An Experimental Investigation of Simultaneous Heat-Flux And

AIRFOIL, PLATFORM, AND COOLING PASSAGE MEASUREMENTS ON A ROTATING TRANSONIC HIGH-PRESSURE TURBINE

DISSERTATION

Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University

Jeremy B. Nickol, M.S.

Graduate Program in Mechanical Engineering

The Ohio State University

2016

Dissertation Committee:

Professor Randall M. Mathison, Advisor

Professor Michael G. Dunn, Co-Advisor

Professor Sandip Mazumder

Professor Jeffrey P. Bons

Jeremy B Nickol

2016

ABSTRACT

An experiment was performed at The Ohio State University Gas Turbine

Laboratory for a film-cooled high-pressure turbine stage operating at design-corrected conditions, with variable rotor and aft purge cooling flow rates. Several distinct experimental programs are combined into one experiment and their results are presented.

Pressure and temperature measurements in the internal cooling passages that feed the airfoil film cooling are used as boundary conditions in a model that calculates cooling flow rates and blowing ratio out of each individual film cooling hole. The cooling holes on the suction side choke at even the lowest levels of film cooling, ejecting more than twice the coolant as the holes on the pressure side. However, the blowing ratios are very close due to the freestream massflux on the suction side also being almost twice as great. The highest local blowing ratios actually occur close to the airfoil stagnation point as a result of the low freestream massflux conditions. The choking of suction side cooling holes also results in the majority of any additional coolant added to the blade flowing out through the leading edge and pressure side rows.

A second focus of this dissertation is the heat transfer on the rotor airfoil, which features uncooled blades and blades with three different shapes of film cooling hole: cylindrical, diffusing fan shape, and a new advanced shape. Shaped cooling holes have

previously shown immense promise on simpler geometries, but experimental results for a rotating turbine have not previously been published in the open literature. Significant improvement from the uncooled case is observed for all shapes of cooling holes, but the improvement from the round to more advanced shapes is seen to be relatively minor. The reduction in relative effectiveness is likely due to the engine-representative secondary flow field interfering with the cooling flow mechanics in the freestream, and may also be caused by shocks and other compressibility effects within the cooling holes which are not present in low speed experiments.

Another major focus of this work is on the forward purge cavity and rotor and stator inner endwalls. Pressure and heat transfer measurements are taken at several locations, and compared as both forward and aft purge flow rates are varied. It is seen that increases in forward purge rates result in a flow blockage and greater pressure on the endwalls both up and downstream of the cavity. Thus, even in locations where the coolant does not directly cover the metal surface, it can have a significant impact on the local pressure loading and heat transfer rate. The heat transfer on the platform further downstream, however, is unchanged by variations in purge flow rates.

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Dedicated to my mother, for instilling my love of learning, and to my father, for creating my obsession with how things work

ACKNOWLEDGEMENTS

This research was partially funded by the Aviation Applied Technology Directorate under Agreement No. W911W6-08-2-0011 and partially funded by the Federal Aviation

Administration under Agreement No. DTFAWA-10-C-00040. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation thereon.

The views and conclusions contained in this document are those of the authors and not should not be interpreted as representing the official policies, either expressed or implied, of the Aviation Applied Technology Directorate, the Federal Aviation

Administration, or the U.S. Government.

Approved for public release: distribution is unlimited.

First I would like to thank my original advisor, Professor Michael G. Dunn, for first giving me the opportunity to work in The Ohio State University Gas Turbine Laboratory, providing me with four years of financial support through a Graduate Research

Associateship, and paying for me to attend conferences in San Antonio, Düsseldorf,

Phoenix, and Seoul. Your door has always been open to me, and I can’t count the times you’ve explained something to me, or helped me see the big picture when bogged down with insignificant details. I’ll also miss our Monday-morning quarterbacking, discussions on the relative merits of flat plates, and all of your great stories and one-liners. It has not v

only been an honor to work for you for five years, but also a great pleasure. “I haven’t had this much fun since the hogs ate my sister!”

Second I’d like to thank my advisor Dr. Randall Mathison. You’ve been my main mentor since I first arrived, teaching me not only the specific processes and systems in place at the GTL, but answering my questions about gas turbine operation and theory, and general engineering and aviation principles as well. You’ve been a great resource to bounce ideas off of, and have always been willing to take the time to point me in the right direction when I got stuck.

I would also like to thank the other two professors on my dissertation committee:

Dr. Sandip Mazumder, and Dr. Jeff Bons. In addition to serving on my committee, they have been two of the best teachers I have had the privilege of learning from.

I would also like to thank Honeywell Engines in Phoenix, Arizona for their continued support of me and this project. Honeywell provided the majority of the engine hardware utilized for this work, as well as much of the funding. In particular, I would like to thank Jong Liu, Kuo-San Ho, and Benjamin Kamrath for performing the CFD computation that is used in this dissertation, Rajiv Rana for extensive work in the design of the experiment, Malak Malak for management of the project, and Mark Morris for many thoughtful comments and contributions.

Thanks also go to fellow graduate student Matt Tomko for performing much of the early analysis on the pressure data in the purge cavity, providing me with a good foundation from which to work.

This dissertation would not have been possible without the technical expertise of

Jeff Barton, Dr. Igor Ilyin, Ken Fout, and Jonny Lutz in the design, building, and instrumenting of the experiment. Additionally, thanks to Josh Guith for assisting me in the machine shop on more than one occasion, and undergraduate research assistants Chris

Cosher, Kevin McManus, Eric Barbe, Miles Reagans, and Richard Celestina for help with the many miscellaneous tasks associated with the experiment.

I am also grateful for the administrative assistance I received. Thanks to Cathy

Mitchell, and Steve Pruchnicki for assistance out here at the GTL with purchasing and travel authorization and reimbursement. Janeen Sands was also instrumental for helping me to cut through the red tape and answering my countless questions about the convoluted processes and copious paperwork required to do anything at this University.

This dissertation is just one in a long line of works on rotating turbine stages presented by previous graduate students at the Gas Turbine Laboratory. While I have never actually met most of them, I am indebted to countless former GTL graduate students, particularly Dr. Charlie Haldeman, James Murphy, Brian Cohen, Dr. Randy Mathison, Dr.

Brian Green, and Dr. Matt Smith for performing previous work that helped lay the groundwork for this experiment, and for learning a number of lessons the hard way so I wouldn’t have to.

Despite the overall good experience that working in the GTL has been, I would have gone crazy long before reaching this point had it not been for the many friends that I met along the way. Thanks go to Sanjay Ramdon, Shauna Adams, Imani Adams, Steven

vii

Ramirez, Arvind Mohan, Bingya Li, Jiazheng Hong, Venkata Subramanian, Yibo Shao,

Xiao Wu, Emily Dreyer, Ben Grier, Anna Wu, and Soohyun Im for helping me to escape work when I needed to. Further thanks go to the friends that surrounded me at work every day. Through academic and intellectual discussions, tea breaks, Friday lunches, debugging expeditions, mutual complaining sessions, football arguments, lab cricket, and after-work drinks, I owe my sanity and perseverance to having you guys around me every day. Thanks to Alex Habib, Jonny Lutz, Anshuman Pandey, Chris Cosher, Hannah Pier, Tim Lawler,

Matt Tomko, Kiran D’Souza, Miles Reagans, Richard Celestina, Eric Kurstak, and Meng-

Hsuan Tien for the countless distractions, conversations, lessons, and for being awesome friends and colleagues.

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VITA

January 3, 1990 ...... Born—Mayfield Heights, Ohio

May 2011 ...... B.S. Mechanical Engineering, Rose-Hulman Institute of Technology

May 2013 ...... M.S. Mechanical Engineering, The Ohio State University

October 2011-Present...... Graduate Research Associate, The Ohio State University Gas Turbine Lab

PUBLICATIONS

 Nickol, J.B., Mathison, R.M., Malak, M.F., Rana, R., Liu, J.S., 2015, "Time-Resolved Heat Transfer and Surface Pressure Measurements for a Fully Cooled Transonic Turbine Stage", ASME J. Turbomach, 137(9), pp. 091009.

 Nickol, J.B., Mathison, R.M., Dunn, M.G., 2014, "Heat-Flux Measurements for a Realistic Cooling Hole Pattern With Multiple Flow Conditions", ASME J. Turbomach, 136(3), pp. 031010.

 Nickol, J.B., Mathison, R.M., Dunn, M.G., Liu, J.S., Malak, M.F., 2016, "Unsteady Heat Transfer and Pressure Measurements on the Airfoil of a Rotating Transonic Turbine with Multiple Cooling Configurations", ASME Turbo Expo 2016, Seoul, Republic of Korea, ASME Paper No. GT2016-57768.

 Nickol, J.B., Mathison, R.M., Dunn, M.G., Liu, J.S., Malak, M.F., 2016, "An Investigation of Coolant Within Serpentine Passages of a High-Pressure Axial Gas Turbine Blade", ASME Turbo Expo 2016, Seoul, Republic of Korea, ASME Paper No. GT2016-57776.

 Nickol, J.B., Mathison, R.M., Dunn, M.G., Malak, M.F., Liu, J.S., 2015, "Heat Transfer and Pressure Measurement Features for a Cooled Single Stage High Pressure Transonic Turbine", ISABE Conference 2015, Phoenix, Arizona, USA, ISABE2015- 20191.

 Nickol, J.B., Mathison, R.M., Malak, M.F., Rana, R., Liu, J.S., 2014, "Time-Resolved Heat Transfer and Surface Pressure Measurements for a Fully-Cooled Transonic Turbine Stage", ASME Turbo Expo 2014, Düsseldorf, Germany, ASME Paper No. GT2014-26407.

 Nickol, J.B., Mathison, R.M., Dunn, M.G, 2013, "Heat-Flux Measurements for a Realistic Cooling Hole Pattern With Multiple Flow Conditions", ASME Turbo Expo 2013, San Antonio, Texas, USA, ASME Paper No. GT2013-94925.

 Nickol, J.B., 2013, "Heat Transfer Measurements and Comparisons for a Film Cooled Flat Plate with Realistic Hole Pattern in a Medium Duration Blowdown Facility", M.S. Thesis, Dept. Mechanical and Aerospace Engineering, The Ohio State University, Columbus, Ohio, USA.

FIELDS OF STUDY

Major Field: Mechanical Engineering

TABLE OF CONTENTS

Abstract ...... ii

Acknowledgements ...... v

Vita ...... ix

List of Tables ...... xiv

List of Figures ...... xv

Nomenclature and Abbreviations ...... xxii

Chapter 1 Introduction ...... 1 1.1 Significance of the Problem ...... 1 1.2 Scope and Contributions of this Dissertation...... 4 1.2.1 Design and Construction of the Experiment Cooling Circuit ...... 4 1.2.2 Internal Cooling Rate Model and Investigation ...... 4 1.2.3 Airfoil Measurements ...... 6 1.2.4 Purge Cavity Investigation ...... 7 1.2.5 Platform Heat Transfer ...... 8 1.3 Literature Review...... 8 1.3.1 Serpentine Coolant Flows ...... 8 1.3.2 Airfoil Measurements ...... 9 1.3.3 Purge Cavity Flows ...... 12 1.3.4 Platform Heat Transfer ...... 14 1.4 A Note on Units ...... 15

Chapter 2 Methodology ...... 17 2.1 Description of the Facility ...... 17

2.1.1 Large Cooling Facility ...... 20 2.2 Turbine ...... 22 2.3 Instrumentation ...... 28 2.3.1 Heat-Flux ...... 28 2.3.2 Pressure Measurements ...... 33 2.3.3 Temperature Measurements ...... 36 2.4 Run Sequence...... 37 2.6 Operating Conditions ...... 40 2.6.2 Complete Run Matrix ...... 42 2.8 Computational Setup ...... 45

Chapter 3 Cooling Circuit Design ...... 49 3.1 Design Requirements ...... 49 3.2 Coolant Circuit ...... 52 3.2.1 LCF Supply Tank, FAV, and Plenum ...... 53 3.2.2 Cooling Massflow Instrumentation ...... 55 3.2.3 Syltherm-to-Coolant Heat Exchangers ...... 57 3.2.4 Syltherm Circuit ...... 59 3.2.5 Cooling Circuit Evactuation System ...... 60 3.2.6 Piping Choices ...... 62 3.3 Metering Chokes ...... 63 3.3.1 Metering Choke A ...... 66

Chapter 4 Data Reduction...... 69 4.1 Heat-Flux ...... 69 4.2 Pressure and Temperature ...... 70 4.3 Coolant Massflow Rates ...... 70 4.4 Encoder Averaging ...... 70

Chapter 5 Uncertainty ...... 72 5.1 Kapton Heat-Flux Gauges...... 72 5.2 Pressure Transducers ...... 74 5.3 Gauge Location ...... 74 xii

5.5 Summary Table of Uncertainties ...... 75

Chapter 6 Internal Flow Model—Necessity and Theory...... 76 6.1 Requirement for the Flow Model ...... 77 6.2 Physical Turbine Cooling Domain...... 82 6.3 Domain of the model ...... 86 6.4 Mathematical Formulation of the Flow Model ...... 89 6.4.1 Passage Flow Equations ...... 90 6.4.2 Cooling Hole Equations ...... 96 6.4.3 Blowing Ratio Definitions ...... 99 6.5 Validation of the Flow Model ...... 101 6.6 A Note on Cooling Hole Shape ...... 102

Chapter 7 Internal Flow Model—Results ...... 104 7.1 Nominal TOBI Case ...... 104 7.2 Variable TOBI Flow Cases ...... 118

Chapter 8 Airfoil Heat Transfer Results ...... 124 8.1 Time-Averaged Results ...... 125 8.3 Time-Resolved Results ...... 135

Chapter 9 Purge Region Pressure Results ...... 141 9.1 Time Averaged Results ...... 142 9.2 Time-Resolved Results ...... 147

Chapter 10 Platform Heat Transfer Results ...... 157 10.1 Time-Average ...... 157 10.2 Time-Resolved ...... 162

Chapter 11 Conclusions ...... 165

Bibliography ...... 169

Appendix A Equation Summary of Internal Model ...... 177

xiii

LIST OF TABLES

Table 2.1: Rig operating conditions ...... 41

Table 2.2: Variable parameter values ...... 41

Table 2.3: Full matrix of all runs ...... 43

Table 3.1: Target cooling circuit flow rates as a percentage of vane-inlet massflow ...... 50

Table 5.1: Summary of experimental uncertainties ...... 75

Table 6.1: Summary of cooling passage information ...... 86

Table 6.2: Summary of discharge coefficients for each cooling row ...... 99

Table 6.3: Comparison of measured TOBI flow to predicted blade flows ...... 102

Table 7.1: Minimum and maximum blowing ratios by row ...... 120

Table 8.1: Summary of cooling blowing ratio for each cooling row ...... 124

Table A.1: Summary of unknown variables for internal model ...... 178

Table A.2: Equation summary of internal model ...... 179

xiv

LIST OF FIGURES

Figure 1.1: Turbine inlet temperature progress for Rolls-Royce engines [2] ...... 3

Figure 2.1: Photo of the TTF shock tunnel (red) with expansion nozzle (yellow) and dump

tank (red) in the background ...... 18

Figure 2.2: Photo of the expansion nozzle connecting to the dump tank ...... 18

Figure 2.3: Schematic of the rig within the expansion nozzle and dump tank (not to scale)

...... 19

Figure 2.4: Photo of the LCF and cooling circuit outside of the dump tank ...... 21

Figure 2.5: Schematic of the entire cooling circuit ...... 21

Figure 2.6: Schematic of the turbine stage with each major flow labeled (not to scale) .. 23

Figure 2.7: Photo of the rotor blade suction and pressure sides for a round-hole blade with

midspan static pressure instrumentation (not to scale) ...... 24

Figure 2.8: Schematic of internal cooling passages within each rotor blade (not to scale)

...... 25

Figure 2.9: Schematic of the different blades in the “rainbow rotor” (not to scale) ...... 26

Figure 2.10: Photos (not to scale) of the three cooling hole shapes: cylindrical (a), fan (b),

and advanced (c) ...... 27

Figure 2.11: Schematics of the three hole shape geometries ...... 28

Figure 2.12: Photo of a Kapton heat-flux gauge from above [69] ...... 29

Figure 2.13: Schematic (not to scale) of a two-sided heat-flux gauge [70] ...... 30

Figure 2.14: Schematic of the blade platform with locations of all platform heat-flux gauges

(not to scale) ...... 32

Figure 2.15: Schematic giving location of blade root pressure transducers (not to scale) 34

Figure 2.16: Schematic showing pressure transducer locations on rotor platform inner

endwall (not to scale) ...... 35

Figure 2.17: Schematic showing pressure transducer locations on stator inner endwall (not

to scale) ...... 36

Figure 2.18: Computational domain (not to scale) ...... 46

Figure 2.19: CFD heat-flux contour illustrating “boxing” method (boxes and airfoil both

not to scale) used to laterally-average pressure and Stanton number for comparison

...... 48

Figure 3.1: Schematic of the full cooling circuit ...... 52

Figure 3.2: Photo of the Large Cooling Facility (LCF) supply tank ...... 54

Figure 3.3: Photo of the LCF FAV and plenum ...... 55

Figure 3.4: Close-up photo of the three massflow meters ...... 56

Figure 3.5: Photo of LCF with lines to Micromotion massflow meters ...... 57

xvi

Figure 3.6: Photo of the Syltherm-to-coolant heat exchangers...... 58

Figure 3.7: Schematic of cooling circuit with evacuation components highlighted ...... 62

Figure 3.8: Needle valve effective throat area experimental circuit ...... 65

Figure 3.9: Picture and schematic of metering choke ‘A’ ...... 67

Figure 3.10: Picture and schematic of metering choke ‘B’ ...... 68

Figure 6.1: Plot of experimental and computational internal and external pressure ...... 80

Figure 6.2: Photograph of suction and pressure sides of an airfoil instrumented with

pressure transducers with cooling rows labeled (not to scale) ...... 82

Figure 6.3: Schematic of labeled airfoil serpentine passages and cooling rows (not to scale)

...... 83

Figure 6.4: Stencil of the numerical mesh ...... 88

Figure 7.1: Normalized internal static pressure with data labeled for the 6.85% TOBI flow

case ...... 105

Figure 7.2: Normalized internal static temperature with data labeled for the 6.85% TOBI

flow case ...... 107

Figure 7.3: Global blowing ratio vs. span for every cooling hole, labeled by row, for 6.85%

TOBI flow ...... 109

Figure 7.4: Normalized airfoil pressure at the ejection location of each cooling hole ... 111

xvii

Figure 7.5: Local blowing ratio vs. span for every cooling hole, labeled by row, for 6.85%

TOBI flow ...... 113

Figure 7.6: Local freestream massflux normalized by the global average ...... 114

Figure 7.7: Local blowing ratio vs. span for every cooling hole, labeled by row, for 6.85%

TOBI flow, zoomed in ...... 116

Figure 7.8: Average local blowing ratio for each cooling row at various TOBI flow rates

...... 119

Figure 7.9: Row averaged isentropic ejection Mach number vs. TOBI flow ...... 123

Figure 7.10: Fraction of maximum flow through a choked hole as a function of the

isentropic ejection massflow ...... 123

Figure 8.1: Computational and experimental airfoil pressure measurements ...... 127

Figure 8.2: Computational and experimental airfoil midspan Stanton number for different

cooling hole shapes ...... 131

Figure 8.3: Time-averaged midspan Stanton number for round holes ...... 133

Figure 8.4: Time-averaged midspan Stanton number for fan-shaped holes ...... 133

Figure 8.5: Time-averaged midspan Stanton number for advanced-shaped holes ...... 134

Figure 8.6: Schematic showing locations of airfoil gauges by %WD ...... 135

Figure 8.7: Stanton number encoder average data for all cooling holes at -27%WD .... 138

Figure 8.8: Stanton number encoder average data for all cooling holes at -50%WD .... 138

xviii

Figure 8.9: Stanton number encoder average data for all cooling holes at -69%WD .... 139

Figure 8.10: Stanton number encoder average data for all cooling holes at +78%WD.. 139

Figure 8.11: Stanton number encoder average data for all cooling holes at +57%WD.. 140

Figure 8.12: Stanton number encoder average data for all cooling holes at +53%WD.. 140

Figure 9.1: Summary of lettered pressure transducer locations ...... 141

Figure 9.2: Time-averaged normalized pressure measurements for purge region and blade

platform ...... 144

Figure 9.3: Zoom-in of blade root gauges of Figure 9.2 ...... 144

Figure 9.4: Vane inner endwall pressures for three different vane passages, angles defined

from Top Dead Center ...... 146

Figure 9.5: FFT of pressure signals for locations A and C at nominal flow rates ...... 147

Figure 9.6: Normalized pressure encoder averages of purge cavity signals ...... 149

Figure 9.7: Encoder average fluctuation from the mean for location A for variable TOBI

flow rates ...... 151

Figure 9.8: Encoder average fluctuation from the mean for location B for variable TOBI

flow rates ...... 151

Figure 9.9: Encoder average fluctuation from the mean for location C for variable TOBI

flow rates ...... 153

xix

Figure 9.10: Encoder average fluctuation from the mean for location D for variable TOBI

flow rates ...... 153

Figure 9.11: Schematic of (blue) vane wakes heading towards locations C and D ...... 155

Figure 9.12: Encoder average fluctuation from the mean for location C for variable aft

purge flow rates ...... 156

Figure 9.13: Encoder average fluctuation from the mean for location D for variable aft

purge flow rates ...... 156

Figure 10.1: Plot of all time averaged platform Stanton numbers for nominal cooling . 158

Figure 10.2: Plot of aft time averaged platform Stanton numbers for nominal cooling . 159

Figure 10.3: Stanton number vs. TOBI flow rate for pressure side upper platform gauges

...... 161

Figure 10.4: Aft edge and pressure Stanton number variation with aft purge cooling flow

...... 161

Figure 10.5: Stanton number encoder average fluctuation for various TOBI flows for gauge

at 54%AD ...... 163

Figure 10.6: Stanton number encoder average fluctuation for various TOBI flows for gauge

at 60%AD ...... 163

Figure 10.7: Stanton number encoder average fluctuation for various aft purge flows for

gauge at 54%AD ...... 164

Figure 10.8: Stanton number encoder average fluctuation for various aft purge flows for

gauge at 60%AD ...... 164

xxi

NOMENCLATURE AND ABBREVIATIONS

Roman

퐴 Area

퐴푐 Passage cross-sectional area

퐴푒푓푓 Choke effective cross-sectional area

퐴ℎ Cooling hole cross-sectional area

퐴푔푒표 Choke geometric (physical) area

퐴푠 Wetted surface area 푎 First power calibration coefficient 푏 Second-power calibration coefficient 퐵푅 Blowing Ratio

퐶푑 Coefficient of discharge

푐푝 Specific heat capacity at constant pressure

퐷ℎ Hydraulic diameter 푑 Kapton thickness 퐷푅 Density Ratio 푒 Turbulator height 퐹퐹 Flow function 푘 Thermal conductivity 푚̇ Massflow rate 푀푎 Mach number 푀푎̿̿̿̿ Capped (at unity) Mach number 푀푅 Momentum Ratio 푁 Engine rotational speed

푁푐 Engine corrected speed xxii

푃 Turbulator pitch 푝 Pressure 푃푟 Prandtl number 푅 Specific gas constant 푟 Radial (spanwise) coordinate 푅푒 Reynolds number 푅표 Rotation number 푆푡 Stanton number 푇 Temperature 푢 Fluid velocity (absolute or arbitrary frame) 푤 Fluid velocity (rotating frame)

Greek

훾 Ratio of specific heats 휃 Angle 휇 Dynamic viscosity 휌 Fluid density Ω Angular velocity

Subscripts

푐 Coolant 푐푒푛푡 Due to centrifugal effects 푐표푟 Due to Coriolis effects 푐표푟푒 Main stage flow 푒 Airfoil external condition 푓 Due to frictional forces 푖 At ith node 푖푛 Stage inlet 푗 Cooling hole jet flow condition 퐿 Lower gauge (on two-sided HFG) xxiii

푀 At midspan node with experimental measurement 푁 At tip (final) node 푛 Normalized (by stage inlet total condition) 푟 In rotating frame 푟푒푓 Atmospheric reference condition (for normalizing) 푡 Total (stagnation) condition in absolute frame 푡푟 Total (stagnation) condition in rotating frame 푈 Upper gauge (on two-sided HFG) 푤 Wall 0 Initial value (before run) ∞ Freestream (turbine core flow)

Superscripts

→ Vector

Other symbols

∇ Nabla (del) operator

Abbreviations ARC The Ohio State University Aerospace Research Center CHT Conjugate Heat Transfer FAV Fast-Acting Valve FFT Fast Fourier Transform GTL The Ohio State University Gas Turbine Laboratory HFG Heat-Flux Gauge HPT High-Pressure Turbine HXR Heat Exchanger LCF Large Cooling Facility OSU The Ohio State University RANS Reynolds-Averaged Navier-Stokes xxiv

RTD Resistance Temperature Detector TDC Top Dead Center TOBI Tangential On-Board Injector TTF Turbine Test Facility URANS Unsteady Reynolds-Averaged Navier-Stokes %AD Percent Axial Distance %WD Percent Wetted Distance

xxv

CHAPTER 1 INTRODUCTION

An experiment is carried out on a full scale high-pressure turbine (HPT) stage manufactured by Honeywell Engines at The Ohio State University (OSU) Gas Turbine

Laboratory (GTL). The experiment investigates several active research targets within the axial gas turbine community simultaneously, all related to the thermal and aerodynamic performance of axial gas turbines subject to various cooling technologies. The goal of this work is to obtain a better understanding of these cooling technologies, enabling their better utilization of cooling flow, with an ultimate goal of greater fuel efficiency and engine reliability.

