1

Step Misaligned and Film Cooled Nozzle Guide

Vanes at Transonic Conditions: Heat Transfer

Luke Emerson Luehr

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

in partial fulfillment of the requirements for the degree of

Master of Science

In

Mechanical Engineering

Wing F. Ng, Chair

Srinath V. Ekkad

Thomas E. Diller

K. Todd Lowe

February 16th 2018

Blacksburg, VA

Keywords: Experimental Heat Transfer, Transonic, Film Cooling, Endwall Heat

Transfer, Secondary Flows, Endwall Aerodynamics

ii

Step Misaligned and Film Cooled Nozzle Guide

Vanes at Transonic Conditions: Heat Transfer

Luke Emerson Luehr

ABSTRACT

This study describes a detailed investigation on the effects that upstream step

misalignment and upstream purge film cooling have on the endwall heat transfer for nozzle

guide vanes in a land based power generation gas turbine at transonic conditions. Endwall

Nusselt Number and adiabatic film cooling effectiveness distributions were experimentally

calculated and compared with qualitative data gathered via oil paint flow visualization

which also depicts endwall flow physics. Tests were conducted in a transonic linear

cascade blowdown facility. Data were gathered at an exit Mach number of 0.85 with a

freestream turbulence intensity of 16% at a Re = 1.5 x 106 based on axial chord. Varied

upstream purge blowing ratios and a no blowing case were tested for 3 different upstream

step geometries, one of which was the baseline (no step). The other two geometries are a

backward step geometry and a forward step geometry, which comprised of a span-wise

upstream step of +4.86% span and -4.86% span respectively.

Experimentation shows that the addition of upstream purge film cooling increases

the Nusselt Number at injection upwards of 50% but lowers it in the throat of the passage

by approximately 20%. The addition of a backward facing step induces more turbulent

mixing between the coolant and mainstream flows, thus reducing film effectiveness

coverage and increasing Nusselt number by nearly 40% in the passage throat. In contrast,

the presence of a forward step creates a more stable boundary layer for the coolant flow,

thus aiding to help keep the film attached to the endwall at higher blowing ratios. Increasing

the blowing ratio increases film cooling effectiveness and endwall coverage up to a certain

point, beyond which, the high momentum of the coolant results in poor cooling

performance due to jet liftoff. Near endwall streamlines without purge cooling generated

by Li et al. [1] for the same geometries were compared to the experimental data. It was

shown that even with the addition of upstream purge cooling, the near endwall streamlines

iii

as they moved downstream matched strikingly well with the experimental data. This

discovery indicates that while the coolant flow will likely affect the flow streamlines three

dimensionally, they are minimally effected by the coolant flow near the endwall as the flow

moves downstream.

iv

Step Misaligned and Film Cooled Nozzle Guide

Vanes at Transonic Conditions: Heat Transfer

Luke Emerson Luehr

General Audience Abstract

Gas turbine engines are commonly used for power production by burning natural

gas. This leads to exceedingly hot temperatures through several stages of the engine. These

temperatures often exceed the melting points of the metal components, especially in the

region immediately following the combustion zone. Relatively cooler air from the

compressor stage of the engine is used to cool these hot regions using sophisticated cooling

schemes (external/internal cooling). The performance of these schemes can be severely

influenced by unintentional but unavoidable geometric discrepancies caused by non-

uniform thermal expansion and manufacturing tolerances of the engine components.

This study investigates the impact of these geometric variations (specifically:

combustor line/nozzle guide vane platform misalignment) on a commonly employed

external cooling scheme (purge cooling) where the cooler air creates a protective layer

between the metal and the hot gases. The geometric variation is found to make significant

impact to the performance of the cooling scheme. The misalignment in one direction is

found to be detrimental to the purge cooling effectiveness, while the other geometric

misalignment helps the cooling scheme. In addition, increasing the amount of cooling does

not necessarily mean better cooling because the increased amount of coolant can jet off of

the surface before it can protect it from the hot gas. Quantitative results explaining the

effects geometric misalignment and purge cooling are presented in the research herein.

v

Acknowledgements

Before I begin thanking those friends and colleagues that have helped me

throughout this process, I would like to thank God for blessing me with the knowledge and

drive to accomplish such a task and also for the support system He has placed around me

to carry me through to the end. I would also like to thank my amazing wife, Evin Luehr,

who without her help, I could not have accomplished such an undertaking and would not

be half the man I am today. She has supported me in the best and worst times in this process

and I would have quit many times over without her. I would also like to thank my Mother,

Jeani Luehr, and Father, Paul Luehr, as well as my Brother, Joel Luehr, for their constant

prayers and support as well as raising me and molding a large part of who I am today.

Without your help and guidance, I wouldn’t have completed my research.

To Dr. Ng, my advisor, a sincere thank you for guiding me and shaping me into

who I am as an engineer. In addition, thank you to my advisory committee Dr. Srinath

Ekkad, Dr. Todd Lowe, and Dr. Thomas Diller, for their help in the research presented in

this paper.

I would also like to thank my colleagues Ridge Sibold, Jaideep Pandit, David Mayo,

John Gillespie, and Stephen Lash. Without your help, day in and day out, on gathering

data, guiding my decision making, and helping with everyday tasks I would not have

completed this project. In addition, a special thanks to the Mechanical Engineering Support

Staff, specifically Diana Israel for an amazing job of supporting the research group without

a single complaint even when they were warranted. I would also like to thank the Virginia

Tech Mechanical Engineering Machine Shop workers; Timothy Kessinger, Bill Songer,

Phillip Long, and Casey Lucas for manufacturing all the parts necessary for my research.

I also had much help from friends and fellow students along the way. To Noah

Allen, a thank you for your help with all my Matlab and LabVIEW questions. To Jonathan

Pfab, another thanks for your help with Matlab and troubleshooting as well as help with

classes that we took together. To all my other friends and family not mentioned, a great

thanks for helping me along the way.

Finally, I would like to thank my industry sponsor, Solar Turbines Inc. and our

direct contacts Dr. Hongzhou Xu and Dr. Michael Fox for their trust, guidance, and funding

which allowed the research presented herein.

vi

Table of Contents

List of Figures ............................................................................................................... vii

List of Tables ................................................................................................................. ix Nomenclature .................................................................................................................. x

Introduction ..................................................................................................................... 1 Relevant Past Studies ...................................................................................................... 1

Experimental Test Facility ............................................................................................... 4 Reduction Technique ....................................................................................................... 9

Results and Discussion .................................................................................................. 10 1. Addition of Upstream Purge Blowing .................................................................... 10

2. Effect of Step Misalignment .................................................................................. 16

3. Effect of Upstream Blowing Ratio ......................................................................... 19

Summary and Conclusions ............................................................................................ 22

General Discussion ........................................................................................................ 23 References ..................................................................................................................... 24

Appendix A: Detailed Vane Geometry .......................................................................... 27 Appendix B: Heat Transfer Data Measurement Method ................................................. 29

Appendix C: Linear Regression Technique .................................................................... 31 Appendix D: Blowing Measurement and Apparatus ...................................................... 34

Appendix E: Uncertainty Analysis Details ..................................................................... 37 Appendix F: CFD Streamlines Plotted Over Flow Visualization .................................... 38

Appendix G: Effect of Adding Blowing for All Geometries .......................................... 39 Appendix H: Effect of Upstream Step Misalignment at BR = 1.0 .................................. 42

vii

List of Figures

Figure 1. Virginia Tech Transonic Wind Tunnel Facility ................................................ 4

Figure 2. Experimental Test Section Vane Cascade Geometry ........................................ 6

Figure 3. Pitch-Wise View of the Endwall Test Geometries ............................................ 7

Figure 4. IR Camera Setup During Wind Tunnel Blowdown .......................................... 8

Figure 5. Oil paint flow visualization before test: Yellow paint (upstream of step), Red

paint (between cooling rows), Green paint (pressure side), Blue Paint (suction side) ..... 11

Figure 6. Flow Visualization Results for Baseline No Step Case Without Upstream Purge

Cooling ......................................................................................................................... 12

Figure 7. Flow Visualization Results for Baseline No Step Upstream Purge Cooling BR

= 2.5 .............................................................................................................................. 12

Figure 8. Baseline No Step Endwall Nu Contour Without Upstream Purge Cooling...... 13

