HEAT TRANSFER AND FRICTION FACTOR AUGMENTATION IN …

The Pennsylvania State University

The Graduate School

Department of Mechanical and Nuclear Engineering

HEAT TRANSFER AND FRICTION FACTOR

AUGMENTATION IN RIB TURBULATED FLOW

A Thesis in

Mechanical Engineering

by

Gaelyn L. Neely

Submitted in Partial Fulfillment

of the Requirements

for the Degree of

Master of Science

August 2009

ii

The thesis of Gaelyn L. Neely was reviewed and approved* by the following:

Dr. Karen A. Thole

Head of the Department of Mechanical and Nuclear Engineering

Professor of Mechanical and Nuclear Engineering

Thesis Advisor

Dr. H. Joseph Sommer III

Professor-In-Charge of MNE Graduate Programs

Dr. Stefan Thynell

Professor of Mechanical and Nuclear Engineering

*Signatures are on file in the Graduate School.

iii

ABSTRACT

Current gas turbine airfoils must survive in an environment where operating conditions

are approaching extreme levels. Increasing the temperature of the combustion gases entering the

turbine improves engine efficiency and power output; consequently, the turbine inlet

temperatures have reached levels exceeding the melting point of the blade materials. Internal

cooling of the turbine blades is vital to maintaining turbine blade longevity and durability. Rib-

roughened channels in the blade core are commonly used to increase turbulence and secondary

flows that aid the transport of energy. In addition, the ribs increase the convective heat transfer

surface area. Past research has focused on two ribbed wall configurations, and worked to

identify the most favorable rib design that will produce maximum heat transfer with minimal

pressure loss. This paper presents an analysis of various rib configurations for a one ribbed wall

configuration, by comparing the effect of pitch, aspect ratio, and rib orientation on both heat

transfer and friction augmentation. Heat transfer measurements were made using infared camera

thermography in the fully developed region of the channel. Additionally, the effect of total

wetted area versus planform area was investigated.

Experimental measurements were taken in a closed-loop recirculating channel with a

parallel-plate channel test section. The channel had varying aspect ratios of 2.86 or 5 with a

constant blockage ratio of 0.2. All ribs were rounded, discontinuous V-shape, at 45° to the flow

with pitch-to-rib height ratios of 5 or 10. Results indicate heat transfer augmentation was higher

with a pitch-to-rib height ratio of 5 compared to 10. Similarly, the pitch-to-rib height ratio of 5

caused higher friction factor augmentation. The results also indicate aspect ratio did not affect

the ribbed side heat transfer augmentation; however, the 2.86:1 aspect ratio cases had higher

augmentation on the unribbed side compared to the 5:1 case. An increase in aspect ratio caused

an increase in friction factor augmentation; thus the 5:1 aspect ratio case had the highest friction

factor augmentation.

iv

TABLE OF CONTENTS

List of Tables………………………………………………………………………. v

List of Figures……………………………………………………………………… vii

Nomenclature……………………………………………………………………… xi

Acknowledgements………………………………………………………………... xiii

Chapter 1. INTRODUCTION…………………………………………………….. 1

1.1 Motivation for Research…………………………………………… 3

1.2 Research Objectives ………………………………………………. 5

Chapter 2. LITERATURE REVIEW……………………………………………… 7

2.1 Effects of Rib Pitch ……………………………………………….. 9

2.2 Effects of Blockage and Aspect Ratio……..……………………… 11

2.3 Effects of Rib Shape……….……………………………………… 13

2.4 Orientation and Angle of Attack..…………………………………. 14

2.5 Measurement Methods Used for Rib Studies …..………………… 15

2.6 Uniqueness of Research …………………………..………………. 18

Chapter 3. DATA ANALYSIS AND EXPERIMENTAL FACILITY……………. 20

3.1 Rib Geometries……………………………………..……………... 20

3.2 Overall Test Facility………………………………………………. 23

3.3 Test Section Design………………………………….……………. 27

3.3.1 Heat Transfer…………………………………..………….. 28

3.3.2 Pressure Penalty………………………………..…………. 38

3.4 Data Reduction………………………………………….………… 39

3.4.1 Heat Transfer Augmentation……………………………… 41

3.4.2 Friction Factor Augmentation…………………….………. 44

3.5 Uncertainty Analysis………………………………………………. 45

Chapter 4. EXPERIMENTAL RESULTS………………………………………… 49

4.1 Benchmarking……………………………………………………... 49

4.2 Heat Transfer Results for Rounded Ribs……..………………….... 59

4.3 Friction Factor Results for Rounded Ribs…..…………………….. 77

Chapter 5. CONCLUSIONS……………………………………………………….. 80

5.1 Rib Spacing Effects…………………………………………………80

5.2 Aspect Ratio Effects…………………………………………..….... 81

5.3 Area Effects………………………………………………………... 81

5.4 Recommendations for Future Work……………………………..… 82

References…………………………………………………………………………. 83

Appendix A. Flowrate Calculations…………………………………………….... 86

Appendix B. Infared Image Data Reduction…………………………………….. 89

Appendix C. Heat Transfer Uncertainty Calculations…………………………… 96

Appendix D. Friction Factor Uncertainty Calculations………………………….. 103

v

LIST OF TABLES

Table 2-1 Summary of Relevant Rib Studies

Table 3-1 Summary of Rib Configurations

Table 3-2 Summary of Rib Configuration Upstream of the IR Window

Table 3-3 Summary of Power Settings for P/e=10, AR=4:1, e/H=0.125

Table 3-4 Thermal Conductivity and Thickness of Materials in the Loss Analysis

Table 3-5 Losses for Rib Configurations

Table 3-6 Uncertainty in Ribbed Heat Transfer

Table 3-7 Uncertainty in Unribbed Heat Transfer

Table 3-8 Uncertainty in Friction Factor Measurements

Table 3-9 Summary of the Repeatability Testing

Table 4-1 Summary of Ribbed Benchmark Configurations

Table 4-2 Test Matrix for All Configurations

Table 4-3 Summary of the Geometries Tested and Compared with Literature for Results

Table A-1 Parameters for the Orifice and Venturi Flow Meters

Table B-1 Calibration Results for Re=40,000, P/e=5, e/H=0.125,

AR=5:1, Ribbed Side


AR=5:1, Smooth Side

Table B-3 Biot Calculations for Each Rib at High and Low Re Numbers

Table C-1 Uncertainty in Reynolds Number

Table C-2 Uncertainty in Heat Transfer Coefficient for the Ribbed Channel Wall

Table C-3 Uncertainty in Heat Transfer Coefficient for the Smooth Channel Wall

Table C-4 Uncertainty in Nusselt Number for the Ribbed Channel Wall

vi

Table C-5 Uncertainty in Nusselt Number for the Smooth Channel Wall

Table C-6 Uncertainty in the Smooth Channel Nusselt Number

Table C-7 Uncertainty in Nusselt Number Augmentation for the Ribbed Channel Wall

Table C-8 Uncertainty in Nusselt Number Augmentation for the Smooth Channel Wall

Table D-1 Uncertainty in Reynolds Number

Table D-2 Uncertainty in Friction Factor

Table D-3 Uncertainty in Smooth Channel Friction Factor

Table D-4 Uncertainty in Friction Factor Augmentation

vii

LIST OF FIGURES

Figure 1-1. Schematic of a turbojet aircraft engine [Hill and Peterson, 1992].

Figure 1-2. Cut-away of the Pratt & Whitney F119 engine [www.pw.utc.com, 2009].

Figure 1-3. Progress of the compression ratio through the years [Han, 2000].

Figure 1-4. Progression of the turbine inlet temperature over the years [Han, 2000].

Figure 1-5. Three methods of turbine blade cooling are jet impingement, rib turbulated

channels, and pin fin banks [Liu et al., 2006].

Figure 1-6. Aspect ratios of the passages depend on the location in the blade core [Huh et al.,

2008].

Figure 2-1. Schematic defining the rib parameters under investigation in this study.

Figure 3-1. Schematic of a rounded-rib cross-section where all dimensions are normalized to

the rib height.

Figure 3-2. Experimental rib configuration shown with discrete V-shaped, rounded cross-

section ribs 45° to the flow, P/e=5, AR=5:1, and e/H=0.125.

Figure 3-3. Wright et al. [2004] rib configuration showing square cross-section, parallel 45°

to the flow, P/e=10, AR=4:1, and e/H=0.125.

Figure 3-4. Schematic of closed loop test facility used for rib turbulator testing.

Figure 3-5. Schematic of the interior components of the plenum.

Figure 3-6. Rounded inlet contraction vanes, made from halved PVC pipes, which aided the

transition of the flow from the plenum into the test section.

Figure 3-7. Schematic of the test section used for rib turbulator testing.

Figure 3-8. Typical developing augmentation profile at Re=30000, in the streamwise

direction for internal channel heat transfer study with rib turbulators configured as

P/e=5, AR=2.86, and e/H=0.2. One side of the channel had rib turbulators (red)

present, while the other remained smooth (blue).

Figure 3-9. Schematic of the Inconel foil strip heaters made for the sidewalls.

Figure 3-10. Cross-section schematic of the Kapton heater used in the test section.

viii

Figure 3-11. Side and top schematics of the Lexan support added to the IR viewing area. The

support reduced the viewing width by 2.5 cm of the heater.

Figure 3-12. Schematic of thermocouples installation in the channel. Thermocouple bead was

secured to the backside of the heaters using Duralco 128 two-part epoxy and the

wire routed out through a bore hole in the MDF.

Figure 3-13. Diagram of heater and power supply set-up. Voltage is measured across the wire

junction, and the current is measured across the precision resistor.