1.1 SIGNIFICANCE OF THE PROBLEM

Rising fuel costs and a better awareness of the environmental impact of power generation have resulted in strong efforts to increase the efficiency of combustion engines of all kinds. Propulsive gas turbines, or jet engines, are of particular interest. Air travel is the dominant mode of transportation over large distances, with total passengers in excess of 3.3 billion annually, and climbing more than 5% per year [1]. Increases in overall fuel economy also have a compounding effect for propulsive applications, as the aircraft don’t have to carry as much fuel, reducing weight and giving a further boost to efficiency.

Additionally, unlike combustion engines for other applications such as automotive and

electricity generation, there are no alternative technologies emerging that have promise to take significant market share away from jet engines.

The effort to improve fuel economy in propulsive applications has many directions.

In addition to improvements in engine efficiency, new aircraft take advantage of computational advances to create more streamlined and aerodynamic profiles. New composite materials also enable significant weight savings in the airframe without sacrificing strength or safety of the craft. That being said, improvements in engine efficiency still have a direct link to reducing fuel consumption.

Within the effort to improve engine efficiency, there are again several active areas of research. There is extensive work in improving compressor efficiency and reliability.

The combustor is also studied intensely as increased temperatures of combustion result in increased generation of nitrous oxides (NOx) and damage to combustor hardware. Possibly the most active area of research is also the subject of this dissertation, the high-pressure turbine (HPT). One of the ways to increase efficiency is to increase the combustion temperatures, and therefore the HPT inlet temperature, but this can only be done to the degree to which the turbine materials can withstand. Figure 1.1 shows the progress in turbine inlet temperature since 1940 for Rolls-Royce engines. Advances in high- temperature materials and thermal barrier coatings have allowed significant increases in temperature, but further advances have also been made through advanced active cooling of the hardware, several forms of which are investigated herein.

Figure 1.1: Turbine inlet temperature progress for Rolls-Royce engines [2]

This dissertation investigates an experiment on a one-stage high-pressure turbine operating at design-corrected conditions. The stage features rotor film cooling with three different shapes of film cooling hole. Additionally, purge cooling flow is provided in various quantities to both forward and aft cavities. These cooling flows are used in every modern gas turbine to protect the high-pressure rotor and disk, but are still not fully understood or reliably predicted by computational tools. The flow physics are very complicated, and conditions in actual engines are too harsh for detailed instrumentation.

Experimental rigs that can capture most of the relevant flow phenomena are rare and expensive to run, making the insight provided by the experiment presented in this dissertation very valuable.

1.2 SCOPE AND CONTRIBUTIONS OF THIS DISSERTATION

This dissertation attempts to address several different research targets. Each of these, and the specific contributions to the literature, are described briefly below.

1.2.1 DESIGN AND CONSTRUCTION OF THE EXPERIMENT COOLING CIRCUIT

The majority of the technical design and construction work for the experiment presented in this dissertation was performed at the GTL, with the turbine hardware mostly being provided directly from Honeywell Engines. It is important to note that the cooling circuit was designed, constructed, validated, and operated during the experiment by the author of this dissertation. The choke manifold design was loosely based off of a design from a previous cooled turbine experiment run by the GTL, however no design methodologies had been written or published previously. The cooling circuit designed herein successfully achieved all of its requirements, and it is one of the goals of this dissertation that the methodology be published so that it could be used as a starting point for similar experiments.

1.2.2 INTERNAL COOLING RATE MODEL AND INVESTIGATION

Film cooling research typically utilizes various non-dimensionalized measurements to quantify film-cooling rates, such as blowing ratio and density ratio. These quantities are easy to calculate for computations, and can be relatively straightforward to measure on simplified geometries such as flat plates and stationary cascade facilities. It becomes much more difficult to measure on rotating geometries. Often averages are found by measuring the total cooling flow rates and the total freestream flow rates and using these, but this

neglects the variability in both coolant and freestream conditions with respect to location on the test article.

Temperature and pressure measurements are taken at midspan in several of the internal cooling passages, and these data are extrapolated to the remainder of the passage using a model designed by the author, and described in this dissertation. This model is then used to determine massflow rates and blowing ratio for each cooling hole, and the results are investigated both as functions of span, and location on the airfoil.

The model is presented in detail and, although the specifics are only applicable to this turbine design, it could easily be modified to work for other geometries as long as similar boundary conditions are available. Analyzing the specific trends for this airfoil is further valuable because the results show how significant the variation in blowing ratio is across an actual gas turbine airfoil. Quantifying this variation is important because most research to date has assumed blowing ratio to be a constant everywhere. This is one of the first works that investigates and attempts to either validate, or discredit this assumption.

The final contribution of this model is simply to provide values of blowing ratio for this airfoil film cooling investigation. In order to compare the cooling effectiveness seen in this experiment with those from other experiments published in the literature, it is important to be able to compare like cooling flow rates, and the model allows this report to present more details blowing ratio data than that from any cooled rotating turbine experiment previously reported.

1.2.3 AIRFOIL MEASUREMENTS

The experiment utilized a rainbow turbine approach, investigating airfoils with three different shaped cooling holes simultaneously, as well as a sector of uncooled airfoils.

The hole shapes are a simple cylindrical hole shape, a diffusing fan-shaped hole, and a novel Honeywell proprietary advanced shaped hole [3, 4]. Shaped cooling holes have been found to produce significant boosts to the coolant’s ability to remain close to the surface of the airfoil, and therefore cool the surface better. Unfortunately all of this research has been either computational, or on simplified geometries. This dissertation (and its accompanying technical paper by the same author [5]) represents the first rotating experiment that investigates shaped cooling holes that will be published in the open literature. This is particularly important because shaped cooling holes are already becoming common in practice, despite the overall lack of open research for engine- representative test sections.

In addition to heat transfer, the airfoil also features static pressure transducers at various locations around midspan. The midspan pressure field, steady and unsteady, is relatively well understood and able to be predictable by computations (see [6, 7] for examples), but it is still important to measure and confirm that any computation can predict pressure before attempting to predict heat transfer.

The heat transfer and pressure on the airfoil is investigated both in time-averaged, and time-resolved bases. At this time, only a steady (time-averaged) computation exists to compare the data to, but the unsteady phenomena are still significant, and it is worth investigating them. Rao et al. [8] and Allan et al. [9] have shown the instantaneous heat

transfer at certain locations on rotating airfoils can be more than double the time-averaged value, while Dunn et al. [10] has shown the same for surface pressure.

1.2.4 PURGE CAVITY INVESTIGATION

Both forward and aft purge coolant flow rates are varied over the run matrix for this experiment. These purge cavities feature complicated flow phenomena. One wall is rotating, with the other stationary, and the rotating wall acts as a centrifugal pump, forcing air radially outward. In the absence of any supplied flow to this cavity, flow gets pumped out on the rotating-wall side, and consequently sucked back in on the stationary side. This gas ingestion is a significant worry because the gas that gets ingested in an engine would be very hot, and could damage the components in the cavity. The gap is kept small, and there is also a labyrinth seal to create a high-resistance flow path, which will reduce the ingestion, but ultimately the only way to eliminate it is to continually supply cool air at the hub. This keeps the net flow of gas out of the purge cavity.

The forward purge cavity is instrumented with numerous pressure transducers in different locations. The total supplied purge flow is varied both above and below an engine- representative nominal flow rate, and an analysis on the transducers gives valuable insight into the flow within the purge cavity.

Additionally, several pressure transducers are located on the inner endwalls of the stator (aft of the airfoils) and the rotor (forward of the airfoils). The purge ejection will result in some blockage to the core flow, and its impact is seen for variable purge flow rates. An unsteady analysis of these pressures also shows the impact of the stator airfoils on the rotor inner endwall, as well as within the purge cavity beneath the labyrinth seal.

The signal’s relative amplitudes show the effect of the seal geometry at preventing unsteady pressure waves from propagating down into the cavity.

1.2.5 PLATFORM HEAT TRANSFER

Heat-flux gauges are also placed on the rotor platform (inner endwall), and on the platform underside. This region may or may not be directly cooled by the purge flow ejection, but as mentioned previously, the ejection will create a blockage that will modify the flow field in the inner endwall region, so it is likely that there will at least be some indirect impact on platform heat transfer.

Gauges are placed at mid-chord between airfoils, as well as aft of the airfoils, and the impact of varying both forward and aft purge flow rates are investigated on both time- averaged and time-resolved bases.

1.3 LITERATURE REVIEW

Gas turbine cooling is a major subject of research, with thousands of technical papers devoted to it in many specific areas. A review of the open literature for the major research targets of this dissertation follows.

1.3.1 SERPENTINE COOLANT FLOWS

Because the experiment reported here is short-duration, heat does not propagate through the metal of the airfoil into these serpentine passages, so the facility is not a good vehicle to investigate internal cooling effectiveness. However the airfoils are production models, and the serpentine passages that feed the film cooling holes are designed with turbulators and turn geometries to maximize heat transfer while minimizing pressure loss.

Optimal design of these passages is a very important research target, and many experiments have been published on the topic, most notably the HOt Section Technology (HOST) experiments funded by NASA [11-16].

The main goal of the model is to determine blowing ratio for each hole on a rotating turbine experiment, which has never been done in detail for an experiment. One of the first film-cooled rotating experiments was performed by Dring et al. [17]. The paper did present blowing ratios, but there was only a single cooling hole on both the pressure and suction sides. Abhari and Epstein [18] performed a rotating experiment with five rows of cooling holes, and quantified average blowing and momentum ratios for two of the rows, but did not quantify blowing for the other rows, or investigate any spanwise variation. A more recent experiment reported by Haldeman et al. [19] quantifies total rotor cooling as a percentage of core flow, but does not quantify fooling flows in a row-by-row basis, or provide blowing ratio values.

1.3.2 AIRFOIL MEASUREMENTS

One of the earliest experiments on film cooling was performed by Papell and Trout

[20] on a flat plate with a single slot for cooling. Since then, thousands of papers have looked at film cooling with respect to many variables. Among these are cooling parameters such as blowing ratio and momentum ratio, freestream conditions such as turbulence and

Mach number, and cooling hole geometry. Unfortunately the vast majority of these papers have used a simplified geometry as the test article. An experiment by Dunn et al. [21, 22] compared results from a rotating experiment to flat plates and found that they were entirely different, while an experiment by Guenette et al. [23] compared to a cascade and found

that the cascade does reasonably well at matching time-averaged results from rotating experiments away from the leading edge. A review of many of the works on non-rotating geometries is provided by Bogard and Thole [24].

Past work on rotating experiments have investigated many individual variables.

Dunn et al. [21, 22] showed that stator trailing edge cooling causes an increase to rotor airfoil heat transfer. Dring et al. [17] and Abhari et al. [18] looked experimentally at the change in heat transfer due to film cooling and found the suction sides experienced much greater drops in heat transfer. Abhari [25] performed an experiment that was simulated computationally in 3D by Garg and Abhari [26] and in 2D by Abhari [27], and showed that the 2D simulation performed adequately at midspan where there was no cooling, and that both predictions were much more successful on the airfoil suction side. Povey et al. [28] and Kahveci et al. [29] investigated the effect of more engine-realistic inlet temperature profiles at the vane inlet (as opposed to a flat profile), showing significant variations on airfoil heat transfer as compared to a “mixed” profile. The significance of unsteady interactions have also been explored by many of these experiments [6, 8, 9, 18, 21, 22, 25].

A further review on rotating axial gas turbine experiments is provided by Dunn

[30]. This work focuses on both aerodynamics, as well as convective heat transfer, in both experimental and computational regards.

The main unique contribution of this thesis with regards to airfoil heat transfer is the examination of shaped cooling holes on a rotating geometry. The first investigation that looked into shaping cooling holes was published by Goldstein and Burggraf [31], and since then significant progress has been made on understanding the physics and behavior of cooling

flow. Haven et al. [32] showed how regular cylindrical cooling jets produce counter- rotating kidney vortices on either side of the cooling flow that act to lift the cooling flow off, while entraining hot gas on the surface intended to be cooled. They continued to explain how diffusing the flow while still in the cooling hole would create vortical motion in the opposite direction, significantly reducing the flow liftoff. Brittingham and Leylek

[33] performed one of the earliest investigations on shaped cooling holes that coupled experiment with CFD, and this enabled them to show significant detail into the actual physics of the counter-rotating vortices found at each cooling hole exit. There are hundreds of other papers detailing specific differences in film cooling performance for different diffuser-shaped holes; a review that summarizes these has been performed by Bunker [34].

One of the disadvantages of non-cylindrical cooling holes is the added cost of manufacturability. For this reason, there are several unique cooling schemes that combine simple cylindrical holes to produce counter vortices. One scheme that features two smaller holes to complement each main cooling hole was investigated computationally by

Heidmann and Ekkad [35], and experimentally by Dhungel et al. [36], and seen to produce cooling results in between that of standalone cylindrical holes, and diffuser-shaped holes.

Another approach is to have a cylindrical cooling hole eject into a crater [37] or trench

[38], which also results in cooling effectiveness between that of the cylindrical and diffuser-shaped holes, and can be manufactured easier than diffusing holes.

At the other end of the spectrum is to utilize more complicated shaped cooling holes that perform even better than diffuser-shaped holes, and accept the greater manufacturing cost as a trade-off. Okita and Nishiura [39] used a cascade facility to compare a literature-

typical laidback fan-shaped hole to an arrowhead-shaped hole designed to counter the kidney vortices that induce liftoff. On the suction-side, the arrowhead-shaped holes were found to provide significantly higher effectiveness for higher blowing ratios (greater than

2.3, which is representative of suction-side cooling). On the pressure side, the arrowhead shape provided better coverage across all blowing ratios presented (0.6-2.3). Other complicated hole shapes that have presented superior film cooling, even to diffuser shaped holes, include a dumbbell shaped, and bean shaped hole presented by Liu et al. [40], as well as a crescent shaped hole, and a converging slot hole presented by Lu [41].

Despite all of the work mentioned, the Honeywell advanced shape hole is novel to the literature. Additionally, there are no studies comparing different film cooling hole shapes on a rotating rig.

1.3.3 PURGE CAVITY FLOWS

The cavity between stationary and rotating disks is an area with a complicated flow field dominated by swirling and secondary flows. For the HPT, the core flow is still hot enough that it is critical to prevent significant ingestion of hot flow into the cavity. Much research has been done previously on this region, to better understand the flows and better insulate the cavity from the core.

Bayley and Owen [42] performed an early study on a simple cavity between one stationary and one rotating disk with gas supplied axially through the center of the stationary disk. Experiments were conducted both with and without a shroud around the stator, and a series of correlations were developed for flow, pressure, and rotor drag at various rotational Reynolds numbers. Since then, studies have been performed on more

realistic seal geometries and external environments. Phadke and Owen performed a series of experiments comparing the performance of seven different seal geometries subject to a quiescent external environment [43], as well as with axisymmetric [44] and nonaxisymmetric [45] external flow conditions.

An experiment on a purge cavity with upstream nozzle guide vane reported by

Green and Turner [46] investigated the ingestion (and thus seal effectiveness) both with and without a downstream blade row for variable rotor speed and core massflow. It was seen that with the blade row installed, at least some small amount of ingestion will occur, even with large amounts of purge cooling flow supplied.

Hills et al. [47] performed a computation of a purge cavity with a nozzle guide vane and blade row, and compared favorably with experimental data originally published by

Hills et al. [48], showing that the presence of the rotor increases the ingestion, and showing the importance of including it in any computational model.

Most of the prior work has been done on simplified cavity geometries, with turbine stages operating far from engine-representative conditions. Green et al. [49, 50] performed an experiment and computation on a stage operating at engine design-corrected conditions using real engine hardware and seals. The computation was able to predict the pressures and temperatures in the cavity both in time-average and time-accurate form. The computation also shows that the forward purge ejection causes a blockage for the core flow close to the hub, ultimately resulting in a reduction of tangential velocities and therefore an increase in suction side incidence and pressure. This results in a reduction of turbine power.

Similar results for a transonic turbine stage are reported by Paniagua et al. [51], who observed large blockage effects due to the purge flow. This important work was further extended by Pau et al. [52] and Pau and Paniagua [53], who investigated the excitation driven by the vane in more detail. It was shown that for the turbine studied, the vane trailing edge shocks played a strong role in shaping the unsteady hub flows. Blockage effects and unsteady interactions were also found to have a significant impact on performance in the work of Schuepbach et al. [54, 55]. In all studies, the inclusion of purge flow was found to reduce the performance of the turbine. Computational efforts have worked to capture these behaviors through both detailed CFD simulations and through simplified models that focus on the unsteady interactions [56].

1.3.4 PLATFORM HEAT TRANSFER

The rotor platform (inner endwall) doesn’t receive as much attention as the airfoil or blade tip in axial gas turbine research. The majority of blade platforms, including the one in this experiment, do not feature any film cooling of their own. The majority of the concern on the inner endwall is limited to cascade flows and is applied to contouring the endwall profile. This was originally used as a way to reduce secondary flow losses, as shown by Harvey et al. [57], but has more recently been expanded in application to also reduce heat transfer into the platform as originally proposed by Saha and Acharya [58].

Heat transfer measurements on rotating rigs are less common. Early tests by Dunn et al. [59, 60] do present platform data from a turbine without purge cooling, but the data are very limited and trends cannot be established. They do however show that platform heat transfer rates are on the same level as those found on the airfoil, and can be significantly higher

than the suction side, so it stands to reason that the platform is an important area to monitor and protect. A more detailed study by Tallman et al. [61] looked into the platform with many more measurement locations, and compared to a steady 3D RANS prediction. The prediction agreed fairly well with the heat transfer data on the platform, giving confidence to the predictive capabilities. Unfortunately, this experiment also featured no supplied purge cooling, and the computation didn’t mesh the purge cavity.

Another rotating experiment reported by Mathison et al. [62, 63] utilized stator film and purge cooling at variable rates. When both cooling circuits were turned off, the Stanton number increased on the platform both upstream and downstream of the airfoil, with a larger drop upstream. When the circuits were decoupled and the purge varied at constant vane film cooling rates, an increase in Stanton number in the case with no purge flow was still seen, but it was smaller and of similar magnitude both up and downstream of the blade. This is an interesting result that forward purge helps to cool the platform aft of the blade because the computational work by Green et al. [49, 50] (performed on the same experiment) showed that the purge flow remains close to the platform upstream of the rotor airfoil, but migrates up the blade soon after as part of the passage vortex, and does not directly cool the platform after the leading edge. It does, however, modify the flow field and it appears to indirectly cool the aft portion of the platform.

1.4 A NOTE ON UNITS

The majority of the final results of this dissertation will be presented in normalized, or non-dimensionalized form. For any quantity that is dimensional, both SI units, and US customary units will be provided. The first value listed (without parenthesis) will be given in units that the quantity was originally specified or measured in, and the second value (in

parenthesis) will be the conversion. Additionally, all pressures in this dissertation will feature an “a” or “g” tag to denote if the pressure is “absolute”, or “gauge”, respectively

(for example kPaa/kPag, psia/psig).

CHAPTER 2 METHODOLOGY

The turbine experiment was performed at The Ohio State University (OSU) Gas

Turbine Laboratory (GTL), using the Turbine Test Facility (TTF). A description of the experimental and computational methodology follows.

2.1 DESCRIPTION OF THE FACILITY

The OSU GTL TTF consists mainly of a shock tunnel connected to a dump tank through a diverging (supersonic) nozzle. The shock tunnel is 100 ft. (30 m) long and has an inner diameter of 18 in. (0.46 m), and is pressurized and operated in blowdown mode.

Where the tunnel opens to the expansion nozzle is a fast-acting valve (FAV) followed by a choke. A photo of the shock tunnel is provided in Figure 2.1, with a close-up of the expansion nozzle shown in Figure 2.2.

Figure 2.1: Photo of the TTF shock tunnel (red) with expansion nozzle (yellow) and dump tank (red) in the background

Figure 2.2: Photo of the expansion nozzle connecting to the dump tank

Within the expansion nozzle sits the inlet piece to the rig. As the flow is supersonic within the nozzle, a bow shock forms upstream of the inlet. How far up or downstream the rig is physically located within the nozzle affects the Mach number within the expansion nozzle at the bow shock, which in turn affects the strength of the shock. Thus the location of the rig inlet can be used to control the stage inlet pressure and Reynolds number. A schematic of the front of the shock tunnel, expansion nozzle, and rig is provided in Figure

2.3.