Figure 9. Baseline No Step Endwall Nu Contour with Upstream Purge BR = 2.5 .......... 14

Figure 10. Baseline No Step Endwall NHFR from no Upstream Purge Blowing to

Upstream Purge BR = 2.5 .............................................................................................. 15

Figure 11. Near Endwall Flow Streamlines Without Blowing for Backward Step,

Baseline, and Forward Step Geometries ........................................................................ 16

Figure 12. Endwall η contours for All Geometries at Upstream Purge BR = 2.5 ........... 16

Figure 13. Baseline No Step Endwall Nu Contour for Upstream Purge BR = 2.5 .......... 18

Figure 14. Backward Step Endwall Nu Contour for Upstream Purge BR = 2.5 ............. 19

Figure 15. Baseline No Step Endwall η Contour for Upstream Purge BR = 1.0 ............. 20

Figure 16. Baseline No Step Endwall η Contour for Upstream Purge BR = 2.5 ............. 21

Figure 17. Baseline No Step Endwall η Contour for Upstream Purge BR = 3.5 ............. 21

Figure 18. Flow Visualization Results Compared to Data Reduction Results for Baseline

BR = 2.5 ........................................................................................................................ 22

Figure 19. Solid Model of the Vane Geometry and Test Section Window ...................... 27

Figure 20. Camera Setup During Transonic Blowdown Test ......................................... 29

Figure 21. Solid Model of the IR Camera Viewing Plane Through Germanium Window

...................................................................................................................................... 30

Figure 22. DLRT Result After Reduction Showing Calculated HTC and η Values ........ 32

Figure 23. Detailed Illustration of the Upstream Purge Blowing Setup .......................... 35

viii

Figure 24. Flow Chart of Uncertainty Analysis Technique ............................................ 37

Figure 25. No Blowing Near Endwall CFD Streamlines Plotted Over Flow Visualization

Results: Baseline No Step BR = 2.5 ............................................................................... 38

Figure 26. Film Effectiveness Contour for Backward Step Geometry BR = 1.0 ............ 42

Figure 27. Film Effectiveness Contour for Baseline No Step Geometry BR = 1.0 ......... 43

Figure 28. Film Effectiveness Contour for Forward Step Geometry BR = 1.0 ............... 43

Figure 29. Endwall Nu Contour for Backward Step Geometry BR = 1.0 ....................... 45

Figure 30. Endwall Nu Contour for Baseline No Step Geometry BR = 1.0 .................... 46

ix

List of Tables

Table 1: Vane Geometry Parameters and Test Conditions ................................................ 7

Table 2: Experimental Test Matrix ................................................................................ 10 Table 3: Effect of Adding Upstream Purge BR = 1.0 for All Geometries ...................... 39

x

Nomenclature

BR Blowing Ratio

C Chord

c Specific Heat

D Diameter

DR Density Ratio

FDM Fused Deposition Modelling

HSV Horseshoe Vortex

HTC Heat Transfer Coefficient

IR Infrared

M Mach Number

η Adiabatic Film Cooling Effectiveness

NGV Nozzle Guide Vane

Nu Nusselt Number 𝐻𝑇𝐶∗𝐶

𝑘

P Pitch

φ Overall Film Effectiveness

q” Endwall Heat Flux

Re Reynold’s Number

St Stanton Number

T Temperature

t Time

Tu Turbulence Intensity

Subscripts

∞ Mainstream Flow

ax Axial

aw Adiabatic Wall

c Coolant Flow

ex Exit

f Film Cooled

o Non-Cooled

r Recovery

w Wall

1

Introduction

In the power generation gas turbine industry, hotter operating fluid temperatures at

the combustor exit lead to higher turbine power generation efficiencies. Consequently, the

vanes of the turbine, specifically nozzle guide vanes directly following the combustor, face

the potential of thermal failure. Internal cooling, showerhead film cooling, and purge flow

film cooling are a few of the ways that manufacturers try to mitigate the malfunctions

caused by increased thermal load on the endwall of NGVs [2].

Upstream purge film cooling has allowed turbines to operate at higher temperatures

by reducing the thermal load on the endwall of the turbine vanes. Purge film cooling does

so by pulling relatively cooler air from the compressor side of the engine and routing it

through to the endwall of the turbine where it can then be ejected onto the endwall of the

turbine passage to create a protective layer of cooler air.

Because of the improvements in cooling schemes, such as upstream purge film

cooling, that have allowed for higher operating temperatures, engines have also seen

changes in the thermal expansion of many of their components. One major component that

sees such expansion is the combustor lining that directly precedes the NGVs in the flow

path of the operating fluid. This expansion of the thin combustor lining can create a span-

wise backward, or forward facing step misalignment that causes different endwall flow

profiles, which alter the overall heat transfer on the endwall. It is important to note that it

is also quite common for the misalignment between the combustor lining and vane endwall

to be a result of manufactured engine components being out of tolerance as well as thermal

transients at engine startup and shutdown. The exact effect of the misalignment on the

endwall heat transfer coupled with upstream film cooling in transonic testing conditions

remains a relatively unexplored field in the turbomachinery industry. The research herein

serves to shed light on these effects in order to try and resolve the issues that they create.

Relevant Past Studies

Endwall aerodynamics for a NGV have well understood flow physics and

secondary flow features. Understanding of these flow physics is a direct result of the

research done by Herzig [3], Sharma and Butler [4], Langston et al. [5], Goldstein and

Spores [6], and Jílek [7], as a few examples. One of the major secondary flow features is

2

the Horseshoe Vortex (HSV), which occurs when the inlet boundary layer stagnates along

the leading edge of the vane and bifurcates into different vortical structures, the pressure

side and suction side horseshoe vortices. As the pressure side leg of the HSV propagates

downstream, endwall crossflows and pressure gradients cause it to merge with the suction

side leg of the horseshoe vortex, becoming the passage vortex. These secondary flow

structures have a large effect on the convection along the endwall in the turbine passage

and contribute to the overall endwall heat transfer within the passage.

In addition to the endwall aerodynamics within a turbine passage, much study has

also been done regarding the heat transfer along the endwall in such passages. Graziani et

al. [8], Kang et al. [9], Ames et al. [10], and Panchal et al. [11] performed studies on the

heat transfer on the endwall of a vane cascade without film cooling. These studies

collectively found that the presence of secondary flows within a vane passage have a large

effect on the patterns and magnitude of HTC along the passage endwall. In addition, they

also proved that contouring of the passage endwall to alter the generation of secondary

flows can have a significant effect on reducing endwall HTC.

Although not much study has been done for heat transfer in the transonic regime,

Laveau et al. [12] studied the effect of Re on the endwall heat transfer. This study found

that increasing the Re by 28% at the inlet boundary has a significant, 37% increase, on the

endwall Nusselt number (Nu). The results of these findings further stress the importance

of testing at engine-representative Re conditions.

In recent years, endwall film cooling has become more prevalent within the

industry. Takeishi et al. [13], Thrift et al. [14], Roy et al. [15], Saxena et al. [16], and Papa

et al. [17] performed studies on the effects of film cooling on the endwall heat transfer and

endwall adiabatic film cooling effectiveness. From these, multiple conclusions may be

drawn. One such conclusion is that the secondary flow from the HSV reduces the

effectiveness of film cooling and increases heat transfer near the leading edge and along

the suction side of the vanes. In addition, at lower BR, the secondary flows dominate the

momentum of the coolant flow and force the coolant towards the suction side of the passage

leaving the pressure side unaffected. The secondary flows dominate the coolant flow until

the BR reaches a point where the coolant momentum can overcome the secondary flows of

the mainstream and provide coverage over more of the endwall. It is important to note that

3

this increase in BR induces more turbulent mixing with the mainstream flow, as well as

possible jet liftoff from the endwall, especially at high freestream Tu conditions.

Two interesting studies that did not involve purge flow film cooling, an

experimental study performed by Mayo et al. [18] and a CFD analysis by Li et al. [1],

investigated the effects of upstream endwall step misalignment on endwall Nu. These

studies found that the presence of a backward facing upstream step has a large effect on

the endwall heat transfer by altering the secondary flows before the leading edge. The

endwall experiences an augmented Nu due to altered endwall vortices in this region. In

addition, the CFD analysis by Li et al. [1] found that the presence of a forward facing step

causes the flow to reattach much farther upstream. The change in reattachment location

creates a more stable boundary layer, decreases the size and strength of the HSV, and

lowers the overall Nu on the endwall. Conversely, the presence of a backward facing step

causes the flow to reattach farther downstream, creating a larger cavity vortex just after the

step, which creates an unsteady boundary layer. In addition, a backward facing step

increases the size and strength of the HSV and increases the overall Nu on the endwall.

