, Supervisor

Frederick Todd Davidson

Atul Kohli

Ofodike A. Ezekoye

Michael E. Webber Variable Incidence Angle Film Cooling Experiments on a Scaled Up Turbine Airfoil Model

Kyle Feliciano Chavez, B.S.; M.S.

Dissertation Presented to the Faculty of the Graduate School of The University of Texas at Austin in Partial Fulfillment

of the Requirements for the Degree of

Doctor of Philosophy

The University of Texas at Austin May 2016 Dedication

This document is dedicated to my family. Dad, you have always been so encouraging, helpful, and levelheaded. If not for all of your help and encouragement, I’m not sure I’d be where I’m at today. To my brother, I’m so happy for the years we spent growing up together. They are some of my fondest memories and I’ll never forget them.

Mom, if you were still here today, you’d be so proud. I think of you all constantly, and I love you all.

Acknowledgements

I would like to first and foremost thank Dr. Bogard, who has supported and taught me so much along the way. Your dedication to your field of research is an inspiration to me, and you’ve helped shape me in to the engineer I am today. You also taught me how great it is to be “mighty fine” all the time, and that’s priceless in and of itself. I’d also like to thank the Pratt & Whitney team who worked on this project in conjunction with our lab. It was great working with you, and thank you for working so hard to make sure that this project was as successful as it was. I’d like to thank all the graduate students I’ve had the pleasure of working with and meeting. Adam, Dave, Ellen, Emily, Gavin, Jabob (hah), James, John, Josh, Noah, Owen, Robbie, Sean, Tom. I’m so sorry ahead of time for forgetting someone’s name, but you’re all included, I promise. Special thanks to those who spent some of those late nights working with me to meet deadlines. I hope you don’t hate me too much for it.

I’d also like to thank all of the undergraduate assistants I’ve had the pleasure of working with – Brad, Chris, Gary, Jennifer, Khanh, Michelle, and Theo. You’ve helped me so much, and I’ll always be thankful for that. Hopefully I taught you something along the way, or at least made you laugh a few times. Finally, I would like to sincerely thank The University of Texas at Austin

Cockrell School of Engineering and the W.M. Keck Foundation for providing me with funding assistance. It is an honor to be one of the students receiving a fellowship such as the one that I did, and it allowed me to truly pursue my goals without having to worry about the additional financial burdens that I would have had to overcome.

v Variable Incidence Angle Film Cooling Experiments on a Scaled Up Turbine Airfoil Model

Kyle Feliciano Chavez, Ph.D. The University of Texas at Austin, 2016

Supervisor: David G. Bogard

This study focused on three main areas of research - the development of a new type of low-speed, closed-loop wind tunnel design to test at varying incidence angles, the investigation of film cooling for gas turbine components at varying incidence angles, and the analysis of the heat transfer and flow field predictive capability of RANS models. In order to develop the closed loop wind tunnel, a rigorous design and validation process was followed. This validated design is unique for low-speed closed-loop facilities. The development of this wind tunnel enabled measurements of adiabatic and overall effectiveness of two highly realistic airfoil models with shaped holes at varying incidence angles. This was accomplished through application of the appropriate aerodynamic and heat transfer scaling parameters for all measurements. Among other results, it was found that the shaped holes at the stagnation row of holes significantly enhanced film cooling effectiveness in the high curvature region of the showerhead depending on the incidence angle tested, and that the incidence angle effect persisted on the matched Biot number model. No previous studies had experimentally investigated the effects of incidence angle effects on overall effectiveness of a full-coverage airfoil. Furthermore, no previous studies had investigated the effect of shaped holes in the showerhead region of a realistic airfoil model such as the one used in this study. Finally, the computational predictive vi capability of various RANS turbulence models were analyzed by predicting the heat transfer coefficient of the model as well as the turbulence production and turning angle of a vertical array of rods used to generate turbulence in the tunnel. It was found that the computational predictions of leading-edge heat transfer were under-predicted due to the shape of the model leading edge. It was also found that the SST-Transition model appropriately predicted downstream turbulence and turning angle of the vertical rod array when compared to experimental results and empirical correlations in the literature. This is the first study to experimentally and computationally investigate the turning angle of a vertical grid array over a range of zero and non-zero inlet flow angles.

vii Table of Contents

List of Tables ...... xv

List of Figures ...... xvii

Nomenclature ...... xxviii

Chapter 1 : Introduction ...... 1

1.1. Gas Turbine Engines ...... 1

1.1.1. Materials and Cooling Technologies ...... 4

1.1.2. Quantification of Cooling Performance...... 7

1.1.3. Quantification of Aerothermal Performance ...... 10

1.2. Experiments and Computational Fluid Dynamics ...... 11

1.2.1. Reynolds-averaged Navier-Stokes computational models ...... 12

1.3. Considerations of Off-Design Incidence ...... 13

1.4. Gas Turbine Airfoil Nomenclature and Coordinate Systems ...... 13

Chapter 2 : Literature Review ...... 15

2.1. External No-Film Heat Transfer Coefficient Testing ...... 15

2.2. Adiabatic Effectiveness Testing ...... 17

2.3. The Matched Biot Number Model Testing ...... 22

2.4. Variable Incidence Angle Wind Tunnel Facilities ...... 24

2.4.1. Adjustable Inlet Duct Linear Cascades...... 25

2.4.2. Adjustable Inlet Contraction Nozzle Linear Cascades ...... 27

2.4.3. Inlet Guide Vane Cascades ...... 29

2.4.4. Rotating Rigs ...... 31

viii Chapter 3 : Dissertation Objectives and Contribution Goals ...... 33

Chapter 4 : Previous Facility and Conceptual Design of New Facility ...... 36

4.1. Previous Facility Components ...... 36

4.2. Conceptual Design of New Facility ...... 38

4.2.1. Initial Concept ...... 39

4.2.2. Improvement of Conceptual Design – Design Criteria ...... 41

4.2.3. Research for Conceptual Design Improvements ...... 42

4.2.4. Improved Designs and Decision Matrix ...... 42

4.2.5. Revised Design Concept ...... 44

Chapter 5 : Detailed Design of Facility Upgrades ...... 46

5.1. Design of Main Components...... 48

5.1.1. Contraction Nozzle ...... 48

5.1.2. Incidence Angle Mechanism ...... 51

5.1.3. Test Section ...... 59

5.1.4. Diffuser ...... 66

5.1.5. Coolant Loop ...... 70

5.1.6. Construction ...... 71

5.2. : Design of Subcomponents ...... 74

5.2.1. Test Airfoils ...... 74

5.2.2. Turning Vanes for Incidence Angle Mechanism ...... 79

5.2.3. Turbulence Rods for Test Section Inlet ...... 85

5.2.4. Construction ...... 87

ix Chapter 6 : Experimental Plan, Instrumentation, and Experimental Setup ...... 89

6.1. Experimental Plan and Test List ...... 90

6.1.1. Experimental Procedure - Wind Tunnel Validation ...... 90

6.1.2. Experimental Procedure – Formal Test Data Collection ...... 90

6.1.3. Complete Experimental Test List ...... 91

6.1.4. Experimental Procedure – Nominal Testing Conditions ...... 91

6.2. Instrumentation...... 93

6.2.1. Mainstream Pressure and Temperature Measurements ...... 93

6.2.2. Coolant Loop Flow Rate and Temperature Measurements ...... 94

6.2.3. IR Camera Locations ...... 95

6.2.4. Pressure Transducers ...... 97

6.2.5. Data Acquisition System ...... 98

6.2.6. Particle Image Velocimetry ...... 99

6.2.7. Hotwire Anemometry ...... 100

6.3. Experimental Calculations ...... 100

6.3.1. Atmospheric Pressure Measurements ...... 100

6.3.2. Mainstream Velocity Measurements ...... 101

6.3.3. Coolant Passage Flow Rate Measurements ...... 102

6.4. Experimental Setup of Initial Pressure Distribution and Stagnation Line Validation ...... 103

6.5. Experimental Setup of Turning Vane Outlet Angle Validation ...... 104

6.6. Experimental Setup of Turbulence Rod Outlet Angle Validation ...... 110

6.7. Experimental Setup of Pressure Distribution Testing (Test Article A) .111

6.7.2. Measuring the Pressure Distribution, CP, TS, Inlet ...... 113 x 6.7.3. Calculating Pressure Distribution, CP, TS, Inlet ...... 115

6.8. Experimental Setup - Heat Transfer Coefficient Testing (Test Article B)116

6.8.1. Measuring the Heat Transfer Coefficient, h ...... 116

6.8.2. Calculating the Heat Transfer Coefficient, h ...... 118

6.9. Experimental Setup - Film-Cooling Hole Discharge Coefficient Testing120

6.9.1. Measuring the Film-Cooling Hole Discharge Coefficients ...... 120

6.9.2. Passage Mass Flow Rates ...... 120

6.9.3. Calculating the Film-Cooling Hole Discharge Coefficients ...... 121

6.10. Experimental Setup - Adiabatic Film Effectiveness Testing (Article C)122

6.10.1. Measuring the Adiabatic Film Effectiveness, η ...... 122

6.10.2. Calculating the Fractional Mass Flow Rate Through Multiple Rows of Holes, F ...... 123

6.10.3. Calculating the Adiabatic Effectiveness, η ...... 124

6.10.4. Correcting the Adiabatic Effectiveness to Account for Conduction Effects ...... 124

6.11. Experimental Setup - Overall Effectiveness Testing ...... 125

6.12. Experimental Data Acquisition ...... 126

6.12.1. Primary Measurements and Derived Variables ...... 126

6.12.2. IR Thermography ...... 127

6.13. Software Setup for HTC, η, and ϕ IR Measurements...... 127

6.13.1. Subprocess A - Processing IR Measurements for Individual Cameras ...... 129

6.13.2. Subprocess B - Combining Multiple HTC, η, and ϕ IR Measurements from Individual Cameras ...... 136

6.13.3. Subprocess C – Processing Data for Uncertainty Calculations 138

xi Chapter 7 : Calibrations and Experimental Uncertainty Analysis ...... 139

7.1. Calibration Methods and Uncertainties of Calibrated Measurements ...139

7.1.1. Atmospheric Pressure ...... 139

7.1.2. Pressure Transducers ...... 140

7.1.3. Thermocouples ...... 143

7.1.4. Orifice Plate Discharge Coefficient, Cd, o ...... 145

7.1.5. IR Camera Surface Temperature, Ts ...... 151

7.2. Uncertainty Analysis of Derived Variables ...... 157

7.2.1. Uncertainty in Pressure Distribution ...... 157

7.2.2. Uncertainty in Turning Vane Incidence Angle α and Mean Flow Field Measurements with PIV, M ...... 159

7.2.3. Uncertainty in External No-Film Heat Transfer Coefficient, h0, e ...174

7.2.4. Uncertainty in Coolant Passage Mass Flow Rate During Film-Cooling Experiments, mcoolant ...... 175

7.2.5. Uncertainty in Hole Discharge Coefficients, Cd, holes ...... 181

7.2.6. Uncertainty in the Fractional Hole Flow Splits, F ...... 182

7.2.7. Uncertainty in Local External Velocities Near Holes, VTS, local .....184

7.2.8. Uncertainty in Velocity Ratio, VR ...... 186

7.2.9. Uncertainty in Adiabatic and Overall Effectiveness η and ϕ ...... 190

xii Chapter 8 : Experimental Results ...... 193

8.1. Pressure Distribution Results ...... 194

8.2. Heat Transfer Coefficient Experiments...... 194

8.3. Adiabatic Effectiveness at β = -30.1° (i=0.1°) ...... 199

8.4. Adiabatic Effectiveness at β = -30.1° (i=0.1°) Full Contours ...... 200

8.5. Adiabatic Effectiveness - Incidence Angle Effects ...... 205

8.5.1. Adiabatic Effectiveness for β=-21.2° (i=-8.8°) ...... 206

8.6. A Note on Conduction Correction η0 ...... 210

8.6.1. Difference in Adiabatic Effectiveness , η(β=-30.1°)-η(β=-21.2°) ....213

8.7. Overall Effectiveness – β =-30.1° (i=0.1°) ...... 216

8.8. Effects of Incidence Angle in the Showerhead Region...... 223

8.9. Effects of Stagnation Line Shift for Conical Shaped Holes ...... 224

8.10. Overall Effectiveness – Effects of Incidence Angle on Showerhead Region ...... 229

8.11. Overall Effectiveness – Predictions of ϕ With ϕ0 ...... 231

8.12. Follow-up Study: Capability of Testing ...... 235

Chapter 9 : Computational Setup ...... 236

9.1. Computational Heat Transfer Predictions ...... 236

9.1.1. Computational Domain ...... 237

9.2. Turbulence Grid Flow Field and Turning Angle Simulations ...... 241

Chapter 10 : Computational Results ...... 245

10.1. Heat Transfer Coefficient Predictions ...... 245

10.2. Turbulence Grid Flow Field and Turning Angle Simulations ...... 251

10.2.1. Comparison of Turbulence Levels to Correlations ...... 253 xiii 10.2.2. Comparison of CFD Outlet Angle to Experimental Data ...... 255

Chapter 11 : Conclusions ...... 259

11.1. Wind Tunnel Design ...... 259

11.2. Wind Tunnel Validation and Computational Predictions of Turbulence Grid Turning Angle ...... 260

11.3. Heat Transfer Coefficient Experiments and Computational Work ...... 262

11.4. Adiabatic Effectiveness Experiments - β = -30.1° ...... 263

11.5. Adiabatic Effectiveness Experiments – β = -21.2°, and Effects of Incidence Angle on Adiabatic Effectiveness ...... 264

11.6. Overall Effectiveness Experiments – β=-30.1° ...... 264

11.7. Prediction of ϕ ...... 265

11.8. Effects of Incidence Angle on the Showerhead Region ...... 266

References ...... 267

Vita ...... 273

xiv List of Tables

Table 4.1: The criteria utilized in assessing conceptual designs...... 42 Table 4.2: The decision matrix used in comparing conceptual designs. Note the final

scores highlighted in green, with a score ranging from 0-500...... 45 Table 5.1: The values of the variables used in Equations 5.1 and 5.2to solve for the

contraction nozzle profile...... 51

Table 5.2: The locations, sizes, and types of film cooling holes used in this study...... 79 Table 5.3: The ideal turning vane outlet angles compared to the outlet angles as

predicted by CFD...... 82

Table 5.4: The turbulence rods designed by Mosberg [56]...... 86

Table 6.1: A summary of the tests performed for this project...... 91 Table 6.2: A summary of the nominal target velocity ratios to be bracketed during the

test...... 92

Table 6.3: A summary of the inlet conditions studied...... 92

Table 6.4: A summary of the predicted PIV settings...... 110

Table 7.1: A summary of the uncertainty in h0, e...... 175

Table 8.1: A summary of the testing conditions for the heat transfer coefficient tests. . 195

Table 8.2: A summary of the velocity ratios tested for the β=-30.10° η experiments. .. 200

Table 8.3: A summary of the velocity ratios tested for the β=-21.2° η experiments. .... 208

Table 8.4: A summary of the velocity ratios tested for the β=-30.10° ϕ experiments .. 217 Table 8.5: A summary of the effective inlet incidence angles studied during the

stagnation line shift test...... 225

Table 9.1: A summary of the boundary conditions specified in the simulations...... 237

Table 9.2: A summary of the fluid properties used in the simulations...... 238

xv Table 9.3: Summary of the computational parametric sweep performed for the

turbulence rods...... 244 Table 10.1: Computational results for parametric sweep of incidence angle over a

range of pitches...... 256 Table 10.2: Predicted difference in turbulence grid deflection in CFD vs.

experimental results...... 258

xvi List of Figures

Figure 1.1: Left - Stages of the Brayton Cycle [4]. Right – Example of the open

Brayton Cycle [4]...... 3

Figure 1.2: Overall thermal efficiency of a gas turbine [5]...... 4

Figure 1.3: Schematics of a typical film cooled turbine blade [6]...... 6

Figure 1.4: Coordinate and angle designations used in the paper...... 14 Figure 2.1: Left - 휂 at M=0.7, 훼 = ±10° [35]. Right - 휂 for all blowing ratios and

incidence angles studied [35]...... 21 Figure 2.2: Left - 휂 [35]. Right - 푚 for all blowing ratios and incidence angles studied

[35]...... 22 Figure 2.3: Schematic of the open loop, variable incidence angle duct-type wind

tunnel used by Lee and Park [47]...... 26

Figure 2.4: Schematic of the open loop, blowdown facility utilized by Gao et al. [36]. .. 27

Figure 2.5: Schematic of the open lop facility utilized by Zhang and Yuan [33]...... 27

Figure 2.6: Schematic of the facility utilized by Jeffries [52]...... 28

Figure 2.7: The EGG facility...... 29

Figure 2.8: Schematic of the open loop facility utilized by Sanger [54]...... 30

Figure 2.9: Another view of the open loop facility utilized by Sanger [54]...... 31

Figure 2.10: Schematic of the open lop, facility utilized by Ahn et al. [31]...... 32 Figure 4.1: Schematic of the recirculating low-speed wind tunnel used for airfoil

testing in the TTCRL. An airfoil with an 훼 = 0° design point is visible in the schematic. Portions of the wind tunnel redesigned in the project

are highlighted in red...... 37

Figure 4.2: Schematic of the previous wind tunnel test section [46]...... 38

xvii Figure 4.3: The initial conceptual design for a 훽 ≠ 0° test section. Note that the turning vanes which redirect the flow were designed to provide a

continuous range of incidence angle variation (푖 ± 0) for airfoils at

approach flows both 훽 = 0° and 훽 ≠ 0°...... 40 Figure 4.4: The three proposed conceptual designs which improved upon the original

concept...... 44

Figure 5.1: Schematic of the redesigned wind tunnel section...... 46 Figure 5.2: CAD model of the redesigned wind tunnel pieces, including the upstream

and downstream flow conditioning sections and the test section (coolant

loop is underneath the wind tunnel)...... 47 Figure 5.3: A schematic of the wind tunnel contraction nozzle side profile adapted from Morel [56], giving a visual indication of the equations used to

design the new contraction nozzle...... 49 Figure 5.4: A graph depicting the change in curvature for the side profile of the

contraction nozzle, where Polanka’s [55] design has been previously used and is shown for comparison to the new curves used in the

redesign...... 50 Figure 5.5: An isometric view of the redesigned contraction nozzle, with flow

entering at the left and exiting to the right in the image...... 51 Figure 5.6: A top-down view of the incidence angle mechanism at both 훽 = −25°

and 훽 = −35°...... 52 Figure 5.7: A detailed view of the first stage of turning vanes installed in the wind tunnel, highlighting where the wind tunnel sidewalls interact with the

turning vane cascade...... 55

xviii Figure 5.8: A detailed view of the bottom track system with set pins and spacers,

which set the final position of the turning vane cascade...... 56 Figure 5.9: A detailed view of the inner acrylic walls (made opaque), with highlighted walls changed for different incidence angles and non-highlighted walls

not changed...... 57 Figure 5.10: A detailed view of the outer wooden walls required to provide the final

seal to the wind tunnel. At the interfaces of all wooden walls, weather

stripping provided the pressure seal...... 58 Figure 5.11: A view of the incidence angle mechanism in the 훽 = 0° configuration,

with a different airfoil model viewable in the test section...... 59 Figure 5.12: A side-by-side comparison of the previous (left) and updated (right) test section airfoil cascades, highlighting which airfoils can be removed and

which cannot, and also highlighting the new lid design...... 61 Figure 5.13: A view of one of the CFD simulations, which showed that the C3X

could be installed in to the tunnel and forced to the periodic condition

through movement of the adjustable walls...... 65 Figure 5.14: A view of the inlet channels immediately under the instrumented airfoil, which provides coolant to the base of the airfoil. Basic dimensions for

the current project (left) and a future project (right) are very similar,

highlighting the interchangeability of the parts...... 66 Figure 5.15: A top view and side view schematic showing the dimensions of the new

diffuser design...... 67 Figure 5.16: A graph adapted from Mehta [57] showing what combinations of whole angle and area ratio lead to appropriately and inappropriately operating diffusers. The red lines and X indicates the current design, and indicates xix that without a screen, the diffuser would most likely contain some

separation...... 69 Figure 5.17: A schematic of the updated coolant loop, showing the new location of

the heat exchanger, and the updated piping system for the tunnel...... 71 Figure 5.18: One of the several acrylic sheet layouts sent to the acrylic manufacturer

for the routing process...... 73 Figure 5.19: A depiction of all four models used in the study, with the film-cooled

model hatch design highlighted on the far right image...... 74

Figure 5.20: Fiducial marks on Test Article B...... 76

Figure 5.21: A picture of the airfoil model hatch and core design...... 77 Figure 5.22: A representative schematic of the airfoil profile showing the locations of

the film cooling holes...... 77 Figure 5.23: A picture of the rib turbulators installed into the inside of the passages in

the film cooling models...... 78

Figure 5.24: The turning vane profiles used in the study...... 80

Figure 5.25: The mesh for the second stage, 훽 = −35° airfoil...... 82

Figure 5.26: A velocity contour plot for the stage 1 turning vanes...... 83

Figure 5.27: An incidence angle contour plot for the stage 1 turning vanes...... 83

Figure 5.28: A velocity contour plot for the stage 2 turning vanes...... 84

Figure 5.29: An incidence angle contour plot for the stage 2 turning vanes...... 84

Figure 5.30: A view of one of the turbulence grids used in the study...... 86 Figure 6.1: A schematic of the wind tunnel contraction nozzle and test section,

showing the location of the thermocouples and pitot-static tubes...... 94 Figure 6.2: A schematic of the coolant loop under the wind tunnel, showing the locations of the pressure taps and thermocouples which were used to xx measure flow rates and temperature measurements for discharge

coefficient and film-cooling experiments...... 95 Figure 6.3: A schematic of the IR camera locations for the two types of tests

performed with IR cameras...... 97

Figure 6.4: Pressure transducers used for pressure distribution measurements...... 98 Figure 6.5: A schematic of PIV setup in order to calculate the outlet incidence angle

of the turning vanes...... 104

Figure 6.6: An image of the camera in the location used for testing...... 105

Figure 6.7: An image showing the PIV setup in the wind tunnel...... 107 Figure 6.8: A camera image of the reference grid after the pitch, roll, and tilt of the

camera was performed to align the grid to the reference image...... 108 Figure 6.9: A schematic of PIV setup in order to calculate the outlet incidence angle

of the turbulence grid...... 111

Figure 6.10: A view of the suction side blower...... 113

Figure 6.11: The power source, and its connections to the airfoil model...... 118

Figure 6.12: 1-D heat flux foil energy balance...... 118 Figure 6.13: Raw temperature data from the five cameras used to measure adiabatic

effectiveness...... 123 Figure 6.14: Raw temperature data from the five cameras used to measure overall

effectiveness...... 126 Figure 6.15: Workflow for the software processing scheme employed for calculating

HTC, 휂, or 휙 data. Blue subprocesses (Labeled A-C) are described more

thoroughly in this chapter...... 128

Figure 6.16: Workflow for subprocess A - processing IR data for a single camera...... 130

Figure 6.17: The pinhole camera model...... 132 xxi Figure 6.18: A raw uncalibrated IR image (left) showing the back-projected S and Z locations in red, and the same image converted to the S and Z coordinate

system...... 135 Figure 6.19: A visual representation of the linear blending function utilized for

overlapping camera images...... 137 Figure 6.20: (Above) IR images collected during an overall effectiveness test.

(Below) The combined data, in S and Z coordinates, and converted to 휙. 138 Figure 7.1: (Left) Typical pressure transducer calibration. (Right) Resultant pressure

transducer curve fit uncertainty as calculated with Equation 7.1, and the

average used in later analyses...... 142

Figure 7.2: Typical thermocouple calibration...... 144 Figure 7.3: (Left) Image of the end cap locations removed for orifice plate calibration

testing. (Right) The orifice plate calibration setup...... 146

Figure 7.4: Measured 퐶푑 for each passage and their uncertainties...... 149

Figure 7.5: Measured 퐶푑 for each passage and their respective uncertainty values...... 150 Figure 7.6: One of the IR images collected during IR camera calibration for ℎ0 testing, with the surface thermocouples used during the calibration

visible in the image...... 152 Figure 7.7: An example of the IR camera ℎ0 calibrations, showing the variations

over a number of tests...... 153 Figure 7.8: One of the IR images collected during IR camera calibration for the film-

cooled experiments, with the surface thermocouples used during the

calibration visible in the image...... 155 Figure 7.9: An example of the IR camera spatial dependence in the showerhead region. (Left) the locations and representative curvature of the model in xxii the showerhead region, and (right) application of the PCHIP interpolation scheme for calibration of a reference surface temperature

of 푇=320 K seen in red...... 157

Figure 7.10: Uncertainty in a typical pressure distribution measurement...... 158 Figure 7.11: Relative uncertainty in the pressure distribution measurements for the

훽 = −30.1° case, where the relative uncertainty is naturally quite high

near the stagnation line...... 159

Figure 7.12: Pixel velocity for the representative case of PIV uncertainty analysis...... 163 Figure 7.13: Percent difference between mean velocity from PIV vs. the pitot static

probe...... 164

Figure 7.14: (Top) Mean 푈 and (Bottom) uncertainty due to sampling...... 167

Figure 7.15: (Top) Mean 푈 and (Bottom) uncertainty due to sampling...... 168

Figure 7.16: (Top) 푀 and (Bottom) uncertainty due to sampling...... 169

Figure 7.17: (Top) 훽 and (Bottom) uncertainty due to sampling...... 170 Figure 7.18: Downstream measurement with PIV with no turbulence grid installed,

compared to a simulation of the 33.76° inlet incidence angle in the same location that the PIV data was collected. This figure shows that the results match well downstream in a location where the flow field is

changing due to the presence of the downstream airfoil...... 173 Figure 7.19: Downstream measurement with PIV with the turbulence grid installed,

compared to a simulation of the 30.1° inlet incidence angle in the same location that the PIV data was collected. This figure shows that the PIV

and simulation results match, and that the 30.1° inlet angle with the grid

installed was the appropriate determination...... 174

xxiii Figure 7.20: (Top) Absolute and (Bottom) relative uncertainty in 푚 for the fore

channel...... 178 Figure 7.21: (Top) Absolute and (Bottom) relative uncertainty in 푚 for the middle

channel...... 179 Figure 7.22: (Top) Absolute and (Bottom) relative uncertainty in 푚 for the aft

channel...... 180

Figure 7.23: Uncertainties in the calculated hole discharge coefficients ...... 181

Figure 7.24: The calculated hole discharge coefficients ...... 182

Figure 7.25: Fractional flow rate for full-coverage testing...... 184 Figure 7.26: Relative elemental uncertainty of the main contributors to 훿푉푙표푐푎푙

plotted for each film cooling hole row on the model...... 185 Figure 7.27: Relative total uncertainty of 훿푉푙표푐푎푙 plotted for each film cooling hole

row on the model...... 186

Figure 7.28: Uncertainty in velocity ratio – Condition 1...... 188

Figure 7.29: Uncertainty in velocity ratio – Condition 2...... 188

Figure 7.30: Uncertainty in velocity ratio – Condition 3...... 189

Figure 7.31: Uncertainty in velocity ratio – Condition 4...... 189

Figure 7.32: Uncertainty in velocity ratio – Condition 5...... 190 Figure 7.33: Uncertainty in 휂 depending on the magnitude of the conduction

correction test (휂0)...... 191

Figure 7.34: In-test repeatability of 휂 for Condition 1, far pressure-side camera ...... 192

Figure 7.35: Test-to-test repeatability of 휂 for Condition 3, far pressure-side camera .. 192 Figure 8.1: A matched pressure distribution (of which the showerhead region is

visible) for the 훽=-30.10° case...... 194

Figure 8.2: Results from the heat transfer coefficient measurement experiments...... 196 xxiv Figure 8.3: Results from the heat transfer coefficient measurement experiments...... 197 Figure 8.4: Results of testing 휂 at the 훽 =-21.23° angle over five VR* conditions, showcasing the effects of increasing VR* for each hole. The predicted

stagnation line location is highlighted a black and white vertical line...... 203

Figure 8.5: 휂 for the 훽=-30.1° experiment ...... 205

Figure 8.6: 휂 for the full coverage experiment by Dyson [70]...... 205 Figure 8.7: Results of testing 휂 for the 훽 =-21.23° angle at five VR* conditions, showcasing the effects of increasing VR* for each hole. The predicted

stagnation line location is highlighted a black and white vertical line...... 209 Figure 8.8: Results of 휂 for the 훽 =-21.23° angle at five VR* conditions, showcasing the effects of increasing VR* for each hole. The predicted stagnation

line location is highlighted a black and white vertical line...... 210

Figure 8.9: 휂0 correction used for both incidence angle conditions tested...... 211

Figure 8.10: The effect of 휂0 on the reported 휂 for 훽=-30.1°...... 212

Figure 8.11: 휂푚푒푎푠푢푟푒푑 for the 훽=-30.1° experiment...... 212

Figure 8.12: 휂 for the 훽=-30.1° experiment ...... 212 Figure 8.13: The difference in 휂 levels for the 훽 =-30.1° and 훽 =-21.23° 휂

experiments...... 214 Figure 8.14: The difference in 휂 levels for the 훽 =-30.1° and 훽 =-21.23° 휂

experiments...... 215

Figure 8.15: 휂 for the 훽=-30.1° experiment...... 216

Figure 8.16: Results of 휂 for the 훽 =-21.23° angle...... 216

Figure 8.17: Contour plots of 휙 magnitudes at the 훽 =-30.1° condition...... 219

Figure 8.18: Contour plots of 휙 magnitudes at the 훽 =-30.1° condition...... 221

Figure 8.19: Contour plots of 휙 magnitudes from the Dyson [70] study...... 222 xxv Figure 8.20: 휙 for both incidence angle conditions tested...... 223 Figure 8.21: 휂 levels for the stagnation line sweep performed at the 훽 =-21.23°

condition after the initial experiments...... 226 Figure 8.22: 휂 levels for the stagnation line sweep performed at the 훽 =-21.23°

condition after the initial experiments...... 228 Figure 8.23: 휂 levels for the stagnation line sweep performed at the 훽 =-21.23°

condition after the initial experiments...... 228

Figure 8.24: 휂 levels for the showerhead region during the stagnation line sweep...... 229

Figure 8.25: Contour plots of 휙 magnitudes at the 훽 =-30.1° condition...... 230

Figure 8.26: 휙 for both incidence angle conditions tested...... 231

Figure 8.27: 휙 and 휙0 for the 훽=-30.1° case...... 234

Figure 8.28: 휙 and 휙푝 for the 훽=-30.1° case...... 235 Figure 9.1: Computational domain for ℎ0 studies (airfoil geometry purposefully

distorted for confidentiality reasons)...... 238 Figure 9.2: Relationship between the longitudinal and integral length scales as shown

by Pope [72]...... 239

Figure 9.3: Computational domain for the turbulence rod studies...... 243 Figure 10.1:The three turbulence models investigates vs. the experimental

measurements for the high turbulence 훽 = 25° case...... 246

Figure 10.2: Low and high turbulence CFD and experimental comparisons...... 247

Figure 10.3: Incidence angle CFD vs experiments for the high turbulence case...... 248

Figure 10.4: Low turbulence results from Dyson’s [70] study...... 250

Figure 10.5: High turbulence results from Dyson’s [70] study...... 250 Figure 10.6: Turbulence levels for the 훽=0° simulations at p/d=5 (top) and p/d=2

(bottom) ...... 252 xxvi Figure 10.7: Turbulence levels for the 훽=55° simulations at p/d=5 (top) and p/d=2

(bottom) ...... 252

Figure 10.8: Vector field for the 훽=55° simulations at p/d=2...... 253 Figure 10.9: CFD and experimental correlations for turubulence intensity downstream

of turbulence grids...... 255

Figure 10.10: Surface fit of CFD data, with test data also shown...... 257

xxvii Nomenclature

퐴 Amperage; Area 푎 Constant 퐴퐵푆 Acrylonitrile butadiene styrene 푐 Constant 퐶 Coefficient 퐶퐴퐷 Computer-aided design 퐶퐹퐷 Computational fluid dynamics 퐶푁퐶 Computer numerical control 퐷 Generic variable 퐷퐴푄 Data acquisition 퐷퐿푇 Direct linear transformation 퐷푅 Density ratio 퐹 Fractional flow rate 푓 Focal length 푔 gravity ℎ Heat transfer coefficient (푊/푚^2 퐾) 퐻 Height 퐼 Momentum flux ratio; Current 퐼푅 Infrared 푘 Thermal conductivity; ratio of specific heats; turbulent kinetic energy 퐿 Length; Temperature lapse rate; Turbulence length scale 퐿퐹퐸 Laminar flow element 푀 Blowing ratio; Molar mass; Magnitude 푚 mass 푀퐷퐹 Medium density fiberboard 푁푎퐶푙 Salt crystal 푁푢 Nusselt Number 푁푑: 푌퐴퐺 neodymium-doped-yttrium aluminum garnet 푁퐼 National Instruments 푃 A point in either 2D or 3D 푃퐼푉 Particle image velocimetry 푃푉퐶 Polyvinyl chloride 푟 ratio 푟표푤 For a given row 푅 Universal gas constant 푅퐴푁푆 Reynolds-averaged Navier-Stokes 푆 Curve length 푇 Temperature 푡 Thickness

xxviii 푇푇퐶푅퐿 Turbulence and Turbine Cooling Research Laboratory 푇푢 Turbulence Intensity 푢 Velocity; x-pixel location 푈퐻퐹 Uniform heat flux 푣 y-pixel location 푉 Velocity; Voltage 푉푅 Velocity ratio 푋 Axial distance 푍 spanwise distance

Greek 훼 Thermal expansion coefficient 훽 Test section inlet incidence angle; ratio of orifice diameter to pipe diameter ∆ difference; change 훿 Uncertainty 휀 Emissivity, turbulence dissipation 휙 Overall effectiveness 휂 Adiabatic effectiveness; efficiency

Λf integral length scale 휆 Taylor scale 휇 dynamic viscosity 휌 Density 휎 Stefan-Boltzmann constant; standard deviation 휓 Blending function; scaling magnification factor

Subscripts 0 Without film cooling 퐴 A known 2D / 3D location 푎푖푟 Of air 푎푣푔 Average 푎푤 Adiabatic wall 푎푥 Axial distance 푏푖푎푠 Bias value 퐵푙푒푛푑푒푑 A spatial linear interpolation of a variable 퐵푟푎푦푡표푛 Brayton cycle 푐 Coolant 퐶푁 At the contraction nozzle 푐표푚푝표푛푒푛푡 푖푛푙푒푡 Located at the inlet to the airfoil model 푐표푛푑 conduction 푐표푛푣 Convection 퐷 Diameter

xxix 푑 Discharge 푑푦푛 dynamic 푒 External surface 푒푓푓 Effective 푒푞푢푖푝푚푒푛푡 PIV equipment uncertainty 푓 With film cooling; in the direction of flow; film;flow 푓표푖푙 heat flux foil 푔푒푛 Generation 푔푟푖푑 Of the grid ℎ푒 Hole exit ℎ표푙푒푠 Of the film cooling holes ℎ표푡푤푖푟푒 Of the hotwire 푖 Internal; x-component; index 푖푛푙푒푡 At the inlet location 푗 y-component 퐿푒푓푡 Left side 퐿퐹퐸 Of the laminar flow element 푙표푐푎푙 At the local position 푚푎푥 Maximum value 푚푒푎푠푢푟푒푑 Measured 푚푖푑푠푝푎푛 At the airfoil midspan 푛 Number 표 Orifice; sea-level 표푢푡푙푒푡 At the outlet location 푝 Pressure; particle 푝푎푟푡푖푐푙푒푠 PIV particle physics uncertainty 푝푖푝푒 In the pipe 푝푖푡표푡 − 푠푡푎푡푖푐 푡푢푏푒 Of the pitot static tube 푝푖푥푒푙푠 Pixels 푝푟표푐푒푠푠푖푛푔 PIV software processing uncertainty 푟 Recovery 푟푎푑 radiation 푅푖푔ℎ푡 Right side 푠푎푚푝푙푖푛푔 PIV sampling uncertainty 푠표푢푟푐푒 Power source 푠푝푎푡푖푎푙 Physical 푠푢푟푓 Surface 푡 Stagnation 푇푆 At the test section 푤 At the wall ∞ mainstream; hot gas path

xxx Superscript ̅ lateral average ̅ Total average ̇ Rate

xxxi Chapter 1: Introduction

This chapter provides an introduction to gas turbine history, topics of interest regarding the current project, and the coordinate systems and definitions utilized throughout the text.

1.1. Gas Turbine Engines

The gas turbine is a type of combustion engine consisting of a compressor, combustor, and turbine. Since its initial development over two-hundred years ago, engineers have transformed the gas turbine in to one of the world’s most complex products to date. Today, the gas turbine is widely used in the aviation, marine, and energy sectors. According to the U.S. Energy Information Administration, 9.5푥1015 BTUs of energy are consumed in the natural gas energy production sector, translating to an expenditure of $32 billion per year in a sector completely reliant on gas turbines. In addition to this, jet fuel containing 3푥1015 BTUs of energy are consumed annually, resulting in a $69 billion dollar per year investment. These two factors alone represent over 13% of the energy industry in the USA [1]. These numbers give an idea of the meaningful effect of increasing the efficiency of gas turbines by even fractions of a percent. Indeed, a growing demand for increased gas turbine efficiency has become a driver for current and future gas turbine technology research. The turbojet revolution is often credited to Englishman Sir Frank Whittle (1907- 1996) and German Hans von Ohain (1911-1998). Their pioneering work built upon the initial patent of John Barber (1734-1801) and dedicated work by Dr. J. Franz Stolze (1836-1910), Dr. Stanford Moss (1872-1976), and numerous other engineers [2]. During this mid-1930’s, Hans von Ohain developed a petrol-fueled jet engine. The third iteration

1 of his engine, the HeS 3, powered the world’s first turbojet powered aircraft, the Heinkel He 178. During the same timeframe, Sir Frank Whittle independently developed the Whittle W1 engine which would fly on the first successful British jet-engine aircraft, the Gloster E.28/39. The flights of the Gloster E.28/39 proved to the world that the turbojet was practical. It was then that Whittle was sent to the United States to teach Americans how to design and build his upgraded W2B jet engine, marking the American’s introduction to gas turbine engine development [3]. Beginning with these accomplishments, a continuous demand for better turbomachinery has propelled the quest for increasing efficiency and technological breakthroughs. In order to quantify the effects of turbomachinery, thermal efficiency is typically compared to the Brayton cycle. The Brayton Cycle is a thermodynamic cycle named after the American engineer George Brayton (1830-1982) who developed it. The Brayton cycle consists of four internally reversible processes: isentropic compression, isobaric heat addition, isentropic expansion, and isobaric heat rejection. The cycle is shown in

Figure 1.1. The Ideal Brayton cycle is typically depicted in two ways. In the case of the turbojet, Figure 1.1 shows the open-loop Brayton cycle, wherein the air is drawn in to the compressor and exhausted to atmosphere.