Figure 2.3: Schematic of the rig within the expansion nozzle and dump tank (not to scale)

Downstream of the rig inlet, the core flow passes through a combustor emulator.

The combustor emulator is a 2 ft. (0.61 m) long honeycomb mesh made of Inconel.

Imbedded throughout the honeycomb are heating rods consisting of simple electric heating elements, and RTDs. Prior to a run, the tank is evacuated of air and the heaters are turned

on. Inconel is chosen for its low thermal conductivity, which allows for temperature gradients to more easily be applied to the mesh by powering some heaters more than others, if that is desired. Previous experiments [6, 19, 62-67] have used radial inlet temperature profiles, as well as tangential hot streak inlet temperature profiles to simulate the unequal heating caused by actual combustors, but the experiment described herein only featured uniform temperature profiles. Due to the low conductivity, the heaters had to be turned on for at least three hours before the run to allow the Inconel to get up to temperature and fully disburse the heat throughout the mesh. The heaters were turned off about one minute before the run.

Two 300-channel slip rings are fixed to the shaft, one forward of the stage, and one aft. These are pointed out in Figure 2.3.

2.1.1 LARGE COOLING FACILITY

The Large Cooling Facility (LCF) is responsible for the coolant circuit for the turbine. The coolant-side of the LCF consists of a large supply tank, three MicroMotion massflow meters operating in parallel, heat exchangers, and a choke manifold to meter the flow. The heat exchangers chill the air using Syltherm as a coolant. Syltherm is chilled outside the tank by a chilling unit, and then a heat exchanger chilled with dry ice. More details in the design and operation of the cooling circuits are provided in Chapter 3. A photo of the LCF supply tank, and the parts of the cooling circuit that are outside the dump tank is provided in Figure 2.4, with a more complete schematic provided in Figure 2.5.

Figure 2.4: Photo of the LCF and cooling circuit outside of the dump tank

Figure 2.5: Schematic of the entire cooling circuit

2.2 TURBINE

The turbine stage is a one-stage high-pressure turbine (HPT) manufactured by

Honeywell Engines. A schematic of the stage cross-section is provided in Figure 2.6, with each of the major flows labeled in a different color. There are three main cooling paths, originating in two circuits. The TOBI flow is shown in green where it is injected into the stage, and promptly splits into the blade cooling flow (blue), and forward purge (purple).

It should be noted that some TOBI flow will also exit the rotor through one of a number of leakage paths through various bearings and seals. The forward purge flow then progresses through a labyrinth seal before ejecting between the stator and rotor. The blade flow enters through the disk of the rotor, proceeds up into the root if the blade, and is then ejected through one of the blade cooling rows, tip cooling holes, or trailing edge cooling slots. The other circuit is for the aft purge flow, ejected downstream of the rotor. The aft purge is metered and controlled separately from the TOBI flow. Both circuit flow rates can be controlled independently, and feature “nominal” settings that match coolant-to-core massflow ratios present in engine operation.

The stator consists of 12 vane doublets, for a total of 24 vane airfoils. The rotor consists of 38 blades.

Figure 2.6: Schematic of the turbine stage with each major flow labeled (not to scale)

The stator vanes are all identical to each other (to within production manufacturing and assembly tolerances). In the actual engine, the vanes are film-cooled, however for this experiment the cooling holes have been plugged to more controllably evaluate other parameters. The blades are all identical in geometric profile as well. A photo of both sides of a rotor blade airfoil is provided in Figure 2.7.

Each blade features seven rows of cooling holes in the airfoil (not including the trailing edge cooling slots). These cooling rows are labeled A through G, starting aft on the pressure side, and moving towards the leading edge, then back towards the trailing edge on the suction side (or clockwise in Figure 2.8), and are labeled (except for E which is not visible) in Figure 2.7.

Figure 2.7: Photo of the rotor blade suction and pressure sides for a round-hole blade with midspan static pressure instrumentation (not to scale)

There are six serpentine passages, labeled 1-6 starting with 1 at the leading edge, moving aft, as shown in Figure 2.8. There is a pressure and temperature transducer at midspan of Passages 2, 4, 5, and 6 (underlined in Figure 2.8) in three different blades (one of each cooling hole shape). More details on the geometry and mechanics of these passages is provided in Chapter 6.2.

Figure 2.8: Schematic of internal cooling passages within each rotor blade (not to scale)

It was previously mentioned that there are four different rotor-cooling configurations, tested simultaneously in a “rainbow turbine” approach. Each style of blade makes up a wedge of the overall rotor, as shown in Figure 2.9. No heat transfer instrumentation is on any blade on the edge of a wedge where there is a different style blade next to it (for example, Blades 7, 8, 14, 15, etc.).

It is also important to note that while there are seven rows of holes, four of the rows are round for all three cooled configurations. These rows are B through E, or the leading edge showerhead rows, with the exception of the furthest suction-side row. The shaped rows are A, F, and G, where the airfoil curvature is lower.

Figure 2.9: Schematic of the different blades in the “rainbow rotor” (not to scale)

The three hole shapes are a simple circular cross-sectioned cylindrical hole, fan- shaped diffuser, and a novel Honeywell advanced-shaped hole. Figure 2.10 provides a photo of all three cooling hole shapes, while Figure 2.11 provides a two-face diagram with angles dimensioned. Both the fan-shaped and advanced-shaped holes are cylindrical in cross-section before expanding to their ejection shape, and the cylindrical entry region is of the same diameter as the fully cylindrical holes. Each blade has the same number of holes in each row, and hole centers are located in identical locations.

Figure 2.10: Photos (not to scale) of the three cooling hole shapes: cylindrical (a), fan (b), and advanced (c)

Figure 2.11: Schematics of the three hole shape geometries

2.3 INSTRUMENTATION

The experiment features hundreds of instruments located to investigate all of the previously mentioned research targets.

2.3.1 HEAT-FLUX

Heat-flux is measured using two different kinds of heat-flux gauges (HFGs). The airfoil measurements on the uncooled blades are measured using one-sided Pyrex heat-flux gauges. These gauges are small cylinders (about 0.040 inch diameter (1.0 mm)) of Pyrex glass embedded such that one face of the cylinder is flush with the airfoil, with an RTD on the outer surface. These gauges operate by assuming the Pyrex starts off at a uniform temperature, and modeling the Pyrex as semi-infinite. The RTD is open to the core flow, and its temperature is used as the boundary condition in a one-dimensional semi-infinite conduction model. The assumption of semi-infinite behavior is obviously limited to short durations, but the experimental runs fall well within this range.

The remaining heat flux measurements, the cooled airfoil heat fluxes and platform heat fluxes, are measured using double-sided Kapton heat-flux gauges. These gauges feature two resistance-based temperature sensors, effectively RTDs, separated by a

0.002 inch (51 μm) Kapton sheet, which acts as a thermal and electrical insulator. The sensors are 0.040 by 0.044 inch (1.0 by 1.1 mm) in cross-sectional area, and less than 1 μm in height. The gauge is then held onto the airfoil by an adhesive. A photo of one gauge up close is shown in Figure 2.12, with a schematic provided in Figure 2.13.

The heat-flux is derived from the upper and lower temperatures using a one- dimensional transient heat transfer numerical model originally developed by Weaver et al.

[68].

Figure 2.12: Photo of a Kapton heat-flux gauge from above [69]

Figure 2.13: Schematic (not to scale) of a two-sided heat-flux gauge [70]

The two styles of heat-flux gauge each have their own advantages. The main advantage of the Pyrex gauge is its robustness. The majority of the Pyrex gauges survived the entire test matrix and didn’t give any significant trouble. The Kapton gauges are much more fragile. The majority of the airfoil gauges failed in the spin-down following the first run, and only a minority of the platform gauges survived the entire run matrix. The advantage of these gauges is that they can be placed almost anywhere. Pyrex gauges require a certain wall depth to hold the entire Pyrex cylinder, and neither the blade platform, nor the cooled airfoils have walls thick enough. Additionally, were this a long duration experiment, the Pyrex gauge model would not be valid, and only the two-sided gauges would be usable. More detail in the operation of both gauges is provided by Murphey [71].

Both types of gauges are able to provide very high-speed data, with frequency response rates in excess of 100 kHz. Like most instrumentation, these heat-flux gauges are

sampled at 500 kHz, which allows for some running-averaging for noise reduction without the loss of any information. The vane-passing frequency is around 5 kHz, and FFT analyses show that unsteady content becomes negligible beyond four times this (20 kHz).

The Pyrex gauges are all located at midspan. There are eight each on Blades 32 and

33 (refer to Figure 2.9), approximately equally spaced apart. The locations are staggered between the two airfoils, for sixteen different locations across the airfoil (although not all survived the run matrix).

The airfoil Kapton gauges were clustered around six main locations, three on each side of the airfoil. Each instrumented airfoil had one strip of gauges on each side of the airfoil, with each strip consisting of two or three gauges. Each style of cooling hole has one such strip of gauges at each of the six locations.

Platform Kapton heat-flux gauges are located in three main locations: the upper and lower sides along the pressure-side lip around mid-chord, and on the upper side along the trailing edge lip. A diagram of the platform with the airfoil and gauge locations is shown in Figure 2.14. For platform gauges, a coordinate system of percent axial distance (%AD) and percent pitch will be used. These coordinates are defined such that 0%AD is along the leading lip on the airfoil, with 100%AD at the trailing lip. Pitch is defined zero at the pressure-side/trailing vertex, and 100% at the suction-side/trailing vertex. The trailing edge is used rather than the leading edge because the gauges whose location varies with pitch are the aft gauges, near the trailing edge. These coordinates are shown in Figure 2.14

PS GAUGE, TOP PS GAUGE, BOTTOM 1.50 AFT GAUGE, TOP 1.25

1.00

PITCH 0.75

0.50

0.25

0.00

-0.25 0.0 0.2 0.4 0.6 0.8 1.0 AXIAL DISTANCE

Figure 2.14: Schematic of the blade platform with locations of all platform heat-flux gauges (not to scale)

2.3.2 PRESSURE MEASUREMENTS

There are five main locations of pressure measurements used in this experiment: airfoil surface static pressures, airfoil internal (serpentine passage) static pressures, purge cavity pressures, rotor and stator inner endwall pressures, and inlet/outlet boundary condition pressures.

Two blades are instrumented with eight airfoil surface static pressure taps each: one round-hole blade, and one fan-shaped blade. The transducers are Kulite XCQ-062-100A transducers. There are four transducers on each side of the airfoil, and the two sets of pressure transducers are located in about the same location to each other. A photo of the round-hole blade was provided in Figure 2.7. These transducers have frequency responses in excess of 50 kHz, although similar to the Kapton HFGs, they do not experience significant unsteady frequency content beyond 20 kHz. They are also sampled at 500 kHz and running averaged to reduce noise.

Three airfoils, one of each cooling hole shape, have internal pressure measurements. Each of these airfoils has four measurements, one each in Passages 2, 4, 5, and 6, as shown in Figure 2.8. The internal pressures are Kulite LE-062-100A transducers.

There are many pressure transducers in the purge cavity, but the two that will be focused on are located on the blade root. A schematic of their location is provided in Figure

2.15. These two locations, labeled “A” and “B”, are repeated on two blades. These two are

Kulite XCEL-25-072-100A transducers.

Figure 2.15: Schematic giving location of blade root pressure transducers (not to scale)

There are also two pressure transducer locations on the blade platform upstream of the airfoil (rotor inner endwall), as well as three on the stator inner endwall downstream of the airfoil. The rotor endwall transducers are mainly analyzed alongside the blade root transducers, so they are also labeled by letters “C” and “D”, as shown in Figure 2.16. The stator endwall transducers are shown in Figure 2.17, and are labeled by their percent pitch of the stator, with 0% being immediately in the wake of an airfoil. All of these transducers are the same model as the airfoil surface pressures, XCE-062-100A.

Figure 2.16: Schematic showing pressure transducer locations on rotor platform inner endwall (not to scale)

Figure 2.17: Schematic showing pressure transducer locations on stator inner endwall (not to scale)

The remaining pressure transducers are used for inlet and outlet boundary conditions. There are five pressure transducers in stagnation rakes and one more measuring static pressure, both up and downstream of the stage. These measurements are used primarily to calculate total-to-total pressure ratio, and to set boundary conditions for computational predictions.

2.3.3 TEMPERATURE MEASUREMENTS

The single-sided Pyrex HFGs directly measure one temperature, and the two-sided

Kapton HFGs measure two, but these temperatures are not directly reported in this

dissertation. There are thermocouples in the same internal serpentine passages as the internal pressure transducers. All 12 of these thermocouples are E type, and are either

0.001 inch (25 μm) or 0.0005 inch (13 μm) diameter. There are also two RTDs embedded within each of the two uncooled blades. The uncooled blades can be heated prior to a run to create a different driving temperature, which can be used in finding the adiabatic wall temperature. These RTDs give the solid blade temperature.

The remaining temperature measurements are thermocouples located within stagnation rakes both up and downstream of the stage. Unlike their corresponding pressure measurements, there are two rakes in both locations. Upstream each rake has 11 thermocouples at 11 different spans, providing a total of 22 measurements. The increased resolution is more important for inlet temperature because the temperature profile will never be perfectly uniform, and recall that the exact temperature profile does have a strong impact on thermal performance [28, 29]. The two downstream rakes each feature five thermocouples.

2.4 RUN SEQUENCE

High-speed data are only collected for three seconds, and the actual time-window used for data lasts only about 20 ms, but the act of making one run takes much of a day.

The evening before a run is to be performed, everything in the dump tank is set as it needs to be for the run. This mainly entails setting the coolant metering chokes to their correct values, and making sure everything is clean and strapped down after the prior run.

Once everything in the dump tank is set, the tank is sealed and evacuated. Once evacuated, the Syltherm circuit is turned on. This entails turning on the Syltherm chiller (which is also

the pump), and filling the dry ice heat exchanger with dry ice. This is left overnight to get the Syltherm as cold as possible, and to chill the metal of the Syltherm-to-coolant heat exchangers inside the dump tank.

In the morning, after checking in on everything, the dry ice is refreshed. The combustor emulator heaters are turned on at least 3 hours prior to a run. It takes about an hour at high-power to get the emulator up to temperature, but at least another two at low power for the heat to soak through the Inconel and reach a fairly constant temperature.

Both the shock tunnel and LCF tank (coolant) are pressurized to their appropriate pressures with dry air. Shortly before a run, the heaters are turned off and the rotor is spun up to approximately 98% of target speed with an air motor. The heaters use a lot of current, and are turned off when the rotor spins primarily as a safety precaution. As the rotor spins up, the speed is monitored, and the trigger is activated when it is at the correct speed.

Upon the trigger being activated, everything else is controlled by an electronic timing system, as high accuracy and precision is essential for run-to-run repeatability.

Immediately after being triggered, the air motor is deactivated and the high-speed data system begins recording. About a quarter of a second after triggering, the coolant circuit opens. The coolant actually causes a further acceleration of the rotor, primarily as reaction from coolant being emitted from the trailing edge cooling slots, but also partially as purge flow (and in past experiments, vane cooling flow) goes through the rotor. At this point, about 150% of the design-coolant is being supplied, with the extra (bypass) flow being used to more quickly fill the cooling cavities and passages. More details on the cooling timing system are provided in Chapter 3.

The coolant is given about a second to fill the cavities and internal passages with the bypass open, and then another half second with the bypass closed to stabilize. The main shock tunnel FAV is opened, and the high-pressure core flow passes through the inlet piece, combustor emulator where it heats up, and finally through the stage. There is an initial transient spike in all of the instrumentation that lasts about 30 ms, and then about 130 ms of mostly-steady operation before the FAV closes. It is from this period that the 20 ms data window, corresponding to four full revolutions of the rotor, is chosen, based on when certain characteristics best match design conditions. The main characteristic that is considered is corrected speed, as the rotor is about 98% design speed when the main FAV is opened, and freely accelerates to about 102% by the end of the core flow period.

After the FAV closes, data are still recorded for about half a second. At this point, the dump tank is pressurized to about half an atmosphere from the run. The rotor freely spins, pulling the air in the tank continuously through the stage as drag slowly brings the rotor to a stop. Because the combustor emulator is still hot, this air that gets sucked continuously through the rotor is heated, and this prolonged exposure to hot gas can be damaging to some of the instrumentation. This mode of operation is in the process of being changed so as to avoid damage to instrumentation in future experiments.

2.6 OPERATING CONDITIONS

The dimensional operating conditions are mostly proprietary, however non- dimensionalized forms of most of the parameters can be published. The experiment is run at engine-representative conditions including corrected speed (Equation (2.1)), flow function (Equation (2.2)), total-to-total pressure ratio, and coolant-to-core flow ratios. The values that are non-proprietary and held constant throughout the matrix are provided in

Table 2.1, while the variable parameters are provided in Table 2.2. Note that temperature ratios in this experiment are not engine representative.

푇푡,푖푛푙푒푡 (2.1) 푁푐 = 푁√ 푇푟푒푓

푇 √ 푡,푖푛푙푒푡⁄ 푇푟푒푓 (2.2) 퐹퐹 = 푚̇ 푐표푟푒 푝푡,푖푛푙푒푡 ⁄푝푟푒푓

Table 2.1: Rig operating conditions

Parameter Value and run-to-run variability Corrected speed (RPM) 9638 ± 660 Total-to-total pressure ratio 3.457 ± 0.093

Table 2.2: Variable parameter values

Parameter Low Nominal High TOBI flow / core flow (%) 5.28 6.85 1 8.03 Aft purge / core flow (%) 0.000 0.516 1 0.971 2 푇푡,푖푛푙푒푡/푇푚푒푡푎푙 1.573 1.813 N/A

1 Value is engine-representative

2 Value is not engine-representative

2.6.2 COMPLETE RUN MATRIX

Table 2.3 provides a full run matrix. The table is spread onto two pages, with the first page displaying the baseline runs, Run 4 which varied the solid blade temperature, and the runs that vary aft purge flow. The second page shows the runs that vary TOBI flow,

Run 11 that runs at a lower stage inlet temperature, and two validation runs (15 and 16) with the heater off. The validation runs are taken as a precaution and baseline to compare to in case there is a suspicion of an uneven profile coming from the combustor emulator, or other issues. Data from these two runs will not be published here.

6.99

9586

3.475

0.971

Nom

Nom 0.9985

continued

6.14

3.463

0.842

10701

Nom

0.9903

7.10

9484

3.496

0.000

Zero

Nom

0.9886

Aft Purge Variation Purge Aft

7.01

9539

3.523

0.000

Zero

Nom

Nom 1.0056 Blade Temp

6.45

9518

3.368

0.491

Nom

Nom Nom

Variation 1.0213

6.85

9550

3.502

0.516

Nom

0.9979

6.53

9423

3.403

0.489

Nom

Nom Nom

0.9987

l matrix of all runs l matrix

Baseline

7.20

8965

3.287

0.535

Nom

Nom Nom

: Ful 1.0193

8.64

9553

3.479

0.649

Nom

Nom 1.0209

Table

Total-to-totalPressure Ratio

Rotor Corrected SpeedCorrected (RPM) Rotor

InletTemp/AVG Total

VaneInlet Target Temp.

Measured aft flowaft Measured

Qualitativeflowaft target

Measured TOBI flow TOBI Measured

Qualitativeflow TOBI target Chronological Run Number Run Chronological Varied Parameter Varied

0.00

9492

3.405

0.000

Zero

Amb

0.5755

Runs

5.34

9506

Validation Validation

3.248

0.741

Amb

Nom 0.5869

Inlet Temp

7.21

9786

3.396

0.481

Low Nom

Variation 0.8590

8.03

9543

3.433

0.525

Nom

0.9949

7.61

9563

3.443

0.516

Nom

Nom 0.9737

7.34

9577

3.462

0.538

Nom

Nom 0.9928

: Continued

5.28

14 9536

3.502 0.482

Low

Nom

TOBI Flow Variation Flow TOBI 1.0029

5.28

13 9488

Table

3.469

0.477

Low

Nom

0.9947

Total-to-totalPressure Ratio

Rotor Corrected SpeedCorrected (RPM) Rotor

InletTemp/AVG Total

VaneInlet Target Temp.

Measured aft flowaft Measured

Qualitativeflowaft target

Measured TOBI flow TOBI Measured

Qualitativeflow TOBI target Chronological Run Number Run Chronological Varied Parameter Varied

2.8 COMPUTATIONAL SETUP

The CFD that will be compared with the experimental data in this dissertation, as well as used for airfoil boundary conditions in the internal model, was run externally by

Honeywell Engines, and was not set up or run directly by the author of this dissertation.

However, the author was in contact with those running the CFD and did provide significant instruction on the computational setup including boundary conditions and convergence criteria. A full description of the computational setup is provided here

The CFD is a 3-D, steady RANS approach. A schematic of the full computational domain is shown in Figure 2.18. It features one stator vane and rotor blade, and uses a mixing plane approach at all stationary/rotating interfaces. The inlet is meshed about one vane chord upstream of the vane, and the outlet is meshed one blade chord downstream of the blade. In addition, the cooling circuits are fully meshed. This includes the aft purge cavity and the rotor (TOBI) cooling circuit. The TOBI flow splits early into two directions: either up a labyrinth seal and to become forward purge flow, or into a plenum that feeds the rotor film cooling at the hub of the blade. The entire serpentine passage system is also fully meshed, complete with turbulators and every film-cooling hole.

The full domain consists of 5.7 million polyhedral cells, in addition to six layers of prism cells around all solid boundaries.

Figure 2.18: Computational domain (not to scale)

The mesh and solver used are both STAR-CCM+. The computation utilized a k-ε turbulence model, and uses a mixing plane approach at the interface midway between the stator and the rotor, as well as a mixing plane shortly after the TOBI inlet region because there are 54 TOBI inlet holes in the physical turbine. Maximum y+ values for solid boundary cells throughout the domain are approximately 3, with the majority of the domain lower than 2. One vane and one blade are each meshed and solved, with a periodic boundary condition on their pitchwise boundaries. Total inlet pressure and temperature, as well as flow angle, are defined at the stator inlet according to the experimental measurements, with both of the coolant inlet boundary conditions being defined based on the experimentally measured massflow rates. Inlet turbulence conditions are taken from prior experiments using the same facility. The exit boundary condition is static pressure, also based on experimental measurements.

The final simulations presented here were run for 200,000 iterations to reach full convergence. This is an unusually high number of iterations, however it was found to be necessary for convergence within the serpentine passages. Originally the simulation was set for 5,000 iterations, based on previously determined best practices from Honeywell for uncooled turbines, and this was falsely validated by observing that each overall domain- totaled residual (mass, momentum, energy, etc.) appeared to stop dropping at around 4,000 iterations. However a small minority of cells in the domain (all within the serpentine cooling passages) had not converged, and their residuals continued to drop as more iterations were performed. After extensive trials, it was found that 200,000 iterations were required for the serpentine passage cells to converge, however these cells made up a sufficiently small minority of total cells that the random fluctuation in residuals due to machine accuracy in the rest of the domain dominated the domain-totaled residual.