One study done by Zhang and Moon [19] combined both upstream step

misalignment, and purge flow film cooling, to find the endwall film cooling effectiveness

in a turbine cascade. They showed that lower BRs can’t overcome the secondary flows

within the passage, but higher BRs are able to penetrate the secondary flow and provide

acceptable endwall cooling coverage. In addition, they found that the presence of a

backward facing step upstream of the vanes creates an unstable boundary layer that induces

coolant mixing immediately after the coolant enters the mainstream, damaging the overall

endwall coverage of the coolant flow. This study, which was done at Mex = 0.72, only

includes film cooling effectiveness and lacks HTC measurements, limiting its ability to

draw complete conclusions regarding endwall heat transfer.

Another major study done at low speed by Piggush and Simon [20] incorporated

upstream step platform misalignment and purge film cooling to find their respective effects

on endwall St and film cooling effectiveness. The study found that the presence of a

forward facing step thins the boundary layer and causes a heat transfer increase, while a

backward facing step thickens the boundary layer and decreases the overall heat transfer

on the endwall. This study was done at very low speed mainstream flow conditions and

4

lacked high freestream turbulence that is seen in actual engine conditions, while the current

study was done at transonic conditions with high freestream turbulence, thus limiting the

validity of drawing meaningful comparisons between the two. The results of the current

study show that the backward facing step actually increases the endwall heat transfer. This

discrepancy is attributed to the effects of compressibility at transonic conditions. In

transonic conditions, there exists a shock within the throat of the passage, which greatly

alters the pattern of the HTC along the endwall

Although much research has been done on endwall heat transfer in a linear turbine

cascade in the presence of purge film cooling, and even some with the addition of upstream

step misalignment, little, if no research, has been conducted to the authors’ knowledge on

endwall HTC and η while combining upstream step misalignment and purge film cooling

on a converging NGV in the transonic regime under engine representative turbulence and

Re levels. This paper serves to shed light on the effects of upstream step misalignment and

upstream purge film cooling on the heat transfer characteristics of an endwall for an engine

representative NGV. The results and conclusions drawn from this study should lead to

improvements on current endwall cooling techniques, allowing for higher operating turbine

temperatures and efficiencies.

Experimental Test Facility

Figure 1. Virginia Tech Transonic Wind Tunnel Facility

5

The Virginia Tech Transonic Wind Tunnel, Figure 1, is a blowdown facility where

aerodynamic and heat transfer measurements are made. The facility is powered by two

Boge Industrial Compressors capable of 1.27 kg/s mass flow at 1207 kPa. To ensure low

moisture content in the air entering the test section, the air is run through an Aircell dryer

where it is dried to -73oC before being stored in a 18930-liter tank. These facilities allow

the wind tunnel to blow down at steady transonic conditions for 30 seconds with a

maximum mass flow rate of 4.5 kg/s.

For heat transfer measurements, the air entering the test section is preheated using

a heat exchanger loop powered by two 36kW heaters shown in Figure 1. Valve 1 is left

open and Valve 2 is closed while a recirculation fan forces air over the heaters. On the top

part of the heating loop, the air passes through copper tubes which serve both as a thermal

capacitor and a flow straightener. The temperature of the air is monitored using a total

temperature thermocouple probe, and once the air reaches the desired temperature,

blowdown can begin after Valve 1 is closed and Valve 2 is opened. A butterfly control

valve upstream of the air inlet in Figure 1 automatically maintains steady downstream

conditions over the course of an experiment. For a more detailed description of the wind

tunnel and capabilities, refer to Arisi et al. [21], Nasir et al. [22], Abraham et al. [23],

Carullo et al. [24], and Smith et al. [25].

The vanes within the test section are manufactured via FDM 3D printing of ABS

P-430 with a Stratasys Fortus 250mc. The printer is capable of handling tolerances within

the required range for vane manufacturing for experimental testing. To ensure the turbine

vanes have smooth surfaces after exiting the printer, they are carefully sanded down until

there are no traces of the stratified 3D printing layers. The vane material has a very low

manufacturer specified thermal conductivity (k =0.188 W/m-K) enabling the assumption

of one dimensional semi-infinite heat conduction through the vane endwall for the duration

of the test when solving for wall heat flux, used to calculate HTC and η as described later.

6

Figure 2. Experimental Test Section Vane Cascade Geometry

The vane cascade shown in Figure 2 consists of 5 vane passages. Behind the top 2

passages exists a tailboard to help ensure the periodicity of the flow through the test section.

A turbulence grid upstream of the test section generates a Tu of 16% to accurately mimic

engine conditions as the working fluid exits the combustor. The method used to calculate

the Tu is described in Nix et al. [26]. A Pitot static probe was placed approximately 2.8 Cax

upstream of the leading edge in order to obtain mainstream flow total and static pressures.

A thermocouple was also placed 4.6 Cax upstream of the leading edge in order to obtain the

test section temperature during blowdown. To gather the inlet and exit static pressures in

the test section, 6 pressure taps evenly spaced in the pitch-wise direction are located 1.4

Cax downstream of the leading edge, and 6 more evenly spaced pressure taps are located

1.4 Cax upstream of the leading edge. To inject upstream purge cooling into the test section,

7

two rows of cylindrical coolant holes are located approximately 0.39 Cax upstream of the

leading edge and inject the coolant into the mainstream flow at an angle of 50o from the

horizontal. Table 1 offers a more detailed representation of the cascade geometry and

blowdown test conditions.

Table 1: Vane Geometry Parameters and Test Conditions

Axial Chord (Cax) 50 mm

True Chord (C) 91.2 mm

Pitch (P) 83.1 mm

Span (S) 152.4 mm

Coolant Injection Angle 50o

Coolant Hole Diameter 2.39 mm

Coolant Hole P/D 3.5

Coolant Hole L/D 5.8

Inlet Angle and Exit Angle 0o and 73.5o

Exit Reynold’s Number (ReCax) 1.5 x 106

Exit Mach Number (Mex) 0.85

Turbulence Intensity (Tu) 16%

To control the film cooling during blowdown, a buffer tank with regulator are used

for supply air. During the experiment the air is passed through an orifice plate meter to

measure the mass flow of the coolant. The mass flow is calculated using pressures upstream

and downstream of the orifice plate as well as the density of the coolant flow and

expansibility factor of the orifice plate. After passing through the orifice plate meter, the

cooling flow continues into an equalizing plenum where the temperatures are measured

before entering the test section through the upstream film cooling holes.

A Netscanner Model 98RK records the Pitot static probe and static pressure port

readings during the course of the tunnel blowdown. All other pressures and temperatures

are recorded using a LabVIEW code and a NI DAQ, and are recorded at a frequency of 18

Hz.

Figure 3. Pitch-Wise View of the Endwall Test Geometries

8

Figure 3 illustrates a detailed pitch-wise view of the baseline test section geometry

and its variants. The baseline case consists of an inner endwall geometry without an

upstream step. The two other geometries to be tested are a forward facing step of 4.86%

span and a backward facing step of 4.86% span. The upstream step is located 0.9 Cax

upstream of the leading edge. The vanes are printed in 3 separate pieces and sealed together

before being installed into the test section.

A FLIR SC325 LWIR camera and a Germanium IR window viewing port were

used to gather endwall temperature history during blowdown testing. A 3D model showing

the view of the IR camera during the blowdown test is illustrated in Figure 4. The vanes

were painted black with a paint of high emissivity in order to accurately capture the endwall

temperature. The camera faced normal to the endwall and was able to capture the full

passage endwall temperature profile during blowdown.