Figure 1.1: Left - Stages of the Brayton Cycle [4]. Right – Example of the open Brayton Cycle [4].

The thermal efficiency of the Brayton cycle is:

1 휂푡ℎ = 1 − 푘−1 푘 1.1 푟푝

Where 푘 is the ratio of specific heats and 푟푝 is the pressure ratio across the compressor. Since the specific heats are taken as contant in a cold air-standard analysis, and since the heat transfer processes occur at constant pressures in the cycle, it follows that:

푘− 1 푇3 푘 = 푟푝 1.2 푇4 And we can therefore simplify the engine efficiency to be:

1 푇 휂 = 1 − = 1 − 4 푡ℎ,퐵푟푎푦푡표푛 푘−1 푇 푘 3 1.3 푟푝 Equation 1.3 shows that a designer is able to increase both pressure ratio and the combustor exit temperature (푇3) in order to affect the thermal efficiency. In reality, the thermal efficiency is dictated by a complex interaction of metallurgical limitations, pressure ratio, and combustion temperature. A graph depicting an example of this 3 interaction is shown in Figure 1.2. From the graph, we see that a higher temperature means more power. The higher a turbine’s output per pound of airflow, the smaller and lighter the gas turbine required. Additionally, for a given operating temperature there exists a specific (yet typically very high) pressure ratio that will lead to an optimal combination of efficiency and output for the product [5]. A soft cap of the maximum turbine inlet temperature is imposed by metallurgical considerations on the turbomachine.

The cap is overcome by employing one or more sophisticated schemes that have been developed to counteract this effect.

Figure 1.2: Overall thermal efficiency of a gas turbine [5].

1.1.1. Materials and Cooling Technologies

Breakthroughs in materials research, materials processing, and manufacturing technologies have resulted in an increase in airfoil material capability in excess of 500° F gains in the past 50 years [3]. The manufacture of superalloys in the 40’s-50’s paved the

4 way for high-temperature turbine component materials. The introduction of directional solidification and single crystal superalloys yielded parts with temperature capabilities over 200° F higher than conventional cast materials. The development of low- conductivity material coatings (or thermal barrier coatings) which can be applied to the external surface of the engine components has also led to a significant reduction in the external part surface temperatures. In addition to these advancements, the manufacturing capabilities have also had to evolve in order to support the development of continuously complex turbine airfoil cooling schemes.

Two types of active cooling schemes have been adopted for use in hot gas-path components. Convection cooling relies on the cooling of the internal cavities of the airfoil by a lower-temperature air bled off from the compressor which leads to lower part temperature and increased part life. Film cooling uses the lower-temperature air to create a thermal barrier between the hot gas and metal. Small film cooling holes of various shapes are strategically added to the airfoil, and the compressor air is ejected from these holes. The ejected coolant flows around the airfoil components, creating a protective layer of coolant on the airfoil components, further reducing part temperatures. It is important to note that a critical step in the active coolant design process is determining the appropriate amount of coolant to bleed off of the compressor, as using any coolant reduces the amount of air available in the combustion process, which leads to the decreased efficiency as seen in Figure 1.2. A diagram of an actively cooled turbine component is shown in Figure 1.3.

Figure 1.3: Schematics of a typical film cooled turbine blade [6].

In addition to advancements in materials and cooling technology, there are a vast number of additional developments which one should also consider. For example, overall compressor design, combustor design, turbine design and control system design all play a critical role in the optimal operation of a turbojet. It is the daunting task of the design team to assess the criticality of the overall design goals and choose the appropriate configuration for a given turbojet in order increase part longevity and produce optimal performance at a reasonable time and cost. Due to the amount of time invested in achieving these goals for a single turbomachine, it is clear how advancing technologies such as film cooling can have a long-lasting impact on the product.

1.1.2. Quantification of Cooling Performance

Conventionally, the performance of a film-cooled component is characterized in terms of the adiabatic effectiveness. For a gas turbine component in high-speed flow conditions, the adiabatic effectiveness is defined as:

푇 − 푇 휂 = 푟,∞ 푎푤,푒 푇푟,∞ − 푇푡,푐,ℎ푒 1.4

Where 푇푟,∞ is the freestream recovery temperature, 푇푎푤,푒 is the adiabatic wall temperature with film cooling (or film temperature) on the airfoil surface, and 푇푡,푐,ℎ푒 is the stagnation temperature of the secondary flow at the exit of the film cooling hole. For low speed flows, this can be written simply as:

푇 − 푇 휂 = ∞ 푎푤,푒 푇∞ − 푇푐,ℎ푒 1.5 Where it is recognized that there is no difference in low speeds between the static and total air temperatures. Equation 1.5 is used throughout the rest of this text since the flow temperatures measured in this project were measured at low-speeds. Equation 1.5 explains the cooling scenario in a cooled gas turbine airfoil - coolant exits from the coolant holes at temperature 푇푐,ℎ푒 and mixes with the mainstream at temperature 푇∞ as the coolant flows downstream, resulting in a constantly increasing coolant temperature. Furthermore, the coolant temperature at the wall will be at the adiabatic wall temperature,

푇푎푤,푒. The bounds of the adiabatic effectiveness can be readily identified in this equation. The film-cooling is not effective at all when the wall temperature is equal to the mainstream temperature, and so 휂 = 0 in this case. Also, the film-cooling is most effective when the wall temperature is equal to the hole-exit coolant temperature, and so in this case 휂 = 1 is a maximum.

It is important to recognize that adiabatic effectiveness does not account for the conjugate heat transfer effects that are present in actual turbine components. As a result, the adiabatic effectiveness of a turbine component is not directly representative of the metal temperature that the component would experience in operation. However, the operating temperature can also be non-dimensionalized and expressed as the overall effectiveness, 휙 for low speed flows, given by:

푇 − 푇 휙 = ∞ 푤,푒 푇∞ − 푇푐,푐표푚푝표푛푒푛푡 𝑖푛푙푒푡 1.6

where 푇∞ is the temperature of the hot gas path, 푇푤,푒 is the external surface temperature of the component wall, and 푇푐표푚푝표푛푒푛푡 𝑖푛푙푒푡 is the temperature of the coolant at the root of the component. It is most appropriate to normalize the overall effectiveness with 푇푐,푐표푚푝표푛푒푛푡 𝑖푛푙푒푡 since the ideal cooling performance of a conducting component with internal cooling occurs when the external wall temperature equals the temperature at the inlet of the component (i.e. 푇푤,푒 = 푇푐표푚푝표푛푒푛푡 𝑖푛푙푒푡 yields 휙 = 1). If 휙 was defined with 푇푐,푒푥𝑖푡 as in 휂, it would be possible to have 휙 > 1 due to the internal convective cooling in the conducting component, and 푇푐,푒푥𝑖푡 is therefore an inappropriate variable to normalize 휙 with. Note that the equation for 휙 is only valid when using a matched Biot number model

Both adiabatic and overall effectiveness measurements have their advantages. The adiabatic effectiveness measurements isolate the conjugate heat transfer effects, highlighting external effects of the coolant. Results display the temperature of the coolant in direct contact with the external surface of the blade. The overall effectiveness measurements show the true normalized surface temperature of the turbine component during operation if the appropriate matched Biot number model (as discussed in Section

2.3) is utilized. The overall effectiveness can therefore directly highlight life-limiting hot- spots over the external surface of the turbine component. It is necessary to attempt to match the difference in densities between the coolant and mainstream gas in order to match the conditions that are typical in an operating engine. The density ratio is defined as:

휌푐 퐷푅 = 휌∞ 1.7 Where the conditions within an engine are typically about DR=2.0. In research experiments, lower density ratio experiments are often performed in order to make experiments realistically possible, as such a high density ratio naturally means large differences in temperatures between the mainstream and coolant flows, which can produce a number of unwelcome effects in a laboratory setting. Therefore, researchers have investigated the scalability of these low density experimental results up to engine conditions, and useful to choose relevant equations which compare the film cooling flow properties to those of the mainstream and are also scalable to engine conditions. In order to analyze the flow physics of the in relationship to the coolant flow, a number of these key parameters are often used in film cooling analysis. One of the most common parameters is the blowing ratio:

휌푐푈 푐 푀 = 1.8 휌∞푈∞

Where 휌푐 and 휌∞ are the coolant and mainstream densities, and 푈푐 and 푈∞ are the coolant velocity exiting a hole and the mainstream velocity directly above the hole breakout location. However, Sinha et al. have [7] shown that there is an implied scalability of the performance of the coolant jet with the momentum of the jet, and so the

9 momentum flux ratio is another common normalizing parameter used extensively in the literature.

2 휌푐푈푐 퐼 = 2 1.9 휌∞푈∞ And most recently, Anderson et al. [8] have shown for shaped holes in particular, the velocity ratio is the best parameter for scaling 휂̅ at variable density ratios. Thus, in light of these recent developments, the velocity ratio is that which is used in the analysis of the results. The velocity ratio is:

푈푐 푉푅 = 1.10 푈∞

1.1.3. Quantification of Aerothermal Performance

Heat transfer to the external surface of a turbine component is dictated solely by the hydrodynamics of the surrounding fluid, and hence the shape of the turbine component and the added effect of the film cooling jets. External heat transfer coefficients with and without film cooling present are both useful parameters to measure and understand. The no-film heat transfer coefficient is given by:

′′ 푞0 ℎ0,푒 = 1.11 푇∞ − 푇푤,푒

′′ where 푞0 is the heat flux, and the denominator of the equation is the temperature difference driving the heat transfer. The heat flux in the actual engine is not known directly, so a number of techniques have been developed to allow for measurement of the external heat transfer coefficient. One technique employs the application of a uniform heat flux (UHF) boundary condition to the external surface of the component, which can be accomplished

10 with a thin, conductive material adhered to the component’s external surface. The surface temperature, mainstream temperature, and applied heat flux are measured in order to directly solve Equation 1.11 for the heat transfer coefficient. The actual method for collecting the surface temperature data varies. Most recently, studies have largely measured surface temperatures with IR thermography or liquid crystals. The heat flux due to convection is calculated by subtracting radiative and conductive losses from the normalized electrical heating of the power source, or:

′′ ′′ 4 4 푞0 = 푞푠표푢푟푐푒 − 휀휎(푇푤,푒 − 푇∞) − 푘(푇푤,푒 − 푇푤,𝑖) 1.12 The external heat transfer with film cooling is also an important parameter be determined. In this case, 푇푎푤 is typically presumed to be the driving temperature potential for heat transfer into the wall of the film-cooled component. The heat transfer coefficient for the cooled turbine component is defined as:

′′ 푞푓 ℎ푓,푒 = 1.13 푇푎푤,푒 − 푇푤,푒

It is not initially apparent that ℎ푓 would differ from ℎ0. However, the presence of the film cooling holes and coolant jets cause hydrodynamic disturbances in the flow and locally increase the heat transfer coefficient near the holes, which is a detrimental consequence of their presence. Therefore, the ratio ℎ푓,푒/ℎ0,푒 is called the heat transfer coefficient augmentation, and is a measure of the unintended enhancement of external convective heat transfer due to the presence of film cooling.

1.2. Experiments and Computational Fluid Dynamics

Increasingly complex turbine component designs are relying more and more upon commercially available computational fluid dynamics (CFD) software or in-house codes

11 to predict key aerodynamic and heat transfer parameters. Although CFD is routinely used to predict some key turbine aerodynamic parameters such as pressure distributions, commercial Reynolds-averaged Navier-Stokes (RANS) codes often lack in their capability to consistently predict heat transfer and film cooling scenarios. Therefore, it is often very useful to compare CFD codes against experimental measurements, especially in more complex scenarios such as new turbine component designs, off-design conditions, varying turbulence levels, etc.

1.2.1. Reynolds-averaged Navier-Stokes computational models

The Navier-Stokes equations govern the velocity and pressure of a flow field. The equations can be decomposed in to mean and fluctuating components, and averaging the equations produce what are known as the Reynolds-averaged Navier-Stokes (RANS) equations, which govern the mean flow. However, due to the nonlinearity of the Navier- Stokes equations the velocity fluctuations of the RANS equations still contain the

′ ′ Reynolds stress term 휌푢̅̅̅푖̅푢̅̅푗. Therefore, to obtain equations that include only the mean velocity and pressure of the flow, the closure problem seeks to ‘solve’ the RANS equations through development of models of the Reynolds stress term. Utilizing these turbulence models in conjunction with RANS equations is much less computationally expensive than direct numerical solutions, but their use is sometimes limited in scope due to the requirement of utilizing the turbulence models. The particular applicability to the RANS simulations used in these studies are discussed during their application in the computational section of this document. It is also worth noting that URANS, LES, and

DNS (higher fidelity simulation methods) are also used, but typically not as regular design tools due to their increased computational demand.

1.3. Considerations of Off-Design Incidence

Each concept discussed so far becomes increasingly complex when studying a turbine’s off-design conditions. Off-design conditions occur during dynamic flight situations and the mixed flight conditions experienced in variable-cycle engines. A thorough understanding of the off-design conditions of variable-cycle engines is required to confidently proceed with designs for the next-generation of aircraft. Therefore, the heat transfer and cooling characteristics must be studied at these off-design conditions, and the capabilities to simulate these characteristics with CFD must be well understood.

1.4. Gas Turbine Airfoil Nomenclature and Coordinate Systems

The following nomenclature was used for the study. First, references to the pressure side and suction side of the airfoil, the axial chord length of the airfoil, and the s- coordinate system (which is the curvature along the airfoil) are all commonplace in this document. In this paper, s=0 represents the geometric leading edge of the airfoil, s is negative towards the pressure side and positive towards the suction side. 훽=0° represents a normal flow direction in the wind tunnel, with decreasing 훽 representing an incidence angle of flow more towards the pressure side of the airfoil. In terms of the engine operating angle 푖, zero refers to the actual inlet operating condition, with positive 푖 being more towards the pressure side. The s coordinate is also often normalized by either the hole diameter, 퐷 or the s- distance along the suction side, 푆푚푎푥. A diagram of this coordinate system and incidence angle and naming designation can be seen in Figure 1.4.

Figure 1.4: Coordinate and angle designations used in the paper.

Chapter 2: Literature Review

2.1. External No-Film Heat Transfer Coefficient Testing

An extensive amount of effort has gone in to measuring the external no-film heat transfer coefficient using the UHF and other techniques, with measurements taking place as early as the 1950’s (see Wilson and Pope). However, the requirements for lower uncertainty and higher spatial resolution have led to a wide array of heat transfer coefficient studies that explore different techniques of measuring heat transfer coefficients. For example, 2D airfoil heat transfer coefficient distributions have been measured in both steady state and transient cascades (see Hylton et al.[9], Schultz [10], and Dunn et al. [11] for examples). Tests have also introduced upstream passing bars which simulate blade and vane row interactions (see Ashworth et al. [12]). Experiments have even explored the effects of freestream turbulence, turbulence length scale, and Reynolds number on heat transfer coefficient. (See Arts et al. [13] and Carullo et al. [14] for examples). These results show an increase in heat transfer coefficients with increasing

Reynolds number, increasing turbulence level, and smaller length scale. Measurements of heat transfer coefficients in both linear and rotating cascades have also been compared by a number of researchers. For example, Baughn et al. [15] compared measurements collected in a linear cascade to that of a rotating rig with liquid crystals at one incidence angle. Guenette et al. [16] compared heat transfer coefficient distributions (measured with heat flux gauges) collected from a linear cascade and a rotating, 3D cascade at one incidence angle. Both found similarities between 2D and 3D data sets, and concluded that mean heat transfer coefficient levels are generally well- predicted by 2D cascades. However, Guenette et al. found an inexplicable over-prediction of HTC at the far-downstream suction-side surface by up to 40% in the 2D rig. Baughn

15 reported an advancement of the transition region on the suction-side of the rotating models, but also reported difficulty setting inlet flow conditions to properly compare tests. Among the extensive amount of heat transfer coefficient measurements on turbine airfoils available in the literature, few measurements have sought to study the effects of incidence angle on the heat transfer coefficient distribution at high-resolution. Although

Arts et al. [13] studied incidence angle changes from -14° to +11°, only midspan thermocouples were used, which provided a limited resolution. Camci and Arts [17] studied incidence angle effects at -10° to +15° off design on a film-cooled blade model, but also only with midspan thermocouples. More recently, Giel et al. [18] provided high- detail heat transfer coefficient data with the liquid crystal technique, but only for ±5° off- design conditions. Beyond this study, high-resolution heat transfer coefficient data is not present in the literature for varying incidence angles. Concerning CFD, Dunn [19] reviewed the current state of the HTC predictive capability of CFD in 2001. Dunn found that many improvements are still required to bring the HTC predictive capability up to that of the aerodynamic predictive capability. Since then, a number of measurement and CFD comparisons have been made, oftentimes with improved or higher order turbulence models. In addition to the high-resolution HTC measurements made, Giel et al. [18] predicted the HTC distribution with a multistage Runge-Kutta 3D Navier Stokes code described by Chima and Yokota [20] but found that while the trends of the experimental and simulated data matched, the predictive capability of the code was wholly unsatisfactory for the parameters studied. Dees et al. [21] compared HTC measurements to an SST-Transition model prediction generated with a Fluent RANS solver, and was able to predict small portions of the showerhead and

16 pressure-side HTC within experimental uncertainty, as well as the overall trends of the HTC distribution. Dees et al. also utilized the Wilcox k-ω model, but with less success. However, Tallman et al. [22] showed that using a modified 3D, compressible, RANS solver with a k-ω model, GE’s TACOMA platform could be used to predict HTC distributions quite well for high-pressure turbine vanes and airfoils, and fairly well for low-pressure turbine vanes. Furthermore, Luo et al. [23] performed a comparative study of various turbulence models on a turbine airfoil and end wall, and found that 3D CFD predictions with the SST model has better accuracy than the k-ε, realizable k-ε, and V2F models, but also agreed that additional studies are needed to address more complex scenarios than those presented in the study. Prior to the current study, there have been few publications of the sensitivity of the external HTC distribution of airfoils to a combination of turbulence and incidence angle variations.

2.2. Adiabatic Effectiveness Testing

Many studies of adiabatic effectiveness have been provided by researchers since the 1960’s. The majority of adiabatic effectiveness utilized simplified geometries in flat plates to reduce the complexity of the problem by removing the aerodynamic effects of a curved turbine component (see Goldstein [24,25] and Hartnett [26] for examples). Since then, thousands of studies have been published which investigate the effects of varying fluid properties, fluid flow rates, hole geometry, turbine component geometry, etc. on film cooling. A review of the current state of film cooling has been provided by Bogard and Thole [27], and a review of the current state of shaped cooling holes in particular was provided by Bunker [28] as a few broad examples. However, among the many studies available on film cooling, few investigate the effects of the inlet incidence angle on airfoil film cooling, especially on a stagnation line 17 row of holes. Most commonly, the effect has been studied in leading edge models. An early study by Cruse et al. [29] used a 3-row leading edge model - one row was located along the stagnation line and one row location on either side of the stagnation line row.

They observed significant decreases in 휂̅ values when the stagnation line was moved above the center row of holes forcing coolant from the center row to move away from the “suction” side. However, when the stagnation line was moved to the bottom of the center row of holes, there was no noticeable increase in 휂̅ values despite the increased coolant flow towards the “suction’ side. Another leading edge model study done by Wagner et al.

[30] used a leading edge model with two rows of holes which were placed at ±3.3d from the stagnation line, including a configuration using shaped holes. They found that the adiabatic effectiveness downstream of both rows of holes increased when the approach angle was changed by 5° resulting in 1d movement of the stagnation line. Consequently this study showed the sensitivity to stagnation line position even when the stagnation line did not directly impact the coolant holes.

Beyond the previous studies, a number of the incidence angle studies specifically examine film cooling effectiveness on the external surface of the turbine component.

Wagner [30] used a simplified leading-edge model to study effectiveness for 0° and +5° design conditions. Wagner tested both cylindrical and shaped holes for M=1.2,2.0, and

3.0, and found decreased performance for the cylindrical suction-side hole (due to exaggerated separation) but increased performance for the pressure-side hole. The shaped holes performed better than the cylindrical holes, although the incidence angle shift had the same effect on the shaped holes. Ahn et al. [31,32] performed PSP experiments on a simplified blade in a rotating rig by varying the rotational speed (no equivalent incidence angles were provided). The blade consisted of three rows of radial-angle cylindrical

18 holes. However, since a 2-dimensional blade design was used in a rig, the stagnation line was slightly inclined with respect to the center row of holes. Ahn et al. found the most pronounced differences on the center row of holes. Most recently, Zhang et al. [33] studied the combined effects of compound angle shaped holes and varying incidence angle on the showerhead and pressure-side effectiveness of a GE-E3 guide vane at −10°, 0, and +10° incidence angles with PSP. Zhang et al. found that the peak effectiveness increases with positive incidence angle, and also found that the peak effectiveness moved downstream with positive incidence. Zhang et al. also found that the effect of incidence angle is most pronounced at the showerhead region, and although Zhang et al. reported that the pressure distribution downstream of the showerhead region was nearly unchanged, no pressure distributions were provided in the paper. Computational studies on the effects of incidence angle on showerhead film cooling have also been performed. Although not a simulation of adiabatic effectiveness,

Montomoli et al. [34] did perform a numerical study on the effect of incidence angle on coolant jets in conjunction with wake passing. The study investigated the leading edge with an in-house URANS CFD solver. Two rows of cylindrical holes were studied at one blowing ratio of M=0.7. Montomoli found a separation region downstream of the pressure side hole whose size was affected by the incidence angle, but these results were overshadowed by the effects of the wake passing in the simulation. This prompted a follow-up study by Benabed et al. [35].

Benabed et al. [35] performed an in-depth numerical study of adiabatic effectiveness on the same AGTB-B1 blade model as that of Montomoli et al. [34].

Benabed studied inlet incidences of −10°, −5°, 0°, +5° and +10° at M= 0.7, 1.1, and

1.5 for two rows of cylindrical holes. Benabed found significant variations in adiabatic effectiveness on both suction side and pressure side of the blade, as can be seen in Figure 2.1. The pressure-side of the model experiences significant jet liftoff at higher blowing ratios as would be expected for cylindrical holes. Due to the shift in the stagnation position at negative incidence angles, the coolant from the suction-side row of holes is forced to the pressure side for some blowing ratios, resulting in very low suction-side effectiveness values for some cases. For positive incidence angles, the suction-side performs quite well. Area averaged film-cooling effectiveness over the whole blade was greatest for the +10° incidence angle for all blowing ratios, which can be seen in Figure 2.2. This result seems to be primarily driven by the interaction of the suction-side jet with the mainstream air. However, predicting realistic effectiveness values require proper simulation of this jet and mainstream interaction within the computational domain. This is an extremely difficult task to accomplish given Benabed’s use of a RANS solver employing the 푘 − 휔 푆푆푇 turbulence model in the simulation. Therefore, although the results of the study begin to reveal the relationship between incidence angle and effectiveness, experimental data is still required, especially for such a complex scenario.

Figure 2.1: Left - 휼 at M=0.7, 휶 = ±ퟏퟎ° [35]. Right - 휼̅ for all blowing ratios and incidence angles studied [35].

Figure 2.2: Left - 휼̿ [35]. Right - 풎̇ for all blowing ratios and incidence angles studied [35].

It is also worth noting that there are some additional studies which have examined the effects of incidence angle on components other than the film-cooled vane itself. As some examples, Gao [36] studied the effects of incidence angle on tip gap cooling. PSP was used in this study, and effectiveness was reported at incidence angles of

−5°, 0°, 푎푛푑 + 5° and blowing ratios of M=0.5, 1.0, and 1.5 for a GE-E3-equivalent squealer tipped blade. In addition to the tip gap, a single row of near-tip pressure-side compound angled shaped holes and radial angled shaped holes were imaged. Zhang et al. [37] studied the effects of incidence angle on endwall film cooling in a linear cascade at

−10°, 0°, and +10° for M=0.7, 1.0, and 1.3. Suryanarayanan et al. [38] studied endwall film cooling effectiveness at 23.2°, 43.4°, and 54.8° (with the stagnation line moving towards the pressure side with increasing incidence) in a rotating blade platform. In both of these cases, the incidence angle changes showed a significant effect on the performance.

2.3. The Matched Biot Number Model Testing

Both 1D and 3D analyses of the scaling parameters required to accurately measure 휙 have been performed by a number of researchers. For example, Davidson [39] 22 showed that a simple 1D analysis reveals 퐵푖 = ℎ푓,푒푡/푘 and ℎ푓,푒/ℎ푓,𝑖 (the ratio of external to internal heat transfer coefficients) are required to be matched to engine conditions in order to accurately measure 휙. In other words, the ratio of the turbine component size, heat transfer coefficient, and thermal conductivity, and the ratio of the external and internal heat transfer coefficient of the model under testing must all be matched to the actual turbine component in order to accurately measure 휙. Further 3D analyses, such as that by Nathan et al. [40] have shown that this concept extends to the 3D realm.

Therefore, it is a requirement to match both 퐵푖 and ℎ푓,푒/ℎ푓,𝑖. Due to the much lower external heat transfer coefficients experienced in scaled-up blade models running in low- speed wind tunnels, a corresponding material with a lower thermal conductivity is chosen to compensate. Furthermore, in order to accurately match ℎ푓,𝑖, scaled-up internal features (such as rib turbulators) must be present in the scaled-up model, and similar internal and external Reynolds numbers similar to engine conditions must be used during the tests. A number of papers have been published that present results of empirical tests on conducting airfoil models. Hylton et al. [41] completed some of the first empirical testing of a conducting airfoil, which led to a number of advancements in the understanding of the thermal properties of a cooled airfoil. Additional studies by Turner et al. [42] and Hylton et al. [43] improved on these tests by incorporating more realistic film-cooling designs. However, these tests did not match both the Biot number and the ratio of internal to external heat transfer coefficients. Nonetheless, these tests still have served as benchmarks for future work for many years.

Albert and Bogard[44], Davidson [39], Dees et al. [45–47], Dyson et al. [48], and Nathan et al. [40] have all expanded on the conducting model concept by testing a scale model of the C3X vane, which is the same turbine vane as that used in Hylton et al.

[49,9]. However, in these cases the vane had been modified (with internal rib turbulators, external TBC, etc.) in order to study a different aspect of film cooling. In these cases, the scaled C3X vane was manufactured out of different material which more closely approximated the true Biot number of the C3X vane in order to collect matched Biot number data. In addition to experimental data, Harrison and Bogard [50] and Shih et al. [51] have both completed computational studies investigating the accuracy of using models with matched Biot numbers. Harrison and Bogard [50] showed that using a matched Biot number model results in a more appropriate boundary condition, and this has been examined afterwards by researchers such as Shih et al. [51]. A number of past experiments that utilize a matched Biot number model have all explored some new facet of research by modifying the base turbine model. This study takes this idea one step farther by testing an airfoil design which is fully cooled, contains realistic shaped holes, realistic internal rib turbulators, and realistic internal channel geometries. This study also seeks to test the effects of incidence angle changes on such a model. Matched Biot number model testing on such a realistic model does not exist in the literature, regardless of the effects of incidence angle on such a model.

2.4. Variable Incidence Angle Wind Tunnel Facilities

There are a number of facilities which are equipped to handle inlet incidence angle changes. A review of many of the facilities was completed in order to determine the feasibility of utilizing a similar design in the recirculating facility. It is worth noting that there were no closed-loop, linear cascade, variable incidence angle wind tunnels found in the literature which are similar to the design undertaken in this project. A short list of some types of variable inlet cascades are presented here in order to familiarize the reader 24 with common techniques which are used to change the inlet flow incidence angle in to an airfoil cascade.

2.4.1. Adjustable Inlet Duct Linear Cascades

One type of design seen repeatedly in the literature is a multiple airfoil rotatable cascade with adjustability in the lengths of walls and tailboard connected to the leading and trailing edges of an airfoil. One such example is the open-loop wind tunnel explained by Lee and Park [47], who studied the effects of incidence angle on enwall convective transport within the cascade. A depiction of which can be seen in Figure 2.3. For this design, a unique inlet duct was manufactured and installed for each incidence angle studied. The size of the inlet duct dictated the total number of airfoils utilized in the cascade, and although the authors are not clear, it is presumed that a new exhaust duct is installed when the number of airfoils being used in the cascade is changed.

Figure 2.3: Schematic of the open loop, variable incidence angle duct-type wind tunnel used by Lee and Park [47].

There are a number of other wind tunnels that employ this basic design. Gao et al. [36] utilized a five blade cascade in a blow-down facility to study effects of incidence angle on blade tip film cooling which is shown in Figure 2.4. However, during these studies the tailboards were not adjusted when incidence angle was adjusted (over ± 5° in the study) – it was assumed by the authors that effects of adjusting the incidence angle had negligible effects on the tests for the shallow angles studied. Zhang and Yuan [33] also utilized a similar design for testing effects of incidence angle on first-stage nozzle guide vanes, as can be seen in Figure 2.5. Although Zhang and Yuan do not specifically state how the inlet duct was readjusted, they utilize the underlying turntable to reposition the vanes as well as the instrumentation which was mounted to the turntable device with an additional support structure.

Figure 2.4: Schematic of the open loop, blowdown facility utilized by Gao et al. [36].

Figure 2.5: Schematic of the open lop facility utilized by Zhang and Yuan [33].

2.4.2. Adjustable Inlet Contraction Nozzle Linear Cascades

A variation on the adjustable inlet duct-type wind tunnels instead includes the adjustability in a more continuously variable configuration which conditions the inlet flow by way of an adjustable contraction upstream of the airfoil cascade. Jeffries [52] highlights the use of a high-speed blow down facility at Carleton University (shown in Figure 2.6 ) which is used extensively for investigations off-design conditions. A similar approach was taken for the Straight Cascade Tunnel Göttingen (EGG), which is also a 27 blow down facility primarily utilized for aerodynamic studies of airfoil cascades. In this design the contraction nozzle and walls upstream of the cascade can be adjusted to provide the appropriate flow in to the cascade. A number of other wind tunnels utilize a very similar, such as the Von Karman Institute CT2 [53] (not shown).

Figure 2.6: Schematic of the facility utilized by Jeffries [52].

Figure 2.7: The EGG facility.

2.4.3. Inlet Guide Vane Cascades

Adjustable inlet guide vane cascades do exist in the literature, such as the wind tunnel presented by Sanger et al. [54] and shown in Figure 2.8 and Figure 2.9. In this open loop configuration, 59 inlet guide vanes approximately ¾ the size of the downstream test airfoils are used to provide inlet flow redirection in to the test section. The authors do not explicitly state whether or not the inlet guide vanes are readjusted

(stagger angle, shaping) to provide different inlet angles, or whether they are simply replaced to test different angles. The author reported that although inlet uniformity and turbulence levels were a potential concern, but that neither were an issue (with inlet turbulence levels of about 2% upstream of the instrumented airfoil cascade). Note that there are several adjustable walls which match the turning angle of the inlet guide vanes, and also that the tunnel is built within a second layer presumably to provide additional

29 sealing. A clear view of the outer casing of the cascade can be seen in the figures below. It is also interesting to note the size of this particular wind tunnel – the test section width is 1.52m, and the whole facility is an open-loop wind tunnel housed on two floors of a building, which provide air to the blower through inlet ducting built around the building, and exhaust the cascade air through a vent on the ceiling of the 2nd floor.

Figure 2.8: Schematic of the open loop facility utilized by Sanger [54].

Figure 2.9: Another view of the open loop facility utilized by Sanger [54].

2.4.4. Rotating Rigs

It is worth noting that although building and utilizing a rotating rig for the work performed on this project was outside of the project scope, it is possible to assess the effects of variable incidence angle within rotating rigs. This would be performed by adjusting the operating speed of the rig, thereby affecting the velocity triangle (inlet flow angle) entering the airfoil stage of interest. Such tests have been performed in the past by universities and research facilities which have access to a rotating rig. A schematic of the rotating facility at Texas A&M used for many research papers (see [31] for example) can be seen in Figure 2.10.

Figure 2.10: Schematic of the open lop, facility utilized by Ahn et al. [31].

Chapter 3: Dissertation Objectives and Contribution Goals

The overall goal of this project was to provide the first thorough empirical assessment of adiabatic and overall effectiveness of a very complex scaled up turbine component at varying incidence angles. The model is fully cooled, contains realistic shaped holes, realistic internal rib turbulators, and realistic internal channel geometries. In the context of this overall goal, several additional studies (experimental and computational) were performed in order to examine incidence angle effects. The specific goals are as follows:

1. Design, manufacture, and validate a new type of wind tunnel test section which will enable testing of a linear cascade of airfoils at varying incidence angles in a closed- loop configuration. In order to accomplish the primary goal, a new wind tunnel test section must be developed and manufactured. In order to verify that the test section can vary incidence angle in a repeatable manner, a series of validation experiments must be performed in the tunnel prior to performing any formal experiments. The design will facilitate the current work as well as future work at varying incidence angles on airfoils in order to gain a better working knowledge of the effects of incidence angle variation as well as to enable testing of both blades and vanes in the facility.

2. Better understand the effects of incidence angle on the adiabatic and overall

effectiveness of film-cooled airfoils. In order to do so, a complex airfoil model will be tested in the new test section. Measurements of the adiabatic and overall effectiveness of the airfoil will be made, and a 33 comparison will be made to measurements completed on less complex models. This will also include a comparison of the overall effectiveness to the adiabatic effectiveness measurements, which will provide additional insight in to the utility testing matched Biot number models.

3. Determine the effects of varying blowing ratios on the adiabatic and overall

effectiveness of film-cooled airfoils. In-line with the main goal, the study seeks to assess a combination of varying blowing ratios and incidence angles on the adiabatic and overall effectiveness of the models. These tests will represent a significant contribution to the literature and to the understanding of the effectiveness of shaped holes in actual turbine components, especially since matched Biot number model testing on such a model does not yet exist. Furthermore, a compilation of the results listed above will represent an extremely useful reference for those seeking to understand the effects of the parameters varied on a realistic turbine model with shaped holes.

4. Better understand the effects of incidence angle on the no-film external heat transfer coefficient.

As an additional goal, the project seeks to build on some work completed in the past which examines the effects of incidence angle on the no-film heat transfer coefficients of airfoils. In order to accomplish this goal, the no-film external heat transfer coefficient will be measured in the new facility and compared to results in the literature.

5. Develop predictions of the no-film heat transfer coefficient and turbulence grid flow field effects through the utilization of RANS models. An attempt to predict the heat transfer coefficients of the two incidence angles will also be presented, and their validity assessed. The comparison of the heat transfer simulations to the experimental results will prove useful to a turbine designer should one need to assess the effect of incidence angle on the heat transfer coefficient. Furthermore, turbulence grid measurements and correlations developed within the framework of this project will be compared to simulations in order to gain a better understanding of the use of turbulence grids in low-speed wind tunnels when when the flow is not normal to the grid. These effects exist in the literature for screens due to their widespread use, but do not exist for a vertical array of cylindrical rods. Therefore, the experimental results and simulations will provide a useful resource for any experimentalist seeking to utilize a turbulence grid in a similar manner.

Chapter 4: Previous Facility and Conceptual Design of New Facility

This chapter details the previous and rebuilt components of the wind tunnel facility which has been used for a number of years on campus at the University of Texas at Austin to perform film cooling experiments. The wind tunnel has gone through a number of iterations over the years, and the last design iteration has been successfully used to test scaled-up gas turbine vanes discussed in some detail. A redesign of the corner test section which has been used to test scaled up gas turbine airfoils was required in order to add the capability to test non-zero inlet incidence angles. In order to do so, the initially proposed conceptual design was updated and refined in order to ensure that the added incidence angle capability would be effective. Furthermore, the new wind tunnel components were designed to be modular in nature, enabling the use of previously existing airfoils in the newly updated facility. New wind tunnel subcomponents were designed in CAD software, including scaled film-cooling test airfoils which would be used in a variable incidence angle study. The components were all manufactured and assembled, completing the conceptual design and construction phase of the project.

4.1. Previous Facility Components

The project was completed using a closed-loop, low-speed wind tunnel currently in operation in the Turbulence and Turbine Cooling Research Laboratory (TTCRL) at the

University of Texas at Austin. A schematic of the recirculating wind tunnel with all the previous components attached can be seen in Figure 4.1. The main loop in the wind tunnel is driven by a 50hp variable-speed, variable-pitch fan which provides mainstream air at constant velocity for testing. A heat exchanger within the main loop enables control of the mainstream fluid temperature between 295K and 315K. A secondary flow loop utilizes a 7.5 hp constant-pitch, constant-speed blower to extract air from the main loop 36 and reroute the air in to the secondary loop heat exchanger. The secondary loop heat exchanger first transfers heat between the mainstream air and liquid nitrogen (provided by a 150-200L liquid nitrogen tank), and then mixes the cooled air with the gaseous nitrogen at the exit of the heat exchanger, thereby providing a cold gaseous nitrogen and air mixture to the test airfoil for film-cooling experiments. Valves are also present in the coolant loop to set the mass flow rate of the cold fluid entering the film-cooled models.

Figure 4.1: Schematic of the recirculating low-speed wind tunnel used for airfoil testing in the TTCRL. An airfoil with an 휶 = ퟎ° design point is visible in the schematic. Portions of the wind tunnel redesigned in the project are highlighted in red.

The most recent test section used in the wind tunnel was a variation of a 3 airfoil, 2 passage test section located in the corner downstream of the contraction nozzle. The most recent test section is shown in Figure 4.2. In the test section, mainstream air flows through a turbulence grid (C), where it is redirected around one fully instrumented test article (G) and two dummy airfoils (F and H) which are only partial representations of the complete airfoil. Flow is redirected through the two main passages around the test article

37 as well as through bleed passages (B). Adjustable blockages and walls (A and E) allow for manipulation of pressure losses through the bleed passages as well as local velocities. These adjustments enable the operator to force a desired flow around the test article. This basic design has been in use for many years but has been upgraded and replaced a number of times in order to accommodate experiments on different vane models. The most recent test section designs have retained the same test section height (549mm) and vane model pitch (457mm), enabling some limited part modularity in the facility. However, the design only allows for testing of airfoil vanes, where the inlet flow is normal to the axis of the airfoil cascade, as in Figure 4.2.

Figure 4.2: Schematic of the previous wind tunnel test section [46].