It should be noted that the computational methodology used for this simulation has some limitations (for example, it neglects time-resolved and unsteady phenomenon), but it is typical of a simulation used in an industry design-phase of actual turbomachinery.

To compare CFD results to the data, the CFD cells are put into “boxes”, each from

40-60% span, and extending 2% WD long. All boundary cells falling within each box are grouped, and their area-weighted average, minimum, and maximum values are used. The minimum and maximum values are presented to give a range for the comparison to data for two reasons. First, the exact span value for the gauges varies from about 40% through

60%. Second, the heat-flux gauge sensing elements are a square with length about 0.040- inch (1.0 mm, or about 2% span), and they provide the average value across that square.

The cooling hole pitch (spanwise gap between adjacent holes) is about twice that size, meaning that exact location of said gauge with respect to the upstream cooling jet can have a significant effect on the film coverage, and therefore the heat-flux at that location. Figure

2.19 shows a contour plot of the CFD heat-flux, with sample “boxes” shown in white dotted lines (boxes not to scale). The figure also shows the strong spanwise gradients in surface heat-flux downstream of each coolant jet that form as a result of non-uniform coolant coverage.

Figure 2.19: CFD heat-flux contour illustrating “boxing” method (boxes and airfoil both not to scale) used to laterally-average pressure and Stanton number for comparison

CHAPTER 3 COOLING CIRCUIT DESIGN

The plumbing circuits responsible for chilling and delivering the coolant flow to the turbine rig was designed by the author of this dissertation, so a chapter will be devoted here to its design and construction.

3.1 DESIGN REQUIREMENTS

The main requirements of the cooling circuit are to transfer the coolant from the supply tank to six inlets on the rig, to meter the flow so each inlet receives close to the correct amount of flow, to measure the flow so that the amount actually delivered is precisely and accurately known, and to chill the coolant as much as possible. During the design-window of the experiment, target nominal values of coolant-to-core massflow ratio have been selected as engine-representative. In addition, “low” and “high” values are set for each circuit to investigate the effect of variable cooling. These target ratios are provided in Table 3.1. Compare this to Table 2.2, which provided the actual measured values.

Table 3.1: Target cooling circuit flow rates as a percentage of vane-inlet massflow

Case TOBI coolant Aft purge coolant Low 5.28% 0.00% Nominal 6.71% 0.50% High 8.12% 1.00%

The coolant supply tank is held at high pressure relative to the experiment itself, at least a factor of three in all cases. Consequently it is assumed that the circuit will choke at the location of smallest area, and the massflow will be independent of the conditions within the rig itself.

While these cooling rates are the targets for the turbine at the design point, a larger coolant flow rate is required during the initial start-up portion of the experiment when the core flow is first established. The additional flow will be referred to as the bypass flow for the duration of this dissertation. This larger coolant flow rate allows the cooling circuit and passage to pressurize more rapidly, and also causes a high pressure in the cooling passages of the turbine blades, which in turn prevents the hot core gas from ingesting into the turbine blade cooling passages, and also prevents the pressure wave from the core flow from compressing the cooling flow and heating it. The exact magnitude of this additional coolant isn’t important, provided that it is “large enough” to prevent ingestion and compression heating (which is verified by looking at the temperature signals from inside the cooling passages and purge cavities), but 50% of the experimental design point is used as a rough target based on previous experiments where this was found to be satisfactory.

The experiment does not match engine-representative temperature ratios between the core flow temperature, metal temperature, and coolant temperature, so there is not a specific design temperature for the coolant. Instead, the goal is simply to chill the coolant to as low a temperature as possible to magnify the effects of the coolant on heat transfer measurements. The chilling is performed in heat exchangers, which transfer heat from the coolant to a liquid called Syltherm. Details on the Syltherm-side of the cooling circuit are provided in Chapter 3.2.4.

3.2 COOLANT CIRCUIT

The complete schematic of the cooling circuit is provided again in Figure 3.1. The cooling system has many components, and each component will be explained individually in the coming sections.

Figure 3.1: Schematic of the full cooling circuit

It was mentioned above that there are six inlets on the rig for coolant. Two of these are for the TOBI flow, 180 degrees apart. The other four are for the aft purge, 90 degrees apart. Ideally, the two TOBI inlets and four aft purge inlets will all provide identical flow

rates. Due to the quantities of massflow required, and the equipment (massflow meters, heat exchangers, etc.) already owned by the GTL, two entirely separate, but identical, circuits are used to supply the TOBI flow. Only one circuit is used to supply the aft purge, as its flow rate is much lower, and this circuit is then split into four passages shortly before entering the rig.

3.2.1 LCF SUPPLY TANK, FAV, AND PLENUM

The cooling circuit begins with the Large Cooling Facility (LCF), which is a tank about 1.27 m3 in total volume, pictured in Figure 3.2. The tank is pressurized with the to- be coolant, which is dry air from The Ohio State University Aerospace Research Center

(ARC) high-pressure air system. The air is dehumidified to a dew point below -130°F (183 K), which is lower than any temperature reached in this experiment, to ensure there is no condensation within the cooling lines.

Figure 3.2: Photo of the Large Cooling Facility (LCF) supply tank

At the outlet of the cooling tank is a hydraulically actuated Fast-Acting Valve, leading to a small plenum, capped off by a flange with four exits: three for cooling lines, and an evacuation line (more details on this provided in Chapter 3.2.5). A picture of this

(as configured for a different experiment) is shown in Figure 3.3. It should be noted that two of the cooling lines are plugged in this photo, as the experiment this photo is from only required one line. The photo also shows the valve actuation lines, which are thin red tubes.

Figure 3.3: Photo of the LCF FAV and plenum

3.2.2 COOLING MASSFLOW INSTRUMENTATION

Three cooling lines come out of the flange downstream of the FAV, and each of these is directed into its own massflow meter. The meters are Coriolis flow meters manufactured by Emerson. They consist of two parallel flow tubes with a forced vibration between them. When flow is present, a Coriolis force caused by the relative motion due to the vibration causes the tubes to vibrate out of phase with each other, and this phase shift is measured to give the massflow rate. More details into the operating principles can be found in the Emerson Micromotion massflow meter data sheet [72].

The two TOBI circuits used larger meters (full model numbers

F100S128CCAAEZZZZ and F100S128CQBAEZZZZ), while the aft circuit used a smaller meter (full model number CMF050M313NQBAEZZZ). A photo of these three massflow meters on their stand is provided in Figure 3.4. Note that there is no line coming out of the meters in this figure. A more zoomed out photo (from the other side) is shown in Figure

3.5. This photo also shows the copper air lines to and from meters. These copper lines go through a bulkhead in the large red dump tank after the meters.

Figure 3.4: Close-up photo of the three massflow meters

Figure 3.5: Photo of LCF with lines to Micromotion massflow meters

3.2.3 SYLTHERM-TO-COOLANT HEAT EXCHANGERS

After entering the evacuated dump tank, the coolant continues through the heat exchangers (HXRs) that transfer their heat to the pre-chilled Syltherm (see Chapter 3.2.4).

These heat exchangers are simple single-pass shell and tube style. Coolant is chilled through these exchangers and continues on to the metering chokes at the low temperature.

A photograph of the heat exchangers is provided in Figure 3.6, although the coolant inlet lines are not yet installed.

There is one heat exchanger for each of the three circuits, all three identical. The heat exchangers are insulated to prevent excessive heat gain from atmosphere anytime the tank is pressurized, although the tank is usually evacuated when the Syltherm lines are active. Syltherm is provided through supply lines (shown in Figure 3.6) and returned through lines on the underside (not visible in Figure 3.6). Each heat exchanger has an RTD that measures the metal temperature of the exchanger. These metal temperatures typically reached 245 K (-19°F) at the time of a run.

Figure 3.6: Photo of the Syltherm-to-coolant heat exchangers

3.2.4 SYLTHERM CIRCUIT

The fluid used to chill the heat exchangers that chill the coolant is Syltherm XLT, manufactured by Dow Chemical Company. Chemically, Syltherm is dimethyl polysiloxane, and it is specially manufactured to be a heat transfer medium for low- temperature applications. More details can be found in the readily available datasheet for

Syltherm XLT [73].

The Syltherm is chilled in two stages. First there is an electronic chiller that the

Syltherm is put through. This chiller is a simple vapor-compression refrigeration cycle.

The output from the chiller continues on to the second phase, which is a heat exchanger outside the dump tank. This heat exchanger is of the same style as the Syltherm-to-coolant heat exchangers, except the Syltherm passes through the main circuit. The secondary circuit (where Syltherm goes in the Syltherm-to-coolant heat exchangers) is blocked off, and the entire heat exchanger is placed in a cooler, and is surrounded by dry ice. This chills the Syltherm below temperatures the chiller can produce alone.

The Syltherm is then passed through the bulkhead and enters the dump tank in one line. This line is then split into three, and provided to each of the three Syltherm-to-coolant heat exchangers. The three return lines then merge into one line, and this one line is returned through the bulkhead and enters the return of the electric chiller.

Typically the Syltherm circuit is turned on overnight before a run, with a fresh load of dry ice applied to the dry ice heat exchanger both the evening before running, and the morning of a run. This allows the metal of all heat exchangers to equilibrate as much as possible, which will help to cool the coolant as much as possible.

It should be noted that all Syltherm lines outside the dump tank (supply and return) are insulated to reduce heat transfer in. Despite this, ice buildup from humidity in the air is common, as the Syltherm is far below the freezing point of water.

3.2.5 COOLING CIRCUIT EVACTUATION SYSTEM

The coolant gas is sufficiently dry air that condensation from it is not a concern for this experiment. However, the cooling circuit is directly connected to the rig, meaning that whenever the dump tank is pressurized, so is the cooling system, and this is with atmospheric air. The dump tank is kept at vacuum as much as possible on run days to allow thermal equilibration in the turbine metal, and to prevent condensation on the outside of the Syltherm-to-coolant heat exchangers (this is mostly harmless, but does create a standing puddle of water that can be mistaken for a Syltherm leak, and also causes the insulation on the heat exchangers to warp), but the tank is brought to atmosphere briefly when quick changes need to be made, as well as after each run for an inspection of any damage. The heat exchangers reach metal temperatures around 245 K (-19°F), which would cause condensation and freezing of any atmospheric humidity within the heat exchanger, leading to a blockage of the gas path. To keep this from happening, the coolant side of these heat exchangers must be prevented from pressurizing even when the dump tank as a whole pressurizes. The cooling circuit evacuation system was designed to accomplish this goal.

Most of this hardware is outside the tank, and it is highlighted in red in the cooling schematic in Figure 3.7. The fourth line coming out of the plenum is the evacuation line.

At the end of the line is a vacuum pump, which pumps the evacuation line down to vacuum.

This pump is only designed to operate at atmospheric pressure or less, so there is a manual

ball valve located early in the evacuation line (this can be seen in in the photo of Figure

3.3). The valve is closed for experiments, or any time that the FAV is open (and therefore the cooling system is pressurized with coolant) to avoid damaging the vacuum pump.

Between the ball valve and vacuum pump is also a relief valve set to open to atmosphere if the evacuation line gets above atmospheric pressure. The relief valve is redundant, and didn’t activate at any time during the experiment, however it was put in place to protect the vacuum pump in case the ball valve was accidentally left open during an experimental run, or if the FAV was accidentally opened when the ball valve was open.

The final component are check valves installed downstream of each heat exchanger.

These check valves only allow flow in one direction, from left to right in the figure. This keeps atmospheric air from the rig passing through the metering chokes and resupplying the heat exchangers as air is pumped out. Downstream of these check valves (for example, in the metering chokes), the cooling passages are pressurized the same as the dump tank, but none of these components are chilled, so there is no concern for condensation or blockage.

Figure 3.7: Schematic of cooling circuit with evacuation components highlighted

3.2.6 PIPING CHOICES

Different types of pipe were used for the coolant circuit flows, mainly chosen based on strength, thermal properties, and cost. The three cooling lines leaving the FAV plenum

1 are 1 inch nominal size copper tubes (1 /8 inch OD, 1.025 inch ID; 28.6 mm OD,

26.0 mm ID) with a maximum pressure of 490 psig (3.38 MPag). Similar copper piping is again used downstream of the massflow meters until shortly before the heat exchangers.

The tubing is then changed to high-pressure polyethylene tubing, 1 inch OD; ¾ inch ID

(25.4 mm OD; 19.05 mm ID) with a maximum rated pressure of 195 psig (1.34 MPag).

This tubing is not as strong, but is significantly more flexible, and the material has a lower thermal conductivity, which will prevent the tubing from heating up the chilled coolant as

much. This polyethylene tubing is the limiting factor in how high the LCF can be pressurized.

3.3 METERING CHOKES

The most important and complicated component of the cooling circuit is the metering choke. Each metering choke is a manifold of PVC pipe with several parallel passages for coolant to flow through. The two TOBI circuits have identical metering choke manifolds (labeled ‘A1’ and ‘A2’) with five passages, while the aft has a different design

(labeled ‘B’) featuring three passages. The manifolds are constructed primarily of schedule

80 PVC piping, ranging in size from ⅜” to 1” (nominal pipe sizes). The minimum rated strength of the piping is 630 psig (4.3 MPag), which is higher than the polyethylene lines supplying the manifold, so this is not a concern.

The manifolds were largely built around components already owned by the GTL, primarily ½” nominal pipe size needle valves and solenoid valves. For all manifolds, 1” nominal pipe size is used at the inlet and outlet. This is then split to either five (TOBI) or three (aft) passages, still at 1”, and only then is reduced to ½”, and in some cases ⅜”.

The theory of designing these manifolds is basic compressible flow because the desired massflows for each cooling case are known, and the throats are assumed choked.

The basic equation for massflow through a choked orifice is shown in Equation (3.1), where Cd is the coefficient of discharge of the orifice, and Ageo is the geometrical area of the orifice. In practice it can be difficult to measure both of those parameters, so they are combined into an effective area, Aeff, as in Equation (3.2), which is used instead.

훾+1 − 푝푡 훾 훾 + 1 2(훾−1) (3.1) 푚̇ = 퐶푑 퐴푔푒표 √ ( ) √푇푡 푅 2

훾+1 − 푝푡 훾 훾 + 1 2(훾−1) (3.2) 푚̇ = 퐴푒푓푓 √ ( ) √푇푡 푅 2

Supplemental experiments were performed before the main experiment to better quantify the areas, using a circuit shown schematically in Figure 3.8. Initially, flow from the LCF was released through just a massflow meter, and then a needle valve, with the needle valve being set to different values across the supplemental run matrix. Schedule 80 piping of various sizes was also used as chokes in some runs (instead of the needle valve) to determine their effective sizes.

Values for total pressure and temperature were obtained from existing instrumentation within the LCF tank, and massflow was measured by the massflow meter.

Equation (3.2) could then be solved for 퐴푒푓푓 for each needle valve setting or pipe size.

Experiments were also performed with one of the heat exchangers as the throat to verify that its effective area was significantly larger than everything else and it would not choke for any conditions in the experiment.

Figure 3.8: Needle valve effective throat area experimental circuit

Unfortunately using Equation (3.2) requires an accurate value for stagnation conditions at the choke, but in the actual experiment there will be significant pressure losses between the LCF (where stagnation conditions are measured) and the metering choke, as well as a temperature drop through the heat exchangers. A preliminary metering choke manifold was designed based on the results of the effective area runs using rough estimates from basic pipe flow equations to approximate the pressure loss that would occur between the LCF and metering choke. The entire coolant path was then put together (except the coolant lines were not yet hooked up to the rig), the dump tank is evacuated, and more supplemental runs are taken. This time the coolant flowed through the massflow meters, heat exchangers, and full metering chokes, and ejected into a vacuum, as would be the case for actual runs in order to measure the massflow with all of the pressure losses.

After analyzing the results it was found that the original metering choke was unable to produce enough massflow for the TOBI case. This is probably because the original estimated pressure losses within the piping were less than the actual pressure loss, likely

because of piping turns and various pipe adapters. The TOBI manifolds were modified by adding a fifth passage, and using a larger size pipe for the always-open passage, and upon further tests, the new design was found to perform adequately. The following sections describe each of the final designs.

3.3.1 METERING CHOKE A

A photo of one of the A metering choke manifolds, and accompanying schematic, is provided in Figure 3.9. At the far left is the check valve (1” pipe size) previously discussed, and seen in Figure 3.1 and Figure 3.7. Note that the color of the line in the schematic corresponds to the size of the pipe, with reducers colored according to the pipe size that feeds them. Each of the five passages also features a ½” union to ease with assembly and disassembly.

Of the five passages, the upper two, and lowest are identical. The 1” line is reduced to ½”, it passes through a ½” needle vale, the ½” union, and then expanded back to 1”.

These three needle valves are all choked during operation, and are adjusted based on the desired amount of coolant flow for any given run. The central passage is reduced to ½”, passes through the union, and then gets further reduced to ⅜” size. This passage is always open and is not adjustable, the choked area is the entirety of the ⅜” pipe (although note that reducers are not rounded, so the effective throat area will be significantly smaller than the geometrical area). From the earlier supplemental experiments, the effective throat area of the schedule 80 ⅜” pipe was found to be about triple that of the wide-open needle valve.

The coolant flow through just this passage is slightly less than the target low TOBI flow.

The final passage, second from the bottom, features a similar ⅜” pipe as the choke, but

there is also an electronically actuated solenoid valve. This passage is responsible for the bypass flow that is required during the startup of a run to prevent coolant compression heating and hot gas ingestion was previously explained. This also means that the magnitude of the bypass flow will be the same, regardless of which TOBI flow is being targeted.

Figure 3.9: Picture and schematic of metering choke ‘A’

The aft purge metering choke “B” is simpler. There are only three passages, all three of which reduce to ½ nominal size, and are controlled by a needle valve. The bypass

(bottom) passage also has an identical solenoid valve to that from the “A” circuits. A photo and schematic are provided in Figure 3.10. The split of the flow path into two, and then four passages downstream of the manifold is also shown.

Figure 3.10: Picture and schematic of metering choke ‘B’

CHAPTER 4 DATA REDUCTION

The data that will be presented in this dissertation have been reduced significantly from their original form. This chapter gives the mathematical details on how to go from the raw data to the completely reduced data.

4.1 HEAT-FLUX

Heat-flux gauges only directly measure unsteady temperature signals. As was previously described, the single-sided Pyrex gauges use the temperature at the top of the

Pyrex and a semi-infinite numerical model to calculate heat flux into the Pyrex, while the two-sided Kapton gauges use upper and lower temperatures in a transient one-dimensional heat transfer model originally developed by Weaver et al. [68].

Heat-flux is then reduced into the Stanton number which is a non-dimensional measure of heat transfer defined as the ratio of the actual heat-flux to the maximum amount of heat-flux that the convecting fluid could theoretically carry away in Equation (4.1). This accounts for other variables such as driving temperature and massflow. In practice, a slightly simplified version of the Stanton number is used, shown in Equation (4.2).

푞" 푆푡 ≡ (4.1) 푇푤 휌∞ 푢∞ ∫ 푐푝 푑푇 푇∞ 푞" 퐴 푆푡 ≈ 푐표푟푒 (4.2) 푚̇ ([푐 푇] − [푐 푇] ) 푐표푟푒 푝 푤 푝 ∞

4.2 PRESSURE AND TEMPERATURE

Raw pressure and temperature measurements in this experiment are proprietary, so they are normalized by the total (stagnation) conditions upstream of the rig, as shown in

Equations (4.3) and (4.4). These normalized values are actually far more useful, as they account for small uncontrollable variations in inlet conditions from one run to another.

푝 (4.3) 푝푛 ≡ 푝푡,푖푛

푇 (4.4) 푇푛 ≡ 푇푡,푖푛

4.3 COOLANT MASSFLOW RATES

Like pressure and temperature, the exact values of massflow rates are all proprietary. The value of core massflow is relatively constant across runs, and is never mentioned in this dissertation. Circuit cooling flow rates (TOBI and aft purge) are normalized by this core massflow rate for each run.

The coolant massflows out of each cooling hole are non-dimensionalized into blowing ratio, as is explained in detail in Chapter 6.4.3 and ultimately defined in Equations

(6.38) and (6.39).

4.4 ENCODER AVERAGING

Unsteady analysis of Stanton number and normalized pressure is performed using both Fourier transforms, and encoder averages. Fourier analysis is standard and won’t be introduced here.

An encoder is fixed to the rotor shaft and used to provide high-precision information on the rotational position of the rotor in time. The data from each revolution is broken into 24 periods (each corresponding to the rotor instrumentation passing one of the 24 vanes), with data from four full revolutions being used, for a total of 96 vane passing periods. The data from these 96 vane passes is then averaged into one encoder average signal. For the purpose of visualization, the encoder average is repeated and shown twice in succession when plotted. More detail into the process of taking the encoder average is described by Nickol et al. [6].

In addition to the true encoder average, sometimes it is helpful to subtract the time- average value from the encoder average when comparing multiple signals. This can be useful in comparing multiple unsteady signals that may have a time-averaged offset between them.

CHAPTER 5 UNCERTAINTY

Quantifying the experimental uncertainty is in essential part of any experimental study. Because of the number of different types of instruments, the propagation of uncertainty will be broken down into several levels, and given its own chapter.

5.1 KAPTON HEAT-FLUX GAUGES

The uncertainty for the two-sided heat flux gauges (HFGs) is complicated because the unsteady heat-flux signal is created via numerical algorithm from two unsteady temperature signals. Additionally, the time-resolved uncertainty for peak-to-peak variation is significantly lower than the gauge-to-gauge time-averaged uncertainty.

While the real heat-flux signal uses a numerical model, an approximation is provided in Equation (5.1). This approximation is used for the uncertainty.

푘 (5.1) 푞" = [ ] (푇푈 − 푇퐿) 푑 푘푎푝푡표푛

The upper and lower temperatures are defined from the resistance of the gauge using a quadratic calibration fit, as shown in Equation (5.2) for calibration coefficients a and b which were determined via individual calibration for each gauge before the experiment. Because only driving temperature is desired, the different between upper and lower temperatures can be rewritten as shown in Equation (5.3). This is important because

typical runs start with an evacuated rig, and it is a safe assumption that the initial temperatures of the upper and lower gauges are the same, and they are actually offset to be equal. In other words, Δ푇0 is defined as zero. This eliminates the largest single contributor of uncertainty. Unfortunately, this assumption does not hold for the early runs from which airfoil heat-flux is taken because of a leak, which supplied small amounts of air into the dump tank. Consequently the airfoil heat-flux has significantly greater uncertainty than the platform heat-flux.