Figure 4. IR Camera Setup During Wind Tunnel Blowdown

9

Reduction Technique

The Cook-Felderman Method [27] is used to transform the endwall temperature history

into endwall heat flux, which is later used to find HTC and η. The Cook-Felderman Method

uses Equation 1 where ρ is density, k is thermal conductivity and cp is the specific heat at

constant pressure. In addition, n is the total number of endwall temperature measurements

taken over time at each respective pixel, Δt is the time step between successive temperature

measurements, and j is the index for each temperature measurement at its respective time

step. The Cook-Felderman method assumes that the endwall can be modeled using one-

dimensional conduction through a semi-infinite solid as mentioned in the previous section

and is made possible due to the low thermal conductivity of the ABS material the vanes are

manufactured from, the thickness of the endwall, and the short duration of the experiment.

𝑞"𝑤(𝑡𝑛) =2√𝑘𝜌𝑐𝑝

√𝜋Δ𝑡∑

𝑇𝑗−𝑇𝑗−1

√𝑛−𝑗−√𝑛+1−𝑗

𝑛𝑗=1 (1)

Once the endwall heat flux is gathered from the temperature data measured and

recorded with the IR camera, a dual linear regression technique (DLRT) developed by Xue

et al. [28] is used in which Equation 2 for the adiabatic film cooling effectiveness can be

modified and combined with Equation 3 to be written as Equation 4 which serves as the

governing equation for the DLRT.

𝑞" = ℎ(𝑇𝑎𝑤 − 𝑇𝑤) (2)

𝜂 =𝑇𝑟−𝑇𝑎𝑤

𝑇𝑟−𝑇𝑐 (3)

𝑞"

𝑇𝑟−𝑇𝑐= ℎ

𝑇𝑟−𝑇𝑤

𝑇𝑟−𝑇𝑐− ℎ𝜂 (4)

In order to retrieve the HTC and η with Equation 4, the DLRT guesses a recovery

temperature and then subsequently calculates an HTC and η. This process is iterated for

each temperature location until the R2 value for the linear regression is maximized. Frome

10

here on, this paper will nondimensionalize HTC as Nusselt Number (Nu) for more

meaningful comparisons to literature.

To calculate the uncertainties in Nu and η, the uncertainties in each of the individual

measurements was conducted using the perturbation method described in Kline and

McClintock [29]. Nu and η are functions of wall temperature, mainstream temperature, and

coolant temperature. Because of this, the wall, mainstream, and coolant temperatures were

all altered by their respective measurement uncertainties (individually and simultaneously).

This led to an average calculated uncertainty of approximately ± 4.0% in Nu and

approximately ± 0.1 in η.

Results and Discussion

The following presents a detailed analysis on the results from the experiments that

took place during this study. They will begin with how the addition of upstream purge

blowing affects endwall heat transfer compared to no purge flow for the baseline of no

step. After which, the effects of step misalignment and the effects of altering upstream

purge blowing on endwall heat transfer will be individually discussed. For a comprehensive

set of test conditions and geometries that will be discussed, refer to Table 2.

Table 2: Experimental Test Matrix

Test Number Upstream Step

Misalignment

Upstream

Purge

Blowing

Ratio

1 Baseline No Blowing

2 Baseline 1.0

3 Baseline 2.5

4 Baseline 3.5

5 Backward Facing 2.5

6 Forward Facing 2.5

1. Addition of Upstream Purge Blowing

Before examining the effects of upstream step misalignment and altering purge BR

on endwall heat transfer, it is important to simply compare the endwall heat transfer of a

no blowing case to one with upstream purge flow. Oil paint flow visualization helps with

this comparison, and is a tool used to capture the endwall flow physics that then helps in

describing the endwall heat transfer. Figure 5 illustrates the application method for the oil

paint onto the vane endwall before a blowdown test.

11

Figure 5. Oil paint flow visualization before test: Yellow paint (upstream of step), Red paint (between

cooling rows), Green paint (pressure side), Blue Paint (suction side)

The blue paint is first applied to the suction side of the vane-endwall interface.

Next, green paint is applied to the pressure side of the vane-endwall interface. Then, red

paint is applied at the point of inflection on the vane endwall upstream of the leading edge,

which for the cooling case, is just between the two rows of coolant holes. Lastly, yellow

paint is applied just upstream of the step misalignment. The oil paint is swept along the

endwall during the course of a test. As stated earlier, qualitative results can be drawn based

upon the shape and patterns of the paint formed by the endwall flows. Figures 6 and 7

depict the results of the flow visualization testing after the tunnel blowdown.

12

Figure 6. Flow Visualization Results for Baseline No Step Case Without Upstream Purge Cooling

Figure 7. Flow Visualization Results for Baseline No Step Upstream Purge Cooling BR = 2.5

Region A of Figure 6 illustrates the region in which the HSV begins to form.

Comparing this to the same region in Figure 7, it is seen that the red paint penetrates into

this region. The implication of this result is that the coolant flow is penetrating through the

secondary flows along the endwall. Penetration of the secondary flows is made possible by

the high momentum of the coolant flow at a BR of 2.5. Region B in Figure 6 depicts the

line where the pressure side leg of the horseshoe vortex is pulled towards the suction side

where it combines with the suction side leg to become the passage vortex for the baseline

case without upstream purge blowing. Because of the crossflow and pressure gradients, the

red paint does not reach the pressure side vane-endwall interface. Instead, there is a region

of green paint between the two. This distance of approximately 8 mm is larger than its

LE LE

TE PS PS

LE LE

TE PS

13

counterpart in Region B of Figure 7. The distance between the pressure side leg of the

horseshoe vortex and the pressure side vane-endwall interface in Figure 7 is only

approximately 6 mm. The closer proximity of the red paint to the pressure side of the

passage is caused by the upstream purge blowing overcoming the pressure gradient and

endwall crossflow, thus permitting it to penetrate through the pressure side leg of the

horseshoe vortex. The last region of interest on Figures 6 and 7 is the Region C of

recirculation upstream of the point of inflection on the endwall. For both the no blowing

and BR 2.5 cases, the yellow paint which was applied upstream of the step does not travel

into the vane passage. This is due to the cavity vortex in this region, which recirculates the

endwall flow within the gap caused by the combustor-endwall interface.

Now that the endwall flow features with and without blowing are better understood,

this paper will compare the endwall Nu distribution between the two cases. Figures 8 and

9 depict the endwall Nu contours for the baseline no purge blowing and baseline BR 2.5

cases respectively.

Figure 8. Baseline No Step Endwall Nu Contour Without Upstream Purge Cooling

14

Figure 9. Baseline No Step Endwall Nu Contour with Upstream Purge BR = 2.5

Comparing Figures 8 and 9, Region A shows an area of increased Nu of about 50%

due to the addition of upstream purge blowing. This is caused by the turbulent mixing

between the coolant flow and endwall boundary layer flow. The increase in endwall Nu

continues until the leading edge of the vanes and to about 0.2 Cax downstream of the leading

edge. The addition of purge coolant flow does, however, decrease the endwall Nu in the

throat of the passage by approximately 20% by shielding the endwall from the hot

mainstream gases.

15

Figure 10. Baseline No Step Endwall NHFR from no Upstream Purge Blowing to Upstream Purge BR =

2.5

The endwall Nu contour does not tell the entire story given the fact that regions of

higher Nu can still have lower heat flux values into the endwall. The parameter used to take

increased Nu at coolant injection into account, as well as the decrease in gas temperature

from coolant injection, is the net heat flux reduction (NHFR). NHFR is given by Equation

5.

𝑁𝐻𝐹𝑅 = 1 −ℎ𝑓

ℎ𝑜(1 −

𝜂

𝜑) (5)

The variable φ is the nondimensional metal temperature given as overall film

effectiveness. A value of 0.6 for φ is a quite common choice for realistic engine coolant,

inlet, and metal temperature for a gas turbine and was first introduced by Mick and Mayle

[30]. In the present study, a value of 0.6 for the overall film effectiveness is also used.

Region A of Figure 10 shows an area of zero to little NHFR due to the addition of purge

cooling. This hints at the possibility of jet liftoff of the coolant flow from the endwall at

these conditions. No appreciable NHFR is seen until 0.1 Cax upstream of the leading edge

in Region B, from which it dissipates in magnitude as it moves downstream. It is important

16

to note, however, that the NHFR does maintain complete endwall coverage, even to the

pressure side of the passage, which is attributed to the high momentum of the coolant flow.