4.2. Conceptual Design of New Facility

At first, there was only one main goal for rebuilding the experimental facility - adding in the capability to test airfoils with nonzero inlet flow angles, 훽 ≠ 0° (a 38 schematic of the incidence angle designation used in this paper can be seen in §1.4). In the past, the wind tunnel test sections have been built to test airfoils at a zero degree inlet incidence angle design condition (훽 = 0°), such as for a number of tests the lab has performed on the C3X model ([21,39,46,47] as some examples). The current project required testing at nonzero incidence angle (훽 ≠ 0°), and traditionally test sections were redesigned and rebuilt for testing of only one airfoil. A basic design concept had been proposed prior to the start of the project. After beginning the project, the initial design concept was further assessed and improved prior to the detailed design stage. In this chapter, the conceptual design and design evolution are explained in detail.

4.2.1. Initial Concept

Prior to proceeding with the detailed design of the wind tunnel sections, the initial conceptual design was assessed. The initial conceptual design for the test section is shown in Figure 4.3. In this design, small turning vanes were placed upstream of a single cascade of continuously variable turning vanes. The airfoil model remained stationary, and so in order to maintain uniform flow in to the test section, a blockage would have been used upstream of the turning vanes. Blockages were also utilized on each side of the outermost dummy airfoils in order to adjust the flow adequately in the outer passages.

Figure 4.3: The initial conceptual design for a 휷 ≠ ퟎ° test section. Note that the turning vanes which redirect the flow were designed to provide a continuous range of incidence angle variation (풊 ± ퟎ) for airfoils at approach flows both 휷 = ퟎ° and 휷 ≠ ퟎ°.

The assessment of the initial conceptual design revealed a number of positive and negative aspects. On the positive side, any incidence angle could be tested since the turning vanes would be designed to provide a continuously variable inlet incidence angle. In addition, the inlet section would not have to be altered except for the addition of the upstream blockage, meaning that only a small part of the wind tunnel would have to be redesigned. However, the design also had some negative consequences. Most notably, it would be extremely difficult and costly to design and manufacture the continuously variable turning vane cascade. Second, due to the proximity of the turning vanes and airfoil model, the wakes generated by the turning vanes could significantly affect the flow, and there would not be a simple way to generate the appropriate levels of turbulence needed for the tests. Lastly, the modularity of the wind tunnel would not stay

40 intact – older models could not be retrofitted to function appropriately in the test section, as the initial conceptual design required a significant change in the airfoil model size and pitch. It was decided that a critical assessment of some concepts which overcame these drawbacks be performed in order to determine whether or not the final design could be improved upon. In order to proceed with the critical assessment, a three-part process was followed. First, design criteria were established, which could be used to assess the feasibility of each design. Second, wind tunnel design methods in the literature were used to develop upgraded concepts which could overcome the drawbacks of the initial conceptual design and which satisfied the design criteria. Third, a decision matrix was created in order to score the designs and ultimately identify the most useful concept based on the list of design criteria and their importance to the project.

4.2.2. Improvement of Conceptual Design – Design Criteria

Following the three-part process above, a list of design criteria was generated which focused on the requirements of the project as well as the design’s modularity. The list of design criteria and their respective weight factors is listed on the left side of Table 4.1. In general, the list focused on ease of IR camera optical access, tunnel flow quality, and tunnel modularity, but there were also additional design criteria for tunnel seal quality, the number of moving parts, test setup time, and cost. This list was referred to while assessing concepts well known in the literature as well as new concepts which would be applicable to this project.

Table 4.1: The criteria utilized in assessing conceptual designs.

Design Criteria Optical Access Downstream Flow Quality Modularity Upstream Flow Quality Seal Quality Moving Piping / Inst. Setup time for β≠0° Setup time for β=0° Cost

4.2.3. Research for Conceptual Design Improvements

Currently existing wind tunnel facilities whose basic designs exist in the literature were examined in order to gain a better understanding of variable incidence wind tunnel testing. The research performed was used as a foundation for developing the new conceptual designs. In general, closed-loop 훽 ≠ 0° linear cascades are almost never utilized, but a number of open-loop designs which can be used to test airfoils at 훽 ≠ 0° do exist. Furthermore, it is necessary to remain in a closed-loop configuration in order to decrease humidity levels within the wind tunnel, enabling low-temperature film-cooling studies. A literature review of the open-loop designs appears in §2.4, where the various design concepts for existing 훽 ≠ 0° wind tunnels are explained.

4.2.4. Improved Designs and Decision Matrix

During this phase in the project, three new designs were generated. The three designs can be seen in Figure 4.4. First, the initial conceptual design was improved, and this improved design was used in place of the initial design. This first design still contained a single turning vane cascade, but the cascade was moved upstream to provide a passage for the flow conditioning to occur and allowed for simpler IR camera access. 42

Although the design ensured appropriate flow conditioning and IR access, this came at the expense of a test section that had to move for each incidence angle tested, resulting in repositioning of the coolant loop and effects of losses downstream of the test section which varied for each incidence angle. Second, a design which contained two turning vane stages instead of one was proposed. In this design, the first turning vane stage (positioned immediately downstream of the contraction nozzle) would direct the flow by a discrete amount, while the second turning vane stage (positioned downstream of the first) would redirect the flow in to the test section. The second turning vane stage would move, while the first turning vane stage and the test section remained stationary. The stationary test section would significantly simplify the coolant loop design and test setup. Finally, a third and more traditional turntable test section was proposed. The turntable design would provide continuously variable incidence angles and completely avoid the use of turning vanes at the expense of a moving test section. However, the turntable design required moving all airfoil models and the coolant piping during an incidence angle change. It also required a complicated design process downstream of the test section to maintain the closed-loop configuration of the tunnel, especially at large incidence angle changes.

Figure 4.4: The three proposed conceptual designs which improved upon the original concept.

4.2.5. Revised Design Concept

After the first two steps were completed, the design criteria and weighting factors were applied to all three designs. The design matrix as well as the final scores for each of the designs can be seen in Table 4.2. Although test section flow quality was potentially affected by the presence of the turning vanes, since the two-stage turning vane cascade mechanism allowed for stationary instrumentation and good camera access, it scored higher than the other two designs. Thus, the double turning vane cascade design was chosen, knowing that the turning vanes would have to be designed and verified through experimentation prior to formal testing.

Table 4.2: The decision matrix used in comparing conceptual designs. Note the final scores highlighted in green, with a score ranging from 0-500.

Score (0-5) Weighted Score (0-500) Weight Single Guide Double Guide Turntable Single Guide Double Guide Turntable (%) Vane Design Vane Design Design Vane Design Vane Design Design Optical Access 30 * 4 4 1 = 120 120 30 Downstream Flow Quality 15 * 1 3 1 = 15 45 15 Modularity 15 * 5 5 3 = 75 75 45 Upstream Flow Quality 15 * 1 1 5 = 15 15 75 Seal Quality 8 * 2 1 4 = 16 8 32 Moving Piping / Inst. 8 * 1 3 1 = 8 24 8 Setup time for β≠0° 3 * 2 2 5 = 6 6 15 Setup time for β=0° 3 * 4 4 5 = 12 12 15 Cost 3 * 3 1 5 = 9 3 15 TOTAL 100 23 24 30 276 308 250

Chapter 5: Detailed Design of Facility Upgrades

The revised design concept was turned in to a feasibly manufacturable design, the final schematic of which is seen in Figure 5.1, and the final CAD model of which is seen in Figure 5.2. The detailed test section design retains all of the features of the revised design concept, but also contains the final methods for which the inlet flow is conditioned prior to entering the first turning vane stage, realistic component mating in order to install and remove all the replaceable parts (turning vanes, airfoil models, etc.), structural integrity, and sealing.

Figure 5.1: Schematic of the redesigned wind tunnel section.

Figure 5.2: CAD model of the redesigned wind tunnel pieces, including the upstream and downstream flow conditioning sections and the test section (coolant loop is underneath the wind tunnel).

Starting upstream in Figure 5.2, flow enters in to the contraction nozzle, which acts as a flow conditioner, and was designed to mate with the incidence angle mechanism immediately upstream of the test section. Next, the flow enters in to the upstream incidence angle mechanism, which contains the two turning vane stages which redirect the flow, as seen clearly in Figure 5.1. The flow then enters in to the upgraded test section, which provides significant part modularity to enable testing of various airfoil types. The flow then exits through the diffuser, which was redesigned to reduce losses incurred downstream of the previous test sections, increasing the maximum wind tunnel velocity. A description of the detailed design of these main components and the subcomponents used in the project is contained within this chapter. 47

5.1. Design of Main Components

5.1.1. Contraction Nozzle

In order to design the contraction nozzle, design techniques from the literature were applied to the previous contraction nozzle designed by Polanka [55]. There were a number of reasons why Polanka’s design was not used immediately for this wind tunnel:  A new contraction nozzle would have to be manufactured regardless of the design, since the horizontal dimensions of the test section were changed

 The nozzle’s horizontal dimension change resulted in a nearly 2D contraction  The previous polynomials generated by Polanka describing the horizontal and vertical contraction only satisfied the requirements for inlet and outlet dimensions – there was no other basis for the polynomials  The uniformity immediately downstream of the contraction nozzle was critical in this design, since turning vanes were located very near the

contraction nozzle outlet The design was updated according to Morel [56], who provides reference charts for 2D contraction nozzle designs generated from inviscid flow equations, and later tested experimentally. The final contraction nozzle design was created using predetermined inlet and outlet dimensions connected by cubic arcs, as seen in Figure 5.3. The family of curves used for the new design is the same as that discussed in Morel. Therefore, the reference charts generated by Morel can be used directly to approximate the quality of the outlet flow conditions entering the first turning vane cascade.

Figure 5.3: A schematic of the wind tunnel contraction nozzle side profile adapted from Morel [56], giving a visual indication of the equations used to design the new contraction nozzle.

In Figure 5.3, the following equations were used to generate the contours:

1 푥3 푥 퐻(푥) = (1 − ) (퐻 − 퐻 ) + 퐻 푓표푟 ≤ 푋 푋2 퐿3 1 2 2 퐿 5.1

퐻 − 퐻 푥 3 푥 퐻(푥) = ( 1 2 ) (1 − ) + 퐻 푓표푟 > 푋 (1 − 푋)2 퐿 2 퐿 5.2 where 푥 is the axial distance along the curve, 푋 is the arc inflection location, 퐿 is the total length of the contraction nozzle, 퐻1 is the inlet size, and 퐻2 is the outlet size. Normally, the design procedure in Morel would produce the arc inflection location from lookup tables depending on the flow quality required by the designer. Instead, in order to compare the results from Morel [56] to that of Polanka [55], X was set at 0.5 or half way along the contraction nozzle, therefore matching the inflection location of Polanka [55]. Since there was the same amount of space available for the contraction nozzle, the length was also not changed. A comparison of the two profiles can be seen in Figure 5.4. Using these values, Morel’s design requirements predict the development of a turbulent boundary layer along the walls of the contraction nozzle, and predict a maximum velocity 49 non-uniformity of 1%. These values were acceptable for the current application, and rather than attempt to improve the design further, it was decided that the curves specified by Morel along with an inflection point at X=0.5 would be used for the final design. The design was therefore a compromise between the previous design and one grounded in experimental results from the literature.

Comparison of Sideview of Nozzle Curvatures 0.9 New Arc 1 New Arc 2 0.8 3rd order Polynomial (Polanka)

0.7

0.6

0.5

Height from Centerline (m) from Height Centerline 0.4

0.3

0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Length (m)

Figure 5.4: A graph depicting the change in curvature for the side profile of the contraction nozzle, where Polanka’s [55] design has been previously used and is shown for comparison to the new curves used in the redesign.

Table 5.1: The values of the variables used in Equations 5.1 and 5.2 to solve for the contraction nozzle profile.

퐻1(푚) 퐻2 (푚) 푋 (−) 퐿 (푚) Vertical Direction 1.524 1.270 0.5 1.829

Horizontal Direction 1.524 0.549 0.5 1.829

Figure 5.5: An isometric view of the redesigned contraction nozzle, with flow entering at the left and exiting to the right in the image.

5.1.2. Incidence Angle Mechanism

The most complicated upgrade to the test section is the capability to change the incidence angle of the flow in to the test section. A top-down view of the designed incidence angle mechanism can be seen in Figure 5.6. This was accomplished by 51 replacing a straight section of the wind tunnel downstream of the contraction nozzle but upstream of the original test section with two stages of turning vane cascades as in the updated conceptual design. As discussed previously, the farthest upstream section of the incidence angle mechanism contained a stationary stage of turning vanes which redirected the flow by a specific angle in to the second stage, which then redirected the flow again, this time in to the test section itself. The second pack of turning vanes was designed to move laterally and be locked in to position, allowing for testing of one discrete test section inlet incidence angle at a time.

Figure 5.6: A top-down view of the incidence angle mechanism at both 휷 = −ퟐퟓ° and 휷 = −ퟑퟓ°.

In order to start the detailed design of the incidence angle mechanism, a multistage process was followed. This included collecting sizing requirements based off of the updated conceptual design, sizing out the turning vane cascades, and developing a feasible concept for reconfiguring the incidence angle mechanism within these design constraints. Next, the turning vane design was integrated in to the incidence angle mechanism in order to secure the turning vanes as well as streamline removal and installation of the vanes out of and in to the incidence angle mechanism. The design

52 requirements were then utilized in SolidWorks to ensure part functionality as well as generate the materials and cutting list during the manufacturing phase. This design phase is detailed in the following subsections.

5.1.2.1. Overall Sizing Requirements

First, previous wind tunnel diagrams in conjunction with accurate measurements of the currently installed hardware were used to restrict the design footprint. The distance between the aforementioned contraction nozzle and the location of the test airfoil cascade leading edge restricted the length of the incidence angle mechanism, while the lab walls, walkways and instrumentation locations restricted the maximum lateral footprint that could be used by the mechanism. These measurements were used throughout the following sections to restrict the overall design to the required footprint size.

5.1.2.2. Design of Turning Vane Cascades

Next, the axial chord length of the turning vanes used to redirect the upstream flow was specified to be 152mm, partly based off of the sizing limitations noted in the previous step, and partly based off of the total number of turning vanes which would be used in the tunnel (which was a function of cost, structural integrity, and predicted test section flow field uniformity). Once the axial chord length of the turning vanes was specified to be 152mm, the pitch of the turning vanes was specified to be 106mm, which meant that exactly 12 turning vanes would be used in each cascade stage. After the basic turning vane dimensions were specified, the detailed turning vane design process was completed which is discussed in the next chapter. The detailed turning vane design provided the detailed dimensions of the turning vanes for each incidence angle being

53 tested, and therefore solidified the dimensional requirements for the incidence angle mechanism walls. A depiction of the pressure-side and suction-side wall of the first turning vane stage at 훽 = 35° can be seen in Figure 5.7, which more clearly highlights the work accomplished to appropriately size the end walls of the turning vane cascades. Since exactly 12 turning vane pitches were to be used in the cascade, the sidewalls in the vane cascades were lined on the suction-side with a vane which contained only the suction- side of the vane cascade. This was done in order to ensure separation did not occur on the suction-side corner of the turning vane cascade. Furthermore, on the pressure side of each turning vane cascade, a flat wall which followed the true chord line of the airfoil was used. This was done since separation would not occur on the pressure side, but the inlet to outlet area of the cascade needed to remain constant – adding a wall which followed the true chord accomplished this requirement, and this was much simpler than adding a pressure-side-only airfoil for this sidewall.

Figure 5.7: A detailed view of the first stage of turning vanes installed in the wind tunnel, highlighting where the wind tunnel sidewalls interact with the turning vane cascade.

As the turning vanes were secured in to the wind tunnel with set pins, the incidence angle mechanism had to be designed to receive the set pins and set the turning vane stagger angle accurately and with high precision. The design also had to be modular to accept turning vanes of the basic dimensions (152mm axial chord, 106mm pitch) for any incidence angle to be tested. The final design was an adjustable recessed floor and track system which could be reconfigured for any incidence angle and any turning vane cascade used, and would also not interfere with the flow in the neutral 훽 = 0° position. The track mechanism can be seen in Figure 5.8. The mechanism contained two recessed, movable 3” wide and 45” long pieces of acrylic with holes for the turning vane set pins at

106 mm spacing. A small gap in the recess was filled with two shaped acrylic pieces which set the stagger angle of the turning vanes. The acrylic pieces in this section were designed with interference fits so that no additional movement was possible on the 55 bottom track. In order to install and remove the track system for a given set of turning vanes, the shaped pieces were first installed, and the 45” long pieces were flexed and installed, providing an immovable bottom space for the turning vanes to be installed. Turning vane cascade ceilings were individually manufactured, which lead to higher cost but lower complexity, since it was difficult to design the same type of track system for the wind tunnel ceiling.

Figure 5.8: A detailed view of the bottom track system with set pins and spacers, which set the final position of the turning vane cascade.

Both the first and second stage of turning vane tracks were designed very similarly, but while the first turning vane stage was stationary, the second stage had to move laterally (as seen previously in Figure 5.6) in order to provide the movement necessary to place the vanes in the appropriate lateral position. Set pins were used in this case to set the cartridge at the appropriate lateral position for each incidence angle configuration.

5.1.2.3. Sealing The Incidence Angle Mechanism

A number of steps were taken to ensure design modularity while simultaneously providing a high-quality seal from the atmosphere. First, inner walls were designed which provided a continuous vertical surface for the far pressure and suction-side walls in the wind tunnel – these were made out of relatively thin 6mm acrylic. Some acrylic wall sections were uniquely designed for each incidence angle being tested, and so when a new incidence angle was to be tested, these sections were removed and replaced.

However, many of the pieces were also generic and could be used for all of the tested incidence angles. An example view of the removable and permanent inner acrylic walls can be seen in Figure 5.9, while an example view of the removable wooden walls which provided the final wind tunnel seal from atmosphere can be seen in Figure 5.10. The interface between the inner walls and the ceilings were taped in order to reduce the leakage in to the inner-to-outer wall space during startup. Beyond the inner walls, outer wooden walls and weather stripping were used to provide the final outer seal to the atmosphere.

Figure 5.9: A detailed view of the inner acrylic walls (made opaque), with highlighted walls changed for different incidence angles and non-highlighted walls not changed.

Figure 5.10: A detailed view of the outer wooden walls required to provide the final seal to the wind tunnel. At the interfaces of all wooden walls, weather stripping provided the pressure seal.

The ceiling of the incidence angle mechanism was also designed to be removable and adjustable. This allowed for the ceiling to be slightly raised while the incidence angle was being changed, allowing for the inner acrylic walls to be moved without an interference fit between the ceiling and floor of the tunnel. Once the incidence angle was set, the ceiling could then be lowered to engage a seal between the wall and the ceiling. Designing the ceiling this way also reduced the load that the thin inner acrylic walls had to bear, but required a cage support system to support the ceiling, which can be seen in Figure 5.2. The cage system could also conveniently be used to remove and install airfoil models since Article D (the conducting model) weighed in excess of 35 kg. Finally, the incidence angle mechanism could be collapsed and all turning vanes removed which provided for the 훽 = 0° testing capability. A view similar to Figure 5.2 but set to the 훽 = 0° testing configuration, and with the C3X model installed, can be seen in Figure 5.11.

Figure 5.11: A view of the incidence angle mechanism in the 휷 = ퟎ° configuration, with a different airfoil model viewable in the test section.

5.1.3. Test Section

The design goals for the updated conceptual design of the test section necessitated the redesign of the dummy airfoils and instrumented airfoil, flow blockages, adjustable walls, inlet and outlet area. The finalized design can be seen in Figure 5.1. First, the dummy airfoils (labeled G and I in the image) in the airfoil cascade were replaced with removable airfoils as opposed to permanent airfoils used in the past. Next, the standard design for the instrumented airfoils was also updated to ensure many different airfoil types could be installed in to the tunnel. Also, utilizing removable dummy airfoils necessitated the redesign of the side passage flow controls (labeled C in the figure), which metered airflow through the side passages. Improvements were also made to the adjustable walls (labeled E in the figure) in order to ensure the flow could be adequately

59 adjusted in the test section. Finally, the test section inlet and outlet area were increased to handle the chance in incidence angles required for 훽 ≠ 0 testing. It’s important to note that the redesign of these components was largely an iterative process, as the locations of the flow blockages changed as the test section area changed, or as the airfoil lid and base size changed, etc. Furthermore, once a design was created in CAD software, CFD simulations were completed on the test section, and another round of iterations took place prior to finalizing the design. This section highlights the main areas of the test section which were upgraded, and will also focus briefly on some of the final CFD simulations that were completed prior to finalizing the test section design.

5.1.3.1. Test Section – Airfoil Cascade

In order to utilize the wind tunnel test section for the current project and other projects without having to redesign and install a new test section, the previously permanent pressure- and suction-side dummy models were replaced by removable models similar to the test model itself. A juxtaposition of the previous and updated test section airfoils can be seen in Figure 5.12. While the shape of the pressure-side model (labeled G in Figure 5.1) matched that of the instrumented model (labeled H in Figure 5.1), the suction-side airfoil model (labeled I in Figure 5.1) only matched about 1/3 of the leading edge of the test model. The downstream portion of the suction-side model was truncated in order to smoothly mate to the adjustable wall.

Figure 5.12: A side-by-side comparison of the previous (left) and updated (right) test section airfoil cascades, highlighting which airfoils can be removed and which cannot, and also highlighting the new lid design.

Second, a universal lid and base for the airfoils was designed which fit old and new models alike. This was accomplished by comparing the size and shape of the current airfoil model with that of previous designs such as the C3X airfoil (used in several studies in the recent past) in order to create a common lid for the airfoils. The lid design was utilized for the dummy airfoils as well, but only the upstream ½ of the lid was utilized for partial dummy airfoil. A comparison between the previous lid design and the current lid design can also be seen in Figure 5.12. Note how the updated airfoil lid shape fits on the newly designed dummy airfoils, which was not possible in the past as the previous tunnel was not designed to handle multiple removable airfoils in the test section.

5.1.3.2. Test Section - Flow Blockages

The previous wind tunnel design provided for adjustments to the mass flow rate through the use of flow blockages which were only designed for use with the C3X model. These flow blockages were insufficient for the current project. The previous blockages were designed only focusing on the C3X, and as a result, contained an inadequate amount of adjustability, critical in appropriately setting the mass flow rate in the bleed passages for the new model. As the bleed passages were required to provide a significantly larger and varying flow rate for the variable incidence angle studies, the flow blockages were redesigned. The upgraded blockages can be seen clearly in Figure 5.1. The upgraded flow blockages could be adjusted with the same accuracy as the previous design, but the area of the flow bleed could be adjusted over a much wider range. This was achieved through the use of a 114mm semicircle attached to adjustable knobs which adjusted the lateral position of the blockage. The knobs were connected to the semicircle blockage with 3/8”-16 threaded rod, which provided adequate strength to keep the blockages stationary but a significantly better accuracy in setting their position, as the pitch of the threaded rod determined how accurately the blockage could be moved. The knobs could also be locked once set in to place in order to ensure that accidental adjustment of the knobs could not occur. In addition to their redesign, the suction-side flow blockage was moved downstream of the straight pipe section, since the flow could be metered downstream with the flow blockage, freeing up a substantial amount of room for the increased inlet width and incidence angle mechanism required for the current project.

5.1.3.3. Test Section - Adjustable Walls

It was clear after the completion of the conceptual redesign that the adjustable wall seen in Figure 4.2 would still be required. This was because the test section used only three airfoils in the cascade as before, but in this design, the adjustable wall position would have to be adapted to the C3X, the current airfoil model, and future designs as well. Although the adjustable wall remained quite similar to the previous design, the first section of the adjustable wall was made much smaller since the smallest radius of curvature typically occurs near the geometric leading edge of model. Therefore, it was easiest to match the overall shape of the airfoils (including the ITB as well as the C3X) with straight walls by including shorter sections of walls upstream, and longer sections of walls downstream. Since it was critical to check whether or not the desired pressure distribution could be set on the model using the straight walls, the primary focus of the simulations (shown in § 5.1.3) focused largely on the straight wall shape.

5.1.3.4. Test Section – Inlet and Outlet Size Optimization

In order to handle the inlet incidence angle variations, the inlet of the test section was increased from 1.02m to 1.27m (more than a 20% increase) to allow for incidence angle variations without requiring a change in test model pitch. This upgrade allows the lab to utilize all airfoil models that the lab has manufactured over the years in addition to the new airfoil model for this project. It was critical to ensure that readjusting the upstream test section walls for 훽 ≠ 0° testing did not interfere with the total mass flow rate that could pass through the side passage bleeds. That is, the airfoils had to be far enough away from the walls so that the flow was metered by the adjustable blockages, and not by the airfoils themselves. Looking at Figure 5.1 it is clear in this image that there is plenty of space between the sidewalls and the straight wall sections upstream of

63 the airfoils, meaning that adjusting the walls to test at 훽 ≠ 0° does not affect the mass flow rate through the passage as much as the blockages can. The outlet area and outlet shape of the test section was also changed. This was completed by identifying the outlet angle of the current project’s airfoil in simulations in order to determine the ideal outlet test section width. As a result, the outlet of the test section was increased from 404mm to 445mm, and this ensured that there was no unnecessary acceleration of the flow beyond what is needed, thereby reducing losses further downstream in the diffuser, and increasing the maximum wind tunnel velocity.

Walls downstream of the airfoil were designed to follow the flow as smoothly as possible, and this was verified in the test section simulations.

5.1.3.5. Test Section – Design Through Simulation

Once the improved designs were modeled in SolidWorks, simulations were completed in Fluent in order to determine whether or not the flow blockages and adjustable walls could adequately force the appropriate stagnation line and pressure distribution on the airfoils. 2D simulations of the test section were completed with the new airfoil model as well as the C3X model to verify compatibility. For these simulations, the position of the adjustable walls and blockages were iterated until the pressure distribution was matched. This was done by adjusting the position of the adjustable mechanisms in the control volume and comparing the simulation results to the ideal pressure distributions, and repeating the process until the change in positions was insignificant. From these simulations, it was shown that the blockages and adjustable wall provided adequate adjustability of the flow to match both the pressure distribution and stagnation line locations on both models. They also provided evidence that the wall sections immediately downstream of the airfoil redirected the flow adequately in to the 64 diffuser, and therefore could provide for a significant increase in the pressure recovery of the flow in the diffuser over the previous design, therefore increasing the maximum wind tunnel operating speed.

Figure 5.13: A view of one of the CFD simulations, which showed that the C3X could be installed in to the tunnel and forced to the periodic condition through movement of the adjustable walls.

5.1.3.6. Test Section – Mating to Coolant Loop

In order to connect the coolant piping to the base of the airfoil, the inlet channel was designed uniquely for the current project, but was designed in such a way that the inlet channel could be swapped out simply and efficiently for different airfoil models.

The inlet channel internal shape changes from the round shape of the PVC in the coolant loop to that of the internal airfoil passage that it is feeding, and then contains a vertical, constant cross-sectional area 250 mm tall in order to ensure that the flow smoothly enters 65 the base of the airfoil. Designing the inlet channel in such a way ensured that the piping downstream of the heat exchanger did not have to be redesigned for each airfoil model, and redesign was only restricted to the inlet channel itself. Thus, the overall interchangeability of the tunnel parts was improved. Seen in Figure 5.14 is the current inlet channel compared with an inlet channel designed and built after the one for the current project. Notice in the figure that the overall dimensions including the mounting holes are the same between the two models. The internal passage shape (not shown) is unique as dictated by the internal geometry of the film-cooled models.

Figure 5.14: A view of the inlet channels immediately under the instrumented airfoil, which provides coolant to the base of the airfoil. Basic dimensions for the current project (left) and a future project (right) are very similar, highlighting the interchangeability of the parts.

5.1.4. Diffuser

The diffuser design was dictated solely by space limitations, the outlet size of the test section, and the inlet size of the downstream tunnel section. As discussed previously, the outlet of the test section was designed to be as large as possible in an attempt to 66 reduce the pressure loss that could occur due to the diffuser. The diffuser was made to be as long as possible in order to reduce the total angle that it diffused prior to intersecting the corner turning vanes downstream. The diffuser measurements can be seen in Figure 5.15, and the only overall size change between the old and new diffuser is the inlet width, which increased from 406mm to 445mm.

Figure 5.15: A top view and side view schematic showing the dimensions of the new diffuser design.

There were a number of factors which caused some concern for this design. First, due to the space limitations, the whole angles were 휃푇퐻=18.9° and 휃푆퐻 = 14.8° in the horizontal and vertical directions, respectively. This was recommended not to exceed 5° for optimal flow steadiness and 10° for pressure recovery. Beyond 10° a significant amount of separation could occur, reducing the pressure recovered by the diffuser. Researchers such as Mehta [57] classify this as a wide-angle diffuser, meaning that special care should be taken to ensure that significant flow separation does not occur in the diffuser. Unfortunately, due to space limitations, little could be done to further change the overall shape of the diffuser beyond what was already done. Second, the area ratio of

67 this design was quite large at 3.26 as a result of the large whole angles 휃푆퐻 and 휃푇퐻. Figure 5.16 shows the successful operating range of diffusers based off of experimental data (as presented by Mehta [57]). In Figure 5.16, the combination of the area ratio and largest whole angle for the current diffuser leads to improper operation without a screen installed. Finally, significant flow separation most certainly occurred in the previous diffuser design, especially at higher test section velocities. This was evident as a loud hum and powerful vibration emanated from the diffuser at high velocities. The pressure loss upstream of the diffuser and downstream of the corner turning vanes (which were themselves immediately downstream of the diffuser) was measured by Mosberg [58], and it was found that 87% of the total loss experienced in the wind tunnel occurred through the diffuser and turning vanes. Therefore, although the previous diffuser design had a slightly larger whole-angle, it was still potentially a problem with the new design.

Figure 5.16: A graph adapted from Mehta [57] showing what combinations of whole angle and area ratio lead to appropriately and inappropriately operating diffusers. The red lines and X indicates the current design, and indicates that without a screen, the diffuser would most likely contain some separation.

The diffuser design was finalized with these risk factors in mind. A radius of 12.7mm was added to sharp edges of the diffuser to provide a smooth transition out of the test section. The newly designed diffuser was made out of a much thicker material in order to provide additional structural integrity, as the previous diffuser was quite thin. This was done to suppress the strong pressure fluctuations that were occurring within the old diffuser at high velocities, reducing the intensity of the sound emanating from the diffuser area. Finally, although a screen was not installed in the diffuser as Figure 5.16 suggests one should be, the appropriate screen size was purchased from a local manufacturer so that it could be used if needed, and other backup plans were also assessed prior to purchasing the diffuser.

5.1.5. Coolant Loop

In order to provide inlet flow conditioning of the coolant, the coolant loop was redesigned. A schematic of the coolant loop can be seen in Figure 5.17. Starting immediately downstream of the heat exchanger, 3” PVC piping was split with a low-loss 4-way fitting (a doubly wye type fitting) into 3 main 3” PVC passages which would eventually feed the three passages in the airfoil. The 3” PVC pipe was then rerouted under the tunnel as opposed to the inside of the wind tunnel loop, reducing the number of bends in the coolant loop and therefore reducing pressure loss. Flanges were added 10 diameters downstream of the start of the straight PVC sections, which affixed three inline orifice plates for flow measurements capability at enough diameters downstream to remain within ASME standards for orifice plate flow measurements. Another flange was attached to the downstream side of the orifice plates, and a short straight section of pipe proceeded farther downstream, where removable couplers were installed, providing for the final attachment to the inlet channels as discussed earlier. Also, as seen in Figure

5.17, dead ends were added downstream of the piping which allowed for calibration of the installed orifice plates with a laminar flow element (LFE) (as discussed in 0). The piping was then insulated to reduce heat loss through the piping system. Separately from the main PVC coolant loop, small diameter copper piping was also replaced on the wind tunnel. This copper piping proceeded from downstream of the diffuser and around to the heat exchanger inlet. This provided a coupling from the liquid nitrogen tanks used as coolant in the heat exchanger. The copper piping was also well insulated in order to reduce the heat loss of the nitrogen as it passes through the piping.

Figure 5.17: A schematic of the updated coolant loop, showing the new location of the heat exchanger, and the updated piping system for the tunnel.

5.1.6. Construction

Both the contraction nozzle and diffuser were manufactured by Miles Fiberglass & Composites, Inc. of Portland, OR. The components were manufactured with a fiberglass-foam-fiberglass sandwich configuration, similar to the construction method of the other walls in the wind tunnel. A temporary mold was made out of MDF, a Duratec coating was applied to yield a smooth, high-gloss inner surface, and the part was then made by applying .022” of white gel coat followed by 3 layers of 1-1/2 oz. Chopped Strand Mat (fiberglass) and 24 oz. Woven Roving (another fiberglass) in alternating 0.25” layers. The 0.25”-0.5” foam layer (#2-#6) was then applied (depending on what was available), and the same laminate was finally applied over the top of the foam. Once the laminate was cured, the structure was deburred and a base coat of the same white gel was applied to the outside. The parts were then delivered to the lab and were ready for installation immediately thereafter. It is clear that the construction of the contraction

71 nozzle and the diffuser is much higher quality than the previous components (built out of very thin fiberglass layers, presumably without a core), at a cost of a slight increase in weight. However, the reduction in vibration due to the sandwich configuration used in their construction was deemed superior. The acrylic for the incidence angle mechanism and test section was mostly manufactured by Krull CNC routing of Midlothian, TX. For this process, the acrylic parts from the CAD model were laid out on 1.22m x 2.44m acrylic sheets ranging from 6mm to 24mm thick depending on our specifications. An example of the sheet layout can be seen in Figure 5.18. The parts were then manufactured by Krull CNC and shipped to the lab. Acrylic parts were mostly attached with Weld-On® 4™ or Weld-On® 16™ depending on the acrylic smoothness at the bonding location. This provided an airtight seal without the use of screws, which can potentially break the acrylic depending on the bond location and part thickness.

Figure 5.18: One of the several acrylic sheet layouts sent to the acrylic manufacturer for the routing process.

The wood pieces used in the incidence angle mechanism were manufactured by Fine Lumber and Plywood of Austin, TX. CAD dimensions were sent to the company, who cut the pieces out of 12.7mm to 19.1mm thick pieces of Baltic birch, which is known for its strength and stability. For the ceiling and floor of the incidence angle mechanism, a gloss coat was applied to the inner surface of the wood in order to protect it from damage and the slightly elevated temperature levels in the tunnel. Some reinforcements were made to the ceiling prior to installing it on to the wind tunnel, but the Baltic birch has held up quite well over the past few years.

5.2. : Design of Subcomponents

5.2.1. Test Airfoils

Four test articles were manufactured to measure pressure distribution (Test Article A), heat transfer coefficient (Test Article B), adiabatic effectiveness (Test Article C), and overall effectiveness (Test Article D) of the airfoil model. A CAD model of each airfoil type can be seen in Figure 5.19. Each model was a scaled up 2D midspan extrusion of the original airfoil design. Scaling the airfoil model to the pitch of the previously existing models (457mm) produced an airfoil with an axial chord length of 퐶푎푥=355 mm and a pitch of 457mm. The airfoil model heights are also set at 549mm, the same as all previously designed test models. The models for this project all use the upgraded top and bottom lids as discussed previously.

Figure 5.19: A depiction of all four models used in the study, with the film-cooled model hatch design highlighted on the far right image.

5.2.1.1. Test Article A – Pressure Measurement Model

Test Article A was made out of a highly machinable closed-cell polyurethane foam. The test article contains a total of 34 pressure taps, with 22 located at 50% span, 6 located at 40% span, and 6 located at 60% span. The locations of these pressure taps

74 allowed for checks on overall pressure distribution as well as radial pressure uniformity. The pressure taps were manufactured out of 0.033” ID steel hypodermic tubing, an ideal size for pressure taps [59]. The steel tubing was connected to flexible silicone tubing and routed through the largely hollow model core and out the top to allow for the measurements to be recorded by external pressure transducers.

5.2.1.2. Test Article B – Heat Transfer Coefficient Measurement Model

Test Article B was manufactured from the same polyurethane foam as Article A due to the foam’s low thermal conductivity (0.044 W/m-K). It was covered in a thin (0.10 mm) stainless steel shim that when energized provides a uniform heat flux. Packard [4] overviews the buildup process of Article B in detail since a number of adhesives, steel shim, and bus bars were tested by Packard during the buildup process. Once the buildup was completed and the foil adhered to the surface, the foil was painted with a matte black paint, and fiducial marks were added to the external surface at every 6.3mm, with the origin of the fiducial marks at the geometric leading edge of the model. This established a curvature coordinate system on the model, and the fiducial marks on the model could be used later during the data processing stages. An image of the airfoil with fiducial marks can be seen in Figure 5.20.

Figure 5.20: Fiducial marks on Test Article B.

5.2.1.3. Test Articles C and D – Adiabatic and Overall Effectiveness Measurement Models

Articles C and D were nearly identical except for the material with which they were made from. As can be seen in Figure 5.21, the test articles had 4 main components: a leading edge hatch, a suction-side hatch, a pressure-side hatch, and a core. The hatches were removable sections of the model that match the external shape of the airfoil, providing internal access to the airfoil model for instrumentation and ease of machining. Each hatch contained one or more rows of shaped holes. The core model contained all the internal passages as well as the portion of the external surface that the hatches did not cover. The cores had 3 main internal passages: a small suction-side channel to feed two of the suction-side rows, a showerhead region with an impingement plate, and an aft u- bend passage. A schematic of the passage locations can be seen in Figure 5.22.

Figure 5.21: A picture of the airfoil model hatch and core design.

Figure 5.22: A representative schematic of the airfoil profile showing the locations of the film cooling holes.

Some internal passages also contained rib turbulators which allowed the model to match the internal-to-external heat transfer coefficient ratio of the engine component. The foam model also contained the rib turbulators since their placement would affect the flow entering the holes. The rib turbulators were manufactured separately and adhered to the internal walls of the model after the corresponding wall-section of the hatch or core was built.

Figure 5.23: A picture of the rib turbulators installed into the inside of the passages in the film cooling models.

Once the rib turbulators were adhered to the airfoils, a total of 118 shaped holes were machined in to the hatches by in-house machinists as well as an external company, Reed Prototype & Machining. A summary of the shaped hole locations and metering hole diameters can be seen in Table 5.2.

Table 5.2: The locations, sizes, and types of film cooling holes used in this study.

d Hole Type s/D (mm) PS1 -46.3 5.4 Fan PS2 -23.8 5.0 SH1 -16.8 5.0 SH2 -11.7 5.0 Conical SH3 -5.4 5.0 SH4 1.0 4.6 SS1 14.7 4.7 SS2 Fan 35.4 4.7 SS3 59.0 4.6

5.2.2. Turning Vanes for Incidence Angle Mechanism

The turning vanes were one of the most critical design components of the wind tunnel. The turning vanes themselves had to be able to provide the appropriate flow turning angles in to the wind tunnel in order to ensure the tests were performed appropriately. Furthermore, the placement of the turning vanes had to be repeatable in the wind tunnel, and so their design for installation was critical. The basic size of the turning vanes was specified in the design of the incidence angle mechanism as 152mm in axial chord length, and their detailed design was finalized from there. For each incidence angle tested, a unique pair of turning vane profiles was designed. The final designed pairs of airfoils for the 훽=-25° and 훽=-35° configurations can be seen in Figure 5.24. The initial design was performed by Pratt & Whitney. However, since the airfoil design tools are not typically used for low-speed airfoil designs, simulations of the prototypes were also performed at the TTCRL in order to verify their designs at low-speed. The low-speed simulation results were then relayed back to Pratt & Whitney, and this process was performed iteratively until all simulated 79 turning vane outlet incidence angles agreed to within 0.2°. Once the simulations converged to within 0.2°, the airfoil profiles were manufactured.