2 2 (5.2) 푇푈 = 푇푈,0 + 푎푈(푅푈 − 푅푈,0) + 푏푈(푅푈 − 푅푈,0)

2 2 푇푈 − 푇퐿 = 훥푇0 + 푎푈(푅푈 − 푅푈,0) + 푏푈(푅푈 − 푅푈,0) (5.3) 2 2 −푎퐿(푅퐿 − 푅퐿,0) − 푏퐿(푅퐿 − 푅퐿,0)

Using calibration uncertainties in Equation (5.3), and plugging these into a standard uncertainty propagation in Equation (5.1). The Kapton has a material k/d uncertainty of

1.3%, as per previous experiments by Murphey [71]). These result in time-averaged uncertainties of 0.24 × 10-3 and 0.43 × 10-3, for platform, and airfoil Stanton numbers, respectively.

Unsteady uncertainties are defined as the uncertainty in one value of an encoder average with respect to another point in the same encoder average, such as the total peak- to-peak variation. The majority of the uncertainty in time-averaged Stanton number comes from the large change in gauge temperature when the main valve opens and the gauges are first put into contact with the core flow. Once the time window has been reached, the gauge temperatures fluctuate only slightly as a result of vane-blade interaction, and the

uncertainty in these smaller fluctuations is the cause of unsteady uncertainty.

Consequently, the unsteady uncertainty for all Stanton numbers is 0.053 × 10-3.

5.2 PRESSURE TRANSDUCERS

The pressure transducers are all calibrated in-situ against a high-accuracy Heise digital pressure transducer by pressurizing the facility dump tank at various times throughout the experimental matrix. Their calibration accuracies were found to be within

±0.1 psi (±0.7 kPa) for each calibration, and within ±0.2 psi (±1.4 kPa) for repeatability throughout the matrix, corresponding to an experimental uncertainty of 0.40% of the rig total inlet pressure.

5.3 GAUGE LOCATION

The locations of gauges are provided in normalized terms, percent span (% span) and percent wetted distance (%WD) on the airfoil, and percent pitch (% pitch) and percent axial distance (%AD) on the platform. These locations are all subject to some error. High- resolution photos of the instrumented blades are taken and overlaid on a computer model of the airfoil to give the location in spatial dimensions. These spatial dimensions are then converted to % span and %WD based on the geometry of the airfoil. Uncertainty in the exact location propagates to ±0.3% span, ±0.6%WD, 0.5% pitch, and 0.2%AD.

5.5 SUMMARY TABLE OF UNCERTAINTIES

A table summarizing all uncertainties is provided below.

Table 5.1: Summary of experimental uncertainties

Measurement Uncertainty Average airfoil Stanton number ± 0.43 × 10−3 Average platform Stanton number ± 0.24 × 10−3 Unsteady Stanton number ± 0.053 × 10−3 Normalized pressure ± 0.40% Percent wetted distance ± 0.6%푊퐷 Percent span ± 0.3% 푠푝푎푛 Percent pitch ± 0.5% 푝푖푡푐ℎ Percent axial distance ± 0.2%퐴퐷

CHAPTER 6 INTERNAL FLOW MODEL—NECESSITY AND THEORY

Film cooling experiments use several non-dimensional measurements to quantify

film cooling flow rates. The most common by far is the coolant-to-freestream flow

massflux ratio, known as the blowing ratio and defined in Equation (6.1). Other common

parameters include the momentum flux ratio and density ratio, defined in Equations (6.2)

and (6.3), respectively.

푚̇ 푐⁄ 휌푐푢푐 퐴푐 (6.1) 퐵푅 = = 푚̇ 휌∞푢∞ ∞⁄ 퐴∞

2 휌푐푢푐 (6.2) 푀푅 = 2 휌∞푢∞ 휌 퐷푅 = 푐 (6.3) 휌∞

Most experiments and computations on film cooling present at least the blowing

ratio, and often at least one of the other parameters, but measuring this is a difficult task in

an engine-representative environment. The only coolant massflow measurements for this

experiment are far upstream of the rig, with the measured TOBI coolant splitting to blade

flow, purge flow, and leakage. Even if the total flow into the blade cooling passages were

measured directly, how the blade flow is split between the different cooling passages, and

how much coolant ejects through each hole is still unknown, which makes any comparison

to other experiments more challenging. For this experiment, static temperature and pressure measurements are taken at midspan in four of the six serpentine passages on three different blades, and about a dozen static pressure measurements are spread across the surface of the airfoil. Each airfoil contains 85 total cooling holes, not counting those on the blade tip or trailing edge, spread out in seven rows of holes. To attempt to quantify the coolant flow rates and other parameters out of each hole, a detailed model is required, and the theory and implementation of this model is the subject of this chapter.

6.1 REQUIREMENT FOR THE FLOW MODEL

Ideally, a full CFD simulation of the experiment would be able to provide full details on the cooling and blowing properties of each cooling hole. In practice, this is a challenging task. The coolant passages inside of the airfoil are not easy to simulate. The passages are turbulated to enhance heat transfer, but this increases the wall surface area significantly, which increases the cell-count requirement. The added turbulence also presents more difficulty for a simple RANS code to model. The turns at the tip and hub of the blade are also challenging to capture accurately, and are by themselves an active area of research, see the work of Chen et al. [74] for example.

There are further complications on the thermal side. The serpentine passages are essentially a heat exchanger. Heat transfer between the metal and coolant is significant, but can be difficult to predict due to the strong vortical structures and high turbulence caused by the turbulators. Research on models of internal passages show very strong gradients in heat transfer [74, 75]. Additionally, these strong heat transfer gradients cause strong temperature gradients in the metal. The solid surface cannot be accurately modeled using

a constant temperature (isothermal) or constant heat-flux boundary condition, requiring the use of a conjugate heat transfer (CHT) model, further complicating matters. Similar challenges exist in predicting the pressure field.

Despite the challenges in predicting the flow field, very high accuracy is required in certain locations. The pressure margin for coolant ejection through the cooling holes on the pressure side is very small (based on midspan experimental measurements). If the CFD is off by only a small amount, it can double or completely negate the pressure margin for coolant ejection.

A previous section of this dissertation introduced a relatively simple CFD prediction of this experiment performed using steady RANS. The domain included the

TOBI inlet, coolant split into purge and blade flows, blade root, serpentine passages, and every cooling hole, as well as the core flow path of the turbine. While the core region was predicted with reasonable agreement, the pressures within the serpentine passages were not.

Figure 6.1 shows the internal and external pressure values for both experiment and computation for the nominal case. The green line shows the computational prediction for the airfoil surface, with the green circles being airfoil data, and the comparison is fairly close except near the trailing edge, and within 3% of vane inlet total pressure where cooling holes are. The internal data, however, are consistently 5-8% of vane inlet total pressure lower than the prediction. This is particularly important at the pressure side row of holes, where the data present a small pressure margin, and the prediction presents one four times

larger. Any coolant ejection rates for this row of holes predicted by this computation cannot be trusted.

EXT CFD INT CFD REG HOLES EXT DATA INT DATA SHAPED HOLES P2

P2 P4 0.60

0.50 P6

T,INLET

P/P 0.40

0.30

0.20 TE A B C D E F G

-100 -50 0 50 100 PRESSURE SIDE %WD SUCTION SIDE

Figure 6.1: Plot of experimental and computational internal and external pressure

The internal data are plotted at the %WD that they eject to for the pressure and suction side rows. For the Passage 2 row, it feeds Passage 1 which then ejects to all showerhead rows, so it is shown at 0%WD. Passage 6 does not eject to a cooling row, so its location is more arbitrary, but it is shown at -60% WD, about where it would eject if there were a row of holes that it ejected through.

The internal data plotted is the average of the values from the three blades that are instrumented. The range bars for the data present the maximum and minimum pressure from these blades, showing that the blade-to-blade range is significantly smaller than the difference from experiment to computation.

6.2 PHYSICAL TURBINE COOLING DOMAIN

A complete description of the airfoil, film cooling holes, and serpentine passages was provided in Chapter 2, but for convenience the relevant information will be repeated here. There are seven rows of cooling holes, with one on each side of the airfoil, and five clustered near the leading edge. These rows are labeled A through G, with A being the pressure side row, and moving clockwise around the blade as oriented in Figure 6.3. The rows are labeled on a photo of the airfoil in Figure 6.2. Note that the trailing edge cooling slots are not included as a row of cooling holes.

Figure 6.2: Photograph of suction and pressure sides of an airfoil instrumented with pressure transducers with cooling rows labeled (not to scale)

There are six serpentine passages, labeled 1-6 starting with 1 at the leading edge, moving aft, as shown in Figure 6.3. There is a pressure and temperature transducer at midspan of Passages 2, 4, 5, and 6 (underlined in Figure 6.3) in three different blades (one of each cooling hole shape).

Figure 6.3: Schematic of labeled airfoil serpentine passages and cooling rows (not to scale)

Coolant is provided at the root of the blade only to Passages 2 and 3. Passage 2 flows up toward the tip, while continuously losing flow through 19 impingement cooling holes to Passage 1. Passage 1 is supplied only by these impingement holes, and it supplies all five leading edge cooling rows (Rows B-F).

Passage 3 flows up without any cooling holes until the tip, where there are several cooling holes in the turn. Passage 4 begins at the tip and flows toward the hub, while ejecting through cooling hole Row G. The remaining coolant turns at the hub and heads back up the blade through Passage 5, while ejecting to the pressure side Row A. The remaining coolant turns to Passage 6, where it is fed through impingement cooling into the trailing edge pin-fin region and out the trailing edge cooling slots.

The six passages within the blade are significantly different from each other in geometry. Cross-sectional area, hydraulic diameter, and even shape all vary from row-to- row (Figure 6.3 is not to scale, but is approximately correct to show the relative shapes and sizes of the six cooling passages at midspan). The parameters of each passage also vary with span, although are fairly constant with the exception of Passage 2, which shrinks significantly. A summary of each passage is provided in Table 6.1. Passage 2 has both hub and tip values provided, while the remaining passages have their information given at midspan. The cross-sectional area 퐴푐 and hydraulic diameter 퐷ℎ are both normalized relative to the hub value of Passage 2.

Passages 2-6 all feature square cross-sectioned turbulators on the leading and trailing wall. These turbulators are perpendicular to the flow. The turbulator pitch-to-height (푃⁄ ) ratio is 11.75 for all rows. The turbulator blockage ratio (푒⁄ ) is 푒 퐷ℎ

not constant across the passages as the hydraulic diameters vary, but this is given for each passage inTable 6.1.

Rotation effects play a large role in the serpentine passages, primarily through a centrifugally-induced pressure gradient towards the tip of each blade, but also through a

Coriolis force. The Rotation number, defined in Equation (6.4), is also variable from row to row, and is also provided in Table 6.1

Note that a Rotation number is not calculated for Passage 1 because its velocity is extremely low, and actually changes directions several times. This is because rather than being fed at one end like all the other passages, it is continuously fed throughout the span of the passage. The low velocity would result in an extremely high and variable rotation number. Additionally, Passage 1 does not have turbulators, so the turbulator properties also are not calculated for this passage. Parameters for Passage 6 are also not calculated because

Passage 6 is downstream of the region of interest and it is not modeled.

훺 퐷ℎ (6.4) 푅표 = 푤

Table 6.1: Summary of cooling passage information

퐴푐 퐷ℎ 푃 푒 Cooling Total Passage 푅표 퐴푐,2,ℎ푢푏 퐷ℎ,2,ℎ푢푏 푒 퐷ℎ Rows holes 1 0.37 0.69 N/A N/A N/A B,C,D,E,F 76 2 1.00 1.00 11.75 0.06 hub 0.075 Imping.3 19 2tip 0.26 0.49 11.75 0.13 3 1.77 1.49 11.75 0.03 0.18 NONE 0 4 1.45 1.31 11.75 0.05 0.16 G 9 5 0.77 0.90 11.75 0.08 0.05 A 16

6.3 DOMAIN OF THE MODEL

The flow model presented here is a one-dimensional numerical model. It has many fundamental similarities to CFD, but is different from any commercially available package in that the boundary conditions are set in the middle of the domain where experimental data exist, rather than at the actual boundaries. Additionally, instead of numerically solving the Navier-Stokes equations, many flow parameters such as friction factor and cooling hole coefficient of discharge are taken from previous research published in the open literature for similar cases. In essence, the goal of the model is to interpolate and extrapolate the experimental data at midspan of certain cooling passages to all span values of every cooling passage.

3 Passage 2 does not have cooling holes to the airfoil, but does have impingement holes

to Passage 1

The model solved Passages 1, 2, 4, and 5. A stencil of the mesh is provided in

Figure 6.4, with each passage shown in a different color. Each passage is split into 푁 nodes, with node 1 being at the hub, and N being at the tip, regardless of the bulk fluid direction in that particular passage. Note that not every node is shown in the figure, there are breaks.

While it is shown as one domain, Passages 1 and 2 are entirely decoupled from Passages 4 and 5 in the model (with one exception, explained later). These will be explained separately, with Passages 1 and 2 being referred to the forward circuit, and Passages 4 and

5 being referred to as the aft circuit.

Both circuits use external airfoil values of pressure and massflux at the outlet of each cooling hole. These values are all obtained from the CFD simulation previously described in this dissertation. Other than those values, the forward circuit uses only a single value of temperature and pressure at a central node in Passage 2 as a boundary condition.

The aft circuit uses just two pressures and temperatures, each at a central node in each passage. Note that because Passage 1 feeds five rows of showerhead holes, some nodes have multiple holes, which is shown on the stencil.

Figure 6.4: Stencil of the numerical mesh

Note that the aft circuit uses two sets of boundary conditions to solve for two passages, while the forward circuit only has one for its two passages. The details of the mathematical formulation of the model follow, but in simple language this can be explained as follows. The aft circuit needs one pressure to set the pressure throughout the domain, and the second pressure to determine the massflow out the tip of Passage 5 (into 6). The forward circuit only needs one pressure because the total massflow in is simply the sum of all ejected massflows. The aft circuit uses the extra temperature measurement (think of it instead as the temperature increase from Passage 4 to Passage 5) to quantify a sort of domain-wide heat transfer effectiveness. This value is then used in the forward circuit (this is the extent of the coupling between the forward and aft circuits).

Because there is no measured data, nor coolant ejection in Passage 3, there is no need to solve for the coolant properties in this passage. The aft circuit begins at the tip of

Passage 4, although these values are extrapolated to the tip turn between Passage 3 and 4 to quantify the tip coolant ejection. This flow is needed to determine the total coolant massflow in to Passage 3 at the root of the blade, which is used in the validation of the flow model and is just a helpful parameter to have.

6.4 MATHEMATICAL FORMULATION OF THE FLOW MODEL

There are two basic components to the model at each node: the passage flow equations which are used to determine the coolant properties inside the cooling passage, and the cooling hole equations that are invoked at any node with cooling holes, which determines the massflow out at that hole. Note that this model is only valid for the round- hole airfoil (see Chapter 6.6 for a detailed explanation).

6.4.1 PASSAGE FLOW EQUATIONS

The passage flow equations are solved as a set of simultaneous equations with a total of fifteen variables and equations defined for each node. Most equations are defined at all N nodes, with the rest being defined at N-1 nodes, requiring a boundary condition to close the system. This is explained in detail below. Note that the cross-sectional area 퐴푐,푖, and hydraulic diameter, 퐷ℎ,푖, do change node by node, but are known constants from the geometry of the blade. A tabular summary of all of these equations (and unknowns) is provided in Appendix A.

The first group of equations is straightforward. Equation (6.5) is well known and comes from a mass balance of any control volume. Equation (6.6) is a form of the ideal gas law, which is used as the equation of state for the coolant. Equations (6.7) and (6.8) are isentropic flow equations used to relate total (stagnation) conditions to static conditions based on the flow Mach number. Note that total conditions and Mach numbers used here are all in the relative (rotating) frame of reference. Equation (6.9) defines the flow (relative) velocity to the (relative) Mach number based on the speed of sound.

(6.5) 푚̇ 푖 = 휌푖푤푖퐴푐,푖

(6.6) 푝푖 = 휌푖푅푇푖

훾 푝 푇 훾−1 (6.7) ( 푖 ) = ( 푖 ) 푝푡푟,푖 푇푡푟,푖

훾 − 훾 − 1 훾−1 (6.8) 푝 = 푝 [1 + 푀푎2 ] 푖 푡푟,푖 2 푟,푖

(6.9) 푤푖 = 푀푎푟,푖 √훾푅푇푖

Total temperature is not a constant throughout the cooling passage due to heat transfer from the metal into the blade. The heat-flux can be expressed in two ways, shown in Equations (6.10), which is the definition of the convective heat transfer coefficient ℎ푖, and (6.11), which comes from a simple energy balance. These are combined into Equation

(6.12) which is defined for every node except 푖 = 1 in Passages 2, 4, and 5. This leaves two equations in the aft circuit, and one in Passage 2. For Passage 2, the temperature boundary condition at midspan closes the system. The total temperature of Passage 1 is assumed equal to Passage 2 (Equation (6.13)). This is an approximation, but it is assumed acceptable because Passage 1 is continuously fed by Passage 2, and the total temperature does not increase very much even through an entire passage.

(6.10) 푞푖" = ℎ푖(푇푤 − 푇푖)

푚̇ 푖 푐푝 (6.11) 푞푖" = (푇푡푟,푖 − 푇푡푟,푖−1) 퐴푠,푖

(6.12) ℎ푖 퐴푠,푖 (푇푤 − 푇푖) = 푚̇ 푖 푐푝(푇푡푟,푖 − 푇푡푟,푖−1)

푇 | = 푇 | (6.13) 푡푟,푖 푃1 푡푟,푖 푃2

For the aft circuit, one of the two required equations is obtained by modifying

Equation (6.12) to link the i=1 nodes from Passage 4 and 5, as the i=1 Passage 4 node directly feeds the i=1 Passage 5 node (this is conceptually the same as Equation (6.12)).

The second equation comes from the Passage 4 boundary condition at midspan. The convective heat transfer coefficient is determined by Equation (6.14), which compares the actual Nusselt number in the passage to the theoretical Nusselt number for fully-developed turbulent flow within a passage according to the Dittus-Boelter/McAdams equation [76].

The value of 푁푢⁄ is a constant for the entire domain, and the Passage 5 temperature 푁푢∞ boundary condition is used to determine it. Reynolds number is defined in Equation (6.15).

ℎ푖퐷ℎ,푖 푁푢 ⁄푘 (6.14) = 푖 푁푢 0.023 푅푒0.8 푃푟0.4 ∞ 퐷ℎ,푖 푖

휌푖 |푤푖| 퐷ℎ,푖 (6.15) 푅푒퐷ℎ,푖 = 휇푖

The thermodynamic properties of viscosity, thermal conductivity, and Prandtl number are all assumed functions of static temperature, and are obtained through a lookup table for dry air at their respective temperatures (Equations (6.16), (6.17), and (6.18)).

(6.16) 휇푖 = 푓(푇푖)

(6.17) 푘푖 = 푓(푇푖)

(6.18) 푃푟푖 = 푓(푇푖)

The pressure is also not constant throughout the span. There are two main phenomena that cause the pressure to change radially: centrifugal effects, and friction. The centrifugal pressure gradient is defined in general form in Equation (6.19), and given more

specifically for this application by Equation (6.20). Note that 푟 is defined such that greater values are further from the axis of rotation, regardless of the flow direction.

(6.19) 훻푝푐푒푛푡 = −휌 훺⃗ × (훺⃗ × 푟 )

휕푝 2 (6.20) | = 휌푖훺 푟푖 휕푟 푐푒푛푡,푖

Frictional losses require a value of the friction factor, which is defined in Equation

(6.21). The instrumentation in this experiment does not allow for direct measurement or calculation of the friction factor, but many past studies have focused specifically on similar serpentine passages, and have published values for friction factor. Similar to Nusselt number in these channels, the friction factor is often normalized by the value of friction factor for fully-developed turbulent flow in a circular channel, 푓∞, which is calculated using a fit of the Kármán-Nikuradse Equation. The work of Chandra et al. [77] on similar, but

푓 stationary, walls provide approximate values of ⁄ for each channel. Liou et al. [78] 푓∞ explore correlations for friction factor for smooth channels as a function of Reynolds and

Rotation numbers, and show that the channel-average friction factor is increased 10-20% due to Rotation numbers on the order seen in this experiment. Combining the results of

푓 these two studies produce final values of ⁄ of 1.1, 4.5, 6.6, and 5.0 for Passage 1, 2, 4, 푓∞ and 5, respectively. It is difficult to estimate how accurate these values of friction factor are, but the final solution is not very sensitive to them. It can be shown that halving or doubling them results in a ±1.2% change to blowing ratio, at most.

Equations (6.21) and (6.22) are combined into Equation (6.23), which is a complete expression for frictional pressure gradient. Equation (6.24) is the second-order accurate discretization for central nodes, with the right-hand side terms coming from Equations

(6.20) and (6.23). The hub nodes of Passage 2 and 4 are discretized by Equation (6.25), and tip nodes of Passage 1 and 5 use Equation (6.26).

휕푝 1 푓 ≡ | (6.21) 4 1 휕푟 푓 ( ) 휌푤2 퐷ℎ 2 푓 푓 = (6.22) 푓 0.046 푅푒−0.2 ∞ 퐷ℎ

휕푝 푓 4 1 | = (−푠푖푔푛(푤 )) 0.046 푅푒−0.2 ( ) 휌 푤2 (6.23) 푖 퐷ℎ,푖 푖 푖 휕푟 푓,푖 푓∞ 퐷ℎ,푖 2

푝 − 푝 휕푝 휕푝 푖+1 푖−1 = | + | (6.24) 2 훥푟 휕푟 푐푒푛푡,푖 휕푟 푓,푖

4푝 − 푝 − 3푝 휕푝 휕푝 2 3 1 = | + | (6.25) 2 훥푟 휕푟 푐푒푛푡,1 휕푟 푓,1

3푝 + 푝 − 4푝 휕푝 휕푝 푁 푁−2 푁−1 = | + | (6.26) 2 훥푟 휕푟 푐푒푛푡,푁 휕푟 푓,푁

One final equation links the hub node of Passage 5 to that of 4, based on the frictional pressure drop in the hub turn. This leaves one pressure equation for every node except the tip node of Passages 2 and 4, and the hub node of Passage 1. The pressure and massflow equations are closely related, so the closure of this will be explained after introducing those equations.

Determining massflow through the domain is relatively simple. Massflow at the inlets of the domain (hub node of Passage 2, and tip node of Passage 4) are initially unknown, but subsequent nodes’ massflows are defined with respect to the upstream nodes and any local ejections and impingement injections through a simple mass balance in

Equation (6.27). This equation is defined for every node except hub (i=1) nodes, with the massflow at the hub of Passage 5 set equal to the massflow at the hub of Passage 4. This leaves one equation missing for the aft circuit, and two missing for the forward circuit.

(6.27) 푚̇ 푖 = 푚̇ 푖−1 + 푚̇ 푖푛 − 푚̇ 표푢푡

Physical limitations can then be invoked to close the system. The tip of Passage 2 features a tip cooling hole, and therefore the massflow there is equal to the tip ejection massflow, providing one additional Equation (6.28). Similarly, the tip of Passage 1 is closed, so its tip massflow is equal to zero, shown in Equation (6.29). Finally, the hub of

Passage 1 leads only to one cooling hole, allowing the massflow at the hub node of Passage

1 to be set to (the negative of) that cooling massflow in Equation (6.30).