2. Effect of Step Misalignment

Another factor that can greatly affect the endwall heat transfer is the addition of

upstream step misalignment. Figure 11 by Li et al. [1] depicts the near-endwall CFD flow

streamlines without any upstream purge blowing between the upstream step and the leading

edge for backward step, baseline, and forward step geometries.

Figure 11. Near Endwall Flow Streamlines Without Blowing for Backward Step, Baseline, and Forward

Step Geometries

Figure 12. Endwall η contours for All Geometries at Upstream Purge BR = 2.5

Although these streamlines are shown without any upstream purge blowing, they

can still be used as guidelines for the tendencies of the secondary flows to help describe

the experimental results with upstream purge blowing at least qualitatively (A CFD

analysis with purge flow will be provided in a future paper). Of the three geometries in

17

Figure 11, the backward facing step has by far the strongest secondary flows. The most

important to note are the cavity vortex and the HSV. The backward step creates a region

of recirculation and thereby causes the reattachment line of the flow to be moved further

downstream, making an unstable boundary layer for the coolant to be injected into. It also

augments the size and strength of the HSV. In contrast, the forward step causes the

reattachment line to move upstream and renders the cavity vortex insignificant in terms of

altering the flow near the point of coolant injection, as well as weakens the HSV. The

movement of the reattachment line further upstream also allows for a more stable boundary

layer for the coolant to be injected into.

Figure 12 illustrates the effects of upstream misalignment on the endwall η at an

upstream purge BR of 2.5. The calculated adiabatic film cooling effectiveness contours

were plotted for all the step heights and then the near endwall streamlines from Li et al. [1]

were overlaid onto the contours. Region A in the backward step geometry of Figure 12

shows a mixing of the coolant flow with the mainstream flow immediately after being

injected into the test section. The recirculation region caused by the backward step takes

much energy from the coolant flow and thus also decreases its effectiveness near the

leading edge. Compare this to the baseline and forward step geometries in the same region,

where the η values are much higher near the leading edge. This is credited to the weaker

cavity vortices and more stable boundary layers for these geometries. In addition, as the

step moves from backward, to baseline, to forward, Region B exhibits an increasing η value

which can be attributed to the gradually weakening HSV as the step height decreases as

well as the increased momentum in the coolant flow as it moves downstream. Looking at

the backward step case in Figure 12, it is apparent that effectiveness values above 0.5 don’t

penetrate past the pressure side leg of the HSV, due to the much weaker coolant momentum

in the backward step geometry. There is also an increase in η, as the step height decreases

in Region C due to secondary flows taking less energy out of the coolant flow as the step

height decreases, allowing it to reach the pressure side. In addition, there is little to no film

effectiveness in the region where the coolant is injected, indicating there may be jet liftoff

from the endwall. However, the forward step geometry has the closest representation of

wakes after the coolant holes, hinting that it aids in keeping the film attached due to the

more stable boundary layer upstream of the leading edge. This hypothesis of jet liftoff will

18

be addressed later on in the paper. It is important to note, however that for the baseline

geometry in Figure 12 there is one hole located at about 0.35 y/P that exhibits a very distinct

wake after the coolant is ejected from it. This is explained by the CFD streamlines overlaid

onto the film effectiveness contours which match the patterns of the film effectiveness

contours strikingly well. Directly above the hole which exhibits the coolant wake on the

baseline geometry, there exists a saddle point. Just below this saddle point is a region of

high pressure, which pushes the coolant air onto the endwall, keeping it attached in this

region. The degree to which the CFD streamlines from Li et al. [1] without any purge

cooling matched and explained the film effectiveness contours shows that while the flow

streamlines will change three dimensionally due to the jets of coolant air exiting the holes,

it has a minimal effect on the streamlines as they travel downstream. This could be due to

the high ReCax in the tests, for which the inertial forces of the mainstream flow are high

enough such that they dominate the formation and shape of the endwall streamlines moving

downstream.

Figure 13. Baseline No Step Endwall Nu Contour for Upstream Purge BR = 2.5

19

Figure 14. Backward Step Endwall Nu Contour for Upstream Purge BR = 2.5

Because the backward facing step causes a much more drastic change in η on the

endwall, the Nu contours for the baseline and backward facings step geometries are also

compared in Figures 13 and 14, while the forward step geometry is not shown because it

was so similar to the baseline geometry. In Region A, there is an area-averaged increase in

Nu of approximately 25% due to the backward step. This is because the stronger

recirculation zone for the backward step at the point of injection initiates more turbulent

mixing with the coolant flow before it continues downstream into the passage. In addition,

Region B shows an increase in Nu upwards of 50%. The cause of this is the lower coolant

momentum and stronger secondary flows in the backward facing step case, which don’t

allow the coolant to be as effective downstream. Lastly, the Nu is approximately 30% lower

for the baseline case in Region C because the coolant flow for the baseline case reaches

downstream more effectively, allowing it to shield the endwall from the hot mainstream

gases.

3. Effect of Upstream Blowing Ratio

Figures 15-17 depict the endwall η contours at the baseline geometry for blowing

ratios of 1.0, 2.5, and 3.5 respectively. In Region A, where the coolant is injected into the

20

mainstream flow, the only BR that exhibits apparent wakes after the cooling rows is the

BR 1.0 case. This points once again to the conclusion that the flow may be experiencing

jet liftoff at the higher BR cases. Although the BR 1.0 case does show the expected cooling

wakes after the holes, η rapidly decreases in magnitude and coverage as it moves

downstream whereas the higher BR cases maintain acceptable coverage throughout the

entire passage. Region B is also of interest. For the two higher BR cases, η values near 0.7

reach to the suction side surface near the leading edge of the vanes, while the lower

momentum BR 1.0 case fails to do so. This indicates that for BR 2.5 and 3.5, the coolant

flow is actually penetrating into the suction side HSV, overcoming the endwall secondary

flow. The last major feature of note between the three cases is the changes seen in Region

C. As the BR increases, η increases in magnitude and reaches closer to the pressure side of

the passage. This is because the lower momentum BR 1.0 lacks the momentum to penetrate

through and overcome the endwall crossflow and pressure gradients. The downside,

however, to increasing the BR to reach to the pressure side of the passage is the possibility

of jet liftoff from the endwall due to increased coolant flow momentum, as well as the

possibility of pulling more air from the compressor side of the engine than is necessary.

Figure 15. Baseline No Step Endwall η Contour for Upstream Purge BR = 1.0

21

Figure 16. Baseline No Step Endwall η Contour for Upstream Purge BR = 2.5

Figure 17. Baseline No Step Endwall η Contour for Upstream Purge BR = 3.5

To further explore the possibility and implications of jet liftoff from the endwall at

the higher BR cases it is prudent to compare the flow visualization results for the baseline

BR 2.5 case with the reduced heat transfer data for the same case.

22

Figure 18. Flow Visualization Results Compared to Data Reduction Results for Baseline BR = 2.5

The major takeaway from Figure 18 is the red paint that splatters across the pressure

side of the vane surface as well as the pools of red paint that remain untouched after the

cooling holes. These two factors confirm that there is jet liftoff of the coolant from the

endwall. Looking at the reduced data on the left side of Figure 18, the coolant flow does

not seem to reattach to the endwall until about 0.1 Cax upstream of the leading edge. The

liftoff could have been caused by two important factors. The first is the very sharp injection

angle of 50o of the coolant into the mainstream flow. Second, for the tests conducted, the

DR for the purge blowing was 1.2, which was not matched for the coolant flow and thus

the coolant may have been caused to liftoff at BR’s lower than are engine representative.

This then leads to the momentum ratio in between the coolant and mainstream air being

higher than that seen in an engine. Thus, it is suggested, that in future testing, the DR be

matched to engine representative values of 2.0 for upstream purge blowing.

Summary and Conclusions

This paper provided a detailed analysis on the effects of upstream step

misalignment and purge film cooling on the endwall heat transfer for nozzle guide vanes

at transonic conditions with high freestream turbulence. The data was gathered at the

Virginia Tech Transonic Wind Tunnel and reduced to provide high resolution Nu and η

contours within the passage. Oil paint flow visualization was also utilized to qualitatively

understand the flow physics and compare with the experimental data. The key findings

from the work are as follows:

23

1) The addition of upstream purge blowing does protect the endwall from hot

mainstream gases, but it can be subject to jet liftoff from the endwall at higher BR’s.