Figure 3-14. Schematic of the heat loss pathways in the test section. Heat that does not enter

the flow is lost to the surroundings and modeled with a 1-D conduction analysis.

Figure 3-15. Pressure taps are located upstream and downstream of the ribbed section of the

channel; the extra length of channel is accounted for in the friction factor

calculations. The upstream and downstream lengths are summed in ∆x.

Figure 3-16. Schematic defining the various areas used in the area-weighted Nusselt number

augmentation.

Figure 4-1. Channel average Nusselt number results for a smooth channel plotted with

smooth, turbulent, fully developed heat transfer correlations.

Figure 4-2. Channel friction factor results plotted with smooth, turbulent, fully developed

correlations.

Figure 4-3. For the benchmark square rib case, two tests were run at Re=30000 to verify

heating the sidewalls did not effect the heat transfer augmentation. The

augmentation development along the centerline of the channel was the same

regardless of whether the sidewalls were heated.

Figure 4-4. Difference between crossed (Mahmood [2003]) and parallel (current study) rib

orientation is the angle of attack of each side of the channel.

Figure 4-5. Heat transfer augmentation for the benchmark case compared with Wright et al.

[2004] and Mahmood et al. [2002] for P/e=10, AR=4:1, and e/H=0.125.

Figure 4-6a. Augmentation contours show the endwall heat transfer for the benchmarking

configuration.

Figure 4-6b. Augmentation contours show the endwall heat transfer for the benchmarking

configuration.

Figure 4-7. Heat transfer augmentation contour, for Re=10,000, from Mahmood et al. [2002],

where the region immediately upstream and downstream of the rib was resolved.

ix

Figure 4-8. Friction factor augmentation for the benchmark case compared with Wright et al.


Figure 4-9. The effect of increasing the pitch is an increase in heat transfer. This increase is

more prominent at lower Reynolds numbers, as shown by the current study ribbed

results (AR=5:1, e/H=0.2) and a Liu et al. [2006] study.

Figure 4-10. Contours from AR=5:1, e/H=0.2, P/e=5 show the secondary flow induced by the

V-shape ribs.

Figure 4-11. Ribbed side augmentation contours for P/e=10, AR=5:1, e/H=0.2.


Figure 4-13. Ribbed side augmentation contours for P/e=10, AR=2.86:1, e/H=0.2.


Figure 4-15. Smooth side augmentation contours for P/e=10, AR=5:1, e/H=0.2.


Figure 4-17. Smooth side augmentation contours for P/e=10, AR=2.86:1, e/H=0.2.


Figure 4-19. Comparing Rhee et al. [2003] with the current study confirms that no aspect ratio

effect was expected on the ribbed side heat transfer augmentation; however, an

increase in pitch from 5 to 10 decreased heat transfer.

Figure 4-20. The smooth side augmentation shows that when only one-wall of the channel was

ribbed, the aspect ratio had an effect of the augmentation. As the aspect ratio

increased, the smooth wall heat transfer decreased.

Figure 4-21. Kunstmann et al. [2009] tested W-shape ribs in a one-ribbed wall channel; the

unribbed side heat transfer augmentation reflected an aspect ratio effect where the

largest aspect ratio has the highest augmentation.

Figure 4-23. The ribbed side, unribbed side, and channel average augmentation for the 2.86:1

aspect ratio cased.

Figure 4-24. The ribbed side, unribbed side, and channel averaged augmentation for the 5:1

aspect ratio cases.

x

Figure 4-25. Channel-averaged heat transfer augmentation reflects the smooth wall

contribution; therefore, the channel average does showed aspect ratio effect for

this rib orientation.

Figure 4-26. Ribbed side heat transfer results for the P/e=10 cases show reduced augmentation

when total wetted area was used relative to planform area.



Figure 4-28. Unribbed side heat transfer results for all cases show minimal change in

augmentation when total wetted area was used relative to planform area.

Figure 4-29. Global average heat transfer results for the P/e=10 cases show reduced




Figure 4-31. Friction factor results for the current study show friction factor increased with

increasing Reynolds. Also, the highest pressure penalty occurred for the P/e=5

and AR=5 configuration.

Figure 4-32. Comparing the current study with the Rhee et al. [2003] showed similar aspect

ratio trends; as AR was changed from 5 to 2.86, the friction factor decreased.

Figure 4-33. A comparison of friction factor augmentation for the current study with Liu et

al.’s [2006] study shows that as pitch increased, friction factor decreased.

Figure A-1. Sample performance curve for the orifice and venturi flow meters shows the

orifice was better suited for resolving low-flow conditions.

Figure B-1. Raw infared image captured with the Flir camera, for square cross-section ribs,

45° parallel to the flow, P/e=10, e/H=0.125, AR=4:1. The thermocouple

locations, window frame, and ribs are identified.

xi

NOMENCLATURE

A = area [m2]

Ac = cross sectional area of flow [m2]

Ap = planform (smooth) heater area [m2]

At = total (wetted) area, heater surface, between ribs, and rib surface area [m2]

AR = channel aspect ratio, W:H

cp = specific heat of air [J/kg·K]

d = depth of the airgap [m]

DH = hydraulic diameter [m]

dP = pressure drop [in H2O]

e = rib height [m]

f = Darcy friction factor of test section

fo = Blasius friction factor correlations for a smooth pipe

g = acceleration due to gravity [m/s2]

h = heat transfer coefficient [W/m2K]

H = channel height [m]

I = measured current through the precision resistor [A]

k = thermal conductivity [W/mK]

L = length [m]

m& = mass flow rate in test section [kg/s]

Nu = Nusselt number

Nuo = Dittus-Boelter smooth channel Nusselt number

P = pressure [in H2O, psi, or PA] or rib pitch [m]

Pr = Prandtl number

Pw = wetted perimeter of channel [m]

q" = heat flux [W/m2]

Q = power [W] or volumetric flowrate [SCFM or m3/s]

R = resistance [Ω] or universal gas constant, 287 [N-m/kg-K]

Rat = Rayleigh number

Re = Reynolds number

T = temperature [K]

ux = uncertainty in value x

V = velocity of flow [m/s] or voltage [V]

W = channel width [m]

∆x = streamwise length of ribbed section [m]

Greek:

α = thermal diffusivity [m2/s] or rib angle of attack [degrees]

β = bore / hydraulic diameter [m] or volumetric expansion coefficient [1/K]

η = thermal efficiency

µ = dynamic viscosity [N-s/m2]

ρ = density [kg/m3]

ν = kinematic viscosity [m2/s]

xii

Subscripts:

variable = line average value

variable = area average value

air = air properties

airgap = air gap between the heater and ZnSe window

amb = ambient room conditions

bulk = denotes the bulk fluid flow in the channel

conv = convective

endwall = denoted ribbed endwall

in = inlet to test section

ins = insulation

loss = denotes the outer wall of test section

mean = average of inlet and outlet conditions

measured = denotes a measured value

MDF = medium density fiberboard

o = conditions outside the rig

out = outlet of test section

rib = denotes rib surface

side = denotes the sidewall

std = denotes properties at standard temperature and pressure

unribbed = denotes a non-ribbed wall of the channel

wall = denotes the heat loss pathway through the MDF wall

window = denotes the heat loss pathway through the ZnSe window

ZnSe = Zinc Selenide window

xiii

ACKNOWLEDGEMENTS

When I graduated from Penn State with my undergraduate degrees, I just wasn’t ready to

leave Happy Valley. Pursuing grad school at Penn State has been challenging and rewarding,

and I will always look back with fond memories. There are a few people I need to thank, for my

success would not have been feasible without them.

First, I would like to thank my advisor, Karen Thole, for the opportunity to work in your

lab, PSU Exccl. I have learned many life lessons that I will carry with me in my career as an

engineer. You have taught me the value of hard work and persistence, skills that certainly will

be useful in life after grad school. I would also like to also acknowledge Pratt & Whitney for the

support of my research, specifically Atul Kohli and Chris Lehane. Your motivation and

encouragement have been instrumental in my achievements.

Spending so many hours in the lab, I couldn’t have done it without my fellow lab mates:

Grant, Seth, Jason, Steve, Weaver, Alan, Mike, Gina, and Sundar. The unending support and

guidance you have all provided me are invaluable. The company during the tough times and the

laughs during the celebrations are things I will never forget. I have made lifelong friends, and

even as we move apart I know we will keep in touch.

A special thanks goes to my parents… Mom and Dad, who have never let me forget who

I am and what I can achieve. My triumphs are most certainly yours as well. Dad, you have

been my role model since I started walking – you are one of the most ingenious and brilliant

people I know. Mom, I couldn’t have stayed on the path without you, you are definitely my

biggest fan, and your support has carried me though more than you will ever know.

In addition, I need to thank Kathy for all your help with my writing; I have a polished

product thanks to you!

Gif, my goodness, I don’t even know how to start thanking you! From the iSponge to

cap and gown, you have been supportive and patient with me. You have made me countless

dinners, let me vent when it was tough, bought Asti when it was time to celebrate, and given me

hugs when I needed them most. Thank you so much for everything, and I can’t wait to start this

next adventure with you!

1

Chapter 1

INTRODUCTION

Gas turbine engines are widely used for land-based power generation, in addition to

aircraft and naval ship propulsion. Because of their efficiency and fast response time, gas

turbines are ideal for commercial, industrial, and residential electrical power generation because

they can accommodate the fluctuations in load. Similarly, for commercial and military aircraft,

gas turbines provide a nearly instantaneous response when more power is needed.