Figure 5.24: The turning vane profiles used in the study.

The turning vane profiles were machined out of 1” thick ABS plastic with a CNC router. The manufacturing and material selection process was determined after a time and cost analysis of several different manufacturing/material pairs. During the selection process, candidates such as casting/resin and selective laser sintering/nylon were determined to be either prohibitively expensive or time-consuming, and so the router/ABS pair was chosen. The profiles were adhered together to create airfoil profiles 549mm tall (the height of the wind tunnel). Small 2 mm thick sheets of very compressible weather stripping were cut to each profile shape and adhered to the end of each turning vane to ensure there were no gaps between the ceiling and the turning vanes. Set pins were installed in to the airfoils (in to the holes seen in Figure 5.24) which protruded from each end by 12 mm which allowed for their installation in to the turning vane tracks.

5.2.2.1. Simulations

2-dimensional periodic simulations were performed in Fluent for each incidence angle tested. The CFD mesh for the second stage, 훽 = −35° turning vane can be seen in Figure 5.26. Inlet conditions were specified at a turbulence level of 1% and a turbulence length scale of 105mm in order to estimate the true turning angle of the turning vanes.

Upstream and downstream distances of 2퐶푎푥 and 3.5퐶푎푥 were specified for the simulations. The CFD domain contained of 52,000 elements on average. The initially simulated outlet turning angles vs. the desired outlet turning angles are specified in Table 5.3. Once the profile shapes for the incidence angles were updated based on the first round of simulations, simulations were repeated two more times, and the final simulated outlet incidence angles can be seen in Table 5.3. Note that the final outlet incidence angles were within 0.2° of the desired outlet incidence angles as specified in the tables. Velocity field and incidence angle contours for the final iteration of the turning vanes can be seen in Figure 5.26-Figure 5.29.

Figure 5.25: The mesh for the second stage, 휷 = −ퟑퟓ° airfoil.

Table 5.3: The ideal turning vane outlet angles compared to the outlet angles as predicted by CFD.

Ideal Outlet ∠ (°) Fluent Outlet ∠ (°) Ideal-Fluent ∠ (°) Stage # Stage # Stage # Iteration (#) β (°) 1 2 1 2 1 2 -25 12.88 -25 12.41 -22.72 0.47 -2.28 1 -35 18.77 -35 19.14 -32.84 -0.37 -2.16 -25 12.88 -25 12.94 -24.99 -0.06 -0.01 2 -35 18.77 -35 18.63 -35.08 0.14 0.08

Figure 5.26: A velocity contour plot for the stage 1 turning vanes.

Figure 5.27: An incidence angle contour plot for the stage 1 turning vanes.

Figure 5.28: A velocity contour plot for the stage 2 turning vanes.

Figure 5.29: An incidence angle contour plot for the stage 2 turning vanes.

5.2.3. Turbulence Rods for Test Section Inlet

New turbulence grids were designed for each incidence angle in order to provide flow conditioning upstream of the test articles. The following correlation, initially developed by Roach [60] was tested by Mosberg [58] for non-zero inlet incidence angles by changing the incidence angle of the grid itself in a straight section of the previous wind tunnel:

5 − 푥푓 7 푇푢% = 퐴 ( ) 5.3 푏

Where 퐴 = 0.8, 푥푓 is the flow distance downstream, and 푏 is the rod diameter. The equation was used to generate designs for the turbulence grids which would generate a turbulence intensity of 푇푢=5%, and an integral length scale of Λf=5% of the axial chord length in each 훽 ≠ 0° configuration. The turbulence grids were designed to span the entire width and height of the wind tunnel. Springs were added to the ends of some of the rods which secured the grid in to place when installed in to the wind tunnel and forced in to the vertical position. Care was taken to ensure that each grid design was located far enough upstream to allow for the wakes of the turbulence grid to merge and to not interfere with the view of IR cameras (as cameras viewed the airfoil model through specific ports on the wind tunnel, so the turbulence grids could potentially obstruct the view of the model). The turbulence grid designs were manufactured out of aluminum rods with horizontal steel sheets near the end of the rods, which provided structural support and reduced any deflection of the rods. The rods were then spray painted matte black as their metallic construction interfered with the particle image velocimetry (PIV) experiments presented in Chapter 8. An image of one of the manufactured turbulence grids can be seen in Figure 5.30: A view of one of the turbulence grids used in the study..

The table of turbulence grids designed by Mosberg [58] can be seen in Figure 5.30, and those used for the current project (the 훽=-25° and 훽=-35° rods) are highlighted.

Figure 5.30: A view of one of the turbulence grids used in the study.

Table 5.4: The turbulence rods designed by Mosberg [58].

Design rig angle (°) 0 -25 -35 훽 > 35 Grid Rod Diameter, b (in) 0.25 0.25 0.25 0.375 Solidity, S 0.25 0.22 0.20 Effective Solidity, 푺휷 0.25 0.25 0.25 0.25

Additional tests were performed by Packard [4] in order to further verify the correlation in the newly installed test section for the 훽 ≠ 0° tests. During validation of the incidence angles entering the test section for this project, it was found that the turbulence grids deflected the flow by 4-5°, which was induced by the mainstream striking the grid at a non-normal angle. The final correlation by Packard allowed for appropriate positioning of the turbulence grid in the tunnel for each incidence angle, and takes in to account the flow deflection through the turbulence grid by including it in the equation. The final equation generated by Packard was:

5 − 7 푥푎푥 cos(훽) 푇푢% = 퐴 ( ) 5.4 푏

Which is the similar to Equation 5.3, but where 푥푓 in the equation was replaced with 푥푎푥 ∗ cos(훽), where 푥푎푥 is the axial distance downstream of the turbulence grid, and 훽 is the outlet angle of the turbulence grid. Since the equation initially used to construct the turbulence grids was not significantly different than that determined by Packard, the already constructed turbulence grids were still used in the experiments, although their position was set by Equation 5.4 when installed in to the wind tunnel for the experiments.

5.2.4. Construction

5.2.4.1. Test Articles

Both foam and Corian test article profiles were manufactured by Maximum Industries, Inc. of Irving, TX. A detailed account of the build-up process of the foam and Corian sections can be seen in the work by Packard [4]. Film-cooling holes were manufactured both in-house and by Reed Prototype and Machining of Austin, TX. All steps in the machining process by the three providers was of high quality.

5.2.4.2. Turning Vanes

The ABS plastic turning vane profiles were manufactured by Boedecker Plastics of Shiner, TX. Some variations were seen in the surface finish of one of the sets of turning vanes due to different bits being used on the machine. There were also some complications in manufacturing the airfoils due a combination of their curved surface and small size, which makes it difficult to secure on the CNC machine. However, the final profiles were of acceptable quality after some light sanding was applied.

In order to adhere the 1” ABS profiles together to make the turning vanes, ABS cement was used in combination with a square jig and the thru-rods, all of which ensured the profiles were held true. The thru-rods were attached to groups of 3-4 profiles at a time after the ABS cement was placed in-between the profiles, and the jig secured the profiles in place while drying. This process was repeated several times until all of the turning vanes were constructed. The final result was lightly sanded after the glue which had squeezed out the seams was removed, resulting in smooth turning vanes.

5.2.4.3. Turbulence Rods

The horizontal turbulence rod holders were manufactured by Heart of Texas Metalworks in Manor TX out of thin in-stock steel sheet. The steel was waterjetted at the facility, which produced parts of high quality and delivered promptly. The turbulence rods themselves were purchased as rod stock from McMaster Carr and cut to size in the lab. The rods and rod holders were epoxied together to create an acceptable bond.

Chapter 6: Experimental Plan, Instrumentation, and Experimental Setup

In order to organize testing, a test plan was generated. This included the order required for completing tests in the wind tunnel. In summary, for a given 훽 configuration, the functionality of the wind tunnel was confirmed through a set of validation experiments, the flow field was set with the pressure distribution airfoil, and then the formal experiments were completed for that configuration. This process was then repeated for each 훽 configuration. The details of this test plan are shown below. Prior to completing any of the validation experiments or formal experiments in the wind tunnel, several sections of the wind tunnel and airfoils were instrumented in order to enable experimental data collection. Instrumentation was added to collect temperature and pressure measurements at various locations in the wind tunnel, which allowed for calculation of static pressure, total pressure, mass flow rates, and velocities.

Thermocouples were added which enabled temperature and density measurements. Finally, in the cases where external surface temperatures of the airfoil were measured, infrared cameras were used, which viewed the airfoils through specific viewing ports around the tunnel test section. The locations and details of all relevant instrumentation are presented in this chapter. Finally, the experimental procedures for measuring all relevant data in this project are explained below. This includes details such as the equations used to calculated all of the derived variables required for the project, details of correcting for radiation and conduction, and software processing.

6.1. Experimental Plan and Test List

6.1.1. Experimental Procedure - Wind Tunnel Validation

In order to verify functionality of some of the wind tunnel components, a number of experiments were planned prior to formal data collection. The tests focused primarily on flow uniformity of the second stage turning vanes, incidence angle through the second stage of turning vanes, and turbulence levels downstream of the turbulence rods. It was discovered through some of the validation tests that the turbulence rods themselves change the incidence angle of the flow significantly enough to require quantification of their turning angle. This was therefore also added to the validation testing list. Therefore, the following experiments were completed prior to formal testing for a given 훽 value:  Complete preliminary test of flow field around airfoil  Determine the outlet angle of the turning vanes  Determine the outlet angle of the turbulence rods  Verify correlation to determine turbulence decay downstream of rods

6.1.2. Experimental Procedure – Formal Test Data Collection

In order to complete any experiment involving the measurement of ℎ, 휂, or 휙, the appropriate flow field around the airfoil had to be set with the pressure distribution model first. For a given round of experiments at one incidence angle, the following steps were taken to ensure the flow field was set appropriately:  Reconfigure the wind tunnel incidence angle mechanism to the configuration of interest

 Install Test Article A (the pressure distribution model) in to the wind tunnel  Complete the steps outlined in Section 6.7 (Pressure Distribution Testing) 90

 Install the test article of interest (B, C, or D) in to the wind tunnel  Complete the experimental steps outlined for the appropriate experiment

6.1.3. Complete Experimental Test List

The following experiments were completed in support of the project as summarized in Table 6.1.

Table 6.1: A summary of the tests performed for this project.

β=-25° β=-35° Flowfield Validation   Turning Vane Validation   Turbulence Rod Validation   Hole Discharge Coefficients   Pressure Distribution   Heat Transfer Coefficient   Adiabatic Effectiveness   Overall Effectiveness  

6.1.4. Experimental Procedure – Nominal Testing Conditions

Experiments were all performed at 305K with a 5.48 m/s inlet flow velocity

(corresponding to an inlet Reynolds number of 푅푒퐶푎푥 =120,000. In order to estimate flow rates for the piping system used in the study, a nominal velocity ratio condition was established for the nine rows of holes in the test model. The nominal conditions which were to be bracketed by the final tests can be seen in Table 6.2. However, as the hole discharge coefficients were individually measured prior to completing the final experiments, the actual velocity ratios listed in the following table are not exactly those completed during testing. The final velocity ratios can be seen in the results section immediately before the results for each individual test, as there was an influence on the

91 velocity ratios due to slight differences in each model manufactured as well as due to incidence angle. Turbulence levels for the heat transfer coefficient experiments were either at Tu=~1% or Tu=5%, depending on the test. The corresponding inlet incidence angle 훽 and engine inlet angle with respect to its nominal condition, 푖 can be seen in Table 6.3. Turbulence levels for the film cooling experiments were set at Tu=5%. The density ratio was set at a constant DR=1.2 for all tests. Incidence angles studied determined by PIV are shown in Table 6.3.

Table 6.2: A summary of the nominal target velocity ratios to be bracketed during the test.

Nominal Target Velocity Ratios PS1 4.55 PS2 2.28 SH1 2.23 SH2 2.19 SH3 2.23 SH4 2.36 SS1 1.72 SS2 1.34 SS3 1.66 Table 6.3: A summary of the inlet conditions studied.

Rig Inlet Engine Inlet Case Angle, 풊 Turbulence Inlet ReCax Angle, 휷

-35° High Tu -30.1° 0.1° 5.0% 120,000

-25° High Tu -21.2° -8.8° 5.0% 120,000

-35° Low Tu -33.7° 3.7° 0.6% 120,000

-25° Low Tu -25.0° -5.0° 0.6% 120,000

6.2. Instrumentation

6.2.1. Mainstream Pressure and Temperature Measurements

In order to collect mainstream pressure and temperature measurements, one permanent and one temporary pitot-static probe were installed in the tunnel, and three gas thermocouple probes were installed around the base of the instrumented airfoil, as seen in Figure 6.1. The permanent (upstream) pitot-static tube was installed 1 chord length upstream of the first stage of turning vanes. This location was chosen since the contraction nozzle area with respect to downstream distance was essentially constant at this location, but the probe was still far enough upstream of the turning vanes that their influence on the velocity was insignificant. The downstream pitot static probe was installed through a port on the adjustable wall. The three thermocouples were installed in to the bottom of the test section through the bottom of the tunnel and protruded in to the flow by about 50mm.

Figure 6.1: A schematic of the wind tunnel contraction nozzle and test section, showing the location of the thermocouples and pitot-static tubes.

6.2.2. Coolant Loop Flow Rate and Temperature Measurements

Flow rate and temperature measurements in the coolant loop were primarily made within the straight pipe sections downstream of the heat exchanger and upstream of the airfoil. A schematic of the instrumentation locations can be seen in Figure 6.2. Pressure taps were located immediately upstream and downstream of the orifice plates, which allowed for measurements of static pressure and a pressure differential across the orifice plates when connected to pressure transducers. Temperature measurements were made downstream of the orifice plates and were used in conjunction with the pressure measurements to calculate density and mass flow rate through the orifice plates. The

94 orifice plate pressure differentials in particular were used extensively in calculations of film-cooling row flow rates, discharge coefficients, and velocity ratios, the values of which are discussed in the results section. Pressure taps and gas thermocouples were also located about 2cm upstream of the base of the airfoil, which were used for density and discharge coefficient calculations.

Figure 6.2: A schematic of the coolant loop under the wind tunnel, showing the locations of the pressure taps and thermocouples which were used to measure flow rates and temperature measurements for discharge coefficient and film-cooling experiments.

6.2.3. IR Camera Locations

For measurements involving the external surface temperature of an instrumented airfoil, IR cameras were placed in various locations either on or next to the wind tunnel

95 test section to view the external airfoil surface through salt crystal (NaCl) or zinc selenide (ZnSe) ports transmissive in the relevant IR spectra. A schematic of the IR camera and viewing port locations for both the heat transfer coefficient tests as well as the adiabatic film and overall effectiveness measurements can be seen in Figure 6.3. Although there were actually five cameras used in the heat transfer coefficient tests (which were performed first) the fifth camera in that case was not used since there was sufficient overlap between the four cameras. The IR cameras were repositioned to the configuration as seen in Figure 6.3 on the right side for the 휂 and 휙 tests performed later. This allowed for measurements further downstream on the pressure side and also expedited testing, since the camera labeled C on the left of Figure 6.3 limited accessibility to the test section on the suction-side.

Figure 6.3: A schematic of the IR camera locations for the two types of tests performed with IR cameras.

6.2.4. Pressure Transducers

In order to make pressure measurements with Test Article A (the pressure distribution model), Omega model P2650-xxx5V pressure transducers were mounted on a plywood board as seen in Figure 6.4 and then attached to the wind tunnel. Pressure tubing then connected all of the pressure taps within the pressure distribution model to the pressure transducers. This setup expedited the process of pressure distribution data collection beyond that used in previous experiments, and was a far less expensive solution than prepackaged multi-channel pressure scanners on the market. Transducers utilized to measure all other pressure transducers were located in an enclosure located

97 under the test section, and were the same Omega brand transducers except the ones used for coolant measurements, which were high-accuracy Omega brand PX653xxx5V transducers. This enclosure can also be seen in Figure 6.4

Figure 6.4: Pressure transducers used for pressure distribution measurements.

The expected measurement range of the pressure transducers were approximated prior to selecting and purchasing the appropriately sized pressure transducers for their specific measurement task (e.g. pressure distribution measurement, coolant piping pressure, mainstream velocity). As a result, pressure transducers with pressure ranges including 0-125 Pa, 0-500 Pa, -1200Pa-1200 Pa, and 0-5000Pa were used.

6.2.5. Data Acquisition System

All data acquisition for pressure and temperature measurements was accomplished with data acquisition hardware from National Instruments. Instrumentation was connected to one of four NI DAQ modules (NI-SCXI-1300 and NI-SCXI-1303 models) which provided a total of 128 voltage inputs. All modules contain onboard sensors for cold junction compensation of attached thermocouples. However, the 1303 models are used for the most critical precision temperature measurements as the 1303

98 enclosure was specifically designed to minimize temperature errors. Each module can collect data from a single channel at a rate of 160-330 kS/s but data collection rates were much lower since many channels of each module were collected simultaneously during testing. An NI-SCXI-1000 module multiplexor was used to house the four modules. The multiplexed data was sent to the computer through a NI-PCI-e-6321 X-Series DAQ card, which was mounted on a computer near the test section. The computer managed the data collection process, which occurred through LabVIEW 2013 or 2014, and ran an in-house LabVIEW code compatible with either version.

6.2.6. Particle Image Velocimetry

All validation PIV experiments were performed with equipment from Litron and TSI. Seed particles were introduced in to the flow with a TSI Model 9301 oil droplet generator containing olive oil. The oil droplet generator dispersed 1휇푚 seed particles in to the flow. A Litron neodymium-doped-yttrium aluminum garnet (Nd:YAG) model

Litron model YAG70-15-QTL laser, cooling unit, and supplementary lightsheet optics were used to generate the laser light sheet pulses at a 15 Hz pulse repetition rate, which highlighted the seed particles in a 2D field and enabled image capture. A TSI model Powerview Plus 2MP camera with a 2 megapixel resolution was used to capture the seed particle locations while the wind tunnel was running. Finally, a TSI 610035 Laser Pulse Synchronizer with a 1ns time resolution was used in conjunction with a computer to synchronize the laser pulse and image capture. The computer also enabled post- processing of the images through TSI Insight 3G software, calculating the required cross correlations of successive image frames in order to calculate the velocity field for image pairs according to user input. The computer and synchronizer were located near the

99 contraction nozzle on the outside of the wind tunnel loop, which was sufficiently close for connecting all the peripheral instrumentation to the computer.

6.2.7. Hotwire Anemometry

All non-PIV turbulence measurements were performed with an A.A. Lab System

AN-1003 Test module connected to a 5휇m hot-wire probe. The probe was mounted to a traverse system enabling lateral movement of the probe across the wind tunnel for measurements of turbulence intensities and length scales.

6.3. Experimental Calculations

6.3.1. Atmospheric Pressure Measurements

Atmospheric pressure was approximated by retrieving the atmospheric pressure from a local weather station. It is standard practice for weather stations to report atmospheric pressure to the public in terms of the equivalent sea level pressure. In order to account for changes in atmospheric pressure due to elevation, the International

Standard Atmosphere ‘station pressure’ (elevation corrected atmospheric pressure) within the lab:

푔푀 퐿ℎ 푅퐿 푝 = 푝 (1 − ) 6.1 푎푡푚 표 푇 + 퐿ℎ

Where 푝표 is the equivalent sea level pressure reported by the weather station, 퐿=0.0065 퐾/푚 is the temperature lapse rate, ℎ is the lab altitude (182m), 푇 is the lab 푚 temperature, 푔 = 9.81 is the gravity, 푀 = 0.029 is the molar mass of dry air, and 푠 퐽 푅 = 8.314 is the universal gas constant. The LabVIEW code was updated to 푚표푙퐾 automatically gather the weather station atmospheric pressure and apply the calculation in Equation 6.1.

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6.3.2. Mainstream Velocity Measurements

It is worth noting that the velocity upstream of the instrumented airfoil and within the test section was not directly measured during the experiments. This was due to the difficulty in placing a pitot-static tube within the upstream portion of the test section, since the inlet flow changed incidence angles for tests (requiring constant readjustment of the probe angle), and the ideal placement of the tube was upstream of the airfoil model near the turbulence rods, which generated local static and total pressure non-uniformities.

Measuring much closer to the upstream edge of the airfoils was also difficult due to the flow field non-uniformities produced in the upstream test section due to the presence of the airfoils. Therefore, as shown in Figure 6.1, mainstream velocity was monitored at the outlet of the contraction nozzle, and the continuity equation was used to calculate the contraction nozzle velocity. This procedure was shown to work extremely well during later experiments where the velocity was measured directly in the tunnel with PIV and hotwire anemometry, but the PIV and hotwire were not used during typical testing to measure 퐶푝, ℎ, 휂, or 휙. The velocity within the contraction nozzle was calculated as:

2푃푑푦푛 푉 = √ 퐶푁 휌 6.2

Where 푉퐶푁 is the contraction nozzle velocity, 휌 is the local fluid density, and

푃푑푦푛 = 푃푇 − 푃푠, where pressure differential 푃푇 − 푃푆 was measured with one of the differential pressure transducers. A contraction nozzle factor was introduced to the equation, since the velocity entering the test section was not equal to the contraction nozzle velocity. For mass continuity through the contraction nozzle and the test section:

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푚̇ 퐶푁 = 푚̇ 푇푆 = 휌퐴퐶푁푉퐶푁 = 휌퐴푇푆푉푇푆 6.3 Where 푚̇ and 퐴 are the mass flow rate and area at the location of interest. Incorporating the incidence angle 훽 in to the calculation of the area:

퐴 = ℎ푤푒푓푓 = ℎ푤퐶푁푐표푠훽 6.4

where h is the wind tunnel height, and the effective width 푤푒푓푓 is a function of the contraction nozzle width 푤퐶푁 and the incidence angle of the flow. If the incidence angle of the flow is 훽 = 0°, Equation 6.4 appropriately reduces to 퐴푇푆 = ℎ푤퐶푁. Since the density of the fluid does not change from its location at the contraction nozzle to its location at the inlet of the test section, Equation 6.3 reduces to:

퐴퐶푁푉퐶푁 ℎ푤퐶푁 푉퐶푁 푉퐶푁 푉푇푆 = = = 6.5 퐴푇푆 ℎ푤퐶푁푐표푠훽 푐표푠훽 And Equations 6.2 and 6.5 can be combined to yield the velocity in the test section:

2푃 √ 푑푦푛,퐶푁 휌퐶푁 6.6 푉 = 푇푆 푐표푠훽

This yields the functional relationship between the measured velocity 푉퐶푁, the measured test section inlet incidence angle 훽, and the test section velocity. During testing the test section velocity was monitored by calculating Equation 6.6 within LabVIEW.

6.3.3. Coolant Passage Flow Rate Measurements

In film cooling studies, the mass flow rate through was determined by measuring the pressure drop and coolant temperature across the orifice plates located in each passage according to the following equation:

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퐶푑 푚̇ = ∗ 퐴표푟𝑖푓𝑖푐푒√2휌푐,표푟𝑖푓𝑖푐푒∆푃 √1 − 훽4 6.7

Where 퐶푑 was the discharge coefficient of the orifice plate, 훽=퐷표푟𝑖푓𝑖푐푒/퐷푝𝑖푝푒 and 휋퐷2 was specified by the manufacturer, 퐴 = 표푟푖푓푖푐푒, 휌 was the density of the 표푟𝑖푓𝑖푐푒 4 푐,표푟𝑖푓𝑖푐푒 fluid flowing through the orifice plate, and ∆푃 was the difference in static pressure across the orifice plate. 퐶푑 was calibrated in-situ, and the uncertainties of 퐶푑 and 푚̇ for the film cooling experiments are presented in 0.

6.4. Experimental Setup of Initial Pressure Distribution and Stagnation Line Validation

In order to assess the capability to set the flow field properly around the airfoil, the pressure distribution model (Test Article A) was installed in to the tunnel, and the pressure distribution was set using the same experimental setup as explained later for formally setting the pressure distribution (§ 6.7.2). However, as the true 훽 angle of the flow hadn’t been determined yet, the pressure distribution set in the wind tunnel during these initial tests were not used for formal testing. Therefore, in the case of these first flow field tests, emphasis was placed on ensuring that the adjustable walls, adjustable blockages, and the airfoil itself were capable of measuring and forcing the pressure distribution of the instrumented airfoil, and the stagnation lines of all three airfoils to their desired theoretical locations. These initial pressure distributions were used during the experimental validation of the turning vane and turbulence rod outlet angle validation studies. It was shown later that the upstream flow field was not altered significantly enough by the slightly incorrect pressure distribution to warrant an iterative approach to the angle validation studies.

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6.5. Experimental Setup of Turning Vane Outlet Angle Validation

Once the first 퐶푝 and stagnation line test was completed, PIV measurements were performed in order to determine outlet angles of the turning vanes. A visual representation of the experimental setup for the PIV system can be seen in Figure 6.5. In order to measure the outlet angle with PIV, seed particles were introduced in to the test section, and the camera viewed the laser light sheet from atop of the tunnel. This enabled capture of about 1.2 pitches worth of flow field data very near to the trailing edge of the second stage of turning vanes. The test intricacies are detailed below.

Figure 6.5: A schematic of PIV setup in order to calculate the outlet incidence angle of the turning vanes.

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Figure 6.6: An image of the camera in the location used for testing.

Prior to measuring the flow field data, the laser was activated on a very low setting, and the laser light sheet plane position was manually adjusted. First, the light sheet was positioned immediately downstream of the second stage of turning vanes and the laser pan was adjusted until the left side of the sheet was aimed as in Figure 6.5 so that it did not reflect off of the turning vanes, since this reflection reduced the uniformity of the laser sheet, introducing bright spots in the flow and making the image capture more difficult. Next, the height of the light sheet was adjusted by raising and lowering the stand supporting the laser, until the light sheet produced a nearly horizontal beam across the mid-span of the tunnel. The tilt and roll of the light sheet was then adjusted with

0.5mm shims until the plane was parallel to the wind tunnel floor and ceiling (as measured by a ruler), setting the position of the light sheet. Next, a temporary 1cm x 1cm numbered paper grid pattern was installed in to the wind tunnel after the laser was deactivated. The paper grid pattern was affixed to a flat wooden surface with legs which could adjust the height and tilt of the surface. The laser was then reactivated, and the grid was adjusted until the light sheet illuminated the paper,

105 therefore guaranteeing that the grid was located in the plane where data would be collected. The grid was aligned to three turning vane trailing edges, and one of the numbered grid markings was set to intersect the trailing edge of one of the turning vanes, thus aligning one set of grid lines to be coplanar with the turning vane trailing edges, and aligning one set of grid lines to be orthogonal to the turning vane trailing edge plane. This established a convenient local coordinate system for the data collection which could be used to accurately determine spatial location of the data in the tunnel. The camera was also adjusted prior to measuring the flow field. The camera was affixed to a tripod and sat on top of the wind tunnel, as seen in Figure 6.7. The camera was adjusted so that it only viewed the light sheet through the clean, polished, acrylic cover on the rectangular viewing ports on the top of the wind tunnel, ensuring a clear view of the laser sheet through the port. The height of the camera was adjusted to ensure that the maximum possible viewing area free of any obstructions (such as the seams of the acrylic cover) was visible. The camera was then rotated until the grid appeared perfectly vertical and horizontal in the camera view, thus setting the camera roll to very near zero with respect to the coordinate system grid. A level was then used to ensure that the pitch and yaw of the camera were set so that the camera-to-grid direction vector was orthogonal to the grid plane. Finally, images of the grid were captured which allowed for a transformation from pixel coordinates to spatial coordinates and also allowed for the identification and removal of a bias error in the manual roll positioning of the camera (as the grid image could be used to quantify the actual camera roll with respect to the grid coordinate system captured). An image of one of the calibration images can be seen in Figure 6.8.

106

Figure 6.7: An image showing the PIV setup in the wind tunnel.

107

Figure 6.8: A camera image of the reference grid after the pitch, roll, and tilt of the camera was performed to align the grid to the reference image.

Once the calibration images were captured, initial estimates of the appropriate ∆푡 parameter necessary to acquire images were calculated. This was completed with the following equation:

푥푝𝑖푥푒푙푠 푥 푠푝푎푡𝑖푎푙 ∆푡 = ∗ ( ) 6.8 푉∞ 푥푝𝑖푥푒푙푠

Where 푥푝𝑖푥푒푙푠 was the desired number of pixels that the flow would traverse over the course of collecting the image pair (which in itself was dependent on the desired 푥푠푝푎푡푖푎푙 number of vectors in the image), 푉∞ was the nominal mainstream velocity, and ( ) 푥푝푖푥푒푙푠

108 was the conversion factor from camera pixel coordinates (푥푝𝑖푥푒푙푠) to the spatial coordinates (푥푠푝푎푡𝑖푎푙). This completed the initial setup of the camera and the software. In order to ensure that the airflow at the location of interest could be visualized, seed particles were introduced with the oil droplet generator in to the airflow at the imaging location (seen in Figure 6.5). The seed particles were introduced in to the top of the contraction nozzle in a small hole created for this purpose. Previous PIV experiments in the lab utilized a constant, accurately positioned low-volume flow of seed particles from a nozzle attached to the generator which crossed the laser light sheet and facilitated image capture. This method was extremely difficult since the wind tunnel cross sectional area was so large and hence there was great difficulty in precisely positioning the outlet of the seed particle generator, even after a nozzle was specifically designed and manufactured for that purpose. Instead, it was found that 3-4 seconds of high-volume seed particle flow from the generator would fill the wind tunnel with enough oil droplets so that a very uniform distribution of seed particles existed at the area of interest after the particles had circulated around the wind tunnel 2 to 3 times. The seed particle distribution persisted in the tunnel for 5-10 minutes before slowly conglomerating and settling on to inner surfaces of the wind tunnel. This high volume dispersal technique allowed for high- quality image capture with the PIV system during the 5-10 minute window.

In order to complete the test, the wind tunnel was turned on and the flow field and temperature were set to their nominal operating conditions. The seed particles were then introduced in to the flow, and a small set of images (about 50) were captured in order to assess final post-processed vector field quality. Through an iterative approach, the ∆푡 estimate calculated with Equation 6.8 was altered in conjunction with the laser brightness, the laser pulse delay, the camera exposure time, and the manual camera iris

109 until the final vector quality was acceptable. The initial settings used can be seen in Table 6.4, and the final settings are shown in the results, as they were dependent on the particular test being performed. In order to make the final measurements of the flow field, additional seed particles were introduced in to the flow, and at least 500 images were captured immediately afterwards. This was a large number of images, but significantly reduced the precision uncertainty of the angle calculation.

Table 6.4: A summary of the predicted PIV settings.

Initial PIV Settings Pulse Rep Rate Hz 14.5 Pulse Delay μs 500 Δt μs 150 Exposure μs 510 Iris Setting - 0 (Smallest) Laser A Power - 200 Laser B Power - 200

6.6. Experimental Setup of Turbulence Rod Outlet Angle Validation

The turbulence grid for the particular 훽 ≠ 0° experiment was then installed, and PIV measurements were made of the flow downstream of the turbulence grid. Test setup and measurements were very similar to those discussed in the previous section. However, the camera and laser sheet were this time aligned so that the laser did not intersect the turbulence grid. It is critical to understand that two sets of flow field were required were actually required to determine the turbulence rod outlet angles. First, flow field data was measured with the turbulence rods installed. There were significant flow field non- uniformities at this location due to the presence of the airfoils. Without moving the camera, the turbulence grid was removed, and the flow field was measured again. The data sets could be subtracted from each other to determine the change in incidence angle 110 between the two flow field cases, thus determining the deflection angle due to the presence of the turbulence rods. Finally, the originally calculated outlet angle from the turning canes could simply be added to the turbulence rod deflection angle to get the final

훽 angle. A view of the setup for the turbulence grid outlet angle experiments can be seen in Figure 6.9.

Figure 6.9: A schematic of PIV setup in order to calculate the outlet incidence angle of the turbulence grid.

6.7. Experimental Setup of Pressure Distribution Testing (Test Article A)

In order to ensure the flow field around the airfoil was matched to the desired flow field, the pressure distribution around the center airfoil was measured with Test

111

Article A (the pressure distribution model) and stagnation line locations were measured for all three airfoils. The results were compared to outlet angles and stagnation line locations predicted with a RANS CFD solver which utilized the same inlet incidence angle, and the tunnel was adjusted until the stagnation line locations and pressure distribution matched the CFD predictions.

6.7.1.1. A Note on Setting Pressure Distributions

While setting the pressure distribution and stagnation line for the first time, it was immediately noticeable that the appropriate mass flow rate through the suction-side bleed passage could not be achieved. It was determined that the loss through the suction-side passage was much higher than that of the simulation. This was due to the pressure losses incurred during the turns through the large piping on the suction-side which was not modeled during the simulation phase of the test section design. Fortunately, increasing the piping diameter along with the addition of a large 12” diameter blower in the suction- side passage, the proper flow-rates could easily be achieved for the tests. An image which includes this suction-side passage can be seen in Figure 6.10.

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Figure 6.10: A view of the suction side blower.

After installation of the fan in the suction-side passage, the above procedure was followed until a pressure distribution and stagnation line location relatively close to the one predicted by CFD was achieved. The first test after the installation of the suction-side fan proved that there was sufficient lateral movement in the adjustable walls, and blockages to force the desired pressure distribution, therefore satisfying the requirements of the initial validation test.

6.7.2. Measuring the Pressure Distribution, 𝑪푷,푻푺,푰풏풍풆풕

In order to complete the test, Article A was inserted in to the tunnel. The static pressure taps inserted in to the airfoil were routed to the pressure transducers used to measure the pressures in the test. The temporary downstream pitot-static tube was installed as seen in Figure 6.1. The predicted stagnation line location for the 훽 angle being tested was marked with a silver paint pen on the surface to the nearest 0.5 mm.

113

Stagnation line tufts made out of 50-70mm long, thin nylon thread strands were placed at 3mm increments near the stagnation line mark. The wind tunnel was then engaged and set to the nominal operating velocity and temperature. The adjustable walls and blockages were first moved from their predicted set locations until the pressure distribution matched closely to that of the CFD prediction. Then, the stagnation line location on each airfoil was determined to within 2mm. In order to do so, the 2-3 tufts clearly being affected most by the stagnation line were repeatedly manually straightened with a very long, thin rod which did not significantly obstruct the flow. This process was repeated several times in order to determine whether or not the thread strand nearest the stagnation line had a tendency to flow to the pressure or suction side of the model. The stagnation line locations were then compared to their ideal locations as marked on the airfoil, which allowed the operator to determine which passage flow rates needed to be adjusted. The adjustable walls and blockages were then readjusted until the stagnation lines matched the predictions. However, this had the effect of altering the pressure distribution on the airfoil, and so the process was an iterative one where the 퐶푝 and the stagnation lines were repeatedly adjusted until the changes made to each became insignificantly small and were matched to the CFD predictions as accurately as possible.

The methods to collect and calculate pressures and pressure measurements greatly simplified the testing procedure for Test Article A. In the past, the limited availability of pressure transducers limited the maximum number of simultaneous pressure measurements which could be made. Furthermore, pressure distribution calculation measurements were made offline after collecting data. In the new experimental design, 22 pressure taps were utilized to capture pressure measurements simultaneously, and the

114 resultant pressure distribution was calculated and plotted in real-time through the use of a newly developed LabVIEW monitoring tool, significantly streamlining the process.

6.7.3. Calculating Pressure Distribution, 𝑪푷,푻푺,푰풏풍풆풕

The desired pressure distribution with respect the inlet conditions can be calculated by:

2 푃푇,푇푆,𝑖푛푙푒푡 − 푃푆,푚𝑖푑푠푝푎푛 푉푇푆,푙표푐푎푙,𝑖푛푙푒푡 퐶푝,푇푆,𝑖푛푙푒푡 = = ( ) 6.9 푃푇,푇푆,𝑖푛푙푒푡 − 푃푆,푇푆,𝑖푛푙푒푡 푉푇푆,𝑖푛푙푒푡 However, the total pressure at the test section was not directly calculated at the inlet since no pitot-static probes were installed immediately upstream of the airfoil in the test section due to the difficulties described in Section 6.3.2. The total pressure was not assumed to be constant between the contraction nozzle measurement location and the test section inlet since the flow proceeded through two turning vane stages and the turbulence rods. In order to overcome this problem, the total pressure was measured in the middle of the passage on the suction-side of the airfoil as depicted in Figure 6.1. The total pressure at this location was equivalent to the test section inlet, and so the outlet pressure distribution could be calculated as:

2 푃푇,푇푆,표푢푡푙푒푡 − 푃푆,푚𝑖푑푠푝푎푛 푉푇푆,푙표푐푎푙,표푢푡푙푒푡 퐶푝,표푢푡푙푒푡 = = ( ) 6.10 푃푇,푇푆,표푢푡푙푒푡 − 푃푆,푇푆,표푢푡푙푒푡 푉푇푆,표푢푡푙푒푡 And this was equivalent to calculating the upstream pressure distribution with a different normalizing value (푃푇,푇푆,표푢푡푙푒푡 − 푃푆,푇푆,표푢푡푙푒푡). Therefore, the CFD 퐶푝.𝑖푛푙푒푡 used as a reference during pressure distribution testing could easily be renormalized by their inlet and outlet conditions in order to determine the equivalent inlet pressure:

2 2 푉푇푆,푙표푐푎푙,표푢푡푙푒푡 푉푇푆,퐶퐹퐷,표푢푡푙푒푡 퐶푝,푇푆,𝑖푛푙푒푡 = ( ) ∗ ( ) 6.11 푉푇푆,표푢푡푙푒푡 푉푇푆,퐶퐹퐷,𝑖푛푙푒푡 115

Where the CFD velocity values were taken to be constants in ehq equation. Therefore, the inlet pressure distribution was just the outlet pressure multiplied by a constant value, or:

푃푇,푇푆,표푢푡푙푒푡 − 푃푆,푚𝑖푑푠푝푎푛 퐶푝,푇푆,𝑖푛푙푒푡 = ∗ 퐶 = 퐶푝,표푢푡푙푒푡 ∗ 퐶 6.12 푃푇,푇푆,표푢푡푙푒푡 − 푃푆,푇푆,표푢푡푙푒푡

6.8. Experimental Setup - Heat Transfer Coefficient Testing (Test Article B)

6.8.1. Measuring the Heat Transfer Coefficient, 풉

Measurement of the heat transfer coefficient was performed with Test Article B. Once the wind tunnel temperature and velocity were set to their nominal operating conditions, the power source was turned on, providing power from the source through the inset bus bars and in to the steel shim affixed to test Article B. The current was slowly increased up to the operating current, which was typically about 100A, and provided a surface temperature as low as 320K and as high as 350K. This temperature ensured the highest accuracy of the final heat transfer coefficient measurement while reducing the chances of delamination of the steel shim from the airfoil surface. Once the mainstream temperature, mainstream velocity, and operating voltage were all set, the heat flux foil and model were allowed to reach steady state, which was monitored by reading both the internal thermocouple temperatures as well as the external IR temperatures. Upon reaching steady state (which took about 15 minutes), measurements were made in LabVIEW of the mainstream flow properties according to the standard procedure outlined in § 6.12.1. Measurements were also made of the external surface temperature through the IR cameras according to the standard IR collection procedure in § 6.12.2. In addition to these measurements, voltage drop across both the heat flux foil and a shunt resistor were recorded. Upon completion of the test, the current was again ramped down 116 slowly to prevent delamination of the heat flux foil, and once this was achieved, the wind tunnel was turned off, concluding the test. An image of the power source and the connections to the airfoil model can be seen in Figure 6.11. Measurements completed during the tests were used to calculate derived variables required for calculating the heat transfer coefficient. First, the current through the foil was calculated by measuring the voltage drop across a shunt resistor which. The shunt resistor was rated to read 1푚푉 for every 3퐴 of current running through it, which enabled conversion from voltage to current. The voltage drop across the heat flux foil was measured directly on the surface of the airfoil upstream of the bus bars but downstream of the measurement locations. This was measured here since there were some variations in the heat flux plate current flow due to its connection to the bus bar, and so measuring away from the bus bar avoided these variations. Mainstream temperatures and velocity were measured with the mainstream instrumentation. External surface temperatures were collected with IR cameras in the locations seen in Figure 6.3. Temperatures inside the airfoil were measured with the internally mounted thermocouples in Test Article B, which provided point-temperature measurements at various locations within the airfoil and allowed for quantification of conduction losses through the model, which is explained later. These temperatures were interpolated, generating a continuous temperature as function of distance around the airfoil, which simplified the final heat transfer coefficient measurements.