2) The influence of a backward facing step of 4.86% span on the endwall heat transfer

was quite significant. It not only decreased endwall film cooling coverage by taking

momentum out of the coolant flow, but it also increased the endwall Nu upwards

of 40% due to increased turbulent mixing with the mainstream flow.

3) The addition of a forward facing step of 4.86% span aids in keeping the film cooling

layer attached to the endwall at the higher BR conditions because it has the most

stable boundary layer at the point of coolant injection out of the three geometries

tested.

4) While increasing the upstream purge BR does improve the film coverage on the

endwall, it may lead to jet liftoff especially for low DR’s. Because of this, matching

DR in future testing may lead to attached film layers even at the higher BR cases.

5) The addition of upstream purge cooling had minimal effect on the formation and

shape of the near endwall streamlines. This could like be due to the high ReCax of

the flow, of which the inertial effects dominated the formation of the endwall

streamlines instead of the coolant flow.

General Discussion

The film effectiveness results done in this study match well with the previous work

done by Zhang and Moon [19]. The two studies were conducted in different facilities with

different techniques, however, the overarching results were very similar. This gives the

authors great confidence in the testing method, facility, and robustness of the data reduction

technique.

The reason that the conclusions from this study did not match those found by Piggush

and Simon [20] is due to the compressibility effects on the endwall heat transfer. At

transonic conditions, a shock occurs within the throat of the passage, which alters the

formation shape and pattern of the endwall heat transfer contours as compared to heat

transfer in the low speed flow regime.

24

References

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Transonic Conditions,” Turbo Expo 2018, Oslo, Norway, GT2018.

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2017, “Effect of Endwall Contouring on a Transonic Turbine Blade Passage: Heat Transfer

Performance,” J. Turbomach., 139(1), p. 11009.

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Measurements on the Stator Endwall of an Axial Turbine,” J. Turbomach., 137(4), p. 41005.

[13] Takeishi, K., Matsuura, M., Aoki, S., and Sato, T., 1990, “An Experimental Study of Heat Transfer

and Film Cooling on Low Aspect Ratio Turbine Nozzles,” J. Turbomach., 112, p. 488.

[14] Thrift, A. A., Thole, K. A., and Hada, S., 2011, “Effects of an Axisymmetric Contoured Endwall on

a Nozzle Guide Vane: Adiabatic Effectiveness Measurements,” J. Turbomach., 133(1), p. 41008.

[15] Roy, A., Jain, S., Ekkad, S. V., Ng, W., Lohaus, A. S., Crawford, M. E., and Abraham, S., 2017,

“Heat Transfer Performance of a Transonic Turbine Blade Passage in the Presence of Leakage

Flow Through Upstream Slot and Mateface Gap With Endwall Contouring,” J. Turbomach.,

139(12), p. 121006.

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[16] Saxena, R., Alqefl, M., Liu, Z., Moon, H.-K., Zhang, L., and Simon, T., 2016, “Contoured Endwall

Flow and Heat Transfer Experiments with Combustor Coolant and Gap Leakage Flows for a

Turbine Nozzle Guide Vane,” Turbo Expo 2016, Seoul, South Korea, GT2016-56675.

[17] Papa, M., Srinivasan, V., and Goldstein, R. J., 2012, “Film Cooling Effect of Rotor-Stator Purge

Flow on Endwall Heat/Mass Transfer,” J. Turbomach., 134(4), p. 41014.

[18] Mayo Jr., D. E., Arisi, A., Ng, W. F., Li, Z., Li, J., Moon, H.-K., and Zhang, L., 2017, “Effect of

Combustor-Turbine Platform Misalignment on the Aerodynamics and Heat Transfer of an

Axisymmetric Converging Vane Endwall at Transonic Conditions,” Turbo Expo 2017, Charlotte,

North Carolina, GT2017-65091.

[19] Zhang, L., and Moon, H. K., 2003, “Turbine Nozzle Endwall Inlet Film Cooling - The Effect of a

Back-Facing Step,” Turbo Expo 2003, Atlanta, Georgia, GT2003-38319.

[20] Piggush, J. D., and Simon, T. W., 2007, “Heat Transfer Measurements in a First Stage Nozzle

Cascade Having Endwall Contouring: Misalignment and Leakage Studies,” J. Turbomach., 129(4),

p. 782.

[21] Arisi, A., Phillips, J., Ng, W. F., Xue, S., Moon, H. K., and Zhang, L., 2016, “An Experimental and

Numerical Study on the Aerothermal Characteristics of a Ribbed Transonic Squealer-Tip Turbine

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[22] Nasir, S., Bolchoz, T., Ng, W.-F., Zhang, L. J., Koo Moon, H., and Anthony, R. J., 2012,

“Showerhead Film Cooling Performance of a Turbine Vane at High Freestream Turbulence in a

Transonic Cascade,” J. Turbomach., 134(5), p. 51021.

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and Numerical Investigations of a Transonic, High Turning Turbine Cascade with a Divergent

Endwall,” FEDSM paper FEDSM-ICNMM2010-30393.

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“The Effects of Freestream Turbulence, Turbulence Length Scale, and Exit Reynolds Number on

Turbine Blade Heat Transfer in a Transonic Cascade,” J. Turbomach., 133(1), p. 11030.

[25] Smith, D. E., Bubb, J. V, Popp, O., Iii, H. C. G., Diller, T. E., Schetz, J. a, and Ng, W. F., 2000,

“An Investigation of Heat Transfer in a Film Cooled Transonic Turbine Cascade , Part I : Unsteady

Heat Transfer,” ASME paper, 2000-GT-0202.

[26] Nix, A. C., Smith, A. C., Diller, T. E., Ng, W. F., and Thole, K. A., 2002, “High Intensity, Large

Length-Scale Freestream Turbulence Generation in a Transonic Turbine Cascade,” ASME paper

No. GT-2002-30523.

[27] Cook, W. J., and Felerman, E. J., 1966, “Reduction of Data from Thin-Film Heat-Transfer Gages -

A Concise Numerical Technique.,” AIAA J., 4(3), pp. 561–562.

[28] Xue, S., Roy, A., Ng, W. F., and Ekkad, S. V., 2015, “A Novel Transient Technique to Determine

Recovery Temperature, Heat Transfer Coefficient, and Film Cooling Effectiveness Simultaneously

in a Transonic Turbine Cascade,” ASME J. Therm. Sci. Eng. Appl., 7, p. 11016.

26

[29] Kline, S. J., and McClintock, F. A., “Describing Uncertainties in Single Sample Experiments,”

Mech. Eng. (Am. Soc. Mech. Eng.) 75 (1953) 3-8.

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Effect Within the Hole Pattern,” J. Turbomach., 110, p. 66.

27

Appendix A: Detailed Vane Geometry

A more detailed illustration of the vane cascade geometry is provided in Figure 19.

The vanes are scaled up 1.5 times engine size in order to fit within the test section and

match an engine representative Re. They are 3D printed via FDM method using a Stratasys

Fortus 250mc printer. The material is ABS P430 with a thermal conductivity of 0.188

W/m-K.

Figure 19. Solid Model of the Vane Geometry and Test Section Window

From Figure 19, the mating lines between the top vane and center vanes as well as

between the bottom vane and center vanes are clearly visible. In addition, the upstream

purge cooling holes as well as the upstream and downstream pressure taps are outlined in

red boxes for better visibility. The upstream step misalignment is located 0.9 Cax upstream

of the leading edge.

The cooling holes are located approximately 0.39 Cax upstream of the leading edge. In

order to obtain the upstream and downstream static pressure used to calculate the flow

conditions, 6 evenly spaced pressure taps are located 1.4 Cax upstream of the leading edge

and 6 more evenly spaced pressure taps are located 1.4 Cax downstream of the leading edge.

28

The pressure taps are 1/16” metal tubes that lay flush in the test section and continue to the

Netscanner Model 98RK which records them during the course of the tunnel run. With the

upstream and downstream static pressure, the inlet and exit M is calculated using Equation

6.

𝑀 = √2

𝛾−1((

𝑃𝑜

𝑃𝑠)

𝛾−1

𝛾− 1) (6)

The inlet and exit Mach numbers are calculated at a frequency of 18 Hz and are recorded

for use in further data reduction.