A turbine is simply comprised of three main components, including the compressor, the

combustor, and the turbine. Air is pulled into the compressor through a diffuser. As the

compressor rotates, work from the blades causes the air pressure to rise. In the combustor, fuel is

mixed with the high-pressure air and is ignited. This generates a highly energetic mixture of

combustion products, which exit the combustor into the turbine. The flow expands as it passes

through the turbine, causing the blades to rotate. Finally, the gases are exhausted back into the

atmosphere. Figure 1-1 shows a basic schematic of a gas turbine engine [Hill and Peterson,

1992].

Figure 1-1. Schematic of a turbojet aircraft engine [Hill and Peterson, 1992].

The turbine is mechanically coupled to the compressor in order to provide the power

necessary to compress the air. All the remaining power is utilized in various manners depending

on the application. In military aircraft engines, the combustion gases exit the turbine and are

accelerated through a nozzle generating thrust. Figure 1-2 shows a cut-away of the Pratt and

Whitney F119 engine used in the F-22 Raptor. Commercial aircraft engines use the power

2

generated to rotate a large fan. Finally, for land-based power generation applications, the power

generated is typically used to rotate a shaft coupled with an electric generator.

Compressor

CombustorTurbine

Figure 1-2. Cut-away of the Pratt & Whitney F119 engine [www.pw.utc.com, 2009].

There are two main parameters that will increase the thermal efficiency and power output

of a gas turbine; they are the compressor pressure ratio and the turbine inlet temperature.

Through research, the compression ratio has increased from approximately 5 in the 1940’s to

nearly 40 in the 2000’s. Work continues to get this value as high as possible in the future.

Figure 1-3 shows the progression of the compression ratio over the years. The second parameter,

and the focus of this work, is increasing the turbine inlet temperature. By increasing the inlet

temperature the specific core power production of the turbine increases. Inlet temperatures

exceed the melting point of the turbine blade material; thus, advanced cooling schemes are

needed to protect the integrity of the blades. Hot combustion gases pass over the blades and

transfer heat to the outer surface; then that heat is conducted through the metal, and internal

coolant passages pull the heat away from the metal. The advances in turbine blade cooling and

the subsequent increase in turbine inlet temperature are shown in Figure 1-4. By reducing the

blade temperature in addition to minimizing the temperature fluctuations, the lifetime of the

turbine blades can be doubled. The main goal is to reduce the thermal stresses that lead to

fractures in order to increase safety, blade durability, and engine longevity. Many enhancements

have been made to the internal and external cooling of blades; however, there is room for

improvement.

3

Figure 1-3. Progress of the compression ratio through the years [Han, 2000].

Figure 1-4. Progression of the turbine inlet temperature over the years [Han, 2000].

1.1 Motivation for Research

Typical blade cooling schemes include thermal barrier coatings, external cooling, and

internal cooling. The first goal of turbine blade cooling is to reduce the amount of heat being

transferred from the hot combustion gases to the blade; the second goal is that any heat that is

transferred to the blade needs to be removed by internal cooling schemes.

4

Thermal barrier coatings (TBCs) are applied to the external surface of the blade and act

as a layer of insulation against the hot mainstream flow. In addition to TBCs, a passive heat

transfer mechanism, the primary active method of external heat transfer is film cooling. Film-

cooling holes are placed on the leading edge of the blade in order to reduce the amount of heat

transferred from the flow to the blade. Cooling air bleed off the compressor is injected, through

the holes, under the boundary layer formed on the blade surface. This creates a protective layer

of cooling air surrounding the blade like a sheath. While film-cooling structurally weakens the

blade, it is the most effective method of reducing external heat transfer. The remaining two

methods, pin-fins and rib turbulated channels, promote internal heat transfer.

Figure 1-5 is a schematic indicating where jet impingement, pin-fins, and rib turbulated

passages are utilized. Pressurized cooling air is extracted from the compressor stage of the

engine and injected into the turbine blade. This air passes through the serpentine passages and

the pin-fn banks, eventually exiting the top or rear of the blade. On the trailing edge of the

turbine blade are pin-fin banks that not only provide structural support in the thinnest part of the

blade but also increase the heat transferred away from the blade. Pin-fins span the area between

the suction side and the pressure side of the blade; this causes a large increase in the convective

area in the most thermally stressed region of the blade.

Figure 1-5. Three methods of turbine blade cooling are jet impingement, rib turbulated

channels, and pin fin banks [Liu et al., 2006].

Rib turbulated serpentine channels comprise the mid-portion of the blade. The ribs break

up the boundary layer in the internal passages, causing turbulence and increased heat transfer.

Driving factors in rib turbulated channels are the channel aspect ratio, rib orientation, and flow

5

Reynolds number. It should be noted that pin-fins are highly efficient in the trailing edge of the

blade, but they would not have the same effectiveness in the mid-portion of the blade. Pin-fins

cause a great amount of drag, and any pressure loss reduces the efficiency of the overall engine.

Ribs are typically smaller and have much less effect of the pressure relative to a pin-fin. The

goal is to obtain a design with the highest overall cooling effectiveness and the lowest possible

penalty on the thermodynamic cycle performance.

1.2 Research Objectives

The work presented in this thesis is part of the larger goal to gain a better understanding

of the internal cooling of turbine airfoils. Of particular interest in this study were the heat

transfer and pressure loss of the serpentine rib turbulated channels in the mid-portion of a turbine

blade. The unique aspect of this work was having only one side of the channel ribbed.

Traditionally, research has focused on channels with two ribbed walls. A variety of parameters,

related to rib channel flow, were varied in order to identify configurations that maximize heat

transfer, while minimizing the pressure penalty. The pitch-to-rib height ratios studied were

P/e=5 and 10, and the aspect ratios studied were AR=2.86:1 and 5:1. The rib height-to-channel

height ratio was constant at e/H=0.2 for all the cases run. Aspect ratio is of particular interest

because different parts of the blade have different aspect ratios as a consequence of the airfoil

shape, shown in Figure 1-6. When quantifying heat transfer, the area used in defining the heat

flux has an effect on the results. Typically, researchers use the planform area of the heaters as

the preferred method, thus investigating the effect of the individual rib configuration on heat

transfer. However, when the total wetted area is used, the advantage of the additional surface

area is removed from the findings. An analysis of both methods is presented in the results.

The remainder of this thesis is organized as follows. Chapter 2 discusses a literature

review of ribbed channel heat transfer and friction factor studies relevant to turbine airfoil

cooling. Also in the review of relevant literature, the various measurement methods used in heat

transfer studies is presented. Chapter 3 describes the test facility, test section, and data reduction

methodology. Temperature measurements were collected in two different manners, and both are

outlined in the methodology section. The rounded rib experimental results are presented in

Chapter 4, in addition to the smooth channel and characteristic geometry benchmarking. Finally,

conclusions and recommendations for future work are presented in Chapter 5.

6

Figure 1-6. Aspect ratios of the passages depend on the location in the blade core [Huh et al.,

2008].

7

Chapter 2

LITERATURE REVIEW

A review of the relevant literature regarding the various parameters in rib turbulated

internal flows revealed numerous studies have been done. Table 2-1, at the end of the chapter,

shows a summary of all the rib geometries and data-collection methods. Rib characteristics

include pitch-to-rib height ratio (P/e), blockage ratio (e/H), channel aspect ratio, rib shape,

orientation, and angle of attack. The data in this thesis is unique, however, because the effects of

pitch and aspect ratio are investigated with a complex rounded rib. In addition, the study utilized

infared camera thermography to measure spatial heat transfer augmentation on the endwall.

Section 2.1 addresses previous work done regarding pitch-to-rib height ratios (P/e), Section 2.2

covers the combined effect of blockage (e/H) and aspect ratio (AR), while in Section 2.3 gives a

review of rib profile effects. Rib orientation and angle of attack are summarized in Section 2.4.

Section 2.5 highlights the various measurement methods used in experimental work. Finally,

Section 2.6 summarizes the uniqueness of the current study.

For internal flow heat transfer and friction factor studies, some common nomenclature

and definitions are used throughout the literature. Figure 2-1 shows a schematic defining the rib

parameters of pitch, rib height, and angle of attack. In rib studies, it is common to define the

Reynolds number with respect to hydraulic diameter of the channel:

(2-1)

P

P = pitch α = angle of attack

e = rib height

eα

Endwall Rib

Figure 2-1. Schematic defining the rib parameters under investigation in this study.

µ

ρ⋅⋅=

VDHRe

8

The hydraulic diameter is defined in Equation 2-2. For large aspect ratio channels, this

can be estimated by two times the channel height:

(2-2)

Likewise, the Nusselt number is defined by using the hydraulic diameter, as shown in

Equation 2-3:

(2-3)

The measured channel Nusselt number is divided by a smooth circular tube correlation.

Studies commonly use the fully developed turbulent correlation developed by Dittus-Boelter

[Incropera], shown in Equation 2-4:

(2-4)

For friction factor, the commonly used correlation is the Blasius correlation shown in

Equation 2-5:

(2-5)

One remaining value used to evaluate the efficiency of the rib turbulators is the thermal

performance, defined in Equation 2-6:

(2-6)

The thermal performance equation was developed by Webb and Eckert [1972] for heat

exchangers with “repeated-rib” roughness tubes. They found generalized friction factor and heat

transfer augmentation correlations for these tubes, then developed the effectiveness equations.

Equation 2-6 is specific for either a specified heat flux boundary condition or a prescribed wall

temperature boundary condition. The relative friction power relation in the original equation is

raised to the one-third power, which originated from the roughness correlations Webb and Eckert

k

DhNu H⋅

=

31

=

o

o

ff

NuNu

η

w

cH

P

AD

⋅=

4

4.08.0 PrRe023.0 ⋅⋅=oNu

25.0Re316.0 −⋅=of

9

developed. The thermal performance for a specific rib configuration is affected by the rib

orientation and the Reynolds number. Generally speaking, these are the definitions used by the

following researchers in discussing rib turbulator internal flow.