117

Figure 6.11: The power source, and its connections to the airfoil model.

6.8.2. Calculating the Heat Transfer Coefficient, 풉

The heat transfer coefficient was calculated through a 1-D steady state energy balance of the foil at each pixel of the IR camera data available. The balance included the uniform Joule heating within the foil, conduction through the underlying foam, radiation heat transfer to the mainstream, and convective heat transfer to the mainstream.

Figure 6.12: 1-D heat flux foil energy balance.

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The generation within the foil was equal to the heat lost through all three means of heat transfer, or:

′′ ′′ ′′ ′′ 푞푔푒푛 = 푞푟푎푑 + 푞푐표푛푣 + 푞푐표푛푑 6.13 Where

′′ 4 푞푟푎푑 = 휀휎(푇푠푢푟푓,푒 − 푇∞) 6.14

′′ 푞푐표푛푣 = ℎ표,푒(푇푠푢푟푓,푒 − 푇∞) 6.15

푘 푞′′ = − (푇 − 푇 ) 푐표푛푑 푡 푠푢푟푓,𝑖 푠푢푟푓,푒 6.16

퐼푉 푞′′ = 푔푒푛 퐴 6.17 Where 휀 was the emissivity of the flat black paint coating the airfoil (0.95), 휎 was the Stefan-Boltzmann constant, 푇푠푢푟푓,푒 and 푇푠푢푟푓,𝑖were the local external and internal surface temperatures of the airfoil, 푇∞was the mainstream temperature, ℎ표,푒 was the convective (no-film) external heat transfer coefficient, 푘 was the thermal conductivity of the underlying foam material, 푡 was the thickness of the underlying foam, 퐼 was the current provided to the foil, 퐴 was the surface area of the foil, and 푉 was the voltage drop across the area of foil just mentioned. These equations were solved for the desired variable ℎ to yield the final equation, which could be solved using the values measured during the experiment:

퐼푉 4 푘 퐴 − 휀휎(푇푠푢푟푓,푒 − 푇∞) + 푡 (푇푠푢푟푓,𝑖 − 푇푠푢푟푓,푒) ℎ표,푒 = 6.18 (푇푠푢푟푓,푒 − 푇∞) The calculations were performed within the software package created for the project. The software contains Equation 6.18 which is automatically solved for every

119 pixel of heat transfer coefficient test data. For more information on the software, please see Section 6.13.

6.9. Experimental Setup - Film-Cooling Hole Discharge Coefficient Testing

6.9.1. Measuring the Film-Cooling Hole Discharge Coefficients

Film-cooling hole discharge coefficients were also measured for each row of holes for both Articles C and D (the film-cooled models). In order to make these measurements for a particular row of holes, the metering holes of all holes not being tested were plugged with cotton swab tips and then taped over with 3M Super 88 electrical tape. In order to complete the test, the wind tunnel temperature and velocity were set to the nominal operating conditions, and the blower in the secondary loop was turned on. For the passage which fed the open row of holes, the throttling valve which controlled the flow rate through the passage was opened until a very small amount of air flowed through the passage. Passage mass flow rate, temperature, and static pressure were then recorded. The mass flow rate was then increased slightly by opening the valve, and this process was repeated until a wide range of flow rates were measured, which encapsulated the flow rate range to be tested in the film-cooling tests. This concluded testing for the particular row of holes, and the process was repeated for all rows of holes on both test articles.

6.9.2. Passage Mass Flow Rates

Mass flow rate through an orifice plate was calculated through the passage according to the following equation:

퐶푑 푚̇ = ∗ 퐴표√2휌푐,표∆푃표 √1 − 훽4 6.19

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Where 퐶푑 was the discharge coefficient of the orifice plate (determined through a calibration), 훽=퐷표/퐷푝 (퐷표 is the orifice plate diameter, 퐷푝 is the pipe diameter at the 휋퐷2 pressure tap location) and was specified by the manufacturer, 퐴 = 표, 휌 was the 표 4 푐,표 density of the fluid flowing through the orifice plate, and ∆푃표 was the difference in static pressure across the orifice plate. The 훽 values used for the project were 훽 = 0.33, 0.55, and 0.53, which coincided with orifice plates located in the front , middle, and back passages respectively. Finally, ∆푃 and 휌 were measured at the pressure tap and thermocouple locations as specified in Figure 6.2 for each orifice plate.

6.9.3. Calculating the Film-Cooling Hole Discharge Coefficients

The following equation from Gritsch [61] was used to calculate the discharge coefficient.

훾+1 훾−1 푃∞,푙표푐푎푙 2훾 2훾 푃푡,푐 훾 퐶푑,푐 = 푚̇ 푐,푙표푐푎푙/ (퐴푐,푙표푐푎푙푃푡,푐 ( ) √ [( ) − 1]) 푃푡,푐 (훾−1)푅푇푡,푐 푃∞,푙표푐푎푙 6.20

In this equation, 푚̇ 푐,푙표푐푎푙 was the mass flow rate through the row of film cooling holes, 퐴푐,푙표푐푎푙 was the total area of the film-cooling hole row, 푃푡,푐 was the internal passage pressure, 푃∞,푙표푐푎푙 was the mainstream static pressure at the location where the metering hole met the surface of the airfoil profile, 훾 was the heat capacity ratio of air, 푅 was the specific gas constant of air, and 푇푡,푐 was the temperature of the air passing through the film-cooling holes, which was measured at the base of the airfoil. Note that this essentially calculates a ‘row averaged’ discharge coefficient, since a single discharge coefficient is calculated with the equation. This has the benefits of decreased uncertainty due to increased mass flow rate through the passage (a whole row as opposed to a single hole) and also has the benefits of utilizing an average hole diameter, since some small variations were seen in hole-to-hole diameter as discussed in Chapter 8. 121

6.10. Experimental Setup - Adiabatic Film Effectiveness Testing (Article C)

6.10.1. Measuring the Adiabatic Film Effectiveness, 휼

Measurements of the adiabatic film effectiveness were performed with Test Article C in the tunnel. Tests were completed at the nominal operating mainstream velocity and temperature. Cameras were setup in the 휂 testing configuration, as seen in Figure 6.3. For a given operating condition, flow rates were held constant through each of the three channels that fed the film-cooling holes. The mass flow rate of liquid nitrogen entering the coolant loop heat exchanger was increased to provide a significant amount of flow, and a ‘cool down’ of the wind tunnel took place until the coolant temperature reached about 260K. The mass flow rate of the liquid nitrogen was then reduced, slowing the rate of cooling until the temperature of the coolant entering the airfoil model was about 250K. The wind tunnel was held at this condition for about 15 minutes until steady state was achieved. Images were then taken along with corresponding measurements of the relevant parameters (passage coolant temperatures, passage flow rates, passage pressures, internal airfoil pressures, internal temperatures, mainstream velocity, and mainstream temperature) according to the data collection procedure. The mass flow rate through the three coolant loop channels was then changed to a new operating condition and the whole process was repeated until data was collected for all operating conditions.

An example of a single round of images produced during the testing process can be seen in Figure 6.13.

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Figure 6.13: Raw temperature data from the five cameras used to measure adiabatic effectiveness.

6.10.2. Calculating the Fractional Mass Flow Rate Through Multiple Rows of Holes, F

In order to calculate the fractional flow split to each of all rows on a passage, the measured discharge coefficients for that passage were used to calculate the functional relationship between all the rows on a channel and the internal pressure of that channel. Since the lowest flow rates measured in the hole discharge coefficient measurements were quite small, small bias errors due to the low pressure reading across the orifice plate were present. As a result, the fractional mass flow rate through the holes at the lowest flow rates led to fractional mass flow rates that were not equal to 100% when calculated in this way. The bias error in the individual discharge coefficients for very low pressures was taken to be equal across all the rows in a channel, and the fractional flow rate equation was renormalized to ensure that the sum of the fractional flow rates added to 100% for all of the channels over all of the flow rates measured through this test. This resulted in a correction of error in mass flow rate of up to 4% for the lowest flow rates in 123 the front passage, but were lower (about 1-2%) for the other two passages at the lowest flow rates. A detailed uncertainty analysis of this procedure is provided in § 7.2.6.

6.10.3. Calculating the Adiabatic Effectiveness, 휼

Initial adiabatic effectiveness levels were measured with an equation very similar to the typical low-speed 휂 equation (Equation 1.5), recognizing the fact that the material used was not truly adiabatic and would contain through-wall conduction effects.

Therefore, the following equation was used:

푇 ∞ − 푇푠 휂푚푒푎푠푢푟푒푑 = 푇∞ − 푇푐,푒푥𝑖푡 6.21

Where 푇∞ is the mainstream temperature, 푇푐,푒푥𝑖푡 is the hole exit temperature, and

푇푠 is the airfoil surface temperature which was used in place of the adiabatic wall temperature, 푇푎푤 as seen in Equation 1.5. Similar to the ℎ calculations, 휂 was calculated automatically within the software package created for this project. In contrast to the ℎ calculations, the 휂 equation was not immediately corrected for conduction and radiation effects. Instead, a separate test was performed which corrected for the conduction present in the model.

6.10.4. Correcting the Adiabatic Effectiveness to Account for Conduction Effects

In order to correct for conduction effects in the model, a conduction correction experiment was completed. In this test, a number of holes in the viewing area were plugged with cotton swabs and covered with 3M Super 88 electrical tape. Flow and tunnel conditions were set identically to the adiabatic film effectiveness test, and images were also taken like the effectiveness test. However, in this case, the following equation was used:

124

푇∞ − 푇푠 휂0 = 푇∞ − 푇푐,푒푥𝑖푡 6.22

Where in this case, 휂0 is a nonzero value which represents the amount that the external surface of the low thermal conductivity model has cooled below mainstream temperature due to wall-normal conduction effects. The originally measured 휂푚푒푎푠푢푟푒푑 was then corrected using the equation

휂푚푒푎푠푢푟푒푑 − 휂0 휂 = 1 − 휂0 6.23

6.11. Experimental Setup - Overall Effectiveness Testing

Overall effectiveness tests were performed almost identically to the adiabatic effectiveness tests, but with Article D in place of Article C. However, there was a longer waiting time for Article D in order to ensure that the model reached steady state (about 30 minutes), which would take longer to occur than Article C. Also for these tests, no conduction correction was necessary since the goal of the overall effectiveness testing was to examine the effects of the conjugate heat transfer that occurs in the thermally and geometrically scaled model. Therefore, Equation 1.6 was used to calculate 휙, and is repeated here for convenience:

푇 − 푇 휙 = ∞ 푤,푒 푇∞ − 푇푐표푚푝표푛푒푛푡 𝑖푛푙푒푡 1.6 Due to the much stronger conduction effects present in the mode, the temperature profile on the outside of the model is quite different compared to the adiabatic effectiveness, and an example of temperature data from the five cameras used in the study can be seen in Figure 6.14

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Figure 6.14: Raw temperature data from the five cameras used to measure overall effectiveness.

6.12. Experimental Data Acquisition

6.12.1. Primary Measurements and Derived Variables

Measurements of temperatures and pressures from the thermocouples and pressure transducers were all captured with an in-house LabVIEW code which has been in development for a number of years in the lab. These measurements were made at a sampling rate of 500-800 Hz, and 5000-8000 samples were averaged for each measurement (resulting in a 10 second wait time per point). Doing so reduced the precision uncertainty experienced in the tests well below the levels needed to get useful data. For tests that involved IR thermography, the 10 second wait time was also convenient since it took up to 10 seconds to take an image with some of the manually operated cameras. Therefore, it was guaranteed that the IR camera measurement was taken within the envelope of the corresponding LabVIEW measurement time.

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6.12.2. IR Thermography

In order to collect data with the cameras, a standard procedure was followed. Starting with the camera viewing the pressure-side of the airfoil model, an image was taken along with measurements the relevant temperature and pressure data. This process was repeated for each camera. The process was repeated for a total of 3-5 rounds of data collection. Finally, the mass flow rate through the three coolant loop channels was changed to a new operating condition and the whole process was repeated until data was collected for all operating conditions. Since there were 5 cameras, a total of 15-25 images and measurements were taken for each operating condition.

6.13. Software Setup for HTC, 휼, and 흓 IR Measurements

A software package was developed in MATLAB for this project. This software package handled most of the required post-processing and uncertainty calculations for tests involving IR thermography. Following the theme of this project, the software was developed to be as interchangeable as possible with current and future projects, as there was not an established standard within the lab to process data. The software can handle IR input from arbitrary airfoil shapes, and can also handle input from the small wind tunnel flat plate models (in which flat plates with film cooling holes can be studied, serving as an excellent benchmarking platform) with no changes in the software. The fundamental concept of the processing algorithms focused on integrating concepts from the computer vision field with an object-oriented software design approach, simplifying complex tasks for the experimentalists. The high-level workflow can be seen in Figure

6.15, and this workflow is explained in the next section in some detail. The sub-processes highlighted in blue in the high level workflow are then explained in more detail in the following sections.

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Figure 6.15: Workflow for the software processing scheme employed for calculating HTC, 휼, or 흓 data. Blue subprocesses (Labeled A-C) are described more thoroughly in this chapter.

Airfoil coordinates and the locations of fiducial marks (as seen on Article B in Figure 5.20) are read in from an input file generated by the user. The 2D image fiducial mark locations and their corresponding real-world 3D coordinates are utilized in a direct linear transformation (DLT) algorithm as discussed by Hartley and Zisserman [62], which enables 3D to 2D and 2D to 2D coordinate system transformations . In this section of the code, the DLT algorithm is employed to convert the 3D real world fiducial mark locations on to the 2D image plane for user verification of the transformation operation,

128 and then uses these results to convert the same data on to the 2D S- and Z- coordinate systems for final processing. This process is repeated for all images taken by a camera in a given test, and is then repeated for all cameras used for a test. Camera information is then combined in order to produce a continuous set of temperature data in the S- and Z- coordinate system, contained in a single variable within the workspace memory as a rectangular grid of data, greatly simplifying future processing. Data from the whole viewing area of interest can be laterally averaged, or integer hole pitches of data can be laterally averaged, depending on the user specifications. The final information is then output to the appropriate data format depending on the sponsor specifications. Separately in this stage, the information collected with this algorithm is fed to a second function which first computes the magnitudes of the derived variables within the test, such as the flow rate through each row, local hole exit velocity, blowing ratio, momentum flux ratio, velocity ratio, etc. Finally, the same algorithm utilizes the derived value equations and magnitudes in order to calculate bias and precision uncertainty for the test, which is also saved for the experimentalist.

6.13.1. Subprocess A - Processing IR Measurements for Individual Cameras

A subprocess within the main workflow was created to process data for the individual cameras. The workflow for this image processing algorithm can be seen in Figure 6.16. First, a camera model is established for each camera which allows the 3d location of each image plane to be calculated. Having measured the locations of the fiducial marks on each model, the 3d location of each fiducial mark is also known. By using both the camera model as well as the 3d locations of each fiducial mark, the algorithm can transform the IR data to the S- and Z- coordinate system. Once this is complete, the spatially dependent calibrations can be applied to the data, and the final 129 calculations can be performed to generate either ℎ, 휂, or 휙, depending on the model being analyzed.

Figure 6.16: Workflow for subprocess A - processing IR data for a single camera.

6.13.1.1. User-Input Fiducial Marks

Each experiment contains a set of 푢 and 푣 coordinates corresponding to the row and column pixel locations of the fiducial marks as seen in the image. The locations of these fiducial marks are instrumental to the success of the image processing algorithm.

As a result, the user of the algorithm carefully manually records the 푢- and 푣- pixel 130 locations of each fiducial marks as seen through each camera during the test. During the experiments, special care was taken to ensure that the camera locations do not move during the experiments, minimizing the error in fiducial mark locations due to camera movement. However, the data is stabilized at a later point in the processing to further remove image stabilization issues. The algorithm begins by reading in the fiducial mark locations previously recorded by the user.

6.13.1.2. Pinhole Camera Model

In order to be able to transform 3D world coordinates in to 2D image coordinates, a pinhole camera model was implemented in to the processing algorithm. A pinhole camera model is a simplified camera model used regularly in machine vision and image processing algorithms. In the pinhole camera model, all rays passing through each 2D/3D point pair intersect at the center of projection, as seen in Figure 6.17. Higher order effects such as radial distortion are typically ignored in the pinhole camera model, as is the case with the algorithm presented here. However, including higher order distortions is possible in this model.

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Figure 6.17: The pinhole camera model.

6.13.1.3. Solution of the Camera Calibration Matrix – The Direct Linear Transformation Method (DLT)

In the pinhole camera model, a camera calibration matrix 퐶 is represented as a 3x4 matrix, which defines the properties of the camera. The camera calibration matrix must be solved in order to convert world coordinates to image coordinates. A solution to the following equation is therefore desired:

푃푐1 = 퐶푃3퐷 6.24

where 푃푐1 is a point on the image plane and 푃3퐷 is a point in 3D world coordinates. The equation can be expanded, first showing the columns of data collapsed in to individual variables and then fully expanded to show all the variables contained within the 3x4 matrix:

푋 푢 퐶푟표푤1 퐶11 퐶12 퐶13 퐶14 [푣] = [퐶 ] 푃 = [퐶 퐶 퐶 퐶 ] [푌] 푟표푤2 3퐷 21 22 23 24 푍 6.25 1 퐶 퐶 퐶 퐶 퐶 푟표푤3 31 32 33 34 1

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where 푢 and 푣 are the row and column pixel locations in the image coordinate system, and 푋, 푌, and 푍 are the corresponding 3D coordinates of the point in world coordinates. Two linear equations can be generated from Equation 6.25 if both the 2D and 3D locations are known:

푢퐴([퐶푟표푤3] ∙ 푃퐴) − [퐶푟표푤1] ∙ 푃퐴 = 0 6.26

푣퐴([퐶푟표푤3] ∙ 푃퐴) − [퐶푟표푤2] ∙ 푃퐴 = 0 6.27 Where the subscript 퐴 indicates a point where both the 2D and 3D locations are known. This scenario occurs for every fiducial mark on the model – the 2D locations in the image as well as the 3D locations in world coordinates are known for all visible fiducial marks. Therefore, two linear equations (Equations 6.26 and 6.27) can be generated for each visible fiducial mark. Since the camera calibration matrix contains 12 unknowns, 6 fiducial marks are needed to generate the 12 equations required to solve the camera calibration matrix.

Almost always, the number of fiducial marks visible in an image exceeds the 6 required to solve the camera calibration matrix. As a result, it is necessary to solve the following over-determined system:

−1 ∙ 푋퐴 ∙ 퐶11,퐴 ⋯ 1 ∙ 푢퐴 ∙ 퐶34,퐴 0 푢 ([퐶 ] ∙ 푃 ) − [퐶 ] ∙ 푃 = 0 → [ ⋮ ⋱ ⋮ ] = [ ] 퐴 푟표푤3 퐴 푟표푤1 퐴 ⋮ 6.28 −1 ∙ 푋푁 ∙ 퐶11,푁 ⋯ 1 ∙ 푢푁 ∙ 퐶34,푁 0

0 ∙ 퐶11,퐴 ⋯ 1 ∙ 푣퐴 ∙ 퐶34,퐴 0 푣퐴([퐶푟표푤3] ∙ 푃퐴) − [퐶푟표푤2] ∙ 푃퐴 = 0 → [ ⋮ ⋱ ⋮ ] = [⋮] 6.29 0 ∙ 퐶11,푁 ⋯ 1 ∙ 푣푁 ∙ 퐶34,푁 0

Where the number of rows in each of Equations 6.28 and 6.29 is equal to the number of fiducial marks visible in the image, and where the total number of equations is two times the number of fiducial marks visible in the image. Although there are a number 133 of methods that exist to solve over determined systems, a least squares solution to the over determined system presented here is solved within the algorithm through singular value decomposition. This yields the final matrix required to project 3D data on to the 2D image plane, solving the direct linear transformation.

6.13.1.4. Conversion of Image Data to the Original Image Plane, and to the Non- Dimensional Coordinate System

Once the camera calibration matrix is solved, Equation 6.25 can be used to map

3D coordinates directly to the 2D coordinate system. However in this case the 3D coordinates of the entire airfoil model are already known. Therefore, a sufficiently high- resolution field of 3d surface coordinates encapsulating the visible fiducial marks is back- projected on to the image with Equation 6.25. A result of the back-projection can be seen in Figure 6.18. This is utilized to verify the success of the DLT algorithm in back- projecting the 3D data on to the 2D surface –the resultant output can be used to determine if the transformation is completed successfully (e.g. if the user has accidently input incorrect fiducial mark pixel locations). With the back-projection complete, a 2D projective geometric transformation algorithm present in MATLAB (imwarp) handles conversion between the 2D coordinate systems. In this case, imwarp is used to convert between the 2D pixel grid to back- projected 2D s/C and z/H- coordinate system. The pixel data is converted to a uniformly spaced s/C and z/H grid, enabling simplified handling of the temperature data and simplifying the process of combining individual camera images. A raw image converted to the non-dimensional coordinate system can be seen in Figure 6.18. It is worth noting that a 2D to 2D DLT could have also been applied to convert data from the 2D back- projected coordinate system to the S and Z coordinate system, or even from the 2D input

134 fiducial marks directly to the S and Z coordinate system. However, it is extremely useful to visually verify user input through plotting the 3D-2D DLT approach prior to proceeding, and so the 3D-2D DLT approach plus imwarp is currently used in the software. It is also worth noting that MATLABs imwarp function would not work without the radial locations calculated through the back-projection, since imwarp can only use interpolation schemes to approximate the variation of the spatial coordinates in the image pairs, and since two rows of fiducial marks are specified by the user, the resultant imwarp function without the additional radial locations results in a very low quality approximation of the transformation.

Figure 6.18: A raw uncalibrated IR image (left) showing the back-projected S and Z locations in red, and the same image converted to the S and Z coordinate system.

6.13.1.5. Application of the Spatially-Dependent IR Temperature Calibration

Applying the spatially-dependent IR temperature calibrations to the spatially transformed (S- and Z-coordinates) images is quite simple. Since the data was converted to a uniformly spaced rectangular grid in the previous steps, each column of temperature data now corresponds to a unique S location. Furthermore, each linear calibration also corresponds to a unique S location. Therefore, both the slope and the intercept of the calibrations are interpolated with a PCHIP scheme in order to generate a unique linear

135 equation for each S/C position in the grid. The unique calibrations are applied to each row, generating a calibrated temperature map.

6.13.1.6. Conversion of Data to ℎ, 휂, or 휙

Upon applying the calibrations to the temperature data, the temperatures can be converted to either ℎ, 휂, or 휙, depending on which test was completed. Equations 6.18, 6.21, or 1.6 can be used along with the IR data and the additional temperature data collected during the test to complete the conversion. Once the data is converted, the individual data sets of temperature and either ℎ, 휂, or 휙 are saved.

6.13.2. Subprocess B - Combining Multiple HTC, 휼, and 흓 IR Measurements from Individual Cameras

6.13.2.1. Generating Consolidated Datasets

Individual camera datasets are consolidated in to one continuous dataset in the last step of the image processing algorithm. Once all of the data for the individual cameras have been processed, the minimum and maximum s/C limits for each camera are imported from a separate input file generated by the user. If the user specifies overlapping s/C limits for two adjacent cameras, the data in the overlapping region is calculated by applying a spatially-weighted average of the overlapping data. That is, a linear blending function of the following form is used:

퐷퐵푙푒푛푑푒푑 = 퐷퐿푒푓푡(1 − 휓) + 퐷푅𝑖푔ℎ푡휓 6.30 Where 휓 represents the percent distance across the spatial distance to be blended, and 퐷 represents some type of 2D data (ℎ,휂 , 표푟 휙) in the S and Z coordinate plane. When the distance between the leftmost and rightmost datasets is equal, 휓 = 0.5 Equation 6.30 simplifies to an average of the two data columns. A visual representation

136 of the blending function can be seen in Figure 6.19. This allows for the generation of a completely continuous dataset over the 5 camera region, and removes any small discontinuities in overlap regions which can be present due to the propagation of uncertainty in the surface contours of 푇, ℎ, 휂, or 휙. The blending function is typically applied over a very short region (about 6 mm) for each overlapping dataset present in the data consolidation process. Once the data is blended, the continuous dataset is saved to a file in order to facilitate simple plotting routines in MATLAB. An image comparing the initial and final images in the combining process can be seen in Figure 6.20.

Figure 6.19: A visual representation of the linear blending function utilized for overlapping camera images.

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Figure 6.20: (Above) IR images collected during an overall effectiveness test. (Below) The combined data, in S and Z coordinates, and converted to 흓.

6.13.3. Subprocess C – Processing Data for Uncertainty Calculations

While processing the data to generate the laterally averaged data, the setup files used to generate the combined images were read in to memory. The setup files contained all the test variables collected for each image, and so contained all of the information which was necessary to provide the relevant uncertainty calculations. The subprocess then calculated all of the uncertainties according to the methods discussed in 0.

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Chapter 7: Calibrations and Experimental Uncertainty Analysis

Uncertainty analysis for the all derived data was performed through application of the error propagation method of Kline & McClintock shown in Equation 7.1. Using this method, the error of a particular variable (in this case R) is achieved through partial differentiation of R with respect to each measured variable (푋𝑖) used to calculate R. If several independent variables existed within the equation, then the uncertainty was calculated as:

푁 1/2 휕푅 2 훿푅 = {∑ ( 훿푋𝑖) } 7.1 휕푋𝑖 𝑖=1 This method was typically most easily achieved using symbolic math within Matlab as explained above. Although some of the uncertainty equations are shown below, some have been omitted due to their length. However, uncertainty analysis was employed as a generic function within the analysis workflow to simplify the final data analysis steps, and Equation 7.1 was used in order to calculate most of the uncertainties. Bias and precision uncertainties were initially segregated to compare their relative magnitude until the final uncertainty calculation was made which included both the bias and precision uncertainties for the variable of interest. For all measurements with the exception of the PIV, the precision uncertainties did not contribute significantly to the total uncertainties.

7.1. Calibration Methods and Uncertainties of Calibrated Measurements

7.1.1. Atmospheric Pressure

As stated in the instrumentation section, the atmospheric pressure was approximated by compensating for local elevation with respect to the sea level equivalent pressure retrieved from the online weather station data. Applying Equation 6.1 was

139 recently shown to be accurate to within 100 pascals when comparing to a sensor that the lab temporarily had available for analysis. Therefore, uncertainty in atmospheric pressure is assumed to be 훿푃퐴푇푀=100 Pa≈0.1%.

7.1.2. Pressure Transducers

All pressure transducers with the maximum range under 2500 Pa were calibrated with a micromanometer over their operating range. The micromanometer had tick marks every 0.25Pa, which thus plays a role in the precision errors in the manometer reading. In order to perform the calibration, the level of the water with both ports open to atmospheric pressure was recorded several times in order to establish the bias error present in the micromanometer reading due to the water reservoir being under- or over- filled. The transducer of interest was then connected to the micromanometer, and at least 10 voltage readings (of at least 500 points each) were made at 10 micromanometer pressure levels in between the minimum and maximum range of the transducer, although the number of averaged measurements was as large as 20 in some cases. Each averaged measurement was considered to be an independent measurement. During the measurement process, the zero reading of both the micromanometer and the pressure transducer were checked to ensure that no bias drift had occurred. A calibration was generated for the pressure transducer by creating a linear fit of the micromanometer reading and the pressure transducer reading. The deviation from this calibration curve is due to the precision errors in the manometer readings due to the precision errors in the monometer reading, and so in order to determine the confidence interval of the calibration curve, a linear least squares fit of the resultant data is calculated as suggested by Montgomery and Runger [63]: e 140

2 1 (푥 − 푥̅) √ 푝 ± 푡훼/2,푛−2푠푦,푥 + 7.2 푛 푆푆푥푥

Where 푡훼/2,푛−2 is the t-distribution of the calculation with n-2 degrees of freedom using a 95% confidence interval, 푠푦,푥 is the standard error of the estimate, 푛 is the number of points used in the calibration 푥푝 is one of the x-coordinate (voltage) samples in the calibration 푥̅ is the mean of the x (voltage) samples, and 푆푆푥푥 is the sum-of squares of x-value (voltage) deviations from the sample mean. This actually produces an uncertainty that is dependent on the voltage since the uncertainty in the slope calculated in the linear regression makes values at the ends of the voltage calibration range less certain than points near the center of the calibration range. Since the pressure values calculated during the project were most typically collected near the center of the voltage range of the pressure transducers, the average of the confidence interval was used in future error propagations in order to simplify the analysis. This results in a conservative estimate of the uncertainty for most values measured in the project, and a liberal estimate for those values that were very near the minimum and maximum range of the pressure transducers. As a result, the confidence intervals reported were typically close to 푠푦,푥 which has shown in the past to be an appropriate representation of the uncertainties of pressure transducers used in the lab. The uncertainty estimates were calculated in this manner for all the pressure transducers utilized in the project. An image showing a typical pressure transducer calibration can be seen in Figure 7.1.

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Figure 7.1: (Left) Typical pressure transducer calibration. (Right) Resultant pressure transducer curve fit uncertainty as calculated with Equation 7.1, and the average used in later analyses.

As mentioned above, a zero drift of the pressure transducers was typically seen during the calibration process, and this zero drift also occurred during testing. Prior to running an experiment, the voltage of the pressure transducer was monitored with both transducer ports open to atmosphere (making ∆푃 = 0 across the transducer), and the ∆푃 reading was forced to read the appropriate pressure value as specified by the linear calibration performed earlier. This was done by adjusting the intercept of the calibration curve until it read the appropriate reading from the linear calibration. In order to account for bias drift during testing, the ∆푃 across all of the transducers after every test were measured again and recorded. The total ∆푃 which occurred during the test was propagated through each experiment as a bias uncertainty, but for the pressure transducers critical to measurement (flow rates and velocity measurements) the resultant bias error was typically less than 0.2 Pa. It is worth noting that this was lower than what some experimentalists in the lab reported in the past, but it was believed that the low testing bias error was due to proper wiring, grounding, and securing of all the pressure transducers and the data acquisition system for the project.

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7.1.3. Thermocouples

All thermocouples used for testing were calibrated against a high accuracy thermistor contained within a temperature-controlled glycol bath. Prior to calibration, the thermocouples to be calibrated were connected to the same data acquisition ports that they would be reading from during testing, eliminating bias in the temperature measurements due to differences in wiring of each port. Then, the thermocouples were placed in the glycol bath for calibration. For thermocouples reading temperature measurements below or near room temperature (such as the thermocouples in the coolant passages), the thermocouples were calibrated from 305K down to 248 K, which was the lowest possible temperature reading the bath could be set to before the glycol began to freeze. For thermocouples reading temperatures near room temperature or far above room temperature (such as the thermocouples attached to the heat flux plate during calibration), the thermocouples were calibrated from 305K to about 370K. A depiction of a typical thermocouple calibration can be seen in Figure 7.2.

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Figure 7.2: Typical thermocouple calibration.

The uncertainty of the temperature measurements was calculated using the same linear fit approach utilized in uncertainty of pressure transducers. In this case, the uncertainty in the thermocouples was on average 0.1K, which includes confidence interval of the calibration curves as well as an assumed maximum bias of 0.05K due to the bias of the thermistor within the glycol bath. It is worth noting that the reference temperature of the bath has been previously measured by Kistenmacher [64] a NIST traceable Fluke temperature meter with a thermistor probe and found to be within uncertainty of the meter/probe pair (which was 훿푇=0.013 K), and found to be uniform to within 훿푇=0.006 K at various points within the bath. However, it had been two years since that calibration, and so the 0.05K was utilized recognizing that this was a conservative estimate and would still provide acceptable accuracy during the measurement process. Upon repeating the uncertainty analysis for ~50+ thermocouples, it was found that there was never a thermocouple with an uncertainty greater than 144

푇푓표푠푠𝑖푙𝑖푧푒푑=0.1K in all cases, and those that were near 0.1K were the thermocouples calibrated at very high temperatures (for the heat flux plate measurements). In order to simplify the error propagation process due to the large number of thermocouples used in the project, 훿푇푓표푠푠𝑖푙𝑖푧푒푑 = 0.1 K was used for all thermocouples. When measuring average mainstream temperature within the wind tunnel with the three mainstream gas thermocouples, it was found that there were variations in the temperature uniformity in the wind tunnel, typically 0.2K but some times as high as 0.5K. Due to the difficulty in utilizing each thermocouple independently in order to estimate the external temperature for each side of the airfoil, an average mainstream temperature was utilized, and the systematic uncertainty of the average mainstream temperature values used during the rest of the calculations was approximated to be:

휎 훿푇∞,푣푎푟𝑖푎푡𝑖표푛푠 = 푡훼/2,3 ∗ √3 7.3 And the final uncertainty of the mainstream was taken to be

2 2 2 훿푇∞ = √훿푇∞.푣푎푟𝑖푎푡𝑖표푛푠 + 훿푇푓표푠푠𝑖푙𝑖푧푒푑 + 훿푇∞,푝 7.4

Which included the bias due to the calibration, bias due to the spatial variations within the tunnel, and precision uncertainty during the actual test.

7.1.4. Orifice Plate Discharge Coefficient, 𝑪풅,풐

Prior to completing the calibration to determine the orifice plate discharge coefficient, the wind tunnel was reconfigured. First, the cavities which fed coolant to the film-cooled model were sealed with either Test Article A (the pressure distribution model) or Test Article B (the heat transfer coefficient model), as these models did not

145 contain openings to allow coolant airflow in to the mainstream. Then, the end cap connected to the same channel as the orifice plate being tested was opened, and a long tube 90 diameters long was affixed to the end cap location. A laminar flow element was then attached to the end of the tube, and another 90 diameter long tube was affixed to the end of the laminar flow element. This effectively caused all flow through the orifice plate to pass through the laminar flow element as well. The piping upstream and downstream of the laminar flow element ensured that there were no upstream or downstream flow effects causing incorrect laminar flow element readings. Finally, a separate pressure transducer was connected to the laminar flow element, enabling measurements of the laminar element mass flow rate. The setup for the calibration can be seen in Figure 7.3.

Figure 7.3: (Left) Image of the end cap locations removed for orifice plate calibration testing. (Right) The orifice plate calibration setup.

The orifice plate discharge coefficients were then determined through a calibration process. During the calibration process, the secondary loop blower was turned

146 on with the throttling valve nearly closed, and upstream pipe pressure, orifice plate static pressure drop, laminar flow element static pressure drop, orifice plate gas temperature, and laminar flow element gas temperature were all recorded. This allowed for the calculation of 퐶푑 in a polynomial form where the independent variable is a function of the pipe Reynolds number, 푅푒퐷푃:

0.75 푛−1 0.75 푛−2 106 106 퐶푑,표(푅푒퐷푃) = 푎𝑖 [( ) ] + 푎𝑖+1 [( ) ] + ⋯ 푎푛 7.5 푅푒퐷푃 푅푒퐷푃

Where 푎𝑖 through 푎푛 were constants developed during the calibration process and

푅푒퐷푃 was the pipe Reynolds number. In order to calculate the Reynolds number, the pressure drop across the laminar flow element was used to calculate the mass flow rate based off of the equation provided by the manufacturer of the laminar flow element:

푚̇ 퐿퐹퐸 = 휌퐿퐹퐸(21.559∆푃퐿퐹퐸 − 0.189) 7.6

Where 휌퐿퐹퐸 is the density of fluid through the LFE, based on the laminar flow element, and for continuity, 푚̇ 표 = 푚̇ 퐿퐹퐸. Therefore, Reynolds number was calculated as: 4푚 ̇ 푅푒 = 퐿퐹퐸 퐷푃 7.7 휇퐿퐹퐸휋퐷푃

Where 휇퐿퐹퐸 was the dynamic viscosity of the fluid through the LFE. This solved all the variables needed to calculate Equation 7.5. Once the values were measured to calculate the first 퐶푑, the throttling valve was opened further, increasing the mass flow rate through the orifice plate and pressure transducer, and measurements were made again. This process was repeated, and the resultant 퐶푑 as a function of the orifice plate

Reynolds number, 푅푒퐷푃 over the range of 푅푒퐷푃 as in Equation 7.5 which would be measured in any future test.