29

Appendix B: Heat Transfer Data Measurement Method

In order to calculate the HTC and η on the endwall for each test, the endwall

temperature history must first be captured. This is done using a FLIR SC325 LWIR camera.

In order for the camera to see clearly into the test section, a Germanium window with a

BBAR coating is used. Figure 20 illustrates the camera setup during the blowdown test.

Figure 20. Camera Setup During Transonic Blowdown Test

Using a scissor jack stand, the camera is vertically aligned with the test section

window. The camera is then adjusted horizontally to ensure that it can see the entire vane

passage within the test section. In order to ensure the camera is aligned in the same place

for every test, a laser level is used with a known point of incidence on the test window. Not

only does the crosshair laser align the camera vertically and horizontally, but it also makes

sure that it is facing normal to the vane endwall. If not, the crosshair leg lengths will not

be the same.

It was imperative for this process that the IR window used would be compatible

with the IR camera. The IR window had to transmit all wavelengths within the LWIR

spectrum (6-13 μm) in order that the camera would be able to accurately record endwall

30

temperature. The Germanium windows was made such that the entire center passage

endwall could be captured during the course of one blowdown test. A detailed illustration

of the IR camera window and endwall passage view is shown in Figure 21.

Figure 21. Solid Model of the IR Camera Viewing Plane Through Germanium Window

Although the IR camera was able to capture the entirety of the endwall for the center

passage, it was unable to reach all the way upstream to the step misalignment. This was a

concession made due to safety concerns of making the window larger and causing a larger

chance of shattering it. It was also decided not to make two viewing windows in order to

minimize the reduction uncertainty. With two windows, a test capturing the endwall

temperature upstream and another capturing the temperature downstream would have to be

taken separately. This would lead to the necessity of stitching the upstream and

downstream data sets together. All in all, the larger window allows for a much more robust

experimental method.

31

Appendix C: Linear Regression Technique

After the endwall temperature history is gathered, it must be transformed into endwall

heat flux, and subsequently, the endwall HTC and η. In order to transform the endwall

temperature history into the endwall heat flux, the Cook-Felderman Method is applied. The

Cook-Felderman Method assumes that the heat transfer through the vane endwall can be

modeled as one dimensional conduction through a semi-infinite solid. This is made

possible due to the low thermal conductivity of the ABS vane material, the short duration

of the test, and the thickness of the vane endwall. Equation 7 offers the governing equation

for the Cook-Felderman Technique. The values k, ρ, and cp are the thermal conductivity,

density, and specific heat constant pressure respectively for the ABS material. The variable

j refers to the index for each temperature recorded at each respective time step, n is the

total number of temperature measurements taken across the endwall, and Δt is the time step

between temperature measurements.

𝑞"𝑤(𝑡𝑛) =2√𝑘𝜌𝑐𝑝

√𝜋Δ𝑡∑

𝑇𝑗−𝑇𝑗−1

√𝑛−𝑗+√𝑛+1−𝑗

𝑛𝑗=1 (7)

Once the heat flux across the vane passage endwall is gathered using the Cook-

Felderman Method, the endwall HTC and η are simultaneously calculated using a dual

linear regression technique (DLRT) described by Xue et al. [28]. The DLRT combines

Newton’s Law of Cooling and the equation for η to obtain the governing equation for

regression. Equations 8-10 show Newton’s law of cooling, adiabatic film cooling

effectiveness, and DLRT governing equation respectively.

𝑞" = ℎ(𝑇𝑎𝑤 − 𝑇𝑐) (8)

𝜂 =𝑇𝑟−𝑇𝑎𝑤

𝑇𝑟−𝑇𝑐 (9)

𝑞"

𝑇𝑟−𝑇𝑐= ℎ

𝑇𝑟−𝑇𝑤

𝑇𝑟−𝑇𝑐− ℎ𝜂 (10)

32

Equation 10 is organized in a linear fashion such that HTC is the slope of the line and

η is the x-intercept. Figure 22 shows a detailed graph of the DLRT result for one point on

the endwall.

Figure 22. DLRT Result After Reduction Showing Calculated HTC and η Values

The DLRT works by guessing an initial recovery temperature, calculating the HTC,

η, and sum of squares error (SSE). The code iterates its recovery temperature guess and is

complete when the SSE is minimized. Figure 22 is the result of the DLRT for one pixel

after all the iterations are completed. In order for the DLRT to work, two different test runs

with film cooling are needed in order to optimize the signal to noise ratio during data

reduction. One test with chilled coolant and one with ambient temperature coolant. Because

the recovery temperature should be the same for both of the tests, the DLRT is still

33

applicable and the endwall HTC and η should be the same for both test cases. Note that the

lower grouping of data points is for the chilled coolant and the higher grouping of data is

the ambient coolant test.

34

Appendix D: Blowing Measurement and Apparatus

In order to supply the test section with upstream purge coolant, a 100-gallon buffer

tank is filled to 120 psi and regulated down based upon the desired purge flow blowing

ratio. The coolant flow then passes through a Lambda Square orifice plate meter which

allows the mass flow rate of the coolant flow to be determined using Equation 11

𝑚𝑐̇ = 𝐶𝜖𝐴2√2𝜌1(𝑝1 − 𝑝2) (11)

where C is the orifice flow coefficient, 𝜖 is the expansibility factor, A2 is the area of the

orifice hole, ρ1 is the upstream fluid density, p1 is the upstream fluid pressure, and p2 is the

downstream fluid pressure. A pressure transducer located upstream measures the pressure

at the orifice entrance and a differential pressure transducer spanning the orifice plate is

used to get the downstream pressure. A thermocouple upstream of the orifice plate allows

the calculation of the upstream density. The coolant then passes through a three-way valve

which is used for the cooling and into the equalizing plenum before being injected into the

mainstream flow. Thermocouples are placed at the plenum entrance to gather coolant

temperature and the plenum is insulated to minimize thermal loss. Before the blowdown

actually begins, the coolant air is chilled to the desired temperature. In order to achieve

this, the coolant air mixes with liquid nitrogen and is exhausted to the atmosphere before

reaching the test section so as not to alter the initial temperature of the vane endwall.

Coolant temperatures are measured during this process until they reach the desired

temperature. After the coolant is lowered to the desired temperature, the liquid nitrogen is

turned off and the rest of it is purged from the lines. The coolant is then held back with a

low temperature solenoid valve that is synced with the tunnel start to ensure it does not

pre-cool the endwall. When the tunnel blowdown begins, the solenoid for the blowing air

is opened at a precise time to supply the test section with cooling air. A more detailed

illustration of the blowing setup is shown in Figure 23.

35

Figure 23. Detailed Illustration of the Upstream Purge Blowing Setup

The metric used in this study to quantify the amount of coolant being supplied to

the cooling holes is blowing ratio (BR). Blowing ratio is a non-dimensional parameter

defined as the density ratio (DR) multiplied by the velocity ratio (VR). The equations for

BR, DR, and VR are shown in Equations 12-14 respectively.

𝐵𝑅 =𝜌𝑐𝑉𝑐

𝜌∞𝑉∞ (12)

𝐷𝑅 =𝜌𝑐

𝜌∞ (13)

𝑉𝑅 =𝑉𝑐

𝑉∞ (14)

36

Another way to write the BR, and the way it was calculated in this study, is the

mass flow ratio (MFR) divided by the area ratio (AR). MFR and AR are defined in

Equation 15 and 16 respectively.

𝑀𝐹𝑅 =𝜌𝑐𝑉𝑐𝐴𝑐

𝜌∞𝑉∞𝐴∞ (15)

𝐴𝑅 =𝐴𝑐

𝐴∞ (16)

Because the area of the test section as well as the area of the holes, and the mass

flow rate through them is known, the last unknown is the mass flow rate through the tunnel.

The mass flow rate through the tunnel is found using Equation 17.

�̇�∞ = 𝜌∞𝑉∞𝐴∞ (17)

The density is calculated via pressure and temperature measurements in the wind

tunnel test section and the velocity is calculated with the help of a Pitot static probe located

along the centerline of the passage. The highly turbulent boundary layer allows for the safe

assumption of a uniform velocity throughout the test section.

37

Appendix E: Uncertainty Analysis Details This appendix serves to show the details behind the method used to find the

uncertainty values in the Nu and η. For this study, a perturbation method similar to that

used by Cline and McClintock [29] was implemented.