(6.28) 푚̇ 푁,푃2 = 푚̇ 푒,푇퐼푃,푃2

(6.29) 푚̇ 푁,푃1 = 0

(6.30) 푚̇ 1,푃1 = −푚̇ 푒,1,푃1

For the forward circuit, these three extra equations combine with the massflow

Equations (6.27) to give one more massflow equation than node. This combines with the pressure boundary condition at midspan of Passage 2, and these two additional equations are used as the “missing” pressure equations mentioned above.

The aft circuit was one pressure equation short, and one massflow equation short, and these are combined with the two pressure boundary conditions to close the system. An easy way to think of this is the Passage 4 pressure measurement boundary condition sets the pressure throughout the Aft circuit, and the second pressure (or more specifically, the pressure drop from Passage 4 to 5) sets the massflow. Appendix A gives a tabular summary of the entire system of equations, which may be easier to understand.

6.4.2 COOLING HOLE EQUATIONS

The next set of equations are those related to coolant ejection, either through cooling holes, or the impingement holes from Passage 2 to Passage 1. Consequently, these equations will only be performed at nodes that have one of these outlets.

The ejection massflow, notated with the subscript “j”, at each location is a function of the total (in the rotating frame) pressure of the supplying node, and the static pressure at the hole outlet. For film cooling holes, this outlet pressure is the pressure on the airfoil surface at the cooling hole, determined using the CFD simulation. For the impingement holes, it is simply the pressure at the node in Passage 1 where the hole ejects. This condition is notated by the subscript “e” for external.

First, however, a small pressure correction must be applied to account for a pitchwise pressure gradient within the cooling channels to account for the Coriolis effect.

The Coriolis pressure gradient is defined in general terms in Equation (6.31). This simplifies for the current application to Equation (6.32), where θ is the angle between the

Coriolis gradient, and the ejection direction. Finally, Equation (6.33) gives the direct increase in pressure from the bulk passage pressure and the pressure at the cooling hole inlet.

(6.31) 훻푝퐶표푟푖표푙푖푠 = −2휌 훺⃗ × 푤⃗⃗

휕푝 (6.32) | = 2 휌 훺 푤 푐표푠(휃) 휕푟 퐶표푟푖표푙푖푠 (6.33) 푝푗,푖 − 푝푖 = 2 휌푖 훺 푤푖 (푦푖 − 푦푗,푖) 푐표푠 (휃푗,푖)

Total ejection pressure is then determined using Equation (6.8), rewritten with the correct subscripts in Equation (6.34).

훾 − 훾 − 1 훾−1 (6.34) 푝 = 푝 [1 + 푀푎2 ] 푗,푖 푡푟,푗,푖 2 푟,푖

The total ejection pressure and external pressures are combined using standard isentropic relations to find the isentropic ejection Mach number, using Equation (6.35), according to a converging nozzle model. This is the Mach number that the coolant would reach if it were accelerated isentropically from its stagnation condition until the pressure reached the ejection pressure. This Mach number does exceed unity on the suction side due

to low external pressures, but this extra velocity does not increase ejection massflow, so a

“capped” ejection Mach number, defined in Equation (6.36), and annotated with a double overbar. This capped ejection Mach number is then used in the equation for compressible flow through an orifice in Equation (6.37), where 퐶푑 is the cooling hole coefficient of discharge, which accounts for the fact that the cooling holes are not ideal.

훾 훾−1 푝 1 (6.35) 푒,푖 = [ ] 푝푡푟,푗,푖 훾 − 1 2 1 + 2 푀푎푗,푖 (6.36) 푀푎̿̿̿̿푗,푖 ≡ 푀퐼푁퐼푀푈푀(푀푎푗,푖, 1)

훾+1 푚̇ 푗,푖 푝푡푟,푗,푖 훾 훾 − 1 2(훾−1) (6.37) = √ 푀푎̿̿̿̿푗,푖 [1 + 푀푎̿̿̿̿푗,푖] 퐶푑퐴ℎ √푇푡푟,푖 푅 2

This coefficient of discharge would be nearly impossible to measure on a rotating rig with more than one cooling hole, but fortunately there are dozens of previously published experiments designed to measure discharge coefficient for a variety of film cooling flow conditions and geometries. A review of these works has been performed by

Hay and Lampard [79], but the discharge coefficient is a function of many parameters including blowing ratio, and ejection angle. For the central three rows of the showerhead

(C-E), 퐶푑 = 0.65 is used as per Tillman and Jen [80]. The extreme pressure and suction side rows (A and G) use 퐶푑 = 0.60 and 퐶푑 = 0.72, respectively as per Hay et al. [81]. The remaining two rows, (B and F) use 퐶푑 = 0.70, again from Hay et al. [81]. The impingement holes are rounded with fillets, as opposed to the sharp cooling holes, and therefore have a

much higher discharge coefficient of 0.93. A summary of these coefficients is provided in

Table 6.2: Summary of discharge coefficients for each cooling row.

Table 6.2: Summary of discharge coefficients for each cooling row

Row Discharge Coefficient A 0.60 B 0.70 C 0.65 D 0.65 E 0.65 F 0.70 G 0.72 Impingement 0.93

6.4.3 BLOWING RATIO DEFINITIONS

Ultimately the work of this model is performed to determine the blowing ratio of each hole. Recall blowing ratio was defined for a general case in Equation (6.1), but it can be adapted in different ways to a turbine because of the definition of freestream massflux.

The coolant massflux will be defined for each hole as the model-predicted massflow out of the hole, divided by the cross-sectional area of the cooling hole. The freestream massflux

will be defined in two different ways. The first way, is the global blowing ratio, defined in

Equation (6.38), which utilizes a stage-averaged value of massflux for the freestream massflux, defined at the stator inlet massflow divided by the choke area of the stage. The global blowing ratio isn’t physically relevant to the flow physics, but it allows for easier comparison of relative coolant flow rates from one hole to the next. Additionally, the majority of rotating and cascade experiments that publish blowing ratio do not go into detail on how they specifically define freestream massflux in their calculation of blowing ratio, but given their distribution of blowing ratios, it is likely they use the global blowing ratio. The second definition is the local blowing ratio, defined in Equation (6.39), and utilizes the value of freestream massflux on the surface of the airfoil at each cooling hole, as predicted by the CFD computation. This blowing ratio is much more physically relevant, however requires additional dependence on CFD, and obscures the relative rates of coolant.

For example, as is shown in Chapter 7, the highest coolant massfluxes occur on the suction side of the airfoil, due to the low freestream pressure. However, the greatest local blowing ratios occur at the leading edge of the airfoil near the stagnation point, due to extremely low freestream massflux.

푚̇ 푗,푖⁄ 퐴ℎ,푖푛푙푒푡 (6.38) 퐵푅 = 퐺푙표푏푎푙,푖 푚̇ 푐표푟푒⁄ 퐴푠푡푎푔푒

푚̇ 푗,푖 ⁄ (6.39) 퐴ℎ,푖푛푙푒푡 퐵푅퐿표푐푎푙,푖 = [휌푤]푒,푖,퐶퐹퐷

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6.5 VALIDATION OF THE FLOW MODEL

The model presented in this paper makes several assumptions and simplifications, and therefore it is important to validate its end results where possible. The simplest comparison is to compare overall massflows. Recall that the model does not utilize massflow measurements in any way—the passage flow rates are calculated entirely from the pressure measurements in Passages 2, 4, and 5, the geometry of the passages, the friction factor, and the CFD external pressure field. Also recall that the TOBI flow measurement is taken upstream in the cooling system before it enters the rig, and this flow splits to the blade cooling flow, the forward purge flow, and the leakage flow. It seems reasonable that the blade flow should make up a similar fraction of the total TOBI flow, regardless of the exact amount of TOBI flow. Table 6.3 shows the measured TOBI massflows and predicted blade massflows (normalized by turbine inlet massflow), and computes the fraction of predicted blade flow to measured TOBI flow. These values are fairly close to each other, between 54.8% and 58.9%.

Additionally, Honeywell Engines independently developed a proprietary flow model to determine the split among these TOBI flow destinations. The details of this model are corporate confidential, but in essence it uses pressure measurements from this experiment in the TOBI region, purge cavity, and seals, as well as the geometry of these components, to estimate the cooling split. Ultimately it predicts that between 60-61% of the TOBI flow will go through the blade for each run, with exact values depending on run.

The model proposed here consistently predicts a lower blade massflow than the Honeywell model, but they are fairly close given that each model use entirely different in

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Table 6.3: Comparison of measured TOBI flow to predicted blade flows

Total measured Blade massflow Predicted blade massflow as TOBI massflow predicted by model fraction of measured TOBI flow 5.28% 3.08% 58.3% 5.28% 3.09% 58.4% 6.85% 3.75% 54.8% 7.34% 4.07% 55.5% 7.61% 4.29% 56.3% 8.03% 4.73% 58.9% 8.64% 5.08% 58.8%

6.6 A NOTE ON COOLING HOLE SHAPE

The converging nozzle model used in calculating coolant ejection rates is designed for a round cooling hole shape, and is therefore only valid for the round-hole blades presented in this dissertation. The diverging portion in fan and advanced shaped holes completely changes the behavior of the flow within the hole. The cross-sectional area of the fan-shaped hole at the outlet of the hole is approximately 3.7 times larger than the entrance (throat) region, with the advanced shaped hole having an even greater expansion ratio. If the these holes are modeled as an ideal converging-diverging (de Laval) nozzle, this large area ratio results in every cooling hole’s pressure ratio being between the first and second critical points. This results in each shaped hole being choked through the round entrance region, with a standing normal shock within the expanding part of the hole.

It is not immediately clear how accurate the de Laval nozzle model is for fan or especially advanced shaped holes, as the expansion comes from sharp corners on certain

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hole sidewalls, and the advanced shaped hole is very complicated in shape. Nonetheless, the high pressure ratios across the hole and general expanding shape definitely begs additional study, especially as the theoretical benefit of shaped holes comes primarily from the changes in local flow physics due to the hole shape. Most, if not all, of the work previously done on shaped holes has been performed on low pressure ratio, entirely subsonic tests, and will therefore not capture any shock or compressibility-related phenomena, and it is the author’s belief that these may be among the most important phenomena affecting cooling effectiveness.

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CHAPTER 7 INTERNAL FLOW MODEL—RESULTS

The internal model provides a lot of detailed information that has rarely, if ever, been published for a realistic experiment such as this. This chapter will go through these results, first looking at just the nominal TOBI flow case in much spanwise detail. Later, the results for each row will be averaged and the effect of varying TOBI flow will be investigated.

7.1 NOMINAL TOBI CASE

The spanwise results are largely independent of TOBI flow, so one case, the nominal 6.85% case, will be focused on to investigate these trends. The most direct purpose of the model is to take the pressure boundary conditions at midspan and extrapolate these to the reminder of the passage. Pressure results, normalized by stage inlet total pressure, are provided in Figure 7.1.

The most obvious trend is the increase in pressure with span, which is primarily a result of the centrifugal pressure gradient. Passages 1 and 2 keep a relatively close difference, which makes sense as Passage 2 continuously feeds into Passage 1. Passages 4 and 5 differ in slope because of a change in the flow direction, shown in arrows on the figure. Passage 4 features flow radially inward, meaning the frictional pressure gradient works with the centrifugal gradient in being radially out (towards high span). Passage 5 features flow travelling radially out, so the frictional pressure losses counteract the

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centrifugal pressure gradient. It should also be noted that Passage 5 is only about half as large as Passage 4 in cross-sectional area, resulting in double the fluid velocity, and four- times the frictional pressure gradient.

PASSAGE 1 PASSAGE 2 0.65 PASSAGE 4 PASSAGE 5 MEASURED DATA

0.60

T,IN

PASSAGE P/P 0.55

0.50

0 20 40 60 80 100 %SPAN

Figure 7.1: Normalized internal static pressure with data labeled for the 6.85% TOBI flow case

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The temperature within the serpentine passages is not as significant as pressure, but for completion it is also included in Figure 7.2, normalized by stage inlet total temperature

(about 550K). Again, Passage 1 is tightly connected to Passage 2, but is consistently higher because the flow is travelling very slowly in Passage 1, while compressibility effects cool the static temperature of the high-speed flow in Passage 2. Passage 4 is of the opposite slope as the other passages because it is the only one travelling from high to low span, and temperature will increase in the flow direction. The hub temperature of Passage 5 is lower than the hub temperature of Passage 4, despite heat input (relative-total temperature increase) in the hub turn because the smaller cross-sectional area of Passage 5 causes an acceleration of the flow. As written on the plot, the internal coolant bulk Mach number increases from about 0.15 to 0.28.

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0.57

0.56

Ma = 0.15

0.55

T,IN Ma = 0.28

0.54

PASSAGE T/T

0.53

~5.5 K

PASSAGE 1 0.52 PASSAGE 2 PASSAGE 4 PASSAGE 5 MEASURED DATA

0.51 0 20 40 60 80 100 %SPAN

Figure 7.2: Normalized internal static temperature with data labeled for the 6.85% TOBI flow case

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Ultimately solving for temperature and pressure is just an intermediate step to the ultimate goal, which is quantifying the cooling flow rates out of each hole (and from there, the blowing ratios). Figure 7.3 presents the global blowing ratio for the nominal cooling rate at each cooling hole, with different symbols for holes from each row. Because the global blowing ratio uses an averaged value for freestream massflux, is can be thought of as a normalized value of cooling massflux.

As would be expected, the highest coolant flows emerge from Rows E, F, and G, the three most on the suction-side. Row F presents the highest of all, despite Row G being furthest on the suction side. This is because Row G is fed by Passage 4, which Figure 7.1 shows has a significantly lower pressure than Passage 1, which feeds E and F. Row F ejects more than double the massflux of the lowest cooling row, which is Row A.

It is also worth noting that for the most part, blowing ratio increases at higher spans, with the exception of Row A. This is because of the centrifugal pressure gradient, which dominates the rotating cooling passages. There is a centrifugal pressure gradient in the freestream flow as well, highlighted by Figure 7.4, but it is not as dominant because there are many other flow features going on. Row A’s exception is actually a little misleading, as Figure 6.2 showed that Row A is not at a constant value of wetted distance. The lower span holes actually bend aft, resulting in lower external pressure (which is shown by the stronger slope for Row A at low span in Figure 7.4), and therefore higher coolant ejection rates.

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2.8

2.4

2.0

1.6

1.2

GLOBALBLOWING RATIO

0.8

0.4 A C E G B D F

0.0 0 20 40 60 80 100 %SPAN

Figure 7.3: Global blowing ratio vs. span for every cooling hole, labeled by row, for 6.85% TOBI flow

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Figure 7.4 shows the external airfoil pressure onto which the coolant ejects into, again as a function of span with each cooling row shown as a different symbol. Note that these data are entirely from the CFD simulation and are independent of the model. In general, the centrifugal pressure gradient increases the external pressure at higher spans.

Row G presents the best standard of comparison for this for the other rows, as there is not much going on at the suction side other than the centrifugal pressure gradient. As previously mentioned, Row A increases in pressure very quickly at low span, because both effects of increasing span, and getting closer to the leading edge are being seen. At mid to high span, it increases mainly just because of the centrifugal pressure gradient.

Rows B through E are complicated because there is another phenomenon occurring.

At low span, the stagnation point of the airfoil is around Row D. At higher span, the stagnation point moves towards the pressure side, towards Rows C and B, away from D and E. This is why the external pressure for Rows B and C increases faster than Row G and the upper span half of Row A. Row D reaches a maximum at its second cooling hole, where it is exactly at the stagnation point, and then drops as the stagnation point moves toward the pressure side. By midspan, the effect of the moving stagnation point becomes less significant than the centrifugal pressure gradient, and the pressure again increases.

Row E however sees its freestream pressure drop significantly as the stagnation point moves further away and it behaves less like a leading edge row, and more like a suction- side row.

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0.55

0.50

0.45

A D G B E 0.40 C F

T,IN

0.35

EXTERNAL P/P

0.30

0.25

0.20 0 20 40 60 80 100 %SPAN

Figure 7.4: Normalized airfoil pressure at the ejection location of each cooling hole

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Figure 7.3 presented the global blowing ratio, which is essentially a normalized comparison of coolant massfluxes through each hole. While many previous experiments using cascades and rotating turbines appear to use this definition of blowing ratio, it is not the physical blowing ratio that should be used when trying to characterize the film cooling physics. Figure 7.5 shows this blowing ratio, using the local freestream massflux as calculated by the CFD, and this plot presents much more complicated trends than the global blowing ratio. Note also that this plot does not give all the needed information. Other parameters are still important to note, such as momentum flux ratio, and the angle between the coolant ejection and freestream flow.

Cooling Rows A, E, F, and G are relatively constant with span compared to Rows

B, C, and D. The more constant rows will be discussed later with Figure 7.7, which is the same plot as Figure 7.5 with the ordinate zoomed in to show the trends in those rows.

The major trends for Rows B through D is that Row D decreases significantly in blowing ratio, while B and C increase in blowing ratio with span. The reason for this was discussed previously with regards to the stagnation point moving, but is also shown in

Figure 7.6, which plots the local freestream massflux for each hole, normalized by the global average. The stagnation point is associated with high pressure, which will reduce the coolant ejection massflux, but it is also associated with low momentum flow, which has a stronger (and positive) effect on local blowing ratio. At low span, Row D ejects to a region of extremely low freestream massflux, resulting in very high blowing ratio, over 2.5 for the first hole. Similar things happen at high span for Rows B and C, the very low freestream massfluxes push the local blowing ratio above 4.

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4.0 A E B F C G D

3.5

3.0

2.5

2.0

LOCAL BLOWING RATIO 1.5

1.0

0.5

0.0 0 20 40 60 80 100 %SPAN

Figure 7.5: Local blowing ratio vs. span for every cooling hole, labeled by row, for 6.85% TOBI flow

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2.0

1.5

1.0

LOCAL/GLOBAL FREESTREAM MASSFLUX RATIO

A E 0.5 B F C G D

0 20 40 60 80 100 %SPAN

Figure 7.6: Local freestream massflux normalized by the global average

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Another thing to note is the chaotic behavior in this region. The second highest spanned hole in Row C ejects to a freestream massflux about half of the global, while the highest-span hole ejects to a region at the global average. In the distance of one cooling hold to the next, the freestream massflux doubles, causing blowing ratio to drop from about

3.7 to 1.8.

For the more constant Rows A, E, F, and G (shown best in Figure 7.7, but note the ordinate scale) the blowing ratios do not change as much mainly because of two conflicting trends. Locations with higher coolant massflux are caused by lower airfoil pressure, which is usually associated with faster moving freestream flows, and therefore higher freestream massflux. Row A is the best example of this: recall from Figure 7.3 how the low-span holes of Row A experience a much higher global blowing ratio (and thus coolant massflux) due to the lower freestream pressure from being further aft on the blade (see Figure 7.4). This lower pressure comes with greater freestream massflux, shown for the low-span region of

Row A in Figure 7.6, and therefore while the global blowing ratio drops a medium amount from 1.6 to 1.2, the local blowing ratio is constrained between about 0.85 and 0.95, illustrated by Figure 7.7.

There are a few minor trends caused by other phenomena. Row E sees an increase in freestream massflux for similar reasons as Row D, as the stagnation point moves away from the suction side. The high and low span holes in Row G see much lower freestream massfluxes with no corresponding trend in external pressure or coolant massflux, resulting in higher local blowing ratios.

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1.3

1.2

1.1

1.0

LOCAL BLOWING RATIO

0.9

A E B F C G D

0.8 0 20 40 60 80 100 %SPAN

Figure 7.7: Local blowing ratio vs. span for every cooling hole, labeled by row, for 6.85% TOBI flow, zoomed in

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These spanwise trends are interesting and important to note, and have never before been examined in as much detail for a realistic turbine. Unfortunately, they are very strongly influenced by the exact geometry of the airfoil, as well as the speed (for example, the stagnation point will move between takeoff and cruise conditions). This means that the information presented above is not directly applicable to future designers, but is rather best used as a sign of caution against oversimplifying film-cooling analysis. Local blowing ratios in the leading edge showerhead region (which is usually the most critical location to cool) can easily vary by a factor of two from just one hole to the next, and a very detailed

3D analysis is called for in this region for any given airfoil geometry, as well as for any rotor speed.

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7.2 VARIABLE TOBI FLOW CASES

The remainder of this chapter will only look at row-averaged results as a function of overall TOBI flow. Because the spanwise trends were more largely determined by freestream massflux, which is independent of TOBI flow, the results for each row will be averaged to simplify analysis.

Figure 7.8 shows row-averaged local blowing ratio for each row as a function of

TOBI flow. Note that there are two separate runs at 5.28% TOBI flow (Runs 13 and 14), but the data from these runs are very similar. As expected, increasing the total TOBI flow increases the overall average blowing out of every row, but it is clear that some rows are affected differently than others. The pressure side and leading edge rows (A through D) increase significantly more than the rows nearer to the suction side (E through G). Table

7.1 provides the numerical value for blowing ratio for one of the 5.28% TOBI flow runs, and the 8.64% TOBI flow run, as well as the ratio between them. This shows that while the total coolant increases by 77%, Rows E, F, and G only increase by 20-30%, while rows B and C increase 86-88%, while Rows A and D more than double in overall massflux ejection.

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3.0

2.5

2.0

1.5

1.0

0.5 A C E G

ROW-AVERAGED LOCAL BLOWING RATIO B D F

0.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 TOBI FLOW (% OF CORE MASSFLOW)

Figure 7.8: Average local blowing ratio for each cooling row at various TOBI flow rates

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Table 7.1: Minimum and maximum blowing ratios by row

Row 5.28% TOBI BRL 8.64% TOBI BRL 8.64% / 5.28% A 0.607 1.351 2.228 B 1.571 2.922 1.860 C 1.663 3.133 1.884 D 1.202 2.664 2.216 E 0.954 1.239 1.299 F 0.975 1.224 1.255 G 1.064 1.275 1.198 WEIGHTED 1.161 2.051 1.767 AVG

The reason for this comes down to basic compressible flow through an orifice.

Recall that the model calculates an isentropic ejection Mach number for each cooling hole based on the ratio of the (relative frame) stagnation pressure within the serpentine passage at the cooling hole inlet, and the external airfoil pressure at the cooling hole exit, using

Equation (6.35), repeated below.

훾 훾−1 푝 1 (6.35) 푒,푖 = [ ] 푝푡푟,푗,푖 훾 − 1 2 1 + 2 푀푎푗,푖

The suction-side rows are ejecting to very low pressures on the airfoil, and consequently the coolant is at a much higher Mach number within the cooling hole. Figure

7.9 shows the row-averaged isentropic Mach number for each row with variable TOBI

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flow. Rows F and G are choked (isentropic ejection Mach number greater than unity) even at the lowest TOBI flow case, so the only way to increase their massflow is by increasing the passage total pressure (recall Equations (6.36) and (6.37), also repeated below).