2.1 Effects of Rib Pitch

One of the goals of this work was to investigate the effect of rib pitch with a complex rib

shape. Many studies have looked at the pitch, but not with the same rib shape as the current

work. This section summarizes a few representative studies regarding pitch and establishes the

expected trends associated with rib spacing.

Han and Park [1988] studied pitch-to rib height ratios of 10 to 20. The cases tested were

characterized by square, brass ribs on two walls, oriented in a parallel angle configuration. This

study used the planform area of the foil heaters in the data reduction, which is consistent with

most internal flow rib turbulator studies. Han and Park [1988] found that P/e=10 yielded higher

heat transfer and higher pressure drop penalty in all cases when compared with P/e=20. For a

P/e=20 ratio the boundary layer was able to redevelop, thus reducing the heat transfer. The

pressure drop was also higher for the P/e=10 ratio because the number of ribs in the channel is

doubled when the pitch changes from 20 to 10, meaning more obstacles for the flow to

encounter.

A 2006 study by Liu et al. investigated the effect of rib spacing on heat transfer and

friction factor, and they summarized their findings as thermal performances (η). Additionally,

they examined the effect of using planform area compared to wetted surface area in their

definition of heat flux. The test section was a two-pass channel with an aspect ratio of 1:2 and

two ribbed walls. For each pitch tested, the square ribs were parallel angled at 45° to the flow

with a blockage ratio held constant at 0.125. Over the span of Reynolds 5,000 to 40,000, the

pitch-to-rib height ratios tested were as follows: 10, 7.5, 5, and 3. To compare Liu et al.’s results

with the current study, only the first pass data was considered; however, the study does report

first-pass, second-pass, and channel-averaged (both passes) values.

When using the planform area, Liu et al. [2006] found that heat transfer augmentation

increased with a decrease in P/e, which is consistent with earlier findings from Han and Park

[1988]. When using the total wetted area, all the augmentation plots converged to one value with

no effect of pitch reported. Friction factor augmentation increased with decreasing P/e from 10

10

to 5. Then as the pitch decreased further to P/e=3, the friction factor augmentation decreased.

Han and Park’s result are consistent with Liu’s, that a decrease in P/e from 10 to 5 caused an

increase in friction factor. Rallabandi et al. [2009] also found for a square channel with 45°

parallel ribs, the heat transfer augmentation decreased when the pitch decreased from 10 to 5.

A study done by Huh et al. in 2008 examined only the effect of pitch on heat transfer

using an average of all the thermocouples placed in the channel. This experiment utilized a two-

pass channel with an aspect ratio of 1:4. Similar to Liu et al. [2006], only results from the first

pass of the channel were considered for comparison purposes. The square ribs were parallel at a

45° angle of attack on two walls. Blockage was constant at e/H=0.125 over the range of

Reynolds numbers tested. Huh et al. tested P/e ratios of 2.5, 5, and 10, given that Liu et al.’s

study showed only a slight variation in heat transfer results when P/e was varied from 7.5 to 10.

Huh et al.’s study used copper blocks to achieve a constant temperature boundary

condition with a lumped capacitance model. Huh et al. [2008] found that heat transfer

augmentation increased with increasing P/e when the total wetted area was used to reduce the

data. The total wetted area was considered to be the smooth area between the ribs and the three

sides of the ribs exposed to the flow. Thus, with total wetted area, they found P/e=10 had the

highest heat transfer augmentation, contradicting the previous findings from Liu et al. [2006] in

which they found using the total area does not result in a pitch effect. Huh et al. did, however,

found that heat transfer augmentation decreased with increasing P/e when the planform area was

used in the data reduction, whereby using planform area, the highest augmentation occurred at

P/e=2.5. In summary, for all the pitches, the augmentation was lower when planform area was

used instead of total wetted area. Using planform area in the data reduction identified a trend

where an increase in P/e caused a decrease in heat transfer.

The current study uses planform area; therefore, it was expected that as P/e increased

from 5 to 10, both the heat transfer and the friction factor would decrease. There is an ideal

range of pitch-to-rib height ratios that is desirable for heat transfer augmentation, while keeping

thermal performance in mind. With a large spacing between ribs, the boundary layer is able to

redevelop, decreasing heat transfer. However, with too little spacing between the ribs, the

boundary layer never reattaches, which also decreases heat transfer. With respect to friction

factor, the fewer obstacles (ribs) the flow encounters, the lower the pressure penalty. So it was

11

expected that a lower P/e would yield a higher pressure drop because there were more ribs

present in the channel.

2.2 Effects of Blockage and Aspect Ratio

Upon examining numerous studies, it became apparent that blockage ratio and aspect

ratio effects typically were not isolated during experiments. Most studies utilized one physical

set of ribs and changed the channel dimensions. As the channel height was changed to

accommodate various aspect ratios, the blockage ratio (e/H) inherently changed.

Bunker [2008] investigated the effects of manufacturing tolerances on thermal boundary

conditions for highly cooled turbine airfoils. For internal flow, he found that blockage was the

main contributor to variation in heat transfer when considering aspect ratio, pitch-to-rib height,

angle of attack, and blockage ratio. It is surprising that more studies in the literature do not focus

solely on the effect of blockage without simultaneously varying the aspect ratio. The current

study did not consider various blockage ratios; however, it did investigate the effect of aspect

ratio on heat transfer with a constant blockage.

The study by Han and Park [1988], summarized in Section 2.1, evaluated the combined

effect of angle of attack and aspect ratio on heat transfer and friction factor. Because a single set

of ribs was used, the blockage ratio changed with aspect ratio. The angle of attack was varied

from 90° to 30°, and the aspect ratio varied from 1:1 to 4:1, with the respective blockage ratios

of 0.047 to 0.125. Han and Park [1988] found that at a 90° angle of attack, the augmentation

development down the centerline of the channel remained constant at x/DH =3; therefore, all the

channel-averaged values were averages from data collected downstream of the fully developed

region in the channel. They determined that the centerline averaged Nusselt numbers and the

averaged friction factors increased with decreasing angles of attack, and the maximum heat

transfer occurred at α=60°. However, the best thermal performance for a constant pumping

power occurred at α=30° for an aspect ratio of 1:1 and α=45° for aspect ratios of 2:1 and 4:1.

When examining the effect of aspect ratio, the friction factor augmentation increased

progressively as the aspect ratio increased from 1:1 to 4:1. It should be noted that as the aspect

ratio increased, the blockage ratio simultaneously increased. Heat transfer, however, increased

only slightly as aspect ratio increased from 1:1 to 2:1, and there was almost no change when

12

aspect ratio increased from 2:1 to 4:1. It became a consistent trend that aspect ratio had a greater

effect on pressure drop than on heat transfer.

In 1992, Park et al. looked at the combined effect of aspect ratio and blockage ratio on

friction factor and heat transfer in a channel with two-ribbed walls that contained square,

parallel, angled ribs placed at a pitch-to-rib height ratio of 10 and blockage ratios of 0.031 to

0.125, respectively. This study used one set of ribs for the rectangular channels and a separate

set of ribs for the square channel; so as the channel height was varied, the e/H ratio also changed.

Foil heaters were used to create a constant heat flux boundary condition, and the flow was

hydrodynamically developing as it contacted the ribs due to a sudden entrance contraction. Park

et al. [1992] found for the same level of heat transfer augmentation, the pressure drop in the wide

aspect ratio channel (4:1) was much larger than in the narrow aspect ratio channel (1:4). Overall,

the narrow aspect ratios had higher heat transfer than the wide aspect ratios, which is inconsistent

with the finding that heat transfer increases with increased blockage and aspect ratio, as shown

by Park [1992] and Han and Park [1988]. This study showed that heat transfer augmentation

increased slightly as aspect ratio increased. Friction factor augmentation notably increased with

increasing aspect ratio and, therefore, increasing blockage ratio.

In a naphthalene sublimation study, Rhee et al. [2003] studied the combined effect of

aspect ratio and blockage ratio on heat transfer and friction factor. The test facility used

naphthalene sublimation in the fully developed region to obtain the heat transfer values. The

aspect ratio was varied from 3:1 to 6.82:1, while the blockage ratios ranged from 0.06 to 0.136,

respectively. The square cross-section ribs were either continuous 60° V-shape or discrete 45°

V-shape and both had a constant P/e=10. For both rib orientations, the maximum heat transfer

augmentation occurred at the centerline of the V-shape and decreased along the outer edges of

the rib. Rhee et al. [2003] found that the centerline augmentation of the V-shape was largely

affected by the aspect ratio, while the near-wall region was not as sensitive. They determined

that the impact of the downward flow decreased as the aspect ratio increased in the centerline

region. As expected, Rhee et al. [2003] found that as Reynolds number increased, heat transfer

augmentation decreased and friction factor augmentation increased. For the channel-averaged

values, the heat transfer decreased with increasing aspect ratio. The opposite trend was observed

with the pressure drop: friction factor augmentation increased as aspect ratio increased. It is

important to keep in mind that as the aspect ratio was increased, the blockage ratio also increased

13

in the Rhee et al. study. It is commonly known that an increase in blockage will increase both

heat transfer augmentation and friction factor augmentation.

Rallabandi [2009] confirmed the effect of various blockage ratios on heat transfer and

pressure drop measurements with 45° rounded ribs. Distinctively, the aspect ratio was held

constant, and the rib height-to-channel height ratio (e/H) varied from 0.19 to 0.38. He found that

with a square channel, as the blockage increased, both the fiction factor augmentation and the

heat transfer augmentation increased.

Overall, it can be summarized that experimental findings show as aspect ratio increased,

there was a larger effect on friction factor augmentation than on heat transfer augmentation.