Nu and η were treated as functions of wall temperature, mainstream temperature,

and coolant temperature. Because of this, the wall, mainstream, and coolant temperatures

were all altered by their respective measurement. This alteration was carried throughout

the heat flux calculations as well as the dual linear regression technique (DLRT). The

alterations of the measurements by their uncertainties were carried out both individually

and simultaneously. A detailed flow chart for the uncertainty calculation technique is

shown in Figure 24.

Figure 24. Flow Chart of Uncertainty Analysis Technique

After the uncertainties for each pixel were found, the mean of the absolute value

for a group pixels covering the entire Nu and η spectrum was found. From this analysis, it

was found that the average uncertainty in the Nu measurement was approximately ±4.0%

and the uncertainty in η was approximately ±0.1.

38

Appendix F: CFD Streamlines Plotted Over Flow Visualization

Figure 25 illustrates the same flow visualization results from the paper with the near

endwall CFD streamlines from Li et al. [1] overlaid on them. Once again, it is apparent that

the near endwall streamlines without blowing match very well with the data gathered with

upstream purge blowing. For example, for the baseline case, the coolant flow penetrated

slightly into through the pressure side leg of the HSV. This is seen in Figure F1 where the

red paint passes through the pressure side leg of the HSV as shown in Region A. In

addition, the region where the coolant flow stays attached most effectively to the endwall

in Region B is once again, in the higher pressure region just below the saddle point.

Figure 25. No Blowing Near Endwall CFD Streamlines Plotted Over Flow Visualization Results: Baseline

No Step BR = 2.5

39

Appendix G: Effect of Adding Blowing for All Geometries

Table 3: Effect of Adding Upstream Purge BR = 1.0 for All Geometries

No Blowing BR = 1.0

Backward

Step

Baseline,

No Step

Forward

Step

40

In the body of the paper, the effects of adding upstream purge blowing on the

endwall Nu was investigated for the baseline geometry case. This paper

nondimensionalized HTC using Nu instead of St for all the figures. Nu is the ratio between

the convection heat transfer and conduction heat transfer within the fluid, while the St is

the ratio between the convection heat transfer and thermal capacity of the fluid. Both

parameters are used in literature, however, one major difference between the two is that

Nu exhibits a much higher sensitivity to Re of the flow. The reason that St was not used to

characterize endwall heat transfer in this paper is because the velocities needed to calculate

St were not measured at each location in the passage. This appendix will serve to illustrate

the effects of adding upstream purge blowing on endwall Nu for all three geometries.

In Region A of the figures in Table 3, there is an increase in Nu moving from the

backward step geometry to the forward step and baseline geometries. This is due to the

increased level of turbulent mixing between the mainstream and coolant flows. The

increase mixing for the backward step geometry is caused by the much larger cavity vortex

which is located where the coolant enters the mainstream for the backward step geometry.

This cavity vortex becomes much weaker as the step moves to the baseline and forward

step cases.

Looking at Region B for the backward step geometry of Table 3, it is apparent that

the addition of adding purge blowing at a BR = 1.0 has a minimal effect in the throat of the

passage. This is due to the high strength of the secondary flows which take energy out of

the coolant flow and don’t allow it to reach as far downstream as would be ideal. The

backward step geometry does, however, exhibit a decrease in Nu of about 25% in region

A due to the addition of upstream purge blowing. This is because, while the coolant flow

for the backward step case does not travel far downstream, region A is very close to the

coolant holes, allowing the coolant flow to protect the endwall from the mainstream gases.

Unlike the backward step geometry, the baseline geometry in Table 3 does show

obvious changes of Nu in the throat of the passage due to the addition of upstream purge

blowing. There is a decrease in Nu in the throat of the passage by about 20% due to the

addition of upstream purge blowing. The reason that the baseline geometry reaches into

41

this region, while the backward step case does not is because the weaker cavity vortex at

the point of coolant injection for the baseline geometry.

The last geometry to investigate is the forward step geometry. Like the baseline

geometry, the forward step geometry exhibits a decrease in Nu of about 20% in the throat

of the passage due to the addition of an upstream purge BR = 1.0. Once again, the reason

that the forward step geometry sees a decrease in Nu in the throat of the passage, while the

backward step geometry does not is because of the stronger cavity vortex in the backward

step geometry.

42

Appendix H: Effect of Upstream Step Misalignment at BR = 1.0

This appendix serves to show the effect of upstream step misalignment on endwall

η and Nu contours for an upstream purge BR = 1.0. Figures 26, 27, and 28 illustrate the

adiabatic film cooling effectiveness contours at a BR = 1.0 for the backward step, baseline,

and forward step geometries respectively. Near endwall CFD streamlines generated in Li

et al. [1] are overlaid onto the contours to illustrate and explain the film effectiveness

patterns.

Figure 26. Film Effectiveness Contour for Backward Step Geometry BR = 1.0

43

Figure 27. Film Effectiveness Contour for Baseline No Step Geometry BR = 1.0

Figure 28. Film Effectiveness Contour for Forward Step Geometry BR = 1.0

44

The first area of interest for the contours in Figures 26-28 is Region A. Here, we

can see the very distinct wakes of high effectiveness after the coolant holes for the baseline

and forward step geometries. In contrast, the backward step does not exhibit the same wake

structure. Instead, the cavity vortex in this region mixes with the coolant flow directly after

it is injected into the mainstream and consolidates it all along the center passage line.

Looking closely, the CFD streamlines on the backward step geometry explain these

phenomena quite well even though they were not generated for cases with upstream

blowing. The pitch-wise streamlines where the coolant holes are located illustrate the

cavity vortex that is mixing with and taking the energy out of the coolant flow.

All of the cases shown are conducted at an upstream purge BR = 1.0. Because of

this, the coolant flow has a low momentum and will struggle to overcome the secondary

flows within the passage. This is illustrated in Region B of Figures 26-28. Looking at the

film effectiveness contours, all three geometric cases show that the coolant flow does not

reach all the way to the pressure side of the passage. This is due to the endwall pressure

gradient as well as the pressure side leg of the HSV creating a barrier that the coolant flow

cannot penetrate. The near endwall CFD streamlines that are overlaid on the figures do a

very good job of illustrating this as well. For each of the geometric cases, the line of the

pressure side leg of the HSV as it moves downstream is quite apparent. For all of the cases,

it is clear that on the coolant flow does not penetrate through the pressure side leg of the

HSV, except perhaps a little bit for the forward step case where the secondary flows are at

their weakest. On the pressure side of the pressure side leg of the HSV, there is little to no

film effectiveness, confirming this finding that the coolant flow struggles to overcome the

secondary flows.

Even though the near endwall CFD streamlines provided by Li et al. [1] were

generated without upstream purge blowing, they matched almost exactly with this paper’s

experimental data gathered with upstream purge blowing. Because of this, it is

hypothesized that the addition of upstream purge blowing may likely alter the three

dimensional flow streamlines, however, it has a minimal effect on altering the near endwall

streamlines as they travel downstream.

Because the forward step and baseline geometries were so similar for the film

effectiveness contours, only the baseline and backward step geometries will be compared

45

for Nu contours. Figures 29 and 30 illustrate the Nu contours at an upstream BR = 1.0 for

the backward step and baseline geometries respectively.

Figure 29. Endwall Nu Contour for Backward Step Geometry BR = 1.0

46

Figure 30. Endwall Nu Contour for Baseline No Step Geometry BR = 1.0

Comparing Region A of Figures 29 and 30, it is apparent that for the backward step

geometry, the Nu is approximately 25% higher in the backward step than in the baseline

geometry. This is due to the increased turbulent mixing between the mainstream and

coolant flow caused by the larger cavity vortex in Region A for the backward step

geometry. There is also an increase in Nu due to the presence of a backward facing step in

Region B near the leading edge upwards of 50% near the pressure side of the passage. This

increase is due to the coolant flow in the backward step case, not having the energy to

penetrate to the pressure side of the passage after mixing with the cavity vortex upstream.

The largest discrepancy between the two geometries is in the throat of the passage indicated

by Region C. The presence of a backward facing step upstream causes an increase in Nu

of nearly 65% in this region. This is, once again, due to the decreased energy of the coolant

flow for the backward facing step geometry, which is not able to effectively create film

layer and protect the endwall from the hot mainstream gases in this region of the passage.