(6.36) 푀푎̿̿̿̿푗,푖 ≡ 푀퐼푁퐼푀푈푀(푀푎푗,푖, 1)

훾+1 − 푚̇ 푝 훾 훾 − 1 2(훾−1) 푗,푖 푡푟,푗,푖 ̿̿̿̿ ̿̿̿̿2 (6.37) = √ 푀푎푗,푖 [1 + 푀푎푗,푖] 퐶푑퐴ℎ √푇푡푟,푖 푅 2

The other rows see increased cooling massflux due to both increased TOBI flow, and increased ejection Mach numbers. The effect of increasing Mach number does have diminishing returns, however. Row E’s isentropic ejection Mach number increases from about 0.85 to 1.15, but that increase only causes about a 2% increase in massflow (due just to Mach number increase). This is illustrated graphically in Figure 7.10, which is essentially a plot of Equation (6.37), in contrast with Row A. Rows A, B, C, and D all see much more significant increases in massflow with higher TOBI flow due to both supply pressure increase, and ejection Mach number increase.

These results are valuable and very applicable to real engines. Because the internal cooling pressures have to be greater than the pressure at both the leading edge, and the pressure side of the airfoil in order to eject coolant, it is common for suction side cooling holes to choke because the freestream pressure on the suction side is usually about half of that at the leading edge and pressure side. This becomes an important factor in determining where the supplied engine coolant goes, particularly in determining changes in cooling rates for each row because of marginal changes in overall flow.

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This also presents another interesting problem that is mostly absent from the literature: the effect of hole choking on shaped cooling holes. The two always-choked cooling rows in this experiment are also two of the three shaped rows. The fan and advanced-shaped cooling holes will likely see supersonic flow as the hole begins to expand, and sustain a standing normal shock in each hole when the hole expands too much. This shock will not change the massflux (or blowing ratio), but will change the momentum flux, and temperature significantly.

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1.2

1.0

0.8 A D G B E C F 0.6

EJECTION MACH NUMBER

ROW-AVERAGED ISENTROPIC 0.4

5.5 6.0 6.5 7.0 7.5 8.0 8.5 TOBI FLOW (% OF CORE MASSFLOW)

Figure 7.9: Row averaged isentropic ejection Mach number vs. TOBI flow

1.0

0.8 ROW A ROW E INCREASE INCREASE 0.6

0.4

0.2

FRACTION CHOKED OF FLOW

0.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 ISENTROPIC EJECTION MACH NUMBER

Figure 7.10: Fraction of maximum flow through a choked hole as a function of the isentropic ejection massflow

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CHAPTER 8 AIRFOIL HEAT TRANSFER RESULTS

This experiment is the first example of shaped cooling holes being tested for film cooling performance in a rotating engine-representative environment to be published in the open literature. The airfoil data primarily come from just one run with the highest TOBI flow rate. Detailed blowing ratio data from the internal flow model for this condition are provided in Table 8.1. The table provides the average local and global blowing ratios, as well as the minimum and maximum local blowing ratios for any individual cooling hole in the row.

Table 8.1: Summary of cooling blowing ratio for each cooling row

Cooling Minimum Average Maximum Average Row BRLocal BRLocal BRLocal BRGlobal A 1.07 1.35 1.46 1.93 B 1.64 2.92 4.18 2.25 C 1.57 3.13 5.90 2.41 D 1.48 2.66 4.85 2.40 E 1.17 1.24 1.30 2.46 F 1.20 1.22 1.24 2.76 G 1.23 1.28 1.38 2.31

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8.1 TIME-AVERAGED RESULTS

The main goal of this work is to investigate heat transfer, but first airfoil surface pressure is reviewed. If the computation does not accurately predict the pressure field, there is no chance for a good prediction of heat transfer. Figure 8.1 presents the airfoil static pressure, normalized by stage inlet total pressure. The CFD presents minimum, mean, and maximum values at each wetted distance. The minimum and maximum at each location are the individual minimum and maximum cell values within each “box”, defined between

40% and 60% span, and every 2%WD long, as was described previously and shown in

Figure 2.19. For pressure, there is no major spanwise variation, and with the exception of immediately within the cooling holes, the spanwise differences are caused by a smooth spanwise gradient.

The prediction presents mixed results. There is good agreement on the pressure side until far aft on the airfoil, close to the trailing edge cooling slots, where it overpredicts the experimental pressure. On the suction side, the simulation underpredicts close to the leading edge, in the shock region. This is likely due to the steady nature of the simulation.

There is an unsteady shock in this area of the airfoil, and it is difficult for a steady simulation to accurately model the flow physics in this area. On the rest of the suction side, the pressure is overpredicted, and gets further off the further aft. It appears the steady simulation predicted the shock further upstream than its true average location, resulting in the underprediction close to the leading edge downstream of where the CFD predicts the shock, but upstream of where the shock actually is. This also results in a weaker shock, which causes an overprediction for the downstream locations. It is unfortunate, but not

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altogether surprising that the steady CFD has trouble. A previous study by Southworth et al. [7] showed that steady simulations can have significant disagreements with the averaged solution of unsteady simulations performed with the same mesh and boundary conditions, and previous studies on similar experiments that utilized unsteady predictions, such as that by Nickol et al. [6], have been able to better predict the airfoil pressure field.

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CFD MEAN 0.48 CFD MAX CFD MIN DATA REG HOLES 0.44 SHAPED HOLES

0.40

0.36

T,INLET

P/P 0.32

0.28

0.24

0.20

-100 -50 0 50 100 PRESSURE SIDE %WD SUCTION SIDE

Figure 8.1: Computational and experimental airfoil pressure measurements

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Despite disagreements with the pressure field, the prediction will continue to be used as a comparison. The results for each cooling hole shape, as well as the uncooled blades, is shown in Figure 8.2. The locations of the film cooling rows are indicated by vertical lines, with dotted lines representing holes that are cylindrical for all blades, and solid lines corresponding to rows featuring the shaped holes.

The data show significant spread at any given location, even among gauges seeing the same shaped cooling hole. This is due both to experimental uncertainty, and the spanwise variation in heat transfer caused by the discreet nature of the film cooling jets.

The cooled gauges at about -25% WD are upstream of any shaped hole, so the results here will not show any variation due to hole shape, and can be used as a sort of control to show spread due to the other phenomenon. With few exceptions, the cooled experimental Stanton numbers fall between the uncooled and cooled Stanton numbers predicted by the CFD, suggesting that the computation over-predicts the effectiveness of the coolant in reducing heat transfer into the airfoil.

The higher Stanton numbers that are observed for the uncooled blade appear to agree well with the prediction, with the exception of close to the trailing edge on both sides of the airfoil—the same location the pressure prediction failed to capture.

Shortly downstream of the shaped row on the pressure-side, the data seems to show the round hole outperforming the advanced shape, but this may be a misleading pattern because the heat-flux gauge near the advanced hole is slightly further downstream than the comparable heat-flux gauge for the round hole, and the Stanton number is increasing moving toward the trailing edge at this location. Further downstream, the Stanton number

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for the advanced shaped hole drops quickly and is seen to outperform the fan shape, but the difference is fairly small and within experimental uncertainty. The CFD on the pressure side shows relatively little variation among the three cooling hole shapes. There is a small trend showing the advanced shape to have superior performance immediately following the cooling holes, with the fan-shaped holes performing better further downstream, and the round holes performing the best at a further distance, but the difference in their average performance is small, especially when compared to the significant difference between the uncooled prediction and any of the cooled computations.

On the suction side downstream of the final row of cooling holes, the advanced- hole blade has two gauges with a very low Stanton number, and two more gauges showing a much higher Stanton number a short distance further downstream. This is consistent with the computation for the advanced-shaped row, which also shows a very low Stanton number followed by a quick spike up in heat transfer after this row of holes, although the exact location and magnitude of this spike is not predicted well. The fan-shaped rows demonstrate a slow climb in Stanton number downstream of this row, which is seen both in the data and CFD. The round-hole data appears relatively flat in this region, and the round-hole prediction is also more flat than the other two.

At the furthest downstream measurement location on the suction side, the data show the advanced shape producing the lowest Stanton number, with the cylindrical and fan- shaped performing similar to each-other, but with a greater heat transfer than the advanced- shape. The computation predicts different results, with the advanced shape clearly resulting

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in the greatest Stanton number, although again, the difference between cooling hole shapes is relatively minor and difficult to distinguish from uncertainty.

Prior experiments on shaped cooling holes on simplified geometries (see Bunker

[34] for a review of such works) tend to show a much stronger improvement in film cooling relative to the round hole than is shown here. It is difficult to say with certainty why the shaped cooling holes present less of an improvement in cooling effectiveness in this test, but there are several possibilities, some or all of which may be at fault.

It is helpful first to recall the physics behind the improved film coverage. Shaped holes help to laterally spread the coolant, reduce the coolant’s momentum off the airfoil, and create vortical structures that tend to cancel out or at least reduce the kidney vortices that lift the coolant off the airfoil. These phenomena are caused by changes in the cooling jet flow field, and are also sensitive to changes in the freestream flow field. One major difference could be the presence of a standing shock in each shaped cooling hole due to the engine-representative hole pressure ratio. This shock will completely change the cooling jet flow dynamics, and could eliminate many of the benefits of the shaped hole, but is not present in most (if not all) of the past work. The freestream flow field is also significantly more complicated, with secondary flows and greater turbulence that could act to modify the way the vortical structures evolve in the mixing region between the coolant and freestream.

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3.0

2.5

2.0

STANTON NUMBER X1000

1.5

CFD ROUND CFD FAN CFD ADV CFD UC DATA ROUND DATA FAN 1.0 DATA ADV DATA UC

-100 -50 0 50 100 PRESSURE SIDE %WD SUCTION SIDE

Figure 8.2: Computational and experimental airfoil midspan Stanton number for different cooling hole shapes

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Although the computation predicts a relatively small difference in average surface heat transfer between the different cooling hole shapes, the spanwise extremes in Stanton number produce more noticeable differences. To make visualization easier, each of the three hole shapes will be plotted separately. Figure 8.3 shows the time-averaged midspan

Stanton number, both average experimental data, as well as lateral minimum, mean, and maximum values from the computation for the round-hole case, while Figure 8.4 does the same for the fan-shaped holes, and Figure 8.5 does the same for the advanced-shaped holes.

There are some very large jumps in maximum and minimum Stanton number immediately at each row of cooling holes. For the most part these are extremely local phenomenon (within one hole-diameter of the hole), which is why the axes aren’t expanded to show their peaks. The minima are usually located within a cooling hole, and are negative

(heat transfer out of the metal). The maxima are usually just to the side of a cooling hole.

Further away from a cooling hole, the Stanton number becomes more uniform and the minimum and maximum Stanton number curves get closer, but the hole shape plays some role in how quickly this occurs. The cylindrical and fan-shaped holes behave fairly similarly, but the advanced-shape hole maximum Stanton number is significantly greater than the other two hole shapes after the shaped rows.

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3.0

CFD MEAN ROUND CFD MIN HOLE 2.5 CFD MAX DATA

2.0

1.5

STANTON NUMBER X 1000 X STANTONNUMBER

1.0

-100 -50 0 50 100 PRESSURE SIDE %WD SUCTION SIDE

Figure 8.3: Time-averaged midspan Stanton number for round holes

3.0 FAN HOLE 2.5 CFD MEAN CFD MIN CFD MAX DATA 2.0

1.5

STANTON NUMBER X 1000

1.0

-100 -50 0 50 100 PRESSURE SIDE %WD SUCTION SIDE

Figure 8.4: Time-averaged midspan Stanton number for fan-shaped holes

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3.0 ADV HOLE 2.5 CFD MEAN CFD MIN CFD MAX DATA 2.0

1.5

STANTON NUMBER X 1000

1.0

-100 -50 0 50 100 PRESSURE SIDE %WD SUCTION SIDE

Figure 8.5: Time-averaged midspan Stanton number for advanced-shaped holes

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8.3 TIME-RESOLVED RESULTS

Time-accurate results are presented in the form of encoder averages. Four full revolutions of the rotor are broken into 96 total vane passings, and these 96 individual signals are averaged into one encoder average. This signal is then repeated in all figures for visual clarity. The encoder average plots each show the data for each cooling configuration at a particular location, labeled by %WD. A schematic of an airfoil with these locations all labeled is provided in Figure 8.6.

Figure 8.6: Schematic showing locations of airfoil gauges by %WD

The available data at each location are provided in following figures: -27%WD in

Figure 8.7, -50%WD in Figure 8.8, -69%WD in Figure 8.9, +78%WD in Figure 8.10,

+57%WD in Figure 8.11, and +53%WD in Figure 8.12. Note that not all locations have a

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nearby Pyrex gauge for uncooled heat transfer, and not all locations have surviving Kapton heat-flux gauges for all three cooling configurations, while some have multiple of certain configurations. All available data are plotted for each location. The cooled gauges are all within ±2%WD of the listed location, while the uncooled are within ±5%WD. The cooled gauges can also be anywhere between 40% and 60% span.

At the first location on the pressure side, -27%WD in Figure 8.7, none of the shaped cooling holes have any effect yet, but there is some variation in both phase, and magnitude of unsteadiness in Stanton number among the cooled gauges, even those with the same shape. This is likely due to strong changes in unsteady behavior seen with small changes in location in this region, as can be seen from the strong slope of the CFD results in Figure

8.2. The remaining locations present much better agreement in unsteady behavior among gauges on the same style of blade. The second location on the pressure side, -50%WD in

Figure 8.8, is just downstream of a shaped cooling row. The round-hold gauges present small phase disagreement with each other, with one lining up with the uncooled gauge.

There is also a factor of two difference in magnitude of unsteady behavior between the two round-hole gauges. This is probably a carryover from the -27%WD location: small changes in location can result in significant variation in behavior. Looking at the advanced-hole signal, a phase-shift of about a quarter of a vane-pass is seen from the uncooled and round- hole. The final location near the trailing edge on the pressure side, -69%WD in Figure 8.9, shows two advanced-shape gauges agreeing in phase and magnitude, but a fan-shaped and uncooled gauge leading them in phase slightly, with the uncooled gauge falling between

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the two cooled configurations in phase, but much greater in average heat transfer, and magnitude of unsteadiness.

At the downstream location on the suction side at +78% WD in Figure 8.10, there are three round-hole gauges and two advanced-shape gauges that all line up in phase, but the three fan-shaped gauges again lead the other shapes in phase.

The first two locations on the suction side, +57%WD and +53%WD in Figure 8.11 and Figure 8.12, respectively, are located very close to each other, and behave similarly.

In both cases, both the phase and magnitude of unsteadiness is close for all shapes of cooling hole, with the fan-shape leading the others slightly at +53%WD, and the round leading at +57%WD.

Previous experiments have shown a phase shift between cooled and uncooled airfoils [6, 18] (which is echoed here), so it follows that the modifying the coolant flow field through variable cooling hole shapes can produce a similar shift. It is likely that spanwise variations in the unsteady pressure field cause coolant ejection in the shaped holes to eject more towards a certain direction during certain moments of a vane passing, resulting in rushed or delayed film coverage as a function of hole shape. Unfortunately, the available data are insufficient to pursue a detailed investigation of the physics surrounding this.

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ROUND -27% WD FAN ADVANCED 3 UNCOOLED

STANTON NUMBER X 1000

0.0 0.5 1.0 1.5 2.0 VANE PASS

Figure 8.7: Stanton number encoder average data for all cooling holes at -27%WD

-50% WD

STANTON NUMBER X 1000 X STANTONNUMBER ROUND ADVANCED 1 UNCOOLED

0.0 0.5 1.0 1.5 2.0 VANE PASS

Figure 8.8: Stanton number encoder average data for all cooling holes at -50%WD

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-69% WD

FAN

STANTON NUMBER X 1000 X STANTONNUMBER ADVANCED UNCOOLED 1

0.0 0.5 1.0 1.5 2.0 VANE PASS

Figure 8.9: Stanton number encoder average data for all cooling holes at -69%WD

+78% WD

STANTON NUMBER X 1000

0.0 0.5 1.0 1.5 2.0 VANE PASS

Figure 8.10: Stanton number encoder average data for all cooling holes at +78%WD

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+57% WD

STANTON NUMBER X 1000 X STANTONNUMBER

0.0 0.5 1.0 1.5 2.0 VANE PASS

Figure 8.11: Stanton number encoder average data for all cooling holes at +57%WD

+53% WD

STANTON NUMBER X 1000

0.0 0.5 1.0 1.5 2.0 VANE PASS

Figure 8.12: Stanton number encoder average data for all cooling holes at +53%WD

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CHAPTER 9 PURGE REGION PRESSURE RESULTS

The forward purge cavity is supplied with coolant flow from the TOBI circuit by engine seal geometry to ensure an engine-representative flow split among purge flow, blade flow, and leakage. The internal model predicts the fraction of TOBI flow that travels through the blade to be relatively constant for the range of TOBI flows presented in this dissertation, so it is safe to assume that the fraction of TOBI flow that becomes purge flow is fairly constant as well. The transducers in this region were introduced and labeled in

Figure 2.15 and Figure 2.16, but Figure 9.1 provides the schematics again.

Figure 9.1: Summary of lettered pressure transducer locations

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9.1 TIME AVERAGED RESULTS

Figure 9.2 presents the time-averaged results for locations A through D. Each data point represents the mean of several runs, while the range bars present total run-to-run variation. There are also transducers at locations A and B on two separate blades, and the results from both gauges are shown. It is seen that the cavity pressures A and B are each about 60% higher than the platform inner endwall pressures C and D. This provides a substantial pressure margin to ensure that the net flow is out of the purge cavity, preventing significant hot-flow ingestion into the cavity. Location C also presents significantly higher pressure than location D. This is understandable as location C is much closer to the pressure side of the airfoil while D is closer to the suction side, even though both transducers are upstream of the airfoil. This shows some upstream influence of the rotor on the inner endwall, despite the high Mach numbers in this region.

The nominal and high TOBI cases on the rotor endwall (C and D) present similar pressures, within their respective run-to-run variations. The low TOBI case, however, presents lower pressure. The purge flow causes a blockage and separation region of the core flow on the inner endwall region. It stands to reason that the size of this blockage appears to be a function of the total purge massflow. The nominal and high TOBI cases appear to create a separation that extends at least to these transducers, resulting in lower velocity flow and therefore higher pressure, although similar pressures to each other. The low TOBI flow case on the other hand, allows for reattachment upstream of the platform transducers, and therefore higher flow velocity and lower static pressures.

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The difference between locations A and B is small, so a zoomed-in plot is shown in Figure 9.3. Location B has higher pressure than location A for all cases. This is caused by the centrifugal pressure gradient which was previously explained in the internal model, and given mathematically in Equations (6.19) and (6.20) (repeated below), as B is at a slightly higher radius than A. Evaluating Equation (6.20) for locations A and B predicts that the pressure at B should be about 1.0% of total inlet pressure higher than that at A, but

Figure 9.3 shows that the difference is only about 0.8% of total inlet pressure. The deviation is because the equation does not fully explain the flow field. First, the actual flow features fictional pressure losses that will fight against the centrifugal pressure gradient.

Additionally, because the purge cavity is a disk with one rotating wall, and one stationary wall, the flow is not purely rotational, so the actual centrifugal pressure gradient will not be as large as the theoretical.

(6.19) 훻푝푐푒푛푡 = −휌 훺⃗ × (훺⃗ × 푟 )

휕푝 2 (6.20) | = 휌푖훺 푟푖 휕푟 푐푒푛푡,푖

The high TOBI flow case is also seen to result in higher pressures in the purge cavity, which makes sense as the higher flow rates require a higher supply pressure. The low TOBI case appears higher than the nominal case, but these are much closer to each other and the difference is not as significant.

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0.45

0.40

0.35

T,INLET

P/P 0.30

5.28% TOBI 0.25 6.85% TOBI 8.03% TOBI

A1 A2 B1 B2 C D POSITION

Figure 9.2: Time-averaged normalized pressure measurements for purge region and blade platform

0.46

0.45

0.44

T,INLET

P/P 0.43

0.42

0.41 A1 A2 B1 B2 POSITION

Figure 9.3: Zoom-in of blade root gauges of Figure 9.2

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In addition to the aforementioned rotor inner endwall measurements, there are pressure measurements on the stator inner endwall downstream of the vanes at three values of stator pitch shown in Figure 2.17. These measurement locations are repeated three times in three separate vane passages, and the results are shown in Figure 9.4. Recall that 0% pitch is located right where the vane wake is expected to be, which results in the pressure at that location to be the highest. 50% pitch is right between airfoils, resulting in a medium pressure, while the 95% pitch location is just aft of the suction side high velocity flow, resulting in the lowest static pressure. There is an exception to this, at the 45° from Top

Dead Center (TDC) location. This is most likely caused by some upstream influence from something like a structural strut, although it could also be caused by vane-to-vane manufacturing or assembly differences. Because this region is subject to large velocity gradients, even small shifts in jet behavior or transducer location could lead to significant differences in the pressure trends.

The effect of variable purge flow is small in this location, and run-to-run variation is larger than the difference between the nominal and high TOBI cases, but there is a general trend of increasing pressure with TOBI flow. The cause of this is similar to that on the rotor endwall: the higher TOBI flow causes a larger flow blockage along the inner endwall, resulting in lower speed flow and possibly separation on the inner endwall.

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(a) VANE AT 45o 0.50

0.45

T,INLET

P/P 0.40 5.28% TOBI 6.85% TOBI 8.03% TOBI 0.35

(b) VANE AT 165o 0.50

0.45

T,INLET

P/P 0.40

0.35

0.45

T,INLET

P/P 0.40

0.35

0 20 40 60 80 100 PERCENT PITCH

Figure 9.4: Vane inner endwall pressures for three different vane passages, angles defined from Top Dead Center

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9.2 TIME-RESOLVED RESULTS

Additional insight can be gained by investigating the time-resolved pressure measurements in these locations. Most of this analysis will be performed using encoder averages, but a Fourier analysis also provides some basic insight into the relative strength of unsteady frequency content at different locations, and helps to ensure that the significant frequencies are all integer multiples of the vane-passing frequency, as other frequencies are eliminated by the encoder averaging process. Figure 9.5 presents an FFT of the pressure signals at location A and C. The vane passing frequency is just above 5000 Hz, and peaks are seen for this, and the first three harmonics at location C. Location A also shows peaks at the vane passing and first harmonic, but the magnitudes are much smaller.

0.04

C 0.03 A

0.02

FLUCTUATION 0.01

NORMALIZED PRESSURE NORMALIZED

0.00 0 5000 10000 15000 20000 25000 FREQUENCY (Hz)

Figure 9.5: FFT of pressure signals for locations A and C at nominal flow rates

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Ultimately the magnitude of unsteadiness at locations A and B is only about 15-

25% that of locations C and D. This indicates that the rim seal does its job of reducing the propagation of wake effects into the purge cavity. By the second harmonic, around 16,000

Hz, location A sees so significant peak in unsteady content.