Also, as the aspect ratio was increased, both friction factor augmentation and heat transfer

augmentation were expected to increase.

2.3 Effect of Rib Shape

Classically, most studies utilize square ribs because of the ease of manufacturing.

Complex rib shapes require machining or casting, while a common cross-section shape, such as a

square, can be purchased off the shelf. With that in mind, studies on the effect of rib shape on

heat transfer and friction factor contribute to a significant amount of research done in gas turbine

cooling studies reported in literature.

Liou and Hwang [1993] measured heat transfer coefficients and friction factors in a

rectangular channel with an aspect ratio of 4:1 for two-ribbed walls with various rib shapes. The

configurations were transversely oriented (90°) ribs with e/H=0.125 and varying P/e=8 to 20.

The rib shapes considered were an isosceles triangle, half-circle, and square cross sections.

Results showed that the square cross-section ribs had both the highest heat transfer augmentation

and the highest pressure drop. Conversely, the half-circle ribs had the lowest heat transfer and

the lowest pressure drop. When the data was evaluated for thermal performance, no significant

effect was identified as a result of changing the rib shape. This result may be driven by the fact

that the heat transfer data reduction used the total wetted rather than the planform area of the

channel. The surface area was different for each rib shape, making direct evaluations on the

benefits or drawbacks of the specific rib shapes difficult.

Viswanathan and Tafti [2005] examined computational models using rounded ribs. The

configuration under investigation was a two-wall angled, staggered 45° rounded ribs, in a square

14

channel (aspect ratio was 1:1), with P/e=10 and e/H=0.1. They investigated only one Reynolds

number of 25,000, and the model had a constant heat flux boundary condition. Most studies use

square ribs, and Viswanathan and Tafti [2005] concluded that the use of rounded ribs in a

staggered, angled configuration did not affect the heat transfer but did have a significant effect

on the friction factor. From comparing similar experimental results from Johnson et al. [1994]

and Chanteloup et al. [2002] with computational models from Abdel-Wahab and Tafti [2004],

Viswanathan and Tafti [2005] found the rounded rib friction factor augmentation was 33 percent

less than that of the square rib configuration.

2.4 Orientation and Angle of Attack

Research began with orthogonal ribs, 90° to the flow with studies including Stephens et

al. [1995] and Liou and Hwang [1993]. The focus then shifted to angled ribs at various angles of

attack: 45°, 60°, and 30° including Rhee et al. [2003] and Kim et al. [2007]. Eventually, more

complex orientations developed, including V-shape and W-shape. Experimental studies focused

on determining the ideal orientation for best overall heat transfer with minimal pressure loss.

This goal drew researchers to investigate parallel versus staggered orientations and continuous

(without gaps) versus non-continuous (with gaps) orientations. The current study focused only

on 45° orientations as it has been widely shown that this angle of attack is ideal for angled or v-

shaped orientations [Johnson et al., 1994].

Han and Park [1988] and Park [1992] investigated the effect of angle of attack on heat

transfer by varying the angle between 90° and 30°. Park et al. [1992] found that the angle of

attack was dependent on aspect ratio. For aspect ratios less than one, the 45° and 60° attack

angle had the highest heat transfer augmentation, while for aspect ratios greater than one, the 90°

and 60° yielded a highest heat transfer augmentation. Consistent with the previous research, a

1994 study by Johnson et al. resulted in a recommendation for angled (45°) over orthogonal

(90°) trips for blade design based on heat transfer results for an aspect ratio of 1:1.

Wright et al. [2004] focused their study on the effect of different rib orientations on heat

transfer and friction factor. Six different rib orientations were investigated: angled, discrete

angled, V-shaped, discrete V-shaped, W-shaped, and discrete W-shaped. This approach

highlighted the differences in heat transfer augmentation and pressure penalty between a

continuous and a non-continuous rib. For each rib orientation, the 4:1 aspect ratio channel had

15

two-ribbed walls with an angle of attack at 45°, P/e=10, and e/H=0.125. Wright et al. [2004]

found the W-shape and discrete W-shape had the best heat transfer augmentation; however, these

orientations also had the highest frictional loss augmentation. The discrete V-shape and discrete

angled ribs had the lowest pressure drop augmentation and, therefore, the lowest friction factor

augmentation. When thermal performance was considered, Wright at al. [2004] found that for a

constant pumping power, the discrete V-shape and discrete W-shape had the best performance,

while the angled rib had the worst. This study was selected to benchmark the current study’s test

rig because of the common rib and channel geometry in addition to the thoroughly reported data.

Lee et al.’s [2005] goal was to determine the effect of rib orientation on heat transfer,

mainly comparing parallel to staggered orientations and continuous (without gaps) to non-

continuous (with gaps) orientations. The configurations all had a 45° angle of attack and

included parallel V-shape without gaps, staggered V-shape without gaps, parallel V-shape with

gaps, parallel angled without gaps, staggered angled without gaps, and parallel angled with gaps.

The channel had a 4:1 aspect ratio with two-ribbed walls. Pitch-to rib height spacing was held

constant at P/e=10, and the blockage ratio was e/H=0.125. Lee et al. [2005] concluded that the

V-shaped produced higher heat transfer augmentation than angled ribs. They also found there

was a negligible effect on heat transfer augmentation when comparing parallel to staggered

orientations without gaps, regardless of whether the ribs were angled or V-shaped. However,

parallel V-shaped without gaps had higher heat transfer than parallel V-shape with gaps. Having

a continuous versus non-continuous orientation affected the secondary flow mechanisms, thus

altering the heat transfer augmentation. The opposite was found for parallel angled orientations,

ribs with gaps showed higher heat transfer augmentation than parallel angled without gaps.

These findings are consistent with those of Wright et al. [2004].

Overall, the V-shaped turbulators had the greatest thermal enhancement and performed

well with regard to minimal pressure drop augmentation. The current study utilized this

knowledge and went a step further in investigating how only one ribbed wall would affect the

heat transfer and friction factor.

2.5 Measurement Methods Used for Rib Studies

A variety of measurement methods exist for determining rib heat transfer coefficients.

Many studies, including Johnson et al. [1994], Wright et al.[2004], Lee et al. [2005], Liu et

16

al.[2006], Ostanek [2008], and Huh et al. [2008], used a lumped capacitance method that

required a constant surface temperature boundary condition. A highly thermal conductive

material, such as copper, was typically used to create the walls of the channel. Each copper

block had a thermocouple embedded within it, which recorded the temperature of that section of

the channel at a steady state. Because the blocks were assumed to be a uniform temperature, an

assumption confirmed by a Biot analysis, this lumped capacitance method was an easy and

reliable method to capture average global heat transfer coefficients.

A need for spatially resolved heat transfer data grew as technology advanced and

questions about the secondary flow structures developed. For example, researchers began

predicting heat transfer and flow structures with numerical simulations, and these computational

results required experimental validation. Additionally, a regionally or globally averaged value

does not indicate where areas of lower augmentation were developing along the channel walls.

A hot spot could lead to intense localized thermal stress, eventually weakening the airfoil.

Methods used in experimental work for spatially averaged data collection include holographic

interferometry, naphthalene sublimation, liquid crystals thermography, and infrared camera

thermography, which is the technique utilized in the current study.

Liou and Hwang [1993] used real-time holographic interferometry to measure the

temperature distribution of the airflow and thermocouples to capture local wall temperatures

under the constant heat flux boundary condition. This method provides spatially resolved

convection coefficients around the perimeter of a two-dimensional rib. Interferometry is not an

accurate method of obtaining surface heat transfer measurements. It is difficult to measure the

change in air temperature so close to the surface, which is why Liou and Hwang [1993]

embedded thermocouples along the surface to capture the near-wall temperature. Similarly,

Ostanek [2008] measured the surface temperature with embedded thermocouples; however, the

focus of that study was to develop a methodology for measuring the heat transfer augmentation

on the rib surface. Another data-collection technique better suited for surface temperature

measurements is naphthalene sublimation.

Naphthalene sublimation utilizes the analogy between heat and mass transfer to

determine heat transfer augmentation. Cho et al. [2003] coated the leading and trailing surfaces

in a channel with naphthalene in order to simulate a cooling channel’s two-sided heating

condition, representative of a gas turbine blade. The naphthalene coated surfaces are analogous

17

to a constant temperature boundary condition, where the uncoated surfaces are comparable to

adiabatic surfaces. Sherwood ratios are calculated by measuring the sublimation depth before

and after an experiment. One limitation of naphthalene is that sublimation occurs under natural

convection; therefore, corrections to the measured depths are needed to account for the time used

to measure, install, and disassemble the test facility. Cho et al. [2003] used the naphthalene

sublimation technique to investigate heat/mass transfer in a two-pass duct for smooth and ribbed

surfaces.

Kim et al. [2007] studied the effects of secondary flow due to angled ribs on heat/mass

transfer by using naphthalene sublimation, but they introduced channel rotation and bleed holes

into the configuration. In addition to Cho et al. [2003] and Kim et al. [2007], similar

experiments using naphthalene sublimation were conducted by Han et al. [2005] and Papa et al.

[2002]. The surfaces of the test section were cast in naphthalene, and the local sublimation depth

was measured to attain mass transfer coefficients at each position by using a linear variable

differential transformer.

Another common data-collection technique uses liquid crystals thermography (LCT) to

obtain iso-contours of the surface temperature. The interior walls of a clear channel are painted

with liquid crystal paint. As the paint is heated, the crystals change color, and the changes are

recorded with an RGB camera. Temperature changes are recorded and then reduced to a

temperature map of the entire interior surface of the channel. Maurer and von Wolfersdorf

[2006] used liquid crystals thermography to measure heat transfer on V-shaped ribs in a 2:1

aspect ratio channel. With the LCT, they were able to obtain spatial augmentation maps for the

ribbed walls instead of only channel-averaged or regional augmentations.