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Uncertainty in the discharge coefficients was calculated by propagating uncertainties in the variables through Equation 7.5. Uncertainties in the discharge coefficients were on the order of 1-2% for the normal operating flow rates, except at the very low flow conditions. Uncertainties at the low flow conditions were dominated by the bias uncertainties of the pressure transducers used during the calibration. At the highest flow rates, the uncertainties were dominated by the calibration provided by the manufacturer of the LFE (Equation 7.6), which had its own confidence interval as provided by the manufacturer. The confidence interval of the curve fit applied in

Equation 7.5 was also determined for each passage, although the uncertainty in the fit was very small with respect to the other elemental uncertainties. The resultant discharge 0.75 106 coefficients and their uncertainties are plotted in Figure 7.4 with respect to ( ) 푅푒퐷푃 which was the independent variable used to develop the curve fits. These plots justify the use of the curve fit equation in calculating the discharge coefficient during testing.

Furthermore, the uncertainties with respect to the passage mass flow rates can be seen in Figure 7.5, where the uncertainty due to the pressure transducer bias is more apparent at the low flow rates.

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Figure 7.4: Measured 𝑪풅 for each passage and their uncertainties.

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Figure 7.5: Measured 𝑪풅 for each passage and their respective uncertainty values.

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7.1.5. IR Camera Surface Temperature, 푻풔

Surface temperatures measured with the IR camera were calibrated with surface thermocouples external to the airfoil model. Two rounds of calibrations were completed since the IR camera setup was unique to the non-film cooled IR measurements (ℎ0) as well as the film-cooled experiments (휂, 휂0, 휙). This was also required since the temperature range for the two types of tests did not overlap (e.g. 푇푠,ℎ0 ≈ 320K-350K,

푇푠,휙 ≈250K-305K).

7.1.5.1. Calibration for ℎ0

Calibrated surface thermocouples were attached to Test Article B with double- sided scotch tape between the heat flux surface and the surface thermocouple lead, and a piece of black electrical tape was placed on top of the thermocouple lead. A total of 12 thermocouples were placed on the model, with one at each camera overlap region, and the rest at periodic intervals around the surface so that there were at least two thermocouples in view of every camera. Thermocouples were placed most densely at the showerhead region of the airfoil in order to capture viewing angle effects in the high curvature region of the showerhead. The test article was then placed in to the wind tunnel. The calibration started by setting the test section velocity to a very low speed (1-2 m/s) and setting temperature to its nominal condition. The heat flux plate was then energized with the current source and several steady-state thermocouple and IR temperature measurements were collected over a range of current levels, until a wide range of surface temperature measurements were made which bracketed the expected range of surface temperatures in formal testing. An example of a surface IR temperature measurement can be seen in Figure 7.6.

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Figure 7.6: One of the IR images collected during IR camera calibration for 풉ퟎ testing, with the surface thermocouples used during the calibration visible in the image.

A calibration curve of thermocouple temperature vs. IR temperature for all of the IR cameras was then developed. In order to avoid temperature errors due to the tape affixed to the surface, IR camera temperature measurements were extracted from the images just below each thermocouple in the IR image. A linear fit of the corresponding thermocouple temperatures was used to generate calibrations for each thermocouple visible to the IR camera. The process was repeated in order to verify that there was test- to-test repeatability in the calibration, and Packard [4] used these repeat calibrations to assess the overall uncertainty in the test-to-test repeatability of the calibrations, which was about 훿푇퐼푅=0.5K for all of the cameras. This included bias due to the affixed thermocouple, the confidence interval of the linear fit, and spread in the repeat calibrations.

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Figure 7.7: An example of the IR camera 풉ퟎ calibrations, showing the variations over a number of tests.

7.1.5.2. Calibration for Film Cooling Experiments

For the film-cooled calibrations, copper coupons were adhered to the thermocouples with a thin layer of super glue and the copper and thermocouples were spray painted matte black (with the same spray paint as the airfoil models). A total of 11 of these copper coupons were taped to the surface of Article C (the low-conductivity model) at each film cooling hole, and at periodic locations in between and downstream of the holes.

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Calibrations for the film cooled model were similar to those for the ℎ0 IR camera calibration. However, in the case of the film cooling calibrations, the coolant loop was engaged and the temperature of the coolant was varied by varying the amount of liquid nitrogen in the coolant loop. Since the thermocouples were typically placed over film cooling holes, varying the temperature in the coolant loop had a direct effect on the temperature of the thermocouples, and so this was the method used to change the temperature of the thermocouples for the calibration. For the farthest downstream affixed thermocouples that were not placed over holes, the thermocouple was affixed in-line with a film cooling jet, and although it did not get as cold as the coupons directly over holes, provided an adequate amount of temperature variations in order to develop an acceptable calibration. Several set points of thermocouple and matching IR surface temperatures were measured in this way, resulting in the same linear calibration curves for each camera, and the uncertainties for the film cooled calibrations were essentially the same as those in the ℎ0 calibrations, or 훿푇퐼푅=0.5K. An example of the film-cooling hole calibration can be seen in Figure 7.8 .

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Figure 7.8: One of the IR images collected during IR camera calibration for the film-cooled experiments, with the surface thermocouples used during the calibration visible in the image.

7.1.5.3. Spatial Dependency of IR Temperature Readings

During the calibration measurements, it was found that in high curvature regions of the airfoil and in regions where the angle difference between the camera-to-surface vector and the surface-normal vector were quite large there was a significant variation in the different thermocouple calibrations for a given camera. This was quite especially in the showerhead regions and was shown to be a repeatable occurrence. It was assumed that this was due to the directional emissivity of the spray paint used on all of the models, especially at large angles. In order to overcome this, spatially dependent camera calibrations were developed for each camera. Figure 7.9 shows an example of a shower head camera calibration. When applying a spatially dependent calibration, the calibration slope and intercept at a location actually measured during a calibration was taken to be exactly that of the calibration. For measurements in between calibration locations, an interpolation of both the slope and intercept were used to determine the surface temperature. Specifically, 155 the piecewise cubic interpolation (PCHIP) scheme was utilized, as it preserves the shape of the data and respects monotonicity. This means that on intervals where the data are monotonic, the interpolation is also monotonic, and at points where data has a local extremum, so does the interpolation. This has a significant advantage over a linear interpolation, which would have produced discontinuities in the first derivative of the calibration (and so spikes would be visible in the images). It has advantages over low- order polynomial fits due to the difficulty in actually matching the variations of the calibrations generated for each camera. It also has an advantage over a high-order polynomial interpolation, which could suffer from oscillations near the end of the available interpolating interval (i.e. Runge’s phenomenon). Therefore a piecewise (spline-type) interpolation was used to overcome these problems.

156

Figure 7.9: An example of the IR camera spatial dependence in the showerhead region. (Left) the locations and representative curvature of the model in the showerhead region, and (right) application of the PCHIP interpolation scheme for calibration of a reference surface temperature of 푻=320 K seen in red.

7.2. Uncertainty Analysis of Derived Variables

7.2.1. Uncertainty in Pressure Distribution

Uncertainties in the pressure distributions were calculated for later propagation through the velocity ratio. The uncertainty in the pressure distribution was calculated at every pressure transducer, and included uncertainty in the outlet pressure transducer from the previous equation determined in Chapter 6:

푃푇,푇푆,표푢푡푙푒푡 − 푃푆,푚𝑖푑 푠푝푎푛 퐶푝,푇푆,𝑖푛푙푒푡 = ∗ 퐶 = 퐶푝,표푢푡푙푒푡 ∗ 퐶 6.12 푃푇,푇푆,표푢푡푙푒푡 − 푃푆,푇푆,표푢푡푙푒푡 And so the uncertainty becomes,

퐶 2 퐶∆푃 2 √ 푚𝑖푑푠푝푎푛 훿퐶푝,푇푆,𝑖푛푙푒푡 = ( 훿∆푃푚𝑖푑푠푝푎푛) + (− 2 훿∆푃표푢푡) 7.8 ∆푃표푢푡푙푒푡 ∆푃표푢푡푙푒푡

For a given test, uncertainty in the averaged measurements were due to the bias of the linear fits for each pressure transducer (typically 훿푃푓표푠푠𝑖푙𝑖푧푒푑=0.5 Pa), a small drift in the pressure measurements that would occur during testing (훿푃푓표푠푠𝑖푙𝑖푧푒푑=0.2 Pa), and 157 precision uncertainty in the measurements (which ranged from 훿푃푝푟푒푐=0.05-0.17 depending on whether the flow being measured was in a low or high velocity location).

For the 훽 = −30.10° case, the resultant precision and bias uncertainties in 퐶푝 for the mid span 퐶푝 readings are shown in Figure 7.10, and Figure 7.11 depicts the relative pressure distribution uncertainties at their 푆/푆푚푎푥 location.

Figure 7.10: Uncertainty in a typical pressure distribution measurement.

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Figure 7.11: Relative uncertainty in the pressure distribution measurements for the 휷 = −ퟑퟎ. ퟏ° case, where the relative uncertainty is naturally quite high near the stagnation line.

7.2.2. Uncertainty in Turning Vane Incidence Angle 휶 and Mean Flow Field Measurements with PIV, 푴̅

Uncertainty in the turning vane angle was determined through a propagation of the uncertainties of many sources of uncertainty through the PIV images. The main sources of error investigated were the uncertainty in the velocity magnitudes due to the equipment and equipment setup, uncertainty due to particle dynamics, uncertainty due to processing and uncertainty in the mean values due to sampling. The uncertainty of a representative case of downstream of the mean flow field and incidence angle 훽̅ at a turning vane wake at the 훽 = −30.10° configuration, and immediately downstream of the turning vanes was analyzed in order to gauge the uncertainty in the incidence angle.

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7.2.2.1. Uncertainty in u and v Due to Equipment Specifications

The uncertainty in velocity due to the equipment used in the analysis was taken to be a function of uncertainty introduced through determining the calibration scale physical length, calibration scale image plane length, image distortion due to aberrations in the lens, distance from the calibration scale to the lens, laser pulse timing, and accuracy of the delay generator. In order to propagate these uncertainties the scaling magnification factor 휓 can be calculated as: 푙 휆 ∗ 퐻푝𝑖푥푒푙 휓 = = 퐿 푓 Where 푙 is a distance value on the calibration grid used (in m), 퐿 is the length of 푙 in pixels as determined through an image of the grid, 휆 is the distance from the calibration scale to the lens, 푓 is the lens focal length used, and 퐻푝𝑖푥푒푙 is the physical size of a single pixel on the CCD sensor on the camera (m). The scaling magnification factor

휓 provides a conversion from pixel dimensions in to physical distance dimensions, and therefore was used to convert the flow field velocity from 푝푥/푠 to 푚/푠. Any given x- or y-direction velocity calculated in the flow field is determined through the distance traversed (in pixels) and the time difference between the given pair of camera images as specified by the operator during an experiment. Taking the uncertainty of focal length to be zero,푢 = 휓(푙, 퐿, 휆), the u-component velocity can be expressed as: ∆푥 푢 = 휓(푙, 퐿, 휆) ∗ ∆푡 And propagation of the uncertainty of all of the variables except ∆푥 (analyzed later) results in: 휕푢 2 휕푢 2 휕푢 2 휕푢 2 휕푢 2 휕푢 2 훿푢 = √( 훿푙) + ( 훿퐿 ) + ( 훿퐿 ) + ( 훿휆) + ( 훿∆푡 ) + ( 훿∆푡 ) 휕푙 휕퐿 1 휕퐿 2 휕휆 휕∆푡 1 휕∆푡 2

160

훿푙 = 05푚푚 is the uncertainty of the lines printed on the graph paper, 훿퐿1 = 1푝푥 is the uncertainty of the grid as measured in the image plane (computed from two points in the image, each with 훿푙 = 0.5푝푥), 훿퐿2 = 0.005 ∗ 퐿 was an approximated error in the image distortion due to lens aberrations as suggested by Lazar et al. [65], 훿휆 = 0.5푚푚 due to error in precisely positioning the grid within the laser plane., 훿∆푡1 = 0.5푛푠 was the laser timing jitter as reported by the manufacturer, and 훿∆푡2 = 0.5푛푠 was the synchronizer pulse generator jitter. The uncertainty in 푢 and 푦 for the equipment was very low, at 0.5% of the reading, and so was negligible. The uncertainty as it relates to the incidence angle and magnitude data was therefore also taken to be negligible.

7.2.2.2. Uncertainty in u and v Due to Seed-Particle Dynamics

Uncertainty of the flow field due to the inability of the seeding particles to actually following the flow is often difficult to determine. Ideally, the slip velocity

(푢푓푙표푤 − 푢푝푎푟푡𝑖푐푙푒) could be solved for over the entire flowfield. The calculation of the slip velocity in PIV data sets has been suggested by a number of researchers, and is detailed Lazar et al. [65]. Lazar proposed using a finite differencing scheme to approximate the acceleration terms required to solve for the slip stream velocity over the entire flow field using an assumed drag coefficient of 퐶푑 = 24/푅푒푝:

2 1 휌푝푑푝 휕푢푝 푑푥푝 휕푢푝 푑푦푝 푢푠푙𝑖푝 = 푢푓 − 푢푝 = ( + ) 7.9 18 휇푓 휕푥푝 푑푡 휕푦푝 푑푡 These equations would certainly be appropriate for the uncertainty analysis of the flow field measured in this project. However, rather than solve for the slip stream velocity and further complicate the uncertainty analysis for this data set, it was assumed that the uncertainty due to the slip velocity affecting data was negligible due to the magnitudes of the variables in Equation 7.9 being tested in this study. 161

7.2.2.3. Uncertainty in u and v Due to Image Analysis

It is also extremely difficult to fully understand the uncertainty in the image analysis techniques employed within the current project. In general, the uncertainty in the image analysis is directly related to the quality of the experimental setup, and so it has been shown that following certain experimental PIV guidelines themselves can reduce the measurement uncertainty in the analysis. The laser sheet was therefore very carefully placed parallel to the flow in the wind tunnel, and this miminized out-of-plane particle loss and thus reduced displacement errors in the image processing. The dynamic velocity range of the seed particles were maximized by utilizing an in-plane displacement at least one-quarter of the interrogation window size. This was accomplished by identifying the mean u- and v- component pixel velocity and comparing to the desired grid size. As seen

Figure 7.12, the pixel displacement per ∆푡 is actually quite small, but that the velocity magnitudes are clustered rather nicely about a central location, implying a repeatability in the measurement and showing the subpixel displacement capability of the processing algorithm. Both of these rules of thumb have the effect of increasing the signal-to-noise ratio in the FFT correlation utilized to determine the actual pixel displacement of the flow, and are thus very important to the success of the image analysis. It is also worth noting in Figure 7.12 that a number of outliers appear in the image analysis. The outliers are removed during the post-processing, as they tend to be at the very edges of the frame, where scratches occur in the viewing window, etc. The clusters are replaced by the local average of the flow field in the neighborhood around the failed vector.

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Figure 7.12: Pixel velocity for the representative case of PIV uncertainty analysis.

In addition to these steps, a brief analysis of the same data sets was performed in order to determine the variations in some processing parameters during the test. An idea of the potential errors introduced during processing can be seen in the data when comparing the predicted test section velocity as calculated with the upstream pitot static probe to the area-averaged mean velocity measured with the PIV for an integer turning vane pitch of flow. This comparison can be seen in Figure 7.13. It is shown in Figure

7.13 that the difference between the ideal and actual test section velocity is actually within 1% of the predicted value with increasing vector field density. Although the figure shows that the difference in the mean flow field with respect to the pitot static probe

163 measurement decreases with decreasing grid size, this is probably not the case, since the uncertainty in the velocity calculated with the pitot static probe is larger than 2%. It does however show that there is a small variation of the mean flow field calculation with the PIV for all different processing techniques analyzed. This also implies that the mean flow as calculated with the PIV is representative of the mean flow across the wind tunnel – the PIV measurements were taken near the center of the test section, where the pitot static probe was taken near the inner side of the wind tunnel.

Figure 7.13: Percent difference between mean velocity from PIV vs. the pitot static probe.

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7.2.2.4. Propagated Uncertainty in u and v to 훽

Finally, the uncertainty in the incidence angle is taken to be the uncertainty of the individual components of the flow propagated through the following equation:

푢 β = atan ( ) 푣 7.10

푣 2 −푢 2 훿훽 = √( 훿푢) + ( 훿푣) 푢2 + 푣2 푢2 + 푣2 7.11

There was an additional effect of bias error in the calculation of 훽. This was because the camera was not perfectly aligned to the grid during the test, and so a roll in the camera was present which was bias error in the measurement. In order to remove as much of this error as possible, the roll of the camera was measured by using the calibration image which was aligned carefully to the trailing edge of the turning vanes and was thus square to the turning vanes. The x and y pixels used to establish the magnification factor in the processing stage were saved, and these were used to determine the bias error angle, 훽푏𝑖푎푠 푒푟푟표푟, and the uncertainty in the angle, 훿훽푏𝑖푎푠,푔푟𝑖푑 the calculation of which was very similar to Equations 7.10 and 7.11:

푥 2 푦2 2 √ 푝 푝 훿훽푏𝑖푎푠,푔푟𝑖푑 = ( 2 2 훿푦푝) + ( 2 2 훿푥푝) 7.12 푦푝 + 푥푝 푦푝 + 푥푝

And 훿푥푝 and 훿푦푝 were taken to each be 1 pixel. For the analysis of this data set,

훽푏𝑖푎푠 푒푟푟표푟=1.55° and 훿훽푏𝑖푎푠,푔푟𝑖푑 ≈ 0°. This is a correction performed during the analysis of the data, since the uncertainty in the correction was low, it had no significant effect on the overall uncertainty.

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7.2.2.5. Uncertainty in the Mean Flow Field Due to Sampling

A simple root-mean-square deviation analysis was performed on the vector fields in order to calculate the uncertainty of the flow field due to the calculation of the average:

푡휎 푡휎 푡휎 푡휎훽 훿푈̅ = 푢 , 훿푉̅ = 푣 , 훿푀̅ = 푀 , 훿훽̅ = √푛 √푛 √푛 √푛 7.13 And it is clear from this equation that uncertainty in any of the flow field contour plots will be higher in high turbulence regions. Furthermore, the uncertainty in the mean will vary depending on the number of images taken (n). In the current analysis, 푛 was only counted if the vector field was successfully calculated for the image pair. That is although the average included failed vectors which replaced by nearest-neighbor interpolation, the sampling uncertainty analysis did not. This rightfully produces higher uncertainty in locations where the flow field was interpolated more often. A comparison of the sampling uncertainties for mean data processed with four grid-sizes can be seen in Figure 7.14 through Figure 7.17. In the first case, a single pass

128x128 interrogation region with 50% overlap in adjacent flow field regions was processed. Then, a 2nd pass was applied at a 64x64 interrogation region with a 50% overlap after the first pass was completed. This process was repeated for a 3rd pass at 32x32 and finally a 4th pass at a 16x16 interrogation region, and the resultant uncertainty in the mean u-component velocity can be seen in these figures.

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Figure 7.14: (Top) Mean 푼̅ and (Bottom) uncertainty due to sampling.

167

Figure 7.15: (Top) Mean 푼̅ and (Bottom) uncertainty due to sampling.

168

Figure 7.16: (Top) 푴̅ and (Bottom) uncertainty due to sampling.

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Figure 7.17: (Top) 휷̅ and (Bottom) uncertainty due to sampling.

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7.2.2.6. Combined Uncertainties

Total uncertainty in the flow field was assessed by the root-sum-of-squares of all the uncertainties discussed so far. This includes uncertainty in all of the equipment, particle flow physics, sampling, and image analysis. For each respective variable of interest:

2 2 2 2 훿푇표푡푎푙 = √훿푒푞푢𝑖푝푚푒푛푡 + 훿푝푎푟푡𝑖푐푙푒푠 + 훿푠푎푚푝푙𝑖푛푔 + 훿푝푟표푐푒푠푠𝑖푛푔 7.14

And this resulted in an uncertainty in inlet incidence angle of ~0.2-0.4° depending on the test, since the uncertainty in the 훽 levels was taken from the low turbulence regions in the PIV flow field. However, it is important to note that the largest uncertainty in the flow was due to the number of images taken during the analysis. This is an uncertainty that can be reduced to a very small value given enough time. Unfortunately due to the time it takes to complete and experiment with the PIV, this is sometimes not easily done. For flow fields downstream of the turbulence grids, were the turbulence was naturally higher than what was seen in this representative case, even more images than this case (500 images) were taken in order to drive down the uncertainty even farther. The ultimate uncertainty of the analysis was dominated by the sampling uncertainty, and was taken to be about 0.2° for this data set (as taken from the lowest-turbulence are in- between the wakes of the turning vanes) which was acceptable for the experiments. It is worth noting that this may be a conservative estimate, since the turbulence levels between the wakes were not measured in exactly the same spot with another reference.

7.2.2.7. Uncertainty of Turning Angle Due to Presence of Turbulence Rods

Uncertainty in the turning angle due to the turbulence rods was performed in much the same manner, although two sets of data were taken as discussed in the

171 experimental setup. Since the turbulence rods were located farther downstream than the turning vanes in the test section, the presence of the airfoils made the flowfield non- uniform downstream of the turbulence rods. However, it was necessary to measure the flow field downstream of the turbulence rods in order to determine the deflection angle of the rods. Therefore, the PIV results were compared with CFD results since the flow field was changing significantly, and this can be seen in Figure 7.18 and Figure 7.19. For the data seen in Figure 7.18 and Figure 7.19, the incidence angle measured farthest upstream (the bottom of the figures) was shown to be much more uniform than the data measured downstream (the top of the figures). In order to determine the incidence angle with the grid in, the difference between the CFD and the PIV results with the grid in was minimized, and this value was used as the final grid-in inlet incidence angle. The final angles used during the tests can be seen in § 6.1.4, and are also presented prior to the experimental results. Uncertainty due to this process was estimated to be about 0.2-0.4° as well, and so the total inlet incidence angle was ~ 0.5°.

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Figure 7.18: Downstream measurement with PIV with no turbulence grid installed, compared to a simulation of the 33.76° inlet incidence angle in the same location that the PIV data was collected. This figure shows that the results match well downstream in a location where the flow field is changing due to the presence of the downstream airfoil.

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Figure 7.19: Downstream measurement with PIV with the turbulence grid installed, compared to a simulation of the 30.1° inlet incidence angle in the same location that the PIV data was collected. This figure shows that the PIV and simulation results match, and that the 30.1° inlet angle with the grid installed was the appropriate determination.

7.2.3. Uncertainty in External No-Film Heat Transfer Coefficient, 풉ퟎ,풆

Uncertainty in the no-film heat transfer coefficient was performed by Packard [4]. The uncertainty analysis included all sources of measurement uncertainty required to solve Equation 6.18, which is repeated here for convenience:

퐼푉 4 푘 퐴 − 휀휎(푇푠푢푟푓,푒 − 푇∞) + 푡 (푇푠푢푟푓,𝑖 − 푇푠푢푟푓,푒) ℎ표,푒 = 7.15 (푇푠푢푟푓,푒 − 푇∞) In the analysis of the uncertainty in Equation 6.18, the uncertainty in the current and voltage measurements were lumped in to one term, 훿ℎ0,푒,𝑖푛푠푡, and the uncertainty in 푘, 휀, 휎, and 푡 were taken to be negligible. The rest of the uncertainty terms and the total uncertainty in the measurement 훿ℎ0,푒 can be seen Table 7.1. 174

It is important to note that in some tests, the theoretically uniform heat transfer coefficient appeared to 3-4 periods of radial temperature non-uniformity variations across the surface imaged. In this case, the uncertainty in the ℎ0,푒 was taken to be: 2휎 훿ℎ0,푒,푣푎푟 = √푛푝푒푟𝑖표푑푠 7.16

Which was lumped in to the uncertainty RSS analysis as seen in Table 7.1. It is worth noting that the uncertainty presented in the table (as initially created by Packard) includes the uncertainty in the radiation and conduction correction, which was a result of the uncertainty in the surface temperatures measured with the surface thermocouples.

Table 7.1: A summary of the uncertainty in 풉ퟎ,풆.

Measurement Uncertainty Source Units 풉ퟎ,풆/풉ퟎ,풆 (%) Uncertainty Mainstream Temperature 푇∞ 퐾 0.5 2.4 IR Surface Temperature 푇푠 퐾 0.5 2.4 2 Lateral Variations 훿ℎ0,푒,푣푎푟 푊/(푚 퐾) 0.4 1.5 2 −3 Heat Flux Foil Area 훿퐴 푚 1.3푥10 0.4 2 Current and Voltage 훿ℎ0,푒,퐼푛푠푡 푊/푚 3.8 0.6 ′′ 2 Radiation Correction 훿푞푅 푊/푚 4.1 0.6 ′′ 2 Conduction Correction 훿푞퐶 푊/푚 1.06 0.2 TOTAL 풉 ퟐ ퟏ.ퟏퟏ ퟎ,풆 /(풎 ) 3.8

7.2.4. Uncertainty in Coolant Passage Mass Flow Rate During Film-Cooling Experiments, 풎̇ 풄풐풐풍풂풏풕

The uncertainties in the coolant passage mass flow rates were determined by propagating test uncertainties through Equation 6.7, shown here for convenience:

퐶푑 푚̇ = ∗ 퐴표푟𝑖푓𝑖푐푒√2휌푐,표푟𝑖푓𝑖푐푒∆푃 √1 − 훽4 6.7

175

Where in the case of the actual film cooling experiments, 훿퐶푑(푅푒퐷푝) was known from the previous orifice plate calibrations. It is useful to note that for the Oripac orifice plates used in this project which were manufactured out of a single piece of thick steel, the 훽 value is not a function of temperature as opposed to the case when the more typical steel ‘paddle’ type orifice plates are inserted in to PVC piping and connected with a flange. Consider the linear thermal expansion equation,

훼퐿표∆푇 = ∆퐿표 7.17

Where 훼 is the thermal expansion coefficient of the material, 퐿표 is the original length of the material, ∆푇 is the temperature change, and ∆퐿표 is the change in the length.

An Oripac orifice plate has a steel pipe wall 퐷푝 and a steel orifice plate metering hole diameter 퐷표, and so Equation 7.17 can be solved for the inner and outer diameters as:

훼푠푡푒푒푙퐷표∆푇 = ∆퐷표 7.18

훼푠푡푒푒푙퐷푝∆푇 = ∆퐷푝 7.19 And assuming the orifice plate was cooled from room temperature to some ∆푇 uniformally, Equations 7.18 through 7.20 can be solved for the final value of 훽, 훽푓 as:

퐷표,푓 퐷표 − ∆퐷표 퐷표 − 훼푠푡푒푒푙퐷표∆ 푇 훽𝑖(퐷푝 − 훼푠푡푒푒푙퐷푝∆푇) 훽푓 = = = = = 훽𝑖 퐷푝,푓 퐷푝 − ∆퐷푝 퐷푝 − 훼푠푡푒푒푙퐷푝∆푇 (퐷푝 − 훼푠푡푒푒푙퐷푝∆푇) 7.20 And so the 훽 is invariant to temperature if the steel Oripac orifice plate is uniformly cooled. Although this is probably not exactly the case, the error in 훽 due to temperature is taken to be 훿훽푇 = 0. There was also some error present in the mass flow rate calculations due to the diameter of the orifice plate changing, and there is also a small amount of variation in the value of the discharge coefficient calculated with a Reynolds number assuming no 176 thermal contraction. Since the change in each of these variables was so small, they did not contribute meaningfully to the uncertainty analysis and were thus ignored. Uncertainty of the flow rates over the range of flow rates studied were dominated by the uncertainty in discharge coefficient previously calculated. The uncertainty was also affected by the orifice plate diameter uncertainty (potential machinist error in manufacturing) as well as the uncertainty in the pressure drop across the orifice plates

(especially at low blowing ratios). A summary of the elemental uncertainties calculated prior to performed the RSS analysis is shown in Figure 7.20 through Figure 7.22.

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Figure 7.20: (Top) Absolute and (Bottom) relative uncertainty in 풎̇ for the fore channel.

178

Figure 7.21: (Top) Absolute and (Bottom) relative uncertainty in 풎̇ for the middle channel.

179

Figure 7.22: (Top) Absolute and (Bottom) relative uncertainty in 풎̇ for the aft channel.

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7.2.5. Uncertainty in Hole Discharge Coefficients, 𝑪풅,풉풐풍풆풔

Uncertainties in the hole coefficients was accomplished through propagation of the uncertainties in the pressure distribution 퐶푝, the orifice plate discharge coefficients

훿퐶푑,푂, and the uncertainty in the pressure transducers used to measure the discharge coefficients during the test. The uncertainties in 퐶푑,ℎ표푙푒푠 were dominated by the uncertainties in the orifice plate discharge coefficients as well as the uncertainty in the pressure transducer at the low flow rates. The uncertainty in the discharge coefficient was on average about 2-4% of the measurement value. The uncertainties vs. their flow rates can be seen in Figure 7.23, and the final 퐶푑,ℎ표푙푒푠 values can be seen in Figure 7.24.

Figure 7.23: Uncertainties in the calculated hole discharge coefficients

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Figure 7.24: The calculated hole discharge coefficients

7.2.6. Uncertainty in the Fractional Hole Flow Splits, F

The fractional flow splits used to estimate the mass flow rate through each hole were calculated from the uncertainties in the hole discharge coefficients, 퐶푑,ℎ표푙푒푠. It is worth noting that although the uncertainties in 퐶푑,ℎ표푙푒푠 were about 4% for the lower flow rates, the uncertainties at the low flow rates were dominated by the orifice plate pressure transducer bias. Since the same pressure transducers and orifice plates used during the discharge coefficient measurements were used during the full-coverage film cooling experiments, a significant amount of the uncertainty during the film-cooling experiments could be removed. By recognizing that the total mass flow rate of coolant through the passages must exit out of the holes, any discrepancy in the total mass flow rate vs. the individual hole mass flow rate calculations from 훿퐶푑,ℎ표푙푒푠 was a result of the bias in the pressure transducer during the initial discharge coefficient calculation. A small portion of the uncertainty in the discharge coefficient tests was due to pressure transducer drift

182 during the 퐶푑,ℎ표푙푒푠 experiment, but this was only about 10% of the total bias uncertainty used to calculate 훿퐶푑,ℎ표푙푒푠. Therefore, a renormalization of the mass flow rates calculated with 퐶푑,ℎ표푙푒푠 effectively removes the bias uncertainty of the initially calculated discharge coefficients that was not due to drift in the pressure transducers. This was accomplished by renormalizing the initially estimated hole mass flow rates by instead using a fractional flow split which would always sum to 100% of the flow through the channel.

In order to generate the fractional flow split and eliminate the need for calculating the individual holes using their discharge coefficients, the process is as follows. First, the mass flow rates from the hole discharge coefficient measurements were summed together at equal internal cavity pressures in order to calculate the total mass flow rate vs. internal pressure for the range of flow rates tested. Then the individual mass flow rates were divided by the total mass flow rate. Thus, a fractional flow rate vs. total channel mass flow rate curve was generated for each channel depending on which holes the channel fed. The result is Figure 7.25, which shows the fractional flow rates which were used during the full-coverage experiments. The uncertainty in the fractional flow rate was then estimated by dividing the average uncertainties of holes tested for a given channel by the number of holes in the channel. Since the uncertainty in discharge coefficient is proportional to the mass flow rate, this resulted in a an estimate of mass flow rate of ~1% within the channels, and so an estimate in the error of the fractional flow rate equation of 1% was used for the full- coverage flow tests.

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Figure 7.25: Fractional flow rate for full-coverage testing.

7.2.7. Uncertainty in Local External Velocities Near Holes, 푽푻푺,풍풐풄풂풍

Uncertainty in the local velocity near the holes was calculated using a reformulation of the pressure distribution equation (Equation 6.9):

2푃 퐶 √ 푑푦푛,퐶푁 푝,푇푆,𝑖푛푙푒푡 휌퐶푁 푉푇푆,푙표푐푎푙 = 푉푇푆,𝑖푛푙푒푡√퐶푝,푇푆,𝑖푛푙푒푡 = 푐표푠훽 7.21

2푃푑푦푛,퐶푁퐶푝,푇푆,𝑖푛푙푒푡 푅푇푇푆 = √ 2 푃퐴푇푀푐표푠훽

And so the local velocity uncertainty includes the uncertainties due to the pressure distribution, test section inlet incidence angle, and the contraction nozzle flow properties.

The elemental uncertainties of 푉푇푆,푙표푐푎푙 were propagated through Equation 7.21 and a summary of the main contributors (훿훽, 훿∆푃퐶푁, 훿퐶푃,𝑖푛푙푒푡) to the uncertainty can be seen in

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Figure 7.26 for each hole. Figure 7.27 shows the relative total uncertainty of the local velocity calculated for each hole. Propagated precision uncertainties for all variables were analyzed and found to be insignificant when compared to the bias uncertainties and only the bias uncertainties are presented here. However, a large uncertainty in the local velocities measured during the project is immediately noticeable for the showerhead holes in Figure 7.26 and Figure 7.27. This is due to the extremely low velocity near the showerhead holes, and since the definition of the velocity ratios for the showerhead holes was includes the approach velocity as opposed to this local velocity, does not play a role in the final uncertainty of the velocity ratio. Local velocity uncertainties for the non- showerhead holes were much lower, around 2-3% for a typical test as seen in Figure 7.27.

Figure 7.26: Relative elemental uncertainty of the main contributors to 푽풍풐풄풂풍 plotted for each film cooling hole row on the model.

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Figure 7.27: Relative total uncertainty of 푽풍풐풄풂풍 plotted for each film cooling hole row on the model.

7.2.8. Uncertainty in Velocity Ratio, 푽푹

7.2.8.1. Non-Showerhead Holes Calculation

Uncertainty in the velocity ratio for the non-showerhead holes was calculated using the definition of the velocity ratio:

푉ℎ 푉푅 = 7.22 푉푙표푐푎푙 The uncertainty analysis is quite complicated as Equation 7.22 was reformulated in terms of all of the most basic variables:

퐹푇 퐶 퐷2 cos β ∆푃 푃 (푃 + 푃 ) 퐶 푑 표 √ 표 퐴푇푀 퐴푇푀 푃𝑖푝푒푠 푉푅 = 2 4 7.23 푛ℎ표푙푒푠푃퐴푇푀퐷ℎ 푇푇푆푇푂(1 − 훽 )∆푃푇푆퐶푝,푇푆,𝑖푛푙푒푡

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And this equation was used to propagate the uncertainties through for the five conditions tested in the experiments for rows PS1, PS2, SS1, SS2, and SS3 (the rows not in the showerhead region.

7.2.8.2. Showerhead Holes Calculation

For showerhead holes, the velocity ratio was calculated according to:

푉ℎ 푉푅 = 7.24 푉∞ And when representing the above equation in terms of the basic variables can be expressed as:

퐹푇 퐶 퐷2 cos β ∆푃 푃 (푃 + 푃 ) 퐶 푑 푂 √ 표 퐴푇푀 퐴푇푀 푃𝑖푝푒푠 푉푅 = 2 4 7.25 푛ℎ표푙푒푠푃퐴푇푀퐷ℎ 푇푇푆푇푂(1 − 훽 )∆푃푇푆

And this equation was used to propagate the uncertainties through for the five conditions tested in the experiments, and for the 4 showerhead rows (SH1, SH2, SH3,

SH4).

7.2.8.3. Uncertainty Results for All Holes

The results of the total and relative uncertainties in the velocity ratio for the experiments are shown below in Figure 7.28 to Figure 7.32. In general, the uncertainty in

VR was about 2%, except for the lowest test conditions, which had an uncertainty of 5%. The uncertainty for the non-showerhead holes and the showerhead holes was dominated by the local pressure distribution uncertainty, the mainstream pressure transducer reading, the channel discharge coefficient, and the orifice plate pressure transducers. The uncertainty for the showerhead holes was similar, although the uncertainty did not directly include the pressure distribution uncertainty in these cases.

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Figure 7.28: Uncertainty in velocity ratio – Condition 1.

Figure 7.29: Uncertainty in velocity ratio – Condition 2.

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Figure 7.30: Uncertainty in velocity ratio – Condition 3.

Figure 7.31: Uncertainty in velocity ratio – Condition 4.

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Figure 7.32: Uncertainty in velocity ratio – Condition 5.

7.2.9. Uncertainty in Adiabatic and Overall Effectiveness 휼 and 흓

Uncertainty in the effectiveness levels in a test was a function of the mainstream temperature 푇∞ as described previously, the airfoil surface temperature 푇푠, as also described previously, and the coolant hole exit temperature. 푇푐,푒푥𝑖푡 was measuread with a gas thermocouple calibrated to the nearest 0.1K in a glycol bath. The uncertainty in 휂 is therefore a propogation of these uncertainties: 휕휂 2 휕휂 2 휕휂 2 훿휂, 훿휙 = √( 훿푇∞) + ( 훿푇푠) + ( 훿푇푐,푒푥𝑖푡) 휕푇∞ 휕푇푠 휕푇퐶,푒푥𝑖푡

This resulted in an uncertainty for the 휂 and 휙 measurements of 훿휂 = 훿휙 = 0.01.

7.2.9.1. Conduction Corrected Adiabatic Effectiveness

As the conduction corrected adiabatic effectiveness takes data from two separate tests, the uncertainty in 휂 is a function of both tests. A pair of 2D plots showing the resultant uncertainty levels for a given final 휂 calculation derived from the two tests can

190 be shown below in Figure 7.33. 휂0 was 0.07 on average, and so the range of uncertainty in the resultant effectiveness levels was 훿휂 ≈ 0.01 − 0.015.

Figure 7.33: Uncertainty in 휼 depending on the magnitude of the conduction correction test (휼ퟎ).

Both in-test and test-to-test repeatability in these measurements was also assessed, and it was found to be similar to tests performed in the past. The repeatability analysis also confirmed that the camera calibrations held from test-to-test, even after changing incidence angles (and thus requiring the IR cameras to temporarily be moved). The in-test and test-to-test for one camera can be seen in Figure 7.34 and Figure 7.35.

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Figure 7.34: In-test repeatability of 휼 for Condition 1, far pressure-side camera

Figure 7.35: Test-to-test repeatability of 휼 for Condition 3, far pressure-side camera

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Chapter 8: Experimental Results

The purpose of this chapter is to provide a more detailed description of the validation experiments performed in the wind tunnel as well as provide a detailed understanding of the effects of incidence angle on the no-film heat transfer coefficient, adiabatic effectiveness, and overall effectiveness levels for this airfoil configuration1. In order to do so, the results of pressure distribution, the PIV incidence angle, ℎ0, 휂0, 휂, and 휙 experiments are presented thereafter. In summary, it was shown that the upstream turning vane incidence angle was adequate in redirecting the flow in a repeatable manner in to the test section, enabling the capability to set the pressure distributions in the wind tunnel to appropriate levels. It was also shown that the ℎ0 levels at the incidence angles studied were quite insensitive to the heat transfer coefficient levels even for the moderate

∆훽 studied. In contrast, the adiabatic and overall effectiveness levels contained significant differences with respect to ∆훽, especially in the showerhead. Furthermore, the

휂 and 휙 experiments revealed the optimal operating conditions for the airfoil, and revealed differences in past experiments due to the realistic internal cavity configuration utilized in the study. Finally, it was shown that the utilization of the overall effectiveness studied provided an avenue for a low-order prediction of overall effectiveness levels at conditions not studied by simply having one pair of adiabatic and overall effectiveness tests at matching conditions.