Looking at encoder averages, Figure 9.6 presents the encoder averages for all four locations for the nominal TOBI and aft purge flow case. As was shown in the time-averaged plots, location B has higher pressure than location A because of the centrifugal pressure gradient, while C is higher than D because it is nearer the pressure side, while D is nearer the suction side. Both A and B see much smaller amplitude of oscillation than C and D, but are comparable to each other. The amplitude of oscillation at location C is about 150% that at location D.

In terms of phase, location A leads location B by about a quarter of a vane passing period. The unsteadiness comes from the core flow above the purge cavity, so it seems counterintuitive that the transducer further away from the core flow would lead the transducer closer to the core flow, but the main flow direction within purge cavities tends to be radially inward along the stationary wall, and radially outward along the rotating wall, so it appears the effect of the vane wake propagates with the flow direction more than against it.

Location D is about 2/3 of a blade pitch in front of location C in the direction of blade movement (if every blade had transducers at locations C and D, a transducer at location D would be twice as close to a transducer at Location C on the adjacent blade, as it is to the transducer at location C on its own blade). Accounting for the 24/38 vane/blade

148

count, D is about 0.42 vane pitches ahead of C, meaning it is expected for D to lead C by about 0.42 vane pass, and this is about what is seen.

The difference in shape of the unsteady waveform is also interesting. Location D looks somewhat like a sine wave, while location C has a relatively long-lasting and flat trough of pressure with one very large peak in pressure. This is discussed in more detail later.

0.40 A B C D 0.35

T,INLET

P/P 0.30

0.25

0.0 0.5 1.0 1.5 2.0 VANE PASS

Figure 9.6: Normalized pressure encoder averages of purge cavity signals

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The flow rate through the forward purge cavity was previously shown to have a strong effect on the time-averaged pressure in the purge cavity (see Figure 9.3), but the overall flow rate does not have a very large effect on the unsteady time signal. Figure 9.7 shows the unsteady fluctuation from the mean (just the raw encoder average with the mean subtracted off to make comparison easier) for location A for low, nominal, and high TOBI flows, while Figure 9.8 does the same for location B. These signals are low amplitude, so note the zoomed-in ordinate scale.

The overall shape of the signals is fairly constant across TOBI flow. The biggest difference may be that the lower TOBI flow results in a more “jagged” signal. At location

A, all three cases have one dominant peak and trough. The high TOBI case also has a secondary local peak and trough, but the corresponding peak for the low and nominal cases is actually split into two sub peaks, with the low TOBI case showing much greater amplitude between the sub-peak and trough. Previously referenced literature [46, 50] show that there exist both ingestion into, and ejection out of the purge cavity at different locations and times regardless of the magnitude of supplied purge flow, resulting in a very unsteady and complicated flow field within the cavity. These results show that higher supplied coolant flow rates will reduce the propagation of the effect of the ingestion into the purge cavity, resulting in a “smoother” overall pressure field within the cavity.

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0.010 LOCATION A 5.28% TOBI 6.85% TOBI 0.005 8.03% TOBI

0.000

FLUCTUATION -0.005

NORMALIZED PRESSURE NORMALIZED

-0.010 0.0 0.5 1.0 1.5 2.0 VANE PASS

Figure 9.7: Encoder average fluctuation from the mean for location A for variable TOBI flow rates

0.010 LOCATION B 5.28% TOBI 6.85% TOBI 0.005 8.03% TOBI

0.000

FLUCTUATION -0.005

NORMALIZED PRESSURE NORMALIZED

-0.010 0.0 0.5 1.0 1.5 2.0 VANE PASS

Figure 9.8: Encoder average fluctuation from the mean for location B for variable TOBI flow rates

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The normalized pressure fluctuation encoder averages for the rotor inner endwall, locations C and D, are shown in Figure 9.9 and Figure 9.10, respectively, for variable TOBI flow rates. The aforementioned unevenness in the shape of the unsteady signal at location

C is easier to see here. About 70% of the vane passing period is spent with the pressure below the average value, but the minimum pressure is only 0.025 (2.5% of total inlet pressure) below the mean, while the maximum pressure is more than 0.06 above the mean.

This high-pressure wave is the low speed wake coming off of the vane trailing edge. It is interesting to note how clearly the vane wake can be seen at location C, while it is much more smoothed out at location D, despite both gauges being at the same axial distance upstream of the airfoil, just at different pitches.

The magnitude of unsteadiness is also greater at location C, even when accounting for the greater pressure at C. The peak-to-peak amplitude at C is about 28% the time- averaged value of pressure, while the amplitude is only 21% at D. This is probably also a result of the smoothing out of the vane wake.

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0.06 5.28% TOBI 6.85% TOBI 0.04 8.03% TOBI

0.02

0.00

FLUCTUATION

-0.02

NORMALIZED PRESSURE LOCATION C -0.04 0.0 0.5 1.0 1.5 2.0 VANE PASS

Figure 9.9: Encoder average fluctuation from the mean for location C for variable TOBI flow rates

0.06 5.28% TOBI LOCATION D 6.85% TOBI 0.04 8.03% TOBI

0.02

0.00

FLUCTUATION

-0.02

NORMALIZED PRESSURE NORMALIZED

-0.04 0.0 0.5 1.0 1.5 2.0 VANE PASS

Figure 9.10: Encoder average fluctuation from the mean for location D for variable TOBI flow rates

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There are several reasons why the wake is very coherent at location C, while more spread out at location D. The first is that based on their respective locations, the wake will hit location C without as much upstream influence. This is illustrated by Figure 9.11, with the wakes being shown as blue arrows and the purple double arrows illustrating the increased distance for any interference to propagate to the wake to spread it out. The second reason is that the flow field at location D is accelerating and starting to bend along the main passage between airfoils. This bending can act to pull the wake in towards location D even after location D has moved past the original destination of the wake, resulting in a longer duration of wake, illustrated by the second blue wake arrow bending towards D. The final reason is that, because the pressure is lower at location D than C, the purge cavity at the pitch of location D will eject much more coolant than the cavity at location C. This localized coolant ejection will likely interfere with the wake and result in additional spatial momentum diffusion.

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Figure 9.11: Schematic of (blue) vane wakes heading towards locations C and D

The effect of varying the forward purge flow rate ultimately does not create a significant change in the unsteady waveform on the rotor endwall. Location C and D are very different from each other, but the variation at each location as purge flow is adjusted is minimal. Figure 9.12 and Figure 9.13 show similar plots for variable aft purge flow and present a similarly small changes in wave form shape, suggesting that the small changes observed for variable TOBI flow are statistically negligible.

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0.06 0% AFT 0.516% AFT 0.04 0.971% AFT

0.02

0.00

FLUCTUATION

-0.02

NORMALIZED PRESSURE NORMALIZED LOCATION C -0.04 0.0 0.5 1.0 1.5 2.0 VANE PASS

Figure 9.12: Encoder average fluctuation from the mean for location C for variable aft purge flow rates

0.06 0% AFT LOCATION D 0.516% AFT 0.04 0.971% AFT

0.02

0.00

FLUCTUATION

-0.02

NORMALIZED PRESSURE NORMALIZED

-0.04 0.0 0.5 1.0 1.5 2.0 VANE PASS

Figure 9.13: Encoder average fluctuation from the mean for location D for variable aft purge flow rates

156

CHAPTER 10 PLATFORM HEAT TRANSFER RESULTS

Rotor inner endwall heat transfer measurements will be investigated both as time- averaged measurements, and encoder averages.

10.1 TIME-AVERAGE

Figure 10.1 shows a plot of all time-averaged Stanton number values for the nominal cooling case as a function of axial distance (%AD). The pressure side (PS) bottom gauges are on the underside of the platform and should ideally be sealed and isolated from the core and coolant flows. If there were no leakage into this cavity then the Stanton numbers would be zero (or centered around zero with some experimental error) as there would be no air to transfer heat into or out of the blade, and the experimental duration is insufficient for heat to flow through the full thickness of the platform. If there were significant coolant leakage into the cavity then there would be heat transfer out of the metal

(thus a negative Stanton number) because the coolant temperature is below the initial metal temperature. Instead every gauge presents a slightly positive value, suggesting that the blade seals are imperfect and allow small amounts of core flow through the gaps between blades platforms.

The Platform top gauges show a general trend, increasing in Stanton number at higher axial distances, and the aft gauges continue this trend. There is more scatter in the

Stanton number at these aft gauges, but this is primarily due to their pitch-wise location

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scatter, as Figure 10.2 shows an increase in Stanton number with pitch (moving from the suction side of one blade to the pressure side of the next). The increasing trend with axial distance is likely due to the increasing speed of the flow as it accelerates through the blade row, as well as the replacement of platform boundary layer flow with hot core flow by the passage vortex and other secondary flows. The increasing trend with pitch is also likely caused by the passage vortex, as it pushes flow along the endwall from one blade’s pressure side towards the previous blade’s suction side, resulting in a boundary layer and decreased heat transfer.

2.4

2.0

1.6

1.2

0.8 PS TOP PS BOTTOM

STANTON NUMBER X 1000 X STANTONNUMBER 0.4 AFT TOP

0.0 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 % AXIAL DISTANCE

Figure 10.1: Plot of all time averaged platform Stanton numbers for nominal cooling

158

2.4

2.0

1.6

1.2

0.8 AFT TOP 0.4

STANTON NUMBER X 1000 NUMBER STANTON 0.0 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 % PITCH Figure 10.2: Plot of aft time averaged platform Stanton numbers for nominal cooling

159

Figure 10.3 plots three representative PS top gauges for variable TOBI flow. There are slight changes in platform Stanton number with TOBI flow, but there is no consistent trend, and the changes are within the run-to-run uncertainty of the gauges, therefore it is observed that variable forward purge cooling flows within the range investigated here does not have a significant effect on time-averaged platform heat transfer (which is in line with what was shown by Mathison et al. [63]).

Figure 10.4 presents a similar plot for the runs varying aft purge, and includes two aft edge gauges. The aft gauges decrease in Stanton number as aft purge is increased, however this change is also within run-to-run variation and therefore cannot conclusively be called a physical trend. The pressure-side gauges further upstream also do not show a consistent trend. It appears that any flow field variation due to the downstream blockage caused by aft purge flow is also has little effect to the time-averaged heat transfer on the rotor platform locations investigated here.

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2.4 2.3 39% AD 2.2 45% AD 57% AD 2.1 2.0 1.9 1.8

1.7 STANTON NUMBER X 1000 NUMBER STANTON 1.6 5.2% 5.6% 6.0% 6.4% 6.8% 7.2% 7.6% 8.0% TOBI FLOW

Figure 10.3: Stanton number vs. TOBI flow rate for pressure side upper platform gauges

2.4 2.3 2.2 2.1 39% AD 92% AD 45% AD 93% AD 2.0 57% AD 1.9 1.8

1.7 STANTON NUMBER X 1000 NUMBER STANTON 1.6 0.0% 0.2% 0.4% 0.6% 0.8% 1.0% AFT PURGE FLOW

Figure 10.4: Aft edge and pressure Stanton number variation with aft purge cooling flow

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10.2 TIME-RESOLVED

Figure 10.5 presents the unsteady Stanton number fluctuation for a gauge at

54%AD for variable TOBI flow rates, and Figure 10.6 presents a similar plot for a gauge further down at 60%AD. Figure 10.7 and Figure 10.8 present the encoder average fluctuations for the same locations for variable aft purge flow rates. Both locations present significant unsteady behavior at both the vane-passing frequency, and twice the vane- passing frequency, with two local peaks and troughs in heat transfer per vane pass. The magnitude of both purge cooling rates, however, doesn’t have a significant effect on the unsteady waveform of heat transfer. This is somewhat expected, given the previous conclusion that both TOBI and aft purge cooling rates do not change the time-averaged rates of heat transfer. There are slight differences in unsteady heat transfer, but these differences are within uncertainty, and are insignificant.

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0.4 54% AXIAL DISTANCE 0.3 5.28% TOBI 6.85% TOBI 0.2 8.03% TOBI

0.1

0.0

-0.1

-0.2

STANTON NUMBER X 1000 X STANTONNUMBER -0.3 0.0 0.5 1.0 1.5 2.0 VANE PASS

Figure 10.5: Stanton number encoder average fluctuation for various TOBI flows for gauge at 54%AD

0.4 60% AXIAL DISTANCE 0.3 5.28% TOBI 6.85% TOBI 0.2 8.03% TOBI

0.1

0.0

-0.1

-0.2

STANTON NUMBER X1000 STANTONNUMBER -0.3 0.0 0.5 1.0 1.5 2.0 VANE PASS

Figure 10.6: Stanton number encoder average fluctuation for various TOBI flows for gauge at 60%AD

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0.4 54% AXIAL DISTANCE 0.3 0% AFT 0.516% AFT 0.2 0.971% AFT

0.1

0.0

-0.1

-0.2

STANTON NUMBER X 1000 X STANTONNUMBER -0.3 0.0 0.5 1.0 1.5 2.0 VANE PASS

Figure 10.7: Stanton number encoder average fluctuation for various aft purge flows for gauge at 54%AD

0.4 60% AXIAL DISTANCE 0.3 0% AFT 0.516% AFT 0.2 0.971% AFT

0.1

0.0

-0.1

-0.2

STANTON NUMBER X 1000 X STANTONNUMBER -0.3 0.0 0.5 1.0 1.5 2.0 VANE PASS

Figure 10.8: Stanton number encoder average fluctuation for various aft purge flows for gauge at 60%AD

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CHAPTER 11 CONCLUSIONS

This dissertation investigates pressure and heat transfer measurements on a film and purge cooled rotating transonic turbine stage operating at design-corrected conditions and presents numerous novel measurements and conclusions.

A model is developed to utilize temperature and pressure measurements within the blade serpentine passages to determine coolant flow rates through every film cooling hole on the airfoil, providing blowing ratios based on both rotor-average and cooling hole local freestream massflux values. It is found that coolant massflux out of different cooling holes varies by more than a factor of two across different cooling holes on the same airfoil, but freestream massflux varies by more than a factor of 5. Actual local blowing ratios vary by more than a factor of 4 when both of these are accounted for together.

Away from the stagnation region of the leading edge, blowing ratios are fairly constant, as the increases in cooling massflux are primarily caused by lower freestream pressures, which are caused by greater freestream velocities, and therefore greater freestream massfluxes. Essentially, both numerator and denominator of blowing ratio tend to change together. The area with large variability comes at the leading edge close to the stagnation region, where freestream massflux changes very quickly, and can result in very low freestream massflux, and therefore high blowing ratio.

165

The suction-side cooling holes are mostly choked, or near-choked, while the leading edge and pressure side cooling holes are far from choked. Consequently as total coolant to the blade is increased, the majority of the additional coolant flows out of pressure side and leading edge cooling holes, with the choked holes only flowing 15-25% as large of a relative increase.

Heat transfer was also examined on the airfoil and compared to a computational prediction for several different cooling hole shapes. These cooling hole shapes have been seen to provide significant cooling benefits on simplified geometries, but have never been tested and published on an engine-representative experiment. The results seen in this experiment differ from those in existing literature, showing that the shaped holes do not perform significantly better, although all cooling hole shapes perform significantly better than the uncooled case. Despite the lack of difference in time-averaged heat transfer, small and repeatable unsteady phase-shifts were observed between cooling hole shapes, and between cooled and uncooled cases.

Pressure within the forward purge cavity and on both stator and rotor inner endwalls are also examined for variable forward purge cooling flow rates. The pressure along the rotating wall of the purge cavity is seen to increase with radial distance away from the axis of rotation due to centrifugal effects, but because of frictional losses and because the cavity is not purely rotational, the increase is only about 85% of the theoretical centrifugal increase.

A separation bubble around the purge cavity is observed by seeing lower pressure for the low purge flow cases, while pressures increase significantly at both nominal and

166

high flow cases. This effect is seen on both stator and rotor inner endwalls. The nominal and high purge flow cases are about the same pressure, but far above the low flow case, as the increased flow causes an upstream blockage and downstream recirculation zone, resulting in low speed flow, and higher pressure.

Unsteady pressure fluctuations within the purge cavity are significantly reduced in magnitude as compared to on the rotor inner endwall, about 15-25% the value. This shows that the rim seal does its job of sealing the purge cavity from the core flow fairly well. No locations monitored by this experiment show a significant variation in unsteady pressure waveform based on the range of coolant flows examined here.

The heat transfer on the rotor inner endwall is seen to increase moving aft, likely a result of the accelerating flow, as well as of the passage vortex developing and replacing endwall boundary layer flow with hot core flow. On the endwall aft of the airfoil, heat transfer increases with pitch, being defined as moving from one blade’s suction side, to the next blade’s pressure side, likely also caused by the passage vortex as it pushes flow along the endwall from high pitch to low. Both time-averaged and unsteady heat transfer along the platform at the locations investigated here is unaffected by varying purge cooling flow rates through both the forward and aft purge cavities.

The experiment presented in this dissertation provides novel measurements in multiple locations for an engine-representative turbine test rig. The results presented here provide new insight into the complicated nature of cooling flow rates for actual engine hardware, argues that shaped cooling holes may not provide as large of a boost to cooling

167

effectiveness as previously thought, and presents the effect of forward and aft purge cavity cooling flow on pressures and heat transfer along the inner endwall of the stator and rotor.

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79. Hay, N. and Lampard, D., 1988, "Discharge Coefficient of Turbine Cooling Holes: A Review," Journal of Turbomachinery, 120: pp. 314-319.

80. Tillman, E.S. and Jen, H.F., 1984, "Cooling Airflow Studies at the Leading Edge of a Film-Cooled Airfoil," Journal of Engineering for Gas Turbines and Power, 106: pp. 214-221.

81. Hay, N., Lampard, D., and Benmansour, S., 1983, "Effect of Crossflows on the Discharge Coefficient of Film Cooling Holes," Journal of Engineering for Power, 105: pp. 243-248.

176

APPENDIX A EQUATION SUMMARY OF INTERNAL MODEL

To make the internal model easier to understand, this appendix provides a tabular summary. Table A.1 gives all of the coolant variables that are solved for at each node, with

Table A.2 giving a list of every equation, which nodes each equation is defined in, and a grouping of equations in a form that makes sense.

177

Table A.1: Summary of unknown variables for internal model

1 푚̇ 푖 4N

2 휌푖 4N

3 푤푖 4N

4 푃푖 4N

5 푃푡푟,푖 4N 6 푇 4N

7 푇푡푟,푖 4N

8 푀푎푟,푖 4N

9 ℎ푖 4N

10 푅푒퐷ℎ,푖 4N 휕푝 11 | 4N 휕푟 푐푒푛푡,푖 휕푝 12 | 4N 휕푟 푓,푖

13 푃푟푖 4N

14 푘푖 4N

15 휇푖 4N

푁푢⁄푁푢∞ 1 TOTAL 64N+1

178

4N 4N 4N 4N 4N 4N 4N 4N Full

domain

equations

continued

2N 2N 2N 2N 2N 2N 2N 2N

eqns

Total Total

N N N N N N N N

       

1 1 1 1 1 1 1 1

5 nodes

Passage Passage

Aft circuit Aft

N N N N N N N N

       

1 1 1 1 1 1 1 1

4 nodes

Passage Passage

2N 2N 2N 2N 2N 2N 2N 2N

eqns

Total Total

N N N N N N N N

       

1 1 1 1 1 1 1 1

2 nodes

Passage Passage

Forward circuit Forward

N N N N N N N N

       

1 1 1 1 1 1 1 1

1 nodes

Passage Passage

) ) )

) ) ) ) )

5 6 7 8 9

: Equation summary of internal model : Equation summary

. . . . . 16 17 18

. . .

6 6 6 6 6

Eq.

No.

6 6 6

( ( ( ( (

( ( (

Table

훾

−

훾

−

]

푖

푟

훾

−

푇

훾

푖

)

푐

푀푎

푖

)

푖

훾푅

)

푖

푇

퐴

푇

푡푟

푖

푇

√

푇

(

푅

푇

(

푖

푤

−

푓

(

푖

푓

푟 푓

휌

훾

휌

푎

= =

+ 푖

푀

푖 푖

푖

)

Equation

푖

̇ 휇 푘

푝

푖

푃푟

[

푖

푚

푖

푝

푡푟

푝

푤

푡푟

(

푝

푖

푝

179

4N 4N 4N 4N

Full

4N+1

domain

equations

continued

0 2

2N 2N 2N 2N

eqns

Total Total

N N N N N

---

    

1 1 1 1 1

5 nodes

Passage Passage

Aft circuit Aft

N N N N N

    

2 1 1 1 1

4 nodes

Passage Passage

2N 2N 2N 2N

eqns

Total Total

N N N N N

---

    

2 1 1 1 1

2 nodes

Passage Passage

continued

Forward circuit Forward

N N N N N

------

    

1 1 1 1 1

1 nodes

Passage Passage

Table

) ) ) ) ) )

12 13 14 15 20 23

......

Eq.

No.

6 6 6 6 6 6

B.C.

( ( ( ( ( (

푖

)

푤

푖

−

휌

푖

1 2

푡푟

)

푖

푇

ℎ

퐷

−

푖

(

푖

푃푟

ℎ

푖

∞

푟

푓

푡푟

푓

푖

푃 푘

퐷

푑푎푡푎

푇

ℎ

푖

⁄ 푖

(

푖 ,

푖

ℎ

퐷

푖

푝

휇

−

ℎ 퐷

푡푟

푐

푤

휌

퐷

푇

푖 푅푒

푅푒

푖

ℎ

푚

휌

푖

046

= 023

푃

Equation

)

푖

)

0 ,

)

푖 푚푒푎푠푢푟푒푑

푐푒푛푡

푖

ℎ

푇

푤

퐷

푡푟

(

푒

푇

휕푟

휕푝

−

∞

푅

푀

푤

푇 푢

푠푖푔푛

푁푢

푇

−

푁

(

푖

푠

푖

퐴

푓

푖

ℎ

휕푟

휕푝

180

Full

domain

equations

3 1

- -

1 1 2 0 0 0

eqns

2N 2N

Total Total

------



5 nodes

Passage Passage

Aft circuit Aft

------



4 nodes

Passage Passage

4 2

- -

1 1 1 1 1 1

eqns

2N 2N

Total Total

------



nodes



Passage Passage

continued

A circuit Forward

N N

------



1 nodes

Passage Passage

Table

) ) ) ) ) ) )

24 25 26 27 28 29 30

......

Eq.

No.

6 6 6 6 6 6 6

B.C.

( ( ( ( ( ( (

푁

푓

휕푟

휕푝

휕푟

휕푝

휕푟

휕푝

표푢푡

푁

푚

푃

푑푎푡푎

푐푒푛푡

−

푒

푐푒푛푡

푇퐼푃

푖푛

휕푟

휕푝

휕푟

푒

휕푝

푚

휕푟

푚

휕푝

−

푃

−

푁

푝

−

Equation

푝

푖

3 푃 푚

푚푒푎푠푢푟푒푑

푃

−

푖

푚 푁

− −

푝

푟 푟 푟

푚

Δ Δ

−

푀

−

푝

푖

푁

푝

2 2

푝

−

푚

푖

푝

푁

푝

181