Diette et al. [2004] also used liquid crystals thermography to map iso-contours of Nusselt

numbers on a rib, ribbed wall, and the opposing smooth wall. The bottom of the rib was filleted

and manufactured from Plexiglass. The constant heat flux boundary condition was achieved

with Inconel foil sheets. Diette et al. [2004] concluded that there was good qualitative agreement

between the numerical simulation and the iso-contours obtained with the liquid crystals;

however, the numerical simulation quantitatively under predicted the heat transfer levels as was

also observed in the Maurer and von Wolfersdorf [2006] study. The liquid crystal thermography

method is limited by the temperature range the crystals can register at a given time. To record a

full spectrum of temperatures, the data is collected in stages and then combined into one image.

18

Infared camera thermography has no limitations on the temperature range that can be recorded at

any given time.

Ames et al. [2007] and Lyall [2006] used infrared camera thermography to take full-

surface endwall heat transfer distributions for pin fin arrays. These studies used a constant heat

flux boundary condition, which was achieved with foil heaters. Both used a zinc selenide

window in order to insulate the heater surface, allowing the infared radiation to pass through.

The test surfaces were coated with flat black paint to reduce issues related to the uncertainty.

Mahmood et al. [2002] used infared camera thermography to image a ribbed channel wall in

order to obtain spatially average Nusselt numbers. A portion of the top channel wall was

removed, and a zinc selenide window was installed in order to image the inside ribbed channel

wall. This provided spatial data on the top surface of the rib. This approach is different from the

Lyall [2006] and Ames et al. [2007] studies, which imaged the back side of the heater. When the

zinc selenide was not in place, an insert with ribs exactly matching the adjacent ribs was

installed. The walls were heated with an etched foil heater, creating a constant heat flux

boundary condition, which is necessary in an IR camera study. This study was selected for

comparison because the configuration is identical to the one used in the current study as well as

the Wright et al. [2004] study. Globally averaged values were determined by spatially averaging

the Nusselt numbers in the fully developed region of the test section, which was reported to be in

the x/DH=6.5-7.1 range. This method allowed the researchers to analyze the secondary flow

effects of the surface heat transfer occurring on and around the rib.

2.6 Uniqueness of Research

As aforementioned, the focus of this work was to identify the effect of pitch and aspect

ratio on heat transfer and friction factor with a complex rounded rib shape. Additionally, the

study focused on a one-ribbed wall configuration, which is uncommon in previously reported

experimental work. The one-ribbed wall work completed showed improved thermal

performance over a two-ribbed wall configuration. Finally, the measurement method utilized

infared camera thermography to provide spatially averaged endwall heat transfer data. It also

allowed the current researcher to examine the secondary flow effects on the endwalls of the

channel with minimal limitations.

19

Table 2-1 Summary of Relevant Rib Studies

InvestigatorData-Collection

Method

Aspect Ratio

(W:H)P/e e/H α

Rib

ShapeOrientation Arrangment Discrete

No. Ribbed

Walls

Cho et al.

[2003]

Naphtalene

Sublimation1:2 7.5 0.1 70°

Rectangle

(2:3)Angled

Parallel

CrossedContinuous 2

Diette et al.

[2004]

Liquid Crystal

Thermography4.67:1 10 0.33 90° Rounded Transverse - Continuous 1

1:1 0.047

2:1 0.063

4:1 0.125

Huh et al.

[2008]

Lumped

Capacitance1:4

2

5

10

0.125 45° Square Angled Parallel Continuous 2

Johnson et al.

[1994]

Lumped

Capacitance1:1 10 0.1 45° Half-circle Angled Staggered Continuous 2

Kim et al.

[2007]

Naphtalene

Sublimation1:1 10 0.055

45°

90°Square Transverse Parallel Continuous 2

2:1 0.04 W-Shape

4:1 0.06 2W-Shape

8:1 0.12 4W-Shape

V-Shape Parallel Discrete

V-Shape Parallel Continuous

V-Shape Staggered Continuous

Angled Parallel Discrete

Angled Parallel Continuous

Angled Staggered Continuous

Liu et al.

[2006]

Lumped

Capacitance1:2

3

5

7.5

10

0.125 45° Square Angled Parallel Continuous 2

Isosceles Triangle

Half-circle

Square

Mahmood et al.

[2002]

Infared Camera

Thermography4:1 10 0.125 45° Square Angled Crossed Continuous 2

Maurer & von

Wolfersdorf

[2006]

Liquid Crystal

Thermography2:1 10

0.042

0.01345° Square V-Shape Parallel Continuous

1

2

Ostanek

[2008]

Lumped

Capacitance1.7:1 8 0.15 45° Rounded V-Shape Staggered Discrete 2

1:4 0.031

1:2 0.031

1:1 0.014

2:1 0.063

4:1 0.125

3:1 0.06

5:1 0.10

6.82:1 0.136

Viswanathan &

Tafti [2005]

Numerical

Simulation1:1 10 0.1 45° Rounded Angled Staggered Continuous 2

Angled Discrete

Angled Continuous

V-Shape Discrete

V-Shape Continuous

W-Shape Discrete

W-Shape Continuous

2.86:1

5:1

5

100.2 45° Rounded V-Shape - Discrete 1

4:1 10 0.125 45° Square Angled Parallel Continuous 2

0.19

0.31

0.38

Rounded Angled 2ContinuousParallelRallabandi et al.

[2009]

Lumped

Capacitance1:1

5

7.5

10

Continuous-45° Square

Neely

[2009]

Infared Camera

Thermography

2ParallelSquareWright et al.

[2004]

Lumped

Capacitance4:1 10 0.125 45°

2

Rhee et al.

[2003]

Naphtalene

Sublimation10

45°

60°

Square V-Shape Parallel

Discrete

(45° only)

Continuous

(60° only)

2

2

4:1

10

30°

45°

60°

90°

Square

8

10

15

20

Continuous

Parallel

45°

ContinuousTransverse

Han & Park

[1988]

Thermocouples

w/ Foil Heaters

Holographic

Interferometry

Liou & Hwang

[1993]

Square Angled Parallel Continuous

Angled Parallel

0.125 90°

Park et al.

[1992]

Thermocouples

w/ Foil Heaters

10

20

30°

45°

60°

90°

Kunstmann et al.

[2009]10

Liquid Crystal

Thermography

2

Lee et al.

[2005]

Lumped

Capacitance4:1 10 0.125 45° Square 2

1

20

Chapter 3

EXPERIMENTAL FACILITY AND DATA ANALYSIS

The goal of this project was to obtain heat transfer and friction factor measurements for a

variety of rib turbulator configurations by examining the effects of pitch, blockage, aspect ratio,

rib shape, and rib orientation. Because the actual size of the channel in a turbine blade is too

small to spatially resolve the physics, the test section was scaled up from actual engine size in

order to obtain the desired measurements with sufficient resolution. Benchmark testing was

done with a smooth channel and a characteristic geometry of parallel square-cross section ribs

45° to the flow on two opposing walls. The remaining geometries tested were discontinuous, V-

shaped, rounded ribs at 45° to the flow on one wall only. This chapter explains the design of the

experimental facility as well as the various data reduction methods.

All the rib geometries tested are summarized in Section 3.1. The overall experimental

facility used was built by a previous graduate student [Lyall, 2006] and was designed to allow

test sections to be interchangeable while maintaining the basic structure of the rig. Lyall et al.

[2006] describe in detail the specifications for all components used in the permanent

experimental facility. A summary of the components used in the experimental facility and

instrumentation is offered in Section 3.2. In Section 3.3, the test section design is explained in

detail.

Once raw data was collected, it was reduced from temperature and pressure readings to

heat transfer coefficients and friction factors. Section 3.4 summarizes heat transfers

augmentation data reduction for both the line and spatial measurements. Section 3.5 presents the

friction factor augmentation data reduction.

3.1 Rib Geometries

The various rib configurations under investigation are summarized in Table 3-1. Figure

2-1, in the previous chapter, defines the rib parameters used and varied in the experiments. Four

configurations were rounded cross-section ribs oriented in a discontinuous V-shape at 45° to the

flow. The pitch-to-rib height ratio was varied from 5 to 10, while the trip-height-to-channel-

height remained constant at 0.2. The rib cross-sectional area with normalized dimensions is

shown in Figure 3-1.

21

Rib

Orientation

Rib

Shape

Aspect

Ratio

Length-to-

Hydraulic

Diameter

No. of

Ribs

Pitch-to-Height

Ratio

Blockage

Ratioα

No. Ribbed

Walls

Entry Length-

to-Hydrualic

Diameter

Entry

Condition

w/H L/DH P/e e/H Lentry/DH

V-shaped rounded 2.86 13.7 20 5 0.2 45° 1 7.3 Heated

V-shaped rounded 2.86 13.7 10 10 0.2 45° 1 7.3 Heated

V-shaped rounded 5.0 14.4 24 5 0.2 45° 1 18.0 Unheated

V-shaped rounded 5.0 14.4 14 10 0.2 45° 1 18.0 Unheated

parallel square 4.0 8.7 9 10 0.13 45° 2 17.7 Unheated

69.5°

Height = 1.0

Radius = 0.25

Width = 1.09

Wal

l L

ength

= 0

.89

Table 3-1 Summary of Rib Configurations

Figure 3-1. Schematic of a rounded-rib cross-section where all dimensions are normalized to

the rib height.