1 This chapter contains information based on articles previously published by the author: 1) Chavez, K. F., Slavens, T. N., and Bogard, D.G., 2016, “Experimentally Measured Effects of Incidence Angle on the Adiabatic and Overall Effectiveness of a Fully Cooled Turbine Airfoil with Showerhead Shaped Holes,” Proc. ASME Turbo Expo, paper GT2016-57982, Seoul, South Korea. 2) Chavez, K. F., Slavens, T. N., and Bogard, D. G., 2016, “Effects of Internal and Film Cooling on the Overall Effectiveness of a Fully Cooled Turbine Airfoil with Shaped Holes,” Proc. ASME Turbo Expo 2016, paper GT2016-57992, Seoul, South Korea. 3) Chavez, K. F., Packard, G., Slavens, T. N., and Bogard, D. G., 2016, “Experimentally Determined External Heat Transfer Coefficient of a New Turbine Airfoil Design at Varying Incidence Angles,” ISROMAC 2016, Honolulu, Hawaii. The experiments and results were completed by the author and modified from the originally published article for inclusion in this paper. 193

8.1. Pressure Distribution Results

An example of the pressure taps readings near the showerhead region vs. the computational predictions of the pressure distribution can be seen in Figure 8.1. It can be seen from these results that the pressure distribution could be set with the wind tunnel, establishing the period condition around the airfoils and appropriately setting the flow field. This was repeated for both incidence angles studied in this project.

Figure 8.1: A matched pressure distribution (of which the showerhead region is visible) for the 휷=-ퟑퟎ. ퟏퟎ° case.

8.2. Heat Transfer Coefficient Experiments

As mentioned previously, four total inlet incidence angles were tested during the heat transfer coefficient experiments. This was possible by performing tests either with or without the turbulence grids installed in the wind tunnel since the turbulence grids slightly changed the flow incidence angle in to the test section. This also had the additional effect of altering the turbulence levels, and so each incidence angle tested was tested at a unique turbulence level. The investigated inlet incidence angles and turbulence levels can be seen in the experimental setup, but are repeated here for convenience: 194

Table 8.1: A summary of the testing conditions for the heat transfer coefficient tests.

Engine Inlet Inlet 휷 휷 푹풆 푻 /𝑪 Angle, 풊 풐 풕풍풆풕 ∞,풊풏풍풆풕 풂 (°) (°) (°) (-) (%) (-) -30.1° +0.1° 5% -21.2° -8.7° 5% 72 120,000 0.06 -33.8° +3.8° 1% -25.0° -5.0° 1%

The Nusselt number of the airfoil, 푁푢퐶푎푥, was calculated as: ℎ 퐶 푁푢 = 0 푎푥 퐶푎푥 8.1 푘푎𝑖푟

Where 푘푎𝑖푟 is the thermal conductivity of the air calculated at the air film temperature:

푇 + 푇 푇 = 푠,표 ∞ 푓 2 8.2

Contour plots of the 푁푢퐶푎푥 measured at the airfoil surface can be seen in Figure 8.2 along with the plotted locations of the stagnation lines and the region of constant curvature at the airfoil in the stagnation region. The laterally averaged Nusselt number can be seen along with the stagnation line locations for each test in Figure 8.3. In the results, a peak Nusselt number of about 푁푢퐶푎푥,푚푎푥 = 630 − 650 can be seen in the low turbulence case, and 푁푢퐶푎푥,푚푎푥 = 50 for the high-turbulence case.

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Figure 8.2: Results from the heat transfer coefficient measurement experiments.

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Figure 8.3: Results from the heat transfer coefficient measurement experiments.

The low turbulence 훽 = −25.03° results contained anomalous radial variations as seen in the bottom image in Figure 8.2. This was theorized to be due to a flow disturbance most likely caused by the presence of the upstream turning vanes. In the case of heat transfer experiments at very low turbulence levels, the sensitivity to any flow field disturbances can have measurable effects on the heat transfer coefficient levels as was the case here. It is theorized the wakes of which were not as thoroughly mixed in to the main flow as was the case for the high turbulence HTC measurements. Notice that the high turbulence measurements are indeed more uniform than the low turbulence cases. An acceptable approximation for uncertainty in the laterally averaged heat transfer coefficient was accomplished by taking the standard deviation of the heat transfer coefficient along the radial direction and dividing by the number of periods of non- uniformity present, and is discussed in 0.

197

The location of the measured stagnation lines can be seen in Figure 8.2. There was significant variation in the stagnation line locations set for each incidence angle tested (as determined by CFD). The uncertainty in the measurement of the stagnation line location was much smaller at <0.005푆/푆푚푎푥. The peak heat transfer location was found to be quite insensitive to the incidence angles studied. Since the change in incidence angles only moved the stagnation line over a region which contained a constant curvature, the peak heat transfer coefficient could be thought of as insensitive to the incidence angle in this range.

Studies have been performed by Gandavarapu and Ames [66] in order to predict the effects of turbulence on the heat transfer coefficient at the leading edge above a low turbulence baseline measurement. The following equation from Gandavarapu and Ames [66] can be used to estimate the enhancement of heat transfer in the leading edge region due to turbulence:

1 3 5 푁푢 퐷 12 = 1 + 0.04 ∗ 푇푢 ∗ ( ) 푅푒퐷 8.3 푁푢0 Λf And this yielded an enhancement of heat transfer due to turbulence levels in the leading edge of 19% for the current study, which was very close to the actual value of about 15%. Therefore, the 푁푢 enhancement due to turbulence as calculated by Equation 8.3 are quite in line with the current analysis. It is also worth noting that the enhancement of turbulence seen in the experiments seems to be greatest at the leading edge, but also exists across the whole airfoil surface. This is shown to be the case in past experiments for regions of the airfoil that have not transitioned to turbulence as is the case for this study.

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8.3. Adiabatic Effectiveness at 휷 = −ퟑퟎ. ퟏ° (풊=ퟎ. ퟏ°)

This section provides the results of the adiabatic effectiveness experiments for the

훽 = −30.1° condition. The experiments were performed at five distinct velocity ratios, which were dictated by the flow rate through the three passages which fed the holes. As a

∗ result, the condition names are referred to by a showerhead averaged velocity ratio, 푉푎푣푔, since each hole actually has a distinct velocity ratio due to the local pressure distribution, hole size, and hole shape. As the hole sizes for the overall effectiveness model differed

∗ slightly from the adiabatic effectiveness model, 푉푅푎푣푔 was taken as the average of both so that a common reference for adiabatic and overall effectiveness experiments could be established. Although the table was shown in the discharge coefficient results, the table of velocity ratios is shown again below in Table 8.2 for convenience. First, results of the contour plots of 휂 are presented, and the effects due to increasing the velocity ratio through the holes are explained in detail. Then, the laterally averaged values of 휂 (휂̅) are presented and discussed thereafter.

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Table 8.2: A summary of the velocity ratios tested for the 휷=-ퟑퟎ. ퟏퟎ° 휼 experiments.

휼 ( 풕풊풄풍풆 𝑪): 풆 풊풎풆풏풕풔,풂풕 휷 = −ퟑퟎ.ퟏ° Tested Condition # (Or Average Velocity Ratio) # 1 2 3 4 5 ∗ 0.49 0.93 1.48 1.98 3.01

PS1 1.06 1.85 2.67 3.49 5.26 PS2 0.51 0.99 1.57 2.09 3.12 SH1* 0.50 0.95 1.51 2.01 3.01 SH2* 0.44 0.85 1.34 1.79 2.70 SH3* 0.47 0.91 1.44 1.92 2.90 SH4* 0.47 0.88 1.39 1.88 2.90 SS1 0.51 0.88 1.21 1.58 2.37 SS2 0.62 1.04 1.38 1.72 2.37 SS3 0.48 0.84 1.20 1.54 2.24

8.4. Adiabatic Effectiveness at 휷 = −ퟑퟎ. ퟏ° (풊=ퟎ. ퟏ°) Full Contours

The results of the experiments are shown on the following page in Figure 8.4, and there are a number of overall trends that can be seen in the contour plots. At the low velocity ratios, the effectiveness for both the pressure side rows are quite low, and the suction side rows quite high in comparison. This is consistent with past experiments by Ito et al. [67] and other researchers which have shown that for low velocity ratios, jets on concave surfaces are pulled away from the wall by the pressure gradient normal to the above the jet (which is present due to the curvature of the airfoil), but for high velocity ratios, the inertia of the jet move towards the curved surface resulting in high effectiveness levels. The effect is also reversed for jets on convex surfaces. In general terms, the showerhead holes all begin separating from the surface at very low velocity ratios as their inertia overcomes the high local pressure located near the stagnation region of the airfoil. The effect is less evident for SH4 in particular as its location is in a region

200 transitioning from a stagnation area to the highly convex curvature on the suction side of the airfoil.

Considering the individual hole 휂 values, there are a number of trends in the data. Starting at hole PS1 (the farthest left hole in the image), the increasing velocity ratio is consistent with the study just mentioned [67], and additional experiments which have shown that the pressure side concavity results in increasing effectiveness levels at high velocity ratios, such as the work performed by Dittmar et al.[68] as just one example. However, in this case, the pressure-side hole velocity ratio is extremely high at the highest velocity ratio (VR=5.26) for the high flow rate conditions, and no decrease in

∗ ∗ effectiveness was seen over this range. Conditions 푉푅푎푣푔=1.48 through 푉푅푎푣푔=3.01 also show a consistently increasing lateral spreading of the film cooling jets. A similar trend is seen for PS2, although the effects are much more subtle since the largest velocity ratio for this hole is still very high at VR=3.12, but not quite as large as that for PS1. For all of the showerhead holes (SH1-SH4), it seems that the jets are lifting off significantly from the surface (which is presumed due to how low 휂 becomes in that region) after even the lowest velocity ratio. The effects in the showerhead region are discussed in detail in § 8.9. For SS1, the film cooling jet is biased to one side of the jet, and this bias is reduced somewhat as VR* is increased. Due to the high Reynolds number in the internal passage which feeds both PS1 and PS2, it is believed that the crossflow effects through the small channel feeding SS1 and SS2, the short 푙/푑 of these two holes due to the very thin wall covering the internal SS1 and SS2 cavity, and finally the location of the hole entrance in this cavity are all significantly skewing the final coolant velocity distribution on the external surface. This effect has been seen in past studies such as that by Thole et al. [69] who noted that the positioning, l/d, and cross flow effects were critical to the resultant

201 velocity profile exiting the jet. The thinning of the jets at high velocity ratios can be seen, especially for SS3. Furthermore, it is worth noting that the effects of the individual holes are further complicated by the fact that the non-staggered array of hole rows produces a significant amount of interaction between the holes (in that the upstream row coolant is almost always in-line at least somewhat with the next row of downstream holes). There are significant portions of the airfoil which were not covered adequately by film cooling. First, the stagnation region highlighted in Figure 8.4, contains extremely low 휂 levels. When considering 휂 results alone, this indicates that the hottest spot on the airfoil will occur the engine will occur at the stagnation line. The non-uniformities are also significant in between holes. This would typically not occur as designers typically stagger rows of holes in an effort to provide a more uniform layer of coolant and reduce this effect. The results of the non-uniformities here are discussed in more detail when 휂 and 휙 are compared for 훽 =-30.1°. This is espsecially evident for holes SS1 and SS2.

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Figure 8.4: Results of testing 휼 at the 휷 =-ퟐퟏ. ퟐퟑ° angle over five VR* conditions, showcasing the effects of increasing VR* for each hole. The predicted stagnation line location is highlighted a black and white vertical line.

It is theorized that the internal impingement passage which feeds the showerhead holes and PS2 has a significant effect on their hole-to-hole uniformity. Looking at row

PS2, it is clear that there is one film cooling jet in particular which does not bias to one side of the hole, and this is on contrast to the rest of the holes in the viewable area. This location coincides with the location of the periodic spacing of the internal impingement passage holes. It is also noted that as PS2 is on the edge of the cavity which is fed by the impingement passage, and so there are presumably additional effects within the airfoil

203 which intensify the non-uniformity seen in Figure 8.4. Considering 휂 alone, this has the potential to cause negative consequences in the operating part, since this will cause radial non-uniformities in the model, which could potentially lead to premature failure. The laterally averaged data for the contour plots presented in Figure 8.4 can be seen in Figure 8.5. In this image, the effectiveness levels are clearly shown to consistently increase downstream of the pressure side holes, and reach a peak at

∗ 푉푅푎푣푔=1.48 downstream of the suction side holes. Comparing to one of the most recent adiabatic effectiveness level experiments performed by Dyson [70] which is seen in

Figure 8.6 , the showerhead effectiveness levels for the current project are quite lower due to the increased stream wise hole spacing compared to the configuration of Dyson

(∆s/D=6 for the current project, ∆푠/퐷 = 2 in Dyson), although the pitch to diameter ratios were the same. It is also potentially due to the non-staggered row configuration of the showerhead, whereas the showerhead in Dyson was staggered. It is an important result since the data from Dyson contains a study in the overall effectiveness, so although the hole shapes and spacings are different, the qualitative differences between the models can be discussed. Additionally, there are no full-coverage and showerhead shaped-hole results in the literature for direct comparison. Furthermore, in contrast to the experiment performed by Dyson, the range of velocity ratios in this experiment was larger (VR*=0.5-

3 vs. 0.83-2.5 from Dyson). As a result, the lowest velocity ratios studied for this project contained significantly larger variations in hole performance vs. Dyson. There was significantly less variation on the pressure and downstream suction sides as well, due to the hole shapes studied by Dyson.

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Figure 8.5: 휼̅ for the 휷=-30.1° experiment

Figure 8.6: 휼̅ for the full coverage experiment by Dyson [70].

8.5. Adiabatic Effectiveness - Incidence Angle Effects

This section provides the results of the adiabatic effectiveness experiments for the

훽 =-30.1° and 훽 =-21.23°experiments. The 훽 =-21.23° experiments were performed by 205 pressurizing the internal cavity of the model to the same levels as the 훽 =-30.1° results. This had a minimal effect on the total mass coolant flow rate through the model, but did have an effect on the velocity ratios through each hole, since the velocity ratio was determined by the local mainstream velocity, which was different in between the two cases. First the results of the contour plots of the 훽 =-21.2° 휂 levels are presented, and the effects due to increasing the velocity ratio through the holes are discussed. Then the data are compared to the 훽=-30.1° case through the subtraction of the contours for each data set for a given velocity ratio. The laterally averaged data for the subtracted contours are shown thereafter.

8.5.1. Adiabatic Effectiveness for 휷=-ퟐퟏ. ퟐ° (풊=-ퟖ. ퟖ°)

The results of the experiment are shown in Figure 8.7. In general, the overall trends are the same between the two experiments with the exception of the showerhead.

PS1 and PS2 have a consistent trend of increasing 휂 with increasing VR. SS1 film cooling jets are biased to one side of the jet, which is reduced somewhat as VR is

∗ increased. SS2 reaches a peak 휂 level at 푉푅푎푣푔=1.48 and thereafter its effectiveness decreases. The thinning of the jet is much more pronounced for SS3, which begins

∗ thinning out after 푉푅푎푣푔=1.48. However, considering the showerhead region, it can be seen in the contour plots that there is a dramatic increase in the effectiveness levels beyond what was seen for the 훽=-30.1° case. This is because the stagnation line was located directly over the stagnation row of holes for this configuration. This enhanced the effectiveness levels on the pressure side of the showerhead by as much as 0.3 immediately to the pressure side of the stagnation row of holes. A ‘blanketing layer’ around SH3 is especially noticeable when comparing effectiveness levels for the lowest velocity ratio and the highest velocity ratio. This enhancement persists downstream on 206 both the pressure and suction sides, but the effect is much more noticeable immediately downstream of the stagnation row of holes. When comparing to 훽 =-30.10°, the suction side effectiveness is actually lower since the SH3 row coolant is being split between the pressure and suction sides instead of all flowing towards the suction side. The enhancement of showerhead cooling due to the stagnation line position has been reported in the literature in some showerhead studies. For example, Cruse et al. [29] showed a maximum adiabatic effectiveness at a blowing ratio of M=2 in contrast to a nominal blowing ratio of M=0.5 found in previous studies for cylindrical compound angle holes, and also found a decrease in effectiveness when the stagnation line was downstream of the first hole row. The increased maximum adiabatic effectiveness was reportedly due to a steep injection angle on the holes in combination with the stagnation line location. Wagner and Vogel [30] also noticed what they called a “slot effect” when the stagnation line was moved directly over the cylindrical holes. This prompted a later investigation in to the showerhead region, as the effects of a non-symmetric, realistic airfoil showerhead could yield more insight in this effect than those performed on the leading edge models. This investigation is discussed after the current section.

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Table 8.3: A summary of the velocity ratios tested for the 휷=-ퟐퟏ. ퟐ° 휼 experiments.

휼 풕풊풄풍풆 𝑪 : 풆 풊풎풆풏풕풔,풂풕 휷 = −ퟐퟏ.ퟐ° Tested Condition # (Or Average Velocity Ratio) # 1 2 3 4 5 ∗ 0.49 0.93 1.48 1.98 3.01

PS1 0.97 1.69 2.45 3.19 4.81 PS2 0.51 0.99 1.57 2.09 3.12 SH1* 0.50 0.95 1.51 2.01 3.01 SH2* 0.44 0.85 1.34 1.79 2.70 SH3* 0.47 0.91 1.44 1.92 2.90 SH4* 0.47 0.88 1.39 1.88 2.90 SS1 0.55 0.94 1.29 1.69 2.54 SS2 0.59 0.98 1.30 1.63 2.24 SS3 0.44 0.77 1.10 1.41 2.05 The laterally averaged plot of effectiveness can be seen in Figure 8.8. The increasing effectiveness levels in the showerhead region are very apparent in the laterally averaged data, as well as the trends seen in the other rows – consistently increasing pressure side effectiveness with increasing VR, and a peak in suction-side effectiveness

∗ ∗ at 푉푅푎푣푔 = 1.48. The low 휂̅ levels on row SH3 for 푉푅푎푣푔 = 0.49 can also be clearly seen in Figure 8.8, which can potentially be attributed to a lower flow rate out of this row of holes due to the difference in external pressure for this 훽 condition. Furthermore, as

∗ ∗ 푉푅푎푣푔 was increased to 푉푅푎푣푔=3.01 , the increase in 휂̅ for the showerhead region is very noticeable in Figure 8.8.

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Figure 8.7: Results of testing 휼 for the 휷 =-ퟐퟏ. ퟐퟑ° angle at five VR* conditions, showcasing the effects of increasing VR* for each hole. The predicted stagnation line location is highlighted a black and white vertical line.

209

Figure 8.8: Results of 휼̅ for the 휷 =-ퟐퟏ. ퟐퟑ° angle at five VR* conditions, showcasing the effects of increasing VR* for each hole. The predicted stagnation line location is highlighted a black and white vertical line.

8.6. A Note on Conduction Correction 휼ퟎ

The conduction correction as discussed in the Experimental Setup did have a significant influence on the effectiveness levels of 휂. The results of the measured 휂̅0 magnitudes can be seen in Figure 8.9. In Figure 8.9, notice that there are two peaks in the measured 휂̅0. This coincides with hole PS1 and with the cavity feeding both SS1 and SS2. PS1 contains one of the highest conduction corrections due to the back-side rib turbulators within the model which result in an enhancement of the internal heat transfer coefficient of the adiabatic effectiveness model. However, they are required to ensure that the discharge coefficient and hole exit velocity distributions are matched between the adiabatic and conducting model. The suction side cavity is a smooth, very thin wall with high internal Reynolds numbers within the cavity. Thus, the enhancement in internal heat transfer coupled with the very thin wall of the cavity result in high values of through-wall conduction, even in the case of the 휂̅0 measurements where there is no coolant flowing out of the holes being investigated (there is only internal crossflow). The measured values of 휂̅0 are as high as 휂̅0 =0.15 in the region of the cavity feeding SS1 and SS2, but were typically about 0.09.

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Effects of conduction correction on the final results are according to Equation 6.23, which in essence is a renormalization of the initially measured effectiveness levels with respect to those measured with only internal cooling. The results of the difference between 휂̅ and 휂̅푚푒푎푠푢푟푒푑 can be seen in Figure 8.10. As can be seen in the figure, the magnitude of correction resulted in a reported 휂̅ that differed from the originally

휂̅푚푒푎푠푢푟푒푑 by as little as 0.02 to much as 0.13, but was on average 0.07. These values were higher than typical levels of conduction corrections performed in the same lab, but it was hypothesized that this was due to the realistic internal features and geometries enhancing the internal heat transfer coefficient more than has been measured in the past.

A comparison of the non-corrected 휂̅ (휂̅푚푒푎푠푢푟푒푑) to the corrected 휂̅ can be seen in Figure 8.12 and Figure 8.11.

The results of this experiment highlights the necessity of correction for 휂̅ in real- world experiments where the thermal conductivity of the model is not sufficiently low enough to completely remove conduction effects, especially on such a realistic model as the one studied in this project, where the goal was to increase the internal heat transfer coefficient values as much as possible.

Figure 8.9: 휼̅ퟎ correction used for both incidence angle conditions tested.

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Figure 8.10: The effect of 휼̅ퟎ on the reported 휼̅ for 휷=-30.1°.

Figure 8.11: 휼̅풎풆풂풔 풆풅 for the 휷=-30.1° experiment.

Figure 8.12: 휼̅ for the 휷=-30.1° experiment

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8.6.1. Difference in Adiabatic Effectiveness , 휼(휷=-30.1°)-휼(휷=-21.2°)

In order to emphasize the effects of the incidence angle change in the showerhead region, 휂 at 훽 =-21.2 was subtracted from 휂 at 훽 =-30.1, and the result was plotted in Figure 8.13. It immediately becomes clear when looking at Figure 8.13 that the effects of changing the incidence angle to 훽 =-30.1° from 훽 =-21,2° decreases the effectiveness

∗ on the pressure side of the showerhead by about 0.25 in 휂 at the highest 푉푅푎푣푔. The opposite effect is also present on the suction side, but is only about 0.1 in 휂 at the highest

∗ 푉푅푎푣푔. Thus the film cooling redirected on to the pressure side of the model due to the shift in incidence angle persists farther downstream on the pressure side than on the suction side. A plot of the difference in the laterally averaged effectiveness levels (∆휂̅ ) can be seen in Figure 8.14 which highlights the same effect, and the laterally averaged data for the two incidence angle conditions are shown again in Figure 8.15 and Figure 8.16 for convenience.

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Figure 8.13: The difference in 휼 levels for the 휷 =-ퟑퟎ. ퟏ° and 휷 =-ퟐퟏ. ퟐퟑ° 휼 experiments.

The results are significant in that they highlight the effects of curvature on variations in incidence angle, and also show the utility of testing a realistic showerhead at variable incidence angles rather than a symmetric leading edge model. It can be seen from the contour differences that in the showerhead region which contains a significant convex curvature, adiabatic effectiveness levels from the showerhead stagnation row of holes (SH3) persist more strongly farther downstream on the pressure side up until the point of concave curvature located at hole PS1. Similar to the typical action of a film cooling hole, the overall addition of coolant to the pressure side which contains a highly convex surface immediately downstream of the stagnation row of holes, coolant is held in 214 toward the wall due to the action of the static pressure force surrounding the film. In contrast, the suction side film travels across the relatively lower convex curvature near holes SS1 and SS2 prior to seeing a high convex curvature downstream of row SB. However, due to the mixing of the coolant after travelling ~40 diameters downstream and through two rows of holes, the effects of the increased curvature downstream of SS2 are not noticeable. The effect is therefore retained within the highly convex curvature area downstream of the stagnation row of holes along the pressure side of the airfoil.

Figure 8.14: The difference in 휼̅ levels for the 휷 =-ퟑퟎ. ퟏ° and 휷 =-ퟐퟏ. ퟐퟑ° 휼 experiments.

215

Figure 8.15: 휼̅ for the 휷=-30.1° experiment.

Figure 8.16: Results of 휼̅ for the 휷 =-ퟐퟏ. ퟐퟑ° angle.

8.7. Overall Effectiveness – 휷 =-ퟑퟎ. ퟏ° (풊=0.1°)

This section provides the results of the overall effectiveness experiments for the

훽 = −30.1° experiments. This is an expansion of film cooling studies such as those by Williams et al. [71], Nathan et al. [40], and Dyson et al. [48] in that the models have become increasingly complex, and more realistically represent gas turbine airfoils. In this case, adiabatic and overall experiments were performed with an airfoil with all shaped holes, which is quite unique, especially since showerhead designs tend to utilize cylindrical holes. The experiments were performed at five distinct velocity ratios matching the coolant flow rates to the 휂, 훽 =-30.1° experiments. The condition names

∗ refer to the showerhead averaged velocity ratio, 푉푎푣푔 just as in the 휂 tests, although

216 predicted levels of VR will be slightly different due to the accurate hole size measurements performed during the setup phase. First, results of the contour plots of 휙 are presented, and the effects due to increasing the velocity ratio through the holes are explained in detail. The laterally averaged results are presented afterwards. Next, as this is the only full-coverage overall effectiveness study to present results for an airfoil with only shaped holes, the closest avenue for comparison between full-coverage experiments is to that of Dyson [70], so this comparison is made. And finally, a comparison of the adiabatic and overall effectiveness for both models is shown for reference. The results from this section highlight the usefulness of the overall effectiveness experiments, as in this case the showerhead overall effectiveness levels are much better than the 휂 levels presented previously.

Table 8.4: A summary of the velocity ratios tested for the 휷=-ퟑퟎ. ퟏퟎ° 흓 experiments

흓 ( 풕풊풄풍풆 ): 풆 풊풎풆풏풕풔,풂풕 휷 = −ퟑퟎ. ퟏ° Tested Condition # (Or Average Velocity Ratio) # 1 2 3 4 5 ∗ 0.49 0.93 1.48 1.98 3.01

PS1 1.12 2.01 2.87 3.76 5.65 PS2 0.55 1.04 1.67 2.23 3.36 SH1* 0.55 1.04 1.67 2.22 3.37 SH2* 0.49 0.93 1.49 1.99 3.03 SH3* 0.55 1.04 1.66 2.22 3.39 SH4* 0.52 0.97 1.55 2.09 3.28 SS1 0.54 0.93 1.26 1.65 2.52 SS2 0.66 1.13 1.47 1.84 2.57 SS3 0.51 0.91 1.28 1.64 2.38

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The results of the experiment are shown in Figure 8.17, and the overall trends in variations between test conditions are discussed here. In terms of the general trends on

∗ the overall 휙 levels, it is clear that the two low 푉푎푣푔 conditions are significantly different than the rest of the plots. At the lower two flow rate conditions, there is insufficient internal flow through the model and this results in warming of the internal coolant beyond the levels required to provide low temperature film-cooling at the hole exits. As the flow rate is increased past the first two conditions, it can be seen in Figure 8.17 that there are only subtle changes in the overall effectiveness with increasing velocity ratio.

This is due to a combination of the film effectiveness changes as seen in the 휂

∗ experiments and the increased internal convection at the highest 푉푅푎푣푔 condition in the 휙 experiments. In other words, the internal convection plays a significant role in the

∗ continual reduction of the external surface temperature at the highest 푉푅푎푣푔 levels.

218

Figure 8.17: Contour plots of 흓 magnitudes at the 휷 =-ퟑퟎ. ퟏ° condition.

For the two farthest downstream holes (PS1 and SS3), the film-cooling traces on

∗ the model are still clearly seen throughout the range of 푉푅푎푣푔 tested for the 휙 experiments. However, the complementary effect of the through-hole convection is also evident on these holes since the flow rates are so high through the serpentine passage. There are significant conduction effects (due to the in-hole convection) upstream of row

PS1 by at least 5 hole diameters. This is due to the very high flow rates through row PS1. The effects are also very clear for row SS1, and this is effect is more visible since the airfoil surface at s/D 7-15 are quite thin.

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For all of the showerhead holes (SH1-SH4), the reduced film effectiveness seen during the 휂 experiments is not as clear for all the holes in the 휙 experiments. However, the film cooling traces are still clearly evident on hole rows SH1 and SH4 in particular, but the 휙 levels stay relatively constant for conditions 3-5 as the film cooling traces disappear and the dominant heat transfer mode becomes the convection effects occurring from the increased mass flow rates at these conditions. Immediately downstream of the gill row of holes (PS2) and in between PS1 and PS2, there is also a noticeable area of much higher temperature, and the film cooling traces downstream of PS2 cannot be seen clearly. This is due to a combination of the somewhat uniform 휂 at this location as well as the presence of an internal passage wall separating the passages – as there is no coolant flowing on the opposite side of the holes downstream of PS2, the different boundary condition at this location has the effect of changing the surface temperature at this location. For the showerhead region, even though the hole spacing of s/D=6 the showerhead holes is so large, the internal impingement passage and convective effects counteract the effect of the hot-spot seen in the 휂 tests. Furthermore, although the radial non-uniformities are still present, they are significantly reduced by the radial conduction and convection effects in the matched Biot number model. In fact, the showerhead performs quite well according to the 휙 experiments as the stream wise temperatures are quite uniform and in line with the rest of the airfoil, and if one was tempted to increase the density of the showerhead holes based on the 휂 levels alone, this could result in an over-cooled showerhead region in comparison to the rest of the airfoil. However, the internal, in-hole, and film cooling effects seem well balanced in the showerhead region, and this is only apparent in the 휙 experiments. This therefore highlights the utility of the

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휙 experiments in complementing 휂 experiments, as only seeing the results from the 휂 experiments could leave one to believe that the showerhead is not performing adequately.

The laterally averaged 휙̅ can be seen in Figure 8.18 and the comparison to Dyson [70] can be made. From Figure 8.18, the previously discussed relatively uniform 휙 values are more easily seen, with variations from 휙̅ from ~0.45-0.7. This is in contrast to the results from Dyson [70], compared to variations as large as 휙=0.35-0.75 when comparing the farthest downstream pressure side hole to the showerhead region. There are also steep drop-offs of as high as 0.2 downstream of some of the holes presented by Dyson, where as the declines in effectiveness downstream of the holes in the current project are overall more gradual.

Figure 8.18: Contour plots of 흓 magnitudes at the 휷 =-ퟑퟎ. ퟏ° condition.

221

Figure 8.19: Contour plots of 흓 magnitudes from the Dyson [70] study.

Finally, in order to show the effects of the film-cooling coverage, 휙̅ was averaged in the s/D direction to produce a single total averaged 휙̅ for the whole range of s/D investigated. The results of this analysis are shown in Figure 8.20. It can be seen that 휙̅ is

∗ increased with increasing total mass flow rates very quickly up to 푉푅푎푣푔 = 1.48 and there are significant diminishing returns thereafter. This is shown in contrast to 휂̅ which

∗ begins decreasing after the same 푉푅푎푣푔 = 1.48, suggesting that the additional cooling

∗ benefits beyond 푉푅푎푣푔 = 1.48 are mostly due to the through-wall conduction facilitated by the internal turbulators.

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Figure 8.20: 흓̅ for both incidence angle conditions tested.

8.8. Effects of Incidence Angle in the Showerhead Region

This section provides the results of the additional experiments performed in the showerhead region to glean additional information about the effects of incidence angle on the adiabatic and overall effectiveness levels for this model. First, at the 훽=-21.2° configuration, the stagnation line was manually shifted towards the suction and pressure side by adjusting the flow blockages in the tunnel while an adiabatic effectiveness experiment was taking place. It was shown during this time that the effects of the enhanced effectiveness at the showerhead region occurred most strongly for the

∗ ∗ 푉푅푎푣푔=1.48 and 푉푅푎푣푔=1.98 conditions. Thus, effectiveness levels were measured with the stagnation line in 4 additional positions for these two velocity ratio conditions. This resulted in a total of 6 positions (two additional stagnation line positions from the

223 nominal stagnation line positions for the two configurations) which were investigated further. Effective inlet incidence angles were estimated by measuring the location on the processed adiabatic effectiveness data and performing a sweep of incidence angles in CFD in order to determine what inlet incidence angle from CFD matched the stagnation line location measured during the experiment. This is in contrast to the other two angles which utilized both PIV, 퐶푝, and stagnation tufts in order to verify the overall flowfield inlet incidence angle and stagnation line position. After this experiment was completed,

∗ an additional overall effectiveness experiment at the 훽=-21.2°, 푉푅푎푣푔=1.98 was performed in order to investigate the effects of incidence angle on the showerhead region of the matched Biot number model, and these results are presented after the stagnation line shift experiments.

8.9. Effects of Stagnation Line Shift for Conical Shaped Holes

The estimated effective inlet incidence angle magnitudes where adiabatic effectiveness levels were measured can be seen in Table 8.5, and a contour plot of the movement of the stagnation lines is shown in Figure 8.21. Note that Position 1 could not be measured with the process used to determine the other angles (as the stagnation line was not on top of a row of holes, making it impossible to determine its location) during the test. Since that inlet incidence angle could not be estimated, it is referred to as

훽<−20.1°. In particular, the significant result of this section is that there is a clear and consistent trend of elevated effectiveness in the showerhead region for any stagnation line location within the footprint of the shaped holes in the showerhead region. This is in contrast to a cylindrical hole that does not have a hole breakout larger than the metering

224 hole, and thus the effect of the stagnation line on the enhancement of effectiveness is presumably quite less in the case of cylindrical holes.

Table 8.5: A summary of the effective inlet incidence angles studied during the stagnation line shift test.

Position 휷 (°) 풊 (°) 1 <-20.1 <-10 2 -20.1 -10 3 -21.2 -8.9 4 -21.7 -8.4 5 -23.5 -6.6 6 -30.1 0

. It is clear that as the stagnation line is passed over the conical holes, there is a significant increase in the near-hole adiabatic effectiveness, especially when the stagnation line is very near the hole. For Positions 3 and 4 (훽 =-21.2° and 훽 =-21.7°), the jets generated a blanket of coolant immediately downstream of the conical holes. This was a repeatable phenomenon for the conical holes that apparently has a significant effect on the adiabatic effectiveness of the showerhead. It is also clear that the effect occurs for various location beyond the metering hole size but within the footprint of the conical hole shape. That is, conical holes benefit from this effect over a wider range than their cylindrical counterparts due to the interaction between the stagnating fluid and the fluid exiting out of the wide hole shape.

225

Figure 8.21: 휼 levels for the stagnation line sweep performed at the 휷 =-ퟐퟏ. ퟐퟑ° condition after the initial experiments.

The effect is presented in terms of laterally averaged adiabatic effectiveness 휂̅ in Figure 8.22, and in terms of 휂̅ (averaged over s/D=-40 to +10) in Figure 8.24. The effect of the stagnation line sweep is a near step-change on either side of the hole at 푠/퐷 ≅ −2.5 and 2.5. The effect persists far on to the pressure-side showerhead region and beyond the shaped pressure-side gill row, as was seen in the full coverage data. It can be seen in Figure 8.23 that Position 2 outperforms all of the other cases in the region near rows PS2, SH1, and SS1 with a decreased effect beyond s/D= 0. However, the effect on

226 the most suction-side part of the showerhead region performs close to that of Position 3, which is the 훽 =-21.2° case. It can be seen in Figure 8.24 that the total average effectiveness, 휂̅, is highest for Positions 2-4 when the stagnation line is within the hole footprint. It is interesting to note that for Position 2, the adiabatic effectiveness for the high momentum flux ratio case is enhanced significantly. Comparing Positions 2 and 6 at the left and right bounds of Figure 8.24, the effectiveness for Position 2 is larger by over

0.1 휂̅ on the pressure-side, but only lower by about 0.06 휂̅ on the suction side. Figure 8.24 also shows that for all of the positions where the stagnation line is located within the shaped hole footprint, elevated levels of effectiveness in the showerhead are experienced above those where the stagnation line is not located over the hole footprint. This benefit would also presumably exist in an operating gas turbine, but would appear as a time- averaged effect - upstream wakes traversing across the airfoil surface due to an upstream vane or other flow structure which affects the incidence angle of the incoming flow to the showerhead would in a time-averaged sense be greater for the conical hole shape since the performance is enhanced over a wider range of inlet incidence angles than for a cylindrical hole. The laterally averaged plots of these two velocity ratios studied can be seen in Figure 8.22 and Figure 8.23, where the enhancement due to the stagnation line shift is more apparent in this case. Finally, a total average effectiveness in the showerhead and gill row region (s/D=-40 to +10) can be seen in Figure 8.24. It is evident from this plot that the higher velocity ratio case contained the greatest enhancement for Position 2, but that the adiabatic effectiveness in the showerhead region was in general higher for the whole region where the stagnation line was closer to the stagnation row of holes.

227

Figure 8.22: 휼̅ levels for the stagnation line sweep performed at the 휷 =-ퟐퟏ. ퟐퟑ° condition after the initial experiments.

Figure 8.23: 휼̅ levels for the stagnation line sweep performed at the 휷 =-ퟐퟏ. ퟐퟑ° condition after the initial experiments.

228

Figure 8.24: 휼̅ levels for the showerhead region during the stagnation line sweep.

8.10. Overall Effectiveness – Effects of Incidence Angle on Showerhead Region

In order to identify trends between the two incidence angles,휂 and 휙 for both incidence angles and for 훽 =-30.1° 훽 =-21.2° were plotted, and this can be seen in Figure 8.25. The laterally averaged effectiveness levels for both of the 휙 tests are shown together in Figure 8.26. It is apparent that there is a change in the overall effectiveness levels for the two incidence angles presented in Figure 8.26. It is interesting to note that the showerhead effectiveness levels do change measurably, and this is directly related to the stagnation line shift and thus the external film cooling, external heat transfer coefficient, and heat transfer coefficient augmentation levels of the jets, since the two velocity ratios for the experiments are identical. However, the difference in overall effectiveness on the far pressure-side of the showerhead region is only increased by about

휙̅ = 0.05. The largest effects are seen in the very near-stagnation region, where differences in 휙̅ of as much as 휙̅ = 0.1 are seen at 푠/퐷 = -8. This is coincident with the large enhancement seen in 휂̅ for the two incidence angle cases. Therefore, for the case of

229 this particular hole spacing, the adiabatic effectiveness plays a large role in the overall effectiveness at the two incidence angles. The velocity ratios (and hence the internal heat transfer coefficient magnitudes) for the two overall effectiveness datasets are identical, and so the changes in overall effectiveness are due to the adiabatic effectiveness, external heat transfer coefficient, and heat transfer coefficient augmentation levels of the jets. As it was shown in the previous section that the no-film heat transfer coefficient was largely unaffected by this magnitude of incidence angle change, the largest effects in the overall effectiveness are due to the augmentation in heat transfer coefficient as well as the adiabatic effectiveness.