The dimensions are given in a normalized format because the actual dimensions of the

ribs changed from configuration to configuration, while the shape remained constant. Finally,

the aspect ratio was varied between 2.86 and 5 for the rounded rib studies. Figure 3-2 shows a

sample rib installation for rounded-cross section, parallel 45° to the flow, P/e=5, AR=2.86, and

e/H=0.2. For all the rounded rib tests, the ribs were installed on one side of the channel, with the

remaining three walls left smooth. Because of the complex rib shape, the ribs were milled at the

machine shop to obtain the proper cross-sectional area shape. Copper alloy 110 was used for all

ribs because of the material’s high thermal conductivity, 400 W/m-K.

22

Figure 3-2. Experimental rib configuration shown with discrete V-shaped, rounded cross-

section ribs 45° to the flow, P/e=5, AR=5:1, and e/H=0.125.

The remaining configuration was a square cross-section, parallel 45° to the flow, P/e=10,

AR=4.0, and e/H=0.125. This specific configuration was designed to replicate a study done by

Wright et al [2004] in order to benchmark the test section. Because the cross section on the rib

was square, copper alloy 110 barstock was purchased in the exact width and height needed, and

then cut to length in the machine shop. Figure 3-3 shows this benchmark configuration.

Figure 3-3. Wright et al. [2004] rib configuration showing square cross-section, parallel 45°

to the flow, P/e=10, AR=4:1, and e/H=0.125.

Because many rib configurations were being tested, the ribs needed to be installed in the

channel with an impermanent technique. Contronics manufactures Duralco 132, a two-part

23

resin-hardener epoxy that is highly thermally conductive. The epoxy has a thermal conductivity

of 5.76 W/m-K. To install the rib, the epoxy was applied to the underside of the rib and then

placed on the clean, dry heater. Once all the ribs were installed, cinderblock weights were used

to hold the ribs in place until the epoxy was completely cured. According to Cotronics [2008],

cure time ranges from 16 to 24 hours depending on the ambient temperature. After a specific

configuration was completely tested, the ribs were removed carefully with Klean Strip adhesive

remover. Some residual epoxy remained on the heater surface, and it was cleaned off using the

same adhesive remover. After the heater was cleaned, it was ready for the next rib installation.

3.2 Overall Test Facility

The overall test facility was a closed-loop, recirculating channel. Figure 3-4 shows a

schematic of the facility with flow moving in the clockwise direction. The system includes a

Model D53-J4 high pressure, low flowrate blower manufactured by Chicago Blower. A Baldor

Motor ID15H415-E variable frequency drive control was used to adjust the mass flowrate in 0.01

Hz increments [Lyall, 2006]. The flow exited the blower through 0.15 meter diameter 40 PVC

piping, which was used throughout the rig and continued to the plenum. Downstream of the

blower, but prior to entering the plenum, a relief valve in the system was left open to allow the

pressure differential between ambient room conditions and the test section to be nearly zero

during testing. The plenum conditioned the flow aerodynamically and thermally before it

entered the test section.

Downstream of the test section, there was a square-to-round expansion joint

manufactured by Bolland Machine of Pittsburgh, Pennsylvania. This joint connected the

rectangular test section to the circular PVC piping leading to the flow meter. A calibrated Oripac

model 4150-P orifice flow meter, manufactured by Lambda Square Inc., was used to calculate

the mass flow rate traveling through the test section. Using the orifice meter limited the flowrate

to 153.5 SCFM, which corresponded to a maximum obtainable Reynolds number of

approximately 40,000. The manufacturers’ specifications require ten pipe hydraulic diameters

of smooth pipe upstream and six pipe hydraulic diameters downstream to ensure flowrate

measurements within a specified accuracy of ±0.6% [Lambda Square Inc.]. Finally, the flow

reentered the blower for recirculation.

24

Figure 3-4. Schematic of closed loop test facility used for rib turbulator testing.

Ple

nu

m

Tes

t S

ecti

on

Rel

ief

Valv

e

Flo

w M

eter

IR C

am

era

Vie

win

g A

rea

Blo

wer

FL

OW

FL

OW

L =

7.9

8 m

25

In the plenum, flow encountered a splash plate and then passed through a heat exchanger

before passing through inlet contraction vanes to the test section. Figure 3-5 shows a schematic

of the interior of the plenum. The inside dimensions of the plenum measured 1.22 m in the flow

direction, 1.22 m in the spanwise direction, and 0.55 m high. The splash plate prevented jets

from forming and aided in expanding the fluid. Aerodynamically, the dispersion of the flow

created uniformity inside the plenum by expanding the flow to ensure a zero-velocity inlet

condition for the test section. The plenum had a cross sectional area of 0.67 m2, which was 46:1

to 81:1 times greater than the test section flow area, depending on the specific aspect ratio being

tested. In general, a ratio of 10:1 is considered acceptable for plenum design. Next the flow

passed through a water-to-air heat exchanger, which was used to maintain a consistent inlet

temperature. The closed loop nature of the test necessitated a heat exchanger because heat was

added to the flow in the test section via viscous and electrical heating. Without a steady inlet

temperature, the bulk fluid temperature would have increased gradually throughout the duration

of a test. The inlet temperature was measured by two type E thermocouples placed downstream

of the heat exchanger, and the maximum variation present in the readings was 0.3°C at steady

state.

Splash

PlateHeat

Exchanger

FLOW

Thermocouple

Pressure

Tap

1.22 m 1.22 m

0.55 m

Figure 3-5. Schematic of the interior components of the plenum.

26

Finally, the flow passed through inlet contraction vanes to aid in the transition from the

plenum to the test channel. The vanes were made from halved pieces of PVC pipe secured to the

interior of the front face of the plenum, as shown in Figure 3-6. They were adjustable in order to

accommodate the various channel aspect ratios studied. A pressure tap was mounted on the front

face of the plenum in order to measure the pressure differential between the plenum and various

test section locations and also the ambient room conditions. The tap itself consisted of a small

brass tube in inserted flush with the medium density fiberboard wall. For more accurate pressure

readings, the interior end of the brass tube was chamfered, creating a seamless joint between the

wood and the tubing.

Figure 3-6. Rounded inlet contraction vanes, made from halved PVC pipes, which aided the

transition of the flow from the plenum into the test section.

Temperature and pressure data were collected by National Instruments (NI) signal

conditioning hardware and software. An SCXI 1100 signal conditioner was used in conjunction

with SCXI 1303 and SCXI 1102 terminal blocks to capture voltage signals from the

thermocouples and pressure transducers, respectively. The single SCXI 1000 chassis housed the

terminal blocks and a 2 Hz low pass filter in order to reduce unwanted noise and frequency

content in the signal. Analog signals were converted to digital signals via a PCI-6034E 16 bit

data acquisition card. LabView 8.0 software was used to make a user-friendly interface for data

acquisition manipulation and viewing the outputs.

27

Type E thermocouples were manufactured in the lab and calibrated in an ice bath with a

maximum bias uncertainty of ±0.2°C. The thermocouples were positioned along the centerline

of the channel and provided line-averaged data. In the IR viewing area the calibration

thermocouples were also type E and manufactured in the lab. Various pressure drops throughout

the rig were measured by using two Setra Model 264 pressure transducers. The accuracy was

quoted to ±1.0% of the full scale in ambient conditions [Setra Systems, 2008a]. A 0-5.0 in H2O

range transducer was used across the orifice flowrate meter, and a 0-1.0 in H2O range transducer

was used for test section measurements.

Because there were various pressure taps at one streamwise location, a mechanical fluid

wafer from Scanivalve was used to switch easily between the different tap locations for data

collection. To obtain the plenum pressure with respect to atmospheric pressure, a Meriam 2100F

smart gauge with a 0-20 in H2O range and accuracy of ±0.05% of full scale was used [Meriam

Instruments]. This gauge was also used to measure the high pressure side of the orifice with

respect to the room atmospheric pressure. Atmospheric pressure in the lab was obtained by

using a Setra Model 370 barometric pressure gauge with a range of 60-110 kPa and an accuracy

of ±0.02% full scale [Setra Systems, 2008b]. While the Setra Model 264 transducers were wired

to the NI data acquisition system, the Meriam 2100F and the Setra Model 370 gauges gave

digital readouts that were used to obtain the pressure data. The next section outlines the details

of the test section design.

3.3 Test Section Design

The test section was designed to fit easily into the overall test facility. A parallel plate

channel was built in order to examine the effects of various rib parameters on heat transfer

augmentation and friction factor. The test section was constructed to accommodate changing

channel dimensions and rib configurations while maintaining the ability to obtain measurements.

The Reynolds numbers of interest were in the range 12000 < Re < 40000. These numbers were

representative of the operational Reynolds numbers for internal cooling of a turbine blade.

A channel was built with a 20.3 cm wide endwall and interchangeable sidewalls of

heights 4.1 cm, 5.1 cm, and 7.1 cm. To change the aspect ratio, width-to-height of the channel,

the sidewalls were replaced by the appropriate height sidewall, while the endwall remained a

constant width of 20.3 cm.

28

The components of the test section are depicted in Figure 3-7. The flow exited the

plenum passing through rounded contraction vanes. Two trip wires that had a 2 mm diameter

were used to ensure that the flow was transitioned to a hydrodynamically fully turbulent profile

prior to the start of the rib turbulators. The wires were placed 5 cm downstream of the inlet of

the channel, spanning the 20.3 cm endwalls. Medium density fiberboard (MDF) was used to

make the channel walls because it was readily available, easy to build with, and capable of

rigidly supporting the heaters. Furthermore, MDF has a relatively low thermal conductivity of

0.12 W/m-K, making it a good insulator.

FLOW

Insulation

MDF

Pressure Tap

Contraction Vanes

Trip Wire

Heater IR Window

Air GapCopper Ribs

L = 2.2 m

Pressure Tap

Figure 3-7. Schematic of the test section used for rib turbulator testing.