Furthermore, the overall effectiveness on the whole is higher for the off-design 훽=-21.2° (푖 =-9°) case due to the enhancement in the shower head region (even though the minimum 휙 is about the same) because the stagnation line was positioned over a row of coolant holes.

Figure 8.25: Contour plots of 흓 magnitudes at the 휷 =-ퟑퟎ. ퟏ° condition.

230

Figure 8.26: 흓̅ for both incidence angle conditions tested.

8.11. Overall Effectiveness – Predictions of 흓 With 흓ퟎ

Dees et al. [46] proposed a method to predict the overall effectiveness levels of a model by only measuring 휙0 and 휂. The method involved a 1D analysis of the scaling parameters for 휙. Realizing that the special case exists without film cooling:

1 휙0 = 8.4 1 + 퐵푖 + ℎ0/ℎ𝑖 A warming factor 휒 was added in to the above equation by Williams et al. [71] in order to refine the analysis. The warming factor, 휒, accounts for the amount that the coolant temperature increases as it passes through the internal cavities of the conducting model, so that 휒 is defined as:

푇 −푇 휒 ≡ ∞ 푐,푒푥𝑖푡 푇∞ − 푇푐,𝑖푛푡푒푟푛푎푙 8.5 And so the final equation can be developed so that:

휙푝 = 휙0(1 − 휒휂) + 휒휂 8.6

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This was a 1D calculation, and it assumes that ℎ0/ℎ𝑖 ≈ ℎ푓/ℎ𝑖 for the analysis, and so it is therefore predicted to fail in the near-hole and the area immediately downstream of film cooling holes, where it is expected that ℎ푓/ℎ𝑖 is enhanced significantly above ℎ0/ℎ𝑖 in this region. It is interesting to note that while both Williams et al. [71] and Dyson et al. [48] used the same 1D analysis in an effort to predict the overall effectiveness levels of their conducting models, Williams reported some success with the analysis, while Dyson reported a consistent over-prediction compared to the experimental case. In the analysis by Dyson, it was theorized that the 1D model was too simple to adequately predict the performance for more complicated, full-coverage scenarios such as those analyzed in that study. However, it is interesting to note that conduction corrections to the adiabatic effectiveness data were made by Williams in order to account for the internal cooling experienced in the ideally adiabatic model. These conduction corrections were not made in the case of Dyson.

In order to collect 휙0 data for an analysis like this, several holes at mid-span in all rows of holes can be blocked after the initial overall effectiveness experiments so that no coolant was ejected from these holes. As a result, the overall cooling effectiveness in the blocked region is due only to the internal cooling. These overall cooling values are designated 휙0 as in Equation 8.4. Equation 8.4 was used to predict overall cooling effectiveness based on the measurement method discussed previously. Note that for the current analysis, the conduction corrected values of 휂 are used. The 휒 values, which quantify the warming of coolant as it passes through the internal channels, were also estimated from gas thermocouples located well within each of the channels at the radial midspan of the airfoil. The 휒 of the channels were measured for each flow rate condition presented. It is

232 extremely important to note here that this is only a very rough estimate of what the true 휒 values are, since significant through-hole warming of the coolant occurs within the metering hole due to the high heat transfer coefficient experienced there. Furthermore, the gas temperature is non-uniform within the channel due to the warming experienced from the heat transfer at the wall, and so measuring closer to the holes would have resulted in better approximations of the warming factors. Nonetheless, for all flow rate conditions, the estimates of 휒 ranged from 0.92< 휒 <0.98, consistent with the possible range of 휒 that Dyson et al. [48] estimated in their analysis, which itself was an estimation from past work performed by Terrell et al. on a different airfoil configuration.

The comparisons of 휙̅ and 휙̅0 can be seen in Figure 8.28. Note that 휙̅0 values are only presented in regions between holes because 휙̅0 over a blocked hole would not be relevant. As expected, the 휙̅0 values systematically increased with increasing coolant flow rates. The 휙̅0 contribution was 60% to 70% of the overall 휙̅ values, but was a high as 80% immediately downstream of the showerhead at s/D = 7, and as low as 50% far downstream on the suction side at s/D =65.

233

̅ ̅ Figure 8.27: 흓 and 흓ퟎ for the 휷=-ퟑퟎ. ퟏ° case.

The calculated values of 휙̅푝 are compared to the measurements of 휙̅, and can be seen in Figure 8.28 In the region -40 < s/D < 60, the predicted overall cooling effectiveness was reasonably close to the measured values, although there is a distinct difference in the trend of the data (reasons for the difference in trends are discussed below). However, in the trailing edge regions, s/D < -50 and s/D > 70, the predicted

휙̅푝푟푒푑 values were significantly higher than the measured 휙̅ values. This is likely due to there being a lack of internal cooling of the trailing edge for the model airfoil tested.

Consequently the trailing edge is warmed by the mainstream, and three dimensional conduction causes a warming upstream of the trailing edge which decrease 휙̅ values below the values predicted by Eqn 2 which is based on a 1D heat transfer analysis. The analysis did deviate from the 휙̅ values significantly immediately downstream of the holes, and the implication here is that the approximation made in the 1D analysis

ℎ0/ℎ𝑖 ≈ ℎ푓/ℎ𝑖 was not appropriate very near the holes.

234

̅ ̅ Figure 8.28: 흓 and 흓 for the 휷=-ퟑퟎ. ퟏ° case.

8.12. Follow-up Study: Capability of Testing

It is worth noting that a follow-up study was performed after these tests. Although the results are out of the scope of this project, they showed the capability to test 훽=0° airfoils, and also verified that the software created for this project could be applied easily to another airfoil with little additional work.

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Chapter 9: Computational Setup

Two sets of computational simulations were completed in order to investigate experimental results seen during the experimental phase of the project2. The first set of simulations investigated the effects of the predictive capability in the prediction of heat transfer with various turbulence models in order to better understand their advantages and shortcomings. The second set of simulations investigated the effects of the turbulence grids used during the project – the goal here was to develop some type of correlation for the turning angle produced by the vertical grids, as well as determine the predictive capability of the turbulence production through the grids in order to compare them to the experiments results. The setup of these simulations is detailed below.

9.1. Computational Heat Transfer Predictions

In order to assess the capability to predict h in the linear cascade, three turbulence models were investigated: the two-equation 푘휔-푆푆푇 model for a reference case, the three equation 푘-푘푙-휔 model, and the four equation 푆푆푇-푇푟푎푛푠푖푡푖표푛 model. All of these models utilize low-Reynolds number treatment (LRN) either automatically depending on near-wall the grid size, or manually as specified with the 푘휔-푆푆푇. This means that RANS equations are integrated up to the viscous sublayer, and therefore requires a fine grid near the wall of a 푦+ ≈ 1. The models were chosen specifically for this purpose, as LRN often yields much better accuracy for heat transfer coefficient results than their high Reynolds number treatment (HRN) counterparts due to the importance of the sub layer in heat transfer coefficient calculations.

2 Section 9.1 contains information based on an article previously published by the author: Chavez, K. F., Packard, G., Slavens, T. N., and Bogard, D. G., 2016, “Experimentally Determined External Heat Transfer Coefficient of a New Turbine Airfoil Design at Varying Incidence Angles,” ISROMAC 2016, Honolulu, Hawaii. The computational setup from the paper above was originally created by the author and modified for inclusion in this paper. 236

The models were tested against both the high and low turbulence heat transfer coefficient experiments completed during the experimental phase of the project. Table 9.1, which depicts the final testing conditions in the heat transfer coefficient tests as presented below for convenience, as these are the same test conditions which were matched in the computational experiments:

Table 9.1: A summary of the boundary conditions specified in the simulations.

9.1.1. Computational Domain

In order to test the turbulence models, a computational domain was created in a

CAD modeling program and imported in to ANSYS ICEM CFD. The computational domain can be seen in Figure 9.1. The computational domain included a mesh 1 axial chord length upstream of the airfoil and 2 axial chord lengths downstream of the model. The mesh was an unstructured quad-dominant mesh, and contained a resolved boundary layer prism mesh with a 푦+ ≈ 1 expanding out at a ratio of 1.15 from the airfoil resulting in a total of 68,000 nodes and 134,000 faces. 2nd order discretization schemes were utilized for all relevant variables. All simulations also utilized the energy equation with a constant heat flux applied to the airfoil surface. The fluid properties utilized in the simulations are shown in Table 9.2.

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Table 9.2: A summary of the fluid properties used in the simulations.

Property Value

3 ρ∞ [kg/m ] 1.15

−5 μ∞ [kg/ms] 1.88x10

T∞ [K] 305

Figure 9.1: Computational domain for 풉ퟎ studies (airfoil geometry purposefully distorted for confidentiality reasons).

Constant pressure conditions were specified at the inlet and outlet, and a target outlet mass flow rate was set in order to achieve the desired upstream Reynolds number. The inlet static pressure was specified at atmospheric pressure which was very close to the experimental case in the low-speed wind tunnel. As a result of an atmospheric inlet condition, the outlet pressure was slightly lower than atmospheric pressure due to the contraction of the area as it passes through the cascade and this was the case in the experiments. For each simulated case, the inlet 훽 (°), Tu (%), and Λf/퐶푎푥 (-) were all adjusted until they matched the corresponding experimental data seen in Table 9.1: A summary of the boundary conditions specified in the simulations.. 238

In order to match the integral length scale 퐿11 (Λ푓) in the simulations, 퐿11 was calculated from turbulence and fluid properties at ½ pitch in between the simulated airfoil model and along the leading edge axis of the cascade at the same location the physical measurements occurred for the experiments. First, the turbulence length scale was calculated as:

3 푘2 퐿 = 9.1 휀 Next, the Taylor-scale Reynolds number was calculated from the relationship since these variables are also defined by the turbulent properties and flow properties:

푘2 3 = 푅2 휀휈 20 휆 9.2

Finally, 퐿11 was calculated from a curve fit of the relationship between the longitudinal integral length scale and the turbulence length scale as documented in Pope [72].

Figure 9.2: Relationship between the longitudinal and integral length scales as shown by Pope [72].

239

퐿 푅 ≅ 0 for the flows being simulated, leading to 11 ≅ 0.5, which was quite 휆 퐿 close to the value of 0.43 which the relationship approaches asymptotically at higher 푅휆 numbers for the model spectrum. In the end, the input for the length scale at the inlet of the computational domain was about 4 times smaller than the value of 퐿11 calculated at the inlet of the cascade. This was partially because the Fluent turbulence length scale is 푘3/2 different than that defined in above (defined in Fluent as 퐿 = 퐶3/4 , and so is 푓푙푢푒푛푡 휇 휀 dependent on the model constants used in the turbulence model, where 퐶휇 = 0.09 by default), and partially because the integral length scale increases with downstream distance from the inlet. Since 퐶휇 is by default 0.09, the constant in front of the turbulence length scale 퐿푓푙푢푒푛푡 is 0.16, and so one would expect combining the equations to solve 퐿 for 퐿 assuming 11 ≅ 0.5 yields 퐿 = 3.1ℓ, or a factor of 3. The final factor of 4 is 11 퐿 11 actually expected, since in real flows, the amalgamation of smaller eddies increases their length scale as a flow moves downstream, and so decreasing the inlet length scale even further than the factor of 3 is necessary to account for this. The factor of 4 is close to literature suggesting an input of a Fluent turbulence length scale of about 6 times smaller than integral length scale to achieve the appropriate scale. The factor of 6 specified by some researchers is also dependent on what software is used, as some specify the turbulence length scale differently. Furthermore, although the difference of a factor of 6 difference may seem somewhat small in order to take the time to calculate, the length scale specification has a strong effect on the turbulence intensity decay from the inlet to the leading edge of the model, and if the length scale is specified incorrectly, the inlet specifications can be unrealistic or difficult to achieve appropriate levels of turbulence at the leading edge of the model. In this case of using the appropriate length scale, the inlet specifications of turbulence intensity were around 9% for the high turbulence simulation,

240 or about 4% higher than that specified at the inlet to the computational domain, since the length scale specified has an effect on the decay rate of the turbulence intensity as it flows downstream from the inlet. Target residuals were set as low as possible, and the simulations were run until the solution no longer changed. This was typically on the order of 10−6 for all residuals, but was sometimes lower. In addition to the residuals, the surface temperature was monitored after this occurred in order to ensure that the temperature profile on the airfoil had reached steady state. Once this was completed, the solution was converged and the data was exported.

9.2. Turbulence Grid Flow Field and Turning Angle Simulations

In order to test the predictive capability of the SST Transition model in predicting the properties of the turbulence grids used during this project, a parametric sweep of 푝/푑 and 훽𝑖푛 was performed in ANSYS Fluent. The parametric sweep enveloped the physical specifications of the turbulence rods used in the lab for this project and for other projects out of the scope of this dissertation. In order to create a generic control volume for testing this parametric sweep, a simple 2D model was created with a rod placed in the vertical center of the control volume. The inlet to the control volume was created 20 diameters upstream of the rod in order to ensure that the uniform inlet velocity specified as a boundary condition was appropriate, and an outlet conditions 50 diameters downstream of the rod ensured that the maximum downstream flow distance was the same as that actually experienced in the physical wind tunnel. A depiction of the computational domain for the turbulence rod studies can be seen in Figure 9.3: Computational domain for the turbulence rod studies. An extremely fine mesh was made for this purpose, and a grid independence study was performed in order to ensure that this grid could be utilized 241 without significant errors due to an unresolved mesh. The mesh was created to be finer closer to the rod, and the rod also contained a prism layer of 25 cells, ensuring the

푦+ ≈ 1 condition necessary for resolved boundary layer computations. It is important to notice that since the pitch was a parameter studied here, the computational mesh size changed for each new pitch studied. However, all the mesh specifications were held constant, and this meant that there were significantly more elements contained in the control volume for the highest pitch studies tested vs. the number of elements in the small pitch studies. For the study, the pitch was varied in order to study p/d ranging from 2-5, and for each of the p/d values studied, the incidence angle was swept from 0 to 55° in order to investigate the effect with p/d held constant. A summary of the tests studied can be seen in Table 9.3.

242

Figure 9.3: Computational domain for the turbulence rod studies.

243

Table 9.3: Summary of the computational parametric sweep performed for the turbulence rods.

Experimental p (in) d (in) p/d (-) S (-) βin (°) βout (°) Δβ (°) 0.87 0.25 3.49 0.29 33.76 30.10 -3.66 0.79 0.25 3.15 0.32 25.03 21.23 -3.80 1.87 0.38 4.98 0.20 55.15 52.46 -2.69

Computational p (in) d (in) p/d (-) S (-) βin (°) 0.50 0.25 2.00 0.50 25.00 0.50 0.25 2.00 0.50 35.00 0.50 0.25 2.00 0.50 45.00 0.50 0.25 2.00 0.50 55.00 0.50 0.25 2.00 0.50 0.00 0.75 0.25 3.00 0.33 25.00 0.75 0.25 3.00 0.33 35.00 0.75 0.25 3.00 0.33 45.00 0.75 0.25 3.00 0.33 55.00 0.75 0.25 3.00 0.33 0.00 1.00 0.25 4.00 0.25 25.00 1.00 0.25 4.00 0.25 35.00 1.00 0.25 4.00 0.25 45.00 1.00 0.25 4.00 0.25 55.00 1.00 0.25 4.00 0.25 0.00 1.25 0.25 5.00 0.20 25.00 1.25 0.25 5.00 0.20 35.00 1.25 0.25 5.00 0.20 45.00 1.25 0.25 5.00 0.20 55.00 1.25 0.25 5.00 0.20 0.00

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Chapter 10: Computational Results

10.1. Heat Transfer Coefficient Predictions

Figure 10.1 shows computational predictions with three turbulence models compared to the actual test data for the 훽 = −30.1° (high turbulence) condition3. In the cases shown here, there is a consistent under-prediction of the leading edge 푁푢 in the leading edge region by as much as 15% when compared to the experimental measurements. The 푘휔-푆푆푇 model predicts a very premature transition on both the suction and pressure sides. The 푘-푘푙-휔 and SST-Transition models both predict transition much later, and this is farther downstream than the data that was collected on both sides.

The 푘-푘푙-휔 and SST-Transition models both predict 푁푢 values quite well for regions outside of the leading edge region, and the 푘-푘푙-휔 predicts 푁푢 best out of all the models. These results are consistent when comparing to all of the other experiments as well. Furthermore, the results from the SST-Transition model are consistent with those shown by Menter et al. [73], in that the formulation of the transition model to automatically determine the near wall treatment makes it an excellent choice for heat transfer predictions, as it is relatively robust.

3 Section 10.1 contains information based on an article previously published by the author: Chavez, K. F., Packard, G., Slavens, T. N., and Bogard, D. G., 2016, “Experimentally Determined External Heat Transfer Coefficient of a New Turbine Airfoil Design at Varying Incidence Angles,” ISROMAC 2016, Honolulu, Hawaii. The computational results from the paper above was originally created by the author and modified for inclusion in this paper. 245

Figure 10.1:The three turbulence models investigates vs. the experimental measurements for the high turbulence 휷 = ퟐퟓ° case.

Figure 10.2 shows a comparison of the turbulence effects in the simulated and experimental high and low Tu data sets for the k-kl-ω model only. In the leading edge region, the percentage enhancement of h due to turbulence is nearly the same in both the simulated and experimental cases. However, the enhancement of h downstream of the showerhead region is much more pronounced in the simulations with a nearly uniform increase in the simulated h distribution.

246

Figure 10.2: Low and high turbulence CFD and experimental comparisons.

Figure 10.3 shows a comparison of the incidence angle effects in the simulated and experimental high Tu data sets, based on the k-kl-ω simulations only. Although the leading edge region is poorly predicted, the results from the computations were consistent with the experiments, in that this particular airfoil model is relatively insensitive to incidence angle shifts. Although the 훽 angle was changed by 10°, since the curvature was essentially constant over this range, the leading edge heat transfer was not significantly changed. Furthermore, since the greatest differences in the hydrodynamic effects are present at the leading edge, the change in 푁푢 in the two incidence angles downstream of the stagnation region is not pronounced.

247

Figure 10.3: Incidence angle CFD vs experiments for the high turbulence case.

The percentage increase in the leading edge heat transfer coefficient is similar between the low and high turbulence CFD and experimental studies. From the results, it can be seen that the simulations do not seem to be able to appropriately capture the flow physics involved in the leading edge region for this particular airfoil leading edge. The difference between the experimental and computational heat transfer in the leading edge could be due to a number of effects. These results were compared to the leading edge heat transfer simulations with similar experiments for a C3X vane, the results of which can be seen in Figure 10.4 and Figure 10.5. In these studies, the 푘-휀 simulations

248 compared well to the low-turbulence leading edge heat transfer coefficient levels, but did not compare well at high turbulence. Furthermore, the 푘-휔 SST studies compared well at high turbulence levels, but not at low turbulence. Therefore, the simulations in the present study and this previous study show that the leading edge heat transfer coefficient levels are predicted poorly for different turbulence models, and also for different leading edge radii. It is thought that in both of these studies, the strong streamline curvature coupled with the production in turbulence at the leading edge play a role in the varying predictability of the turbulence models. Although a number of these turbulence models contain corrections for the streamline curvature, they still seem to poorly predict the leading edge heat transfer in these simulations. It would be very useful to investigate the predictability of the leading edge heat transfer with a higher fidelity model (perhaps LES or DES), although the computational resources required for these simulations would be higher than the turbulence models presented here. Furthermore, the effect of not utilizing the curvature correction in certain models, and comparing the resultant leading edge heat transfer would also shed light on this effect. A more in-depth study which focuses on this specific effect has been proposed for future work.

249

Figure 10.4: Low turbulence results from Dyson’s [70] study.

Figure 10.5: High turbulence results from Dyson’s [70] study.

250

10.2. Turbulence Grid Flow Field and Turning Angle Simulations

A graph depicting the turbulence levels of the 훽 = 0° turbulence rod simulations at p/d=2 and p/d=5 can be seen in Figure 10.6. It is interesting to note that for the smallest pitch studied, the turbulence generation predicted immediately downstream of the turbulence rods is quite high at 푇푢=30%. This is due to a combination of the extremely strong shear flow generated between the very high Reynolds number flow in between the rods as well as the very low velocity wake downstream of the rods. The simulation therefore predicts significantly more uniform turbulence levels due to the stronger mixing in this upstream region, and also due to small pitch of the turbulence rods. Figure 10.6 also shows turbulence levels for the same p/d values, but at the highest inlet incidence angle studied. Once again, the turbulence levels are much more uniform than the high pitch 훽 = 0° case, since here the acceleration region through the grid is a function of the flow velocity, which is higher through the non-normal rod array. The turning of the flow is also very evident in Figure 10.7 as evidenced by the downstream wake of the turbulence rods. The flow turning and velocity field in the near-cylinder region of the p/d=2 and 훽=55° simulations can be seen in Figure 10.8.

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Figure 10.6: Turbulence levels for the 휷=0° simulations at p/d=5 (top) and p/d=2 (bottom) .

Figure 10.7: Turbulence levels for the 휷=55° simulations at p/d=5 (top) and p/d=2 (bottom) .

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Figure 10.8: Vector field for the 휷=55° simulations at p/d=2.

10.2.1. Comparison of Turbulence Levels to Correlations

The results at the extreme end of the parametric sweep were compared to the correlation used in the wind tunnel to position the turbulence rods, and these results can be seen in Figure 10.9. In this case, both the Roach correlation [60] and adapted by Mosberg for non-normal flow [58], as well as the adapted correlation suggested by Packard [4] can be seen in the figure. Both correlations predict a 5% turbulence level at about 푥푓/푏=50. The computational results compare quite well to the correlation except the low pitch, high turning angle simulation which contained extremely high levels of turbulence immediately downstream of the rods as discussed previously. However, even this simulation is within about 2% of the turbulence level predicted by the correlations.

253

It is also worth noting that in the original formulation, Roach [60] determined the correlation constant utilizing distance downstream of the turbulence rods in the formulation. Mosberg [58] called this in to question after several turbulence measurements downstream of the grid were made which indicated that the original Roach correlation constant was a function of the downstream distance. Mosberg theorized that this was potentially due to the short distance downstream of the grid where turbulence is non-isotropic, as has been observed widely in the literature. Therefore, accounting for this could lead to a change in the final formulation of the empirical correlation. However,

Mosberg did not explore this directly since this would have required accurate measurements of the turbulence field very close to the grid, which was not necessary for the current project. In the end, both Mosberg and Packard utilized the same origin as that specified in Roach with good results. It is however interesting to note that a non-isotropic decay region does indeed exist in the CFD, and this partially accounts for the deviations from the experimental correlations, especially very near the downstream edge of the grid, but most of the data collapses on the correlations well downstream of the grid.

254

Figure 10.9: CFD and experimental correlations for turubulence intensity downstream of turbulence grids.

10.2.2. Comparison of CFD Outlet Angle to Experimental Data

The results of the parametric sweep of inlet incidence angle and rod pitches can be seen in Table 10.1. In general, the trends of increasing ∆훽 with increasing inlet incidence angle 훽𝑖푛 are present in the results. Most notably, the pitch has an extreme effect on the turning angle of the turbulence grid. For even the widest p/d tested, the incidence angle changed by more than 2°, and changes as large as 15° were seen for the smallest pitch studied.

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Table 10.1: Computational results for parametric sweep of incidence angle over a range of pitches.

p (in) d (in) p/d (-) S (-) βin (°) βout (°) Δβ (°) 0.87 0.25 3.49 0.29 33.76 30.10 -3.66 0.79 0.25 3.15 0.32 25.03 21.23 -3.80 1.87 0.38 4.98 0.20 55.15 52.46 -2.69

Computational p (in) d (in) p/d (-) S (-) βin (°) βout (°) Δβ (°) 0.50 0.25 2.00 0.50 25.00 15.47 -9.53 0.50 0.25 2.00 0.50 35.00 22.45 -12.55 0.50 0.25 2.00 0.50 45.00 30.52 -14.48 0.50 0.25 2.00 0.50 55.00 40.00 -15.00 0.50 0.25 2.00 0.50 0.00 0.00 0.00 0.75 0.25 3.00 0.33 25.00 20.33 -4.67 0.75 0.25 3.00 0.33 35.00 28.95 -6.05 0.75 0.25 3.00 0.33 45.00 38.01 -6.99 0.75 0.25 3.00 0.33 55.00 47.44 -7.56 0.75 0.25 3.00 0.33 0.00 0.00 0.00 1.00 0.25 4.00 0.25 25.00 22.03 -2.97 1.00 0.25 4.00 0.25 35.00 31.07 -3.93 1.00 0.25 4.00 0.25 45.00 40.32 -4.68 1.00 0.25 4.00 0.25 55.00 49.87 -5.13 1.00 0.25 4.00 0.25 0.00 0.00 0.00 1.25 0.25 5.00 0.20 25.00 22.80 -2.20 1.25 0.25 5.00 0.20 35.00 32.04 -2.96 1.25 0.25 5.00 0.20 45.00 41.45 -3.55 1.25 0.25 5.00 0.20 55.00 51.00 -4.00 1.25 0.25 5.00 0.20 0.00 0.00 0.00

The results were compared on a 훽𝑖푛 vs 푝/푑 plane in order to investigate trends over the parametric sweep of data. A plot containing the CFD as well as experimental data can be seen in Figure 10.10. It was found that there was a smooth trend between the

nd variations of 푝/푑 and 훽𝑖푛 in the computational results, and a 2 order polynomial was

256 developed from the computational data in order to produce an equation which could predict the outlet angle 훽표푢푡 with respect to the inlet angle and 푝/푑:

푝 푝 푝 2 훽 = −13.32 + 5.1 푥10−1훽 + 8.103 ( ) + 1.8푥10−3훽2 + 0.06 8훽 ( ) − 1.111 ( ) 표푢푡 𝑖푛 퐷 𝑖푛 𝑖푛 퐷 퐷 10.1

Figure 10.10: Surface fit of CFD data, with test data also shown.

The polynomial was then used to predict the outlet angle of the turbulence rods which have been used in this project as well as another project out of the scope of this dissertation. These results can be seen in Table 10.2. The polynomial predicted the outlet angle to within a degree for two out of the three turbulence rods, which is close to the experimental uncertainty for the incidence angles as tested with the PIV, but were consistently larger than the experimental measurements. Therefore, the CFD data can

257 serve as a valid prediction if it is desired to generate similar turning rods in the same Reynolds number, pitch, and inlet incidence angle regime as those tested here. This is particularly useful since there is currently no data in the literature on predicting the turning caused by turbulence rods at non-normal incidence angles to the flow.

Table 10.2: Predicted difference in turbulence grid deflection in CFD vs. experimental results.

Experimental CFD CFD-Experimental p/d S βin βout ΔβExp ΔβCFD ΔβCFD-ΔβExp 3.15 0.32 25.03 21.23 -3.80 -4.40 -0.60 3.49 0.29 33.76 30.10 -3.66 -4.81 -1.15 4.98 0.20 55.15 52.46 -2.69 -3.01 -0.32

258

Chapter 11: Conclusions

The purpose of this chapter is to provide a brief overview of some of the conclusions as a result of this study. In short, a new wind tunnel design was created in order to enable testing of linear cascades of airfoils at varying incidence angles in a closed-loop setting. The work culminated in the testing of an airfoil at varying incidence angle in order to better understand the effects of incidence angle on the no-film heat transfer, as well adiabatic and conjugate effects of active cooling for an airfoil with multiple rows of shaped holes. During the cooling tests, various rates of coolant were used in order to better understand the effects of the incidence angle variations. This provided a new wind tunnel design for use in closed-loop facilities, provided a better understanding of the effects of incidence angle on shaped holes in the showerhead of a realistic airfoil, provided the first experimental investigation of a conjugate model with all shaped holes, and provided additional insights in to the use of RANS models for predicting heat transfer and flow field effects in the context of these experiments. These results should highlight the utility of conjugate experiments in heat transfer to complement adiabatic effectiveness experiments, which are performed much more often.

11.1. Wind Tunnel Design

The original goal of the wind tunnel design was to enable the capability for testing airfoils at 훽 ≠ 0° in a closed-loop, low-speed, linear cascade facility. This was completed through an approach which included separate project stages including a literature review, conceptual design, finalized design, construction, and validation. As a result, a number of conceptual designs were assessed, and a new wind tunnel design was created for closed- loop, variable incidence angle testing. In the end, it was found that the new design produced acceptably uniform inlet flow over a range of incidence angles. It was verified 259 that the adjustable walls and adjustable blockages built in to the design were able to appropriately set the flow through the cascade in order to force an infinite cascade condition. Furthermore, the two stages of turning vanes utilized for turning the upstream flow were also verified to work quite well in the design. Although out of the scope of the project, it is worth noting that a follow up study verified that the wind tunnel was quite capable of its previous 훽 = 0° testing capability, as a number of studies at 훽 = 0° on a different airfoil cascade have been successfully completed. The design is recommended for low-speed wind tunnels which wish to utilize a closed-loop configuration for 훽 ≠ 0° testing purposes, such as the needs addressed in the current research.

11.2. Wind Tunnel Validation and Computational Predictions of Turbulence Grid Turning Angle

In order to verify the flow field within the new wind tunnel test section, a number of validation experiments were performed, including turbulence intensity and length scale characterization with hotwire and flow field analysis with PIV. It was found through this testing that the flow was relatively uniform through the wind tunnel. When the turbulence grids were not installed, some turbulence was generated by the downstream wakes of the turning vanes, and this potentially affected some of the low-turbulence studies performed during the heat transfer coefficient experimentation phase of the project. The turbulence levels downstream of the turning vanes at the leading edge of the airfoil models would be somewhere on the order of 1% on average, although the turning vanes led to uniformities across this average. When the turbulence grid was installed in order to test turbulence levels at Tu=5% at the leading edge of the airfoil, the turbulence rods generated a sufficient level of turbulence which washed out the effects of the turning vanes, resulting in uniform heat transfer coefficient results. As testing at turbulence levels above 5% in

260 the lab is rather typical, the effects of the turning vanes are therefore almost never an issue. In order to generate turbulence upstream of the test section, a vertical linear array of circular rods were utilized. Due to the unique wind tunnel test section, the inlet flow through the turbulence grids was non-normal to the axis of the linear array of rods. As a result, the flow through the rods was deflected so that the outlet angle was not equal to the inlet angle upstream of the rods. In order to test the effects of the presence of the rods, the downstream incidence angle was tested through PIV, and it was found that the rods turned the flow by 3°-5° depending on the solidity of the rod array. Although this has been seen for wind tunnel screens, this has not been documented in the literature for a vertical linear array of rods. Therefore, a small computational follow up study was performed in order to assess the predictive capability of the SST-Transition turbulence model in predicting the turning angle of the flow through the rods, and the results of this follow up study showed that the turning angle was well predicted.

Finally, a correlation for the turbulence levels downstream of the non-normal rod array was also developed by Packard [4] which was a slight adaptation to that proposed by Roach [60], and adapted by Mosberg [58] for non-normal flow. This was found to work very well in the wind tunnel, and the developed correlations were used extensively in order to design and manufacture new turbulence rods and successfully perform experiments at the 5% turbulence level target for this project. The same follow up study to assess the turning angle of the flow was also used to predict the turbulence levels downstream of the turbulence rods for multiple incidence angles and solidity levels. It was found that the model predicted the turbulence levels downstream of the rods quite well except for the highest solidity studies tested.

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11.3. Heat Transfer Coefficient Experiments and Computational Work

Heat transfer coefficient experiments were performed in the wind tunnel at a total of four incidence angles – two incidence angles at low turbulence, and two incidence angles at high turbulence. It was found that heat transfer coefficient distribution was largely unaffected by the change of incidence angles (~10°). This is presumably due to the fact that the airfoil contains a constant curvature at the leading edge over the range of incidence angles tested. However, the heat transfer at the leading edge was enhanced by

15-20% when the turbulence levels were increased in the tunnel with the addition of a turbulence grid. In addition to the experiments, a number of empirical correlations were used to gauge the leading edge turbulence level enhancement due to addition of the turbulence rods for the high heat transfer coefficient experiments. It was found that the empirical correlations were able to predict the enhancement of the leading edge heat transfer coefficient quite well. The enhancement of turbulence at the leading edge was found to be ~15% and was predicted to be ~19%. A number of RANS computations were performed in order to test the predictive capability of RANS models for heat transfer coefficient distribution. It was found that the RANS turbulence models were not able to predict the leading edge heat transfer adequately, and that a number of the models predicted transition to turbulence quite early. The inability to predict the leading edge heat transfer coefficient is thought to be due to a combination of the ability for the models to predict the development of the turbulence of the approach flow due to the presence of the airfoil, as well as the shape of the airfoil. The incorrect prediction of transition to turbulence on the airfoil due to the models is still a current area of research in the CFD field, and it so it was not completely unexpected

262 that some of the models were unable to predict the appropriate location of transition. It was found through all of the testing that the k-kl-휔 turbulence model is able to predict the heat transfer coefficient levels over the region where data was collected. It was also found that although these models were not able to predict the heat transfer coefficient magnitudes at the leading edge, they were able to predict the percent increase in the heat transfer coefficient magnitudes due to the additional turbulence introduced with the turbulence rods (which was simply prescribed as a higher inlet turbulence boundary condition in the software). This is similar to the predictions seen in the experimental portion of the project, where although the low- and high-turbulence leading edge heat transfer themselves were not well predicted, the percentage increase in heat transfer between the two cases was.

11.4. Adiabatic Effectiveness Experiments - 휷 = −ퟑퟎ. ퟏ°

The adiabatic effectiveness levels of an airfoil with the same external shape as that used in the heat transfer coefficients was tested at a 훽=-30.1° incidence angle. It was found through the experiment that the adiabatic effectiveness levels in the showerhead were very low and this was presumably due to separation even at the very low velocity ratio conditions tested during the study. For the pressure side holes, the effectiveness levels consistently improved, and this was thought to be due to the high momentum of the film cooling jets at the highest conditions tested, especially those of the farthest downstream pressure side holes. In contrast, the suction-side holes had peak laterally averaged adiabatic effectiveness levels in the middle of the range of velocity ratios tested, and consistent decreased thereafter. This was due to the thinning of the jet, which could have possibly been due to the increased momentum of the jet which can induce separation of the jet from the wall. However, as only the adiabatic effectiveness levels of 263 the model were measured and not thermal fields downstream of these jets as well, this is only a presumption. It was also found that the magnitude of the conduction correction used in the study was much higher than those seen in the past in the lab, and this was due to the realistic internal features such as the impingement passage and the internal rib turbulators.

11.5. Adiabatic Effectiveness Experiments – 휷 = −ퟐퟏ. ퟐ°, and Effects of Incidence Angle on Adiabatic Effectiveness

The effectiveness levels were also tested at a second incidence angle condition, and it was found that the complete pressure side of the showerhead was enhanced due to the movement of the stagnation line over a showerhead row of holes for this incidence angle. This effect was strengthened as the velocity ratio through the showerhead holes was increased. It was found through a subtraction of the 훽=-21.2° and 훽=-30.1° data sets that the enhancement of the adiabatic effectiveness levels at the 훽=-21.2° condition was essentially restricted to the high curvature region in the pressure side of the showerhead.

Although the suction side of the showerhead was enhanced at the 훽=-30.1° incidence angle, the level of enhancement for that configuration was not as strong, and it was theorized that this was due to the lower levels of curvature in the near showerhead, suction side region of the airfoil. Therefore, the enhancement persisted and was strengthened for the highest five velocity ratios over the high curvature region of the showerhead. These experiments highlighted the utility of testing realistic showerhead configurations, as the curvature effects can be accounted for.

11.6. Overall Effectiveness Experiments – 휷=-30.1°

The overall effectiveness of the same airfoil configuration (albeit with made out of a different material such that the Biot number was matched to the engine part) was 264 tested at the 훽=-30.1° incidence angle. It was found that the effectiveness levels were quite uniform over the complete airfoil. This was in contrast to the very low levels of adiabatic effectiveness seen in the showerhead region in the adiabatic effectiveness experiments. The enhancement of the effectiveness in the showerhead region was due to the internal convection of the impingement passage as well as the through-hole convection through the shaped holes in the showerhead. Significant cooling was also seen around the shaped holes due to the convection through the holes. The airfoil also had a relatively uniform radial temperature, and this was in contrast to the adiabatic effectiveness results, since the rows were not staggered. Finally, continuous addition of coolant resulted in continuous decreases in external surface temperature due to the internal convection in the model, but there were diminishing returns of this effect as the adiabatic effectiveness levels reached their peak in the middle of the range of velocity ratios tested for this study. When compared to the only other airfoil with a fully cooled configuration, it was found that the airfoil measured in the current project was more uniform. Although the spacing of the showerhead holes was much larger in the current study, the convective cooling in the showerhead region made up for the lack of film cooling in the leading edge. The study highlighted the utility of measuring the overall effectiveness levels of an airfoil in addition to its adiabatic effectiveness levels. Whereas one may assume that the showerhead not receive adequate cooling from the adiabatic effectiveness results alone, the overall effectiveness results show that the showerhead performed quite well.

11.7. Prediction of 흓

The overall effectiveness levels were predicted with a simple 2d equation which has been used in the past to predict overall effectiveness levels with a 휙0 measurement in 265 addition to an 휂 measurement. It was found that the prediction worked quite well after the

휂0 correction had been applied to the 휂 data. The prediction here highlighted the effects of the heat transfer coefficient augmentation and 3D conduction effects surrounding the holes, as the prediction worked quite well, but only far away from the holes.

11.8. Effects of Incidence Angle on the Showerhead Region

Finally, the effect of the stagnation line location on the showerhead region of the adiabatic effectiveness model was also investigated on both the adiabatic and overall effectiveness models in more detail. It was found that the movement of the stagnation line across the whole footprint of the conical shape enhanced the film effectiveness. The overall effectiveness of the showerhead was measured at 훽=-21.2° and it was found that the effects of the stagnation line location affected the overall effectiveness levels, although by a smaller amount. The results here were important in that the enhancement in effectiveness for conical holes seem to persist over the whole footprint of the conical shape, which in the case of this project was quite large.

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Vita

Kyle Chavez was born and raised in Tijeras, New Mexico. He earned his B.S. and M.S. in mechanical engineering from the New Mexico Institute of Mining & Technology in 2009 and 2011 respectively. He then enrolled in the mechanical engineering program at the University of Texas at Austin in 2012. Upon graduating he will begin working at

Williams International as an engineer in the gas turbine industry.

Permanent email: [email protected]

This dissertation was typed by the author.

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