3.3.1 Heat Transfer

To create a constant heat flux boundary condition, heaters were installed on all four walls

of the test section. Rib turbulators disturb the flow by adding increased mixing motions and

disrupting the boundary layer. Early tests led to the finding that an insufficient length of heated

and ribbed channel existed upstream of the IR camera window. Initial channel configurations

permitted only 4 ribs, or 2.7 hydraulic diameters, upstream of the IR camera viewing area. Flow

was not reaching a fully developed state prior to the area where IR measurements were collected,

thus creating misleading results. Because the location of the IR camera viewing area could not

be changed, additional heaters and ribs were installed upstream of the initial heater location in

order to gain the extra hydraulic diameters needed to collect data in the fully developed region.

For the rounded rib configurations with an aspect ratio of 2.86:1, the entry region was heated and

7.3 hydraulic diameters long. The rounded rib configuration with an aspect ratio of 5:1 had an

29

Rib

Orientation

Rib

Shape

Aspect

Ratio

No. Ribs

Upstream of IR

Length-to-

Hydraulic Diameter

Upstream of IR

No. Ribs

Upstream of IR

Length-to-

Hydraulic Diameter

Upstream of IR

w/H

V-shaped rounded 2.86 4 5.5 7 8.2


V-shaped rounded 5.0 7 7.5 - -

V-shaped rounded 5.0 13 7.5 - -

parallel square 4.0 3 5.2 - -

Original Extended

unheated entry region that was 18 hydraulic diameters long. Finally, the square rib configuration

had an unheated entry region that was 17.7 hydraulic diameters long.

Typically, a rib turbulated channel requires approximately five to six rib pitches before

becoming thermally and hydrodynamically fully developed turbulent flow. Graham, Sewall, and

Thole [2004] showed that based on friction factor measurements, the flow became

hydrodynamically fully developed by the third to fifth rib. Similarly, Han and Park [1988]

showed that the flow is thermally fully developed by the sixth rib based on surface heat transfer

measurements.

After retrofitting the channel, the IR camera window was positioned a minimum of 7 ribs

downstream for the rounded rib cases; however, this length varied from 7 to 14 pitches

depending on the specific configuration being tested. Table 3-2 summarizes the original and

extended rib configurations. A plot of the general heat transfer augmentation development in a

ribbed channel along the streamwise axis is show in Figure 3-8. Heat transfer augmentation is

on the ordinate, and the distance along the streamwise direction normalized by hydraulic

diameter is on the abscissa. The augmentation development is for a rib configuration

characterized by P/e = 5, AR = 2.86:1, and e/H = 0.2 with ribs on one wall only. Thermocouples

were permanently installed 6.6 cm apart down the centerline of the channel on both endwalls;

this length corresponded to one of the hydraulic diameters of a specific configuration. The

hydraulic diameter varied depending on the aspect ratio being tested, and 6.6 cm was selected as

the thermocouple spacing because it was the smallest hydraulic diameter being tested.

Table 3-2 Summary of Rib Configuration Upstream of the IR Window

The flow underwent entrance and exit effects caused by the transition from the plenum to

the test section and similarly from the test section to round PVC pipe, as shown in Figure 3-8.

For this example, the entrance length was heated, and the ribs began at x/DH=4.4, causing a large

30

jump in augmentation on the ribbed side of the channel at x/DH=4.4. The augmentation

development on the ribbed wall was characterized by a spike; then it converged to a constant

value in the fully developed region. On the unribbed wall, the augmentation gradually increased

until it remained level in the fully developed region. Augmentation on both sides of the channel

converged at the same x/DH distance from the start of the ribs, confirming that the flow was

thermally fully developed. Slight variations in augmentation values in the fully developed region

were the result of the sensitivity of thermocouple placement.

0

1

2

3

4

5

6

7

0 5 10 15 20

Rib SideNo Rib Side

Nu

Nuo

x

DH

Fully Developed

Region

Exit

Effects

Entrance

Effects

Figure 3-8. Typical developing augmentation profile at Re=30000, in the streamwise

direction for internal channel heat transfer study with rib turbulators configured as

P/e=5, AR=2.86, and e/H=0.2. One side of the channel had rib turbulators (red)

present, while the other remained smooth (blue).

Kapton resistance heaters, manufactured by Electrofilm in Valencia, California, were

purchased for the permanent endwalls, and Inconel strip heaters were manufactured in the lab for

the smaller interchangeable sidewalls. Each 20.3 cm by 97.5 cm Kapton heater was rated to

460.8 watts; thus, each heater was able to generate 2325 W/m2. For the sidewalls, single strip

Inconel foil heaters were manufactured in the lab. As shown in Figure 3-9, a strip of Inconel foil

was cut to 1 hydraulic diameter in height. Due to the thin foil, a 0.8 mm thick copper busbar was

soldered to the end of the strip for stability so that a lead wire could be soldered securely to the

31

heater. The individual strip heaters ranged in resistance depending on the height and length of

the strip. For example, the 7.1 cm wide heaters had a resistance of 1.1 Ω, while the 4.1 cm wide

heaters had a resistance of 1.3 Ω.

Inconel foilCopper strip Lead wire

H = 1 DH

Figure 3-9. Schematic of the Inconel foil strip heaters made for the sidewalls.

A cross-section schematic of the Kapton heater is shown in Figure 3-10. Serpentine

inconel strips were laminated between layers of Kapton and then backed with a 28.3 gram layer

of copper. The copper backing created a more uniform heat flux distribution than the

Kapton/Inconel surface alone. Finally, the copper side was spray painted black in the IR window

viewing area in order to create a highly emissive surface. A typical emissivity value for the

heater was 0.96, and the background temperature ranged from 20 to 28 °C.

Copper

Kapton

Kapton

Flow Side

76.2 µm

76.2 µm

50.8 µm

50.8 µmInconel

1.9 cmMDF

Figure 3-10. Cross-section schematic of the Kapton heater used in the test section.

To image the heater, a portion of the MDF endwall was removed so the backside of the

heater was visible. The window area was oriented at 45° to the flow in order to image the entire

length of a rib spanning the channel at 45° to the flow. A zinc selenide (ZnSe) window,

measuring 29.2 cm by 14.0 cm, was installed in the opening to prevent losses yet still allow

infared waves to pass through. Outside the IR viewing area, the heater was adhered to the MDF

32

wall with model 401B double-sided paper tape manufactured by 3M Company. This silicon-

based adhesive stuck well to both the copper side of the heater and the MDF sidewall. In the IR

viewing area, the ZnSe window extended past the edges of the channel. Because the heater was

the exact width of the channel, 20.3 cm, Lexan supports were added to provide rigidity to the

heater. This adjustment prevented the heater from wrinkling and limited vibrations during

testing.

IR images taken with the supports were of higher quality than those taken without

supports, thus justifying their need. Figure 3-11 shows a schematic of the heater supports. At

the edge of the heater, 1.3 cm of viewing area on each side was sacrificed in order to install the

support. This trade-off was determined to be acceptable because of the resulting improvements

in data collection. The footprint of the supports matched that of the IR window in order to

prevent any surfaces from coming into contact with, and damaging, the surface of the ZnSe.

MDF

Lexan

Support

17.8 cm

20.3 cm

Rib

ZnSe

Air Gap

Lexan

Support

MDF

Insulation

Side View Top View

0.6cm

0.3cm

Heater

Figure 3-11. Side and top schematics of the Lexan support added to the IR viewing area. The

support reduced the viewing width by 2.5 cm of the heater.

Prior to installing the heaters in the channel, the Type E thermocouples were placed at

equidistant locations, 6.6 cm, along the streamwise centerline of the heater. Duralco 128, highly

thermal conductive, electrically resistive epoxy, was used to secure the thermocouple bead to the

backside of the heater. Each thermocouple was placed in the center of an inconel strip to yield

the most accurate readings. Then the thermocouple wires were routed out through a bore hole in

the MDF channel wall, as shown in Figure 3-12. A small counter sink was drilled in the channel

wall on the flow side of the bore hole so that the thermocouple bead would not disrupt the

33

IVQ ⋅=

smoothness of the heater surface. Strips of the 401B double-sided tape were placed along the

length of the channel, and small areas were removed, to accommodate the counter sinks for the

thermocouples. To mount the heater in the channel, the thermocouple wires were fed through

the channel walls. Gradually, the backing of the tape was removed as the heater was rolled into

place with consistent pressure from a hand-held roller. This ensured solid contact and minimal

air gaps among the MDF channel wall, the tape, and the heater.

Heater

MDFThermocouple Bead

Thermocouple Wire

Bore Hole with Countersink

Flow

Duralco Epoxy

Tape

1.9 cm

229 µm254 µm

Figure 3-12. Schematic of thermocouples installation in the channel. Thermocouple bead was

secured to the backside of the heaters using Duralco 128 two-part epoxy and the

wire routed out through a bore hole in the MDF.

Because of slight variations in the individual heater resistances, all the heaters were

independently powered by Lambda EMI Model GEN100-15 DC power supplies. During testing

each heater was connected in series with a Lambda power supply and 1 Ω precision resistor.

Figure 3-13 shows the circuit for the heaters, power supplies, and precision resistors. A voltage

and current were passed through the heater in order to generate a heat flux. To accurately

quantify the power generated by each heater, the current was measured across the 1 Ω precision

resistor, and the voltage was measured across the heater itself with a digital multimeter. Because

the system was connected in series, the current passing through the resistor was equal to the

current passing through the heater. Equation 3-1 shows how the heater power was calculated.

(3-1)

34

Heater

1Ω Precision Resistor

Current Measured Here

Power Supply

Wire Junction

Voltage Measured Here

+

-

Figure 3-13. Diagram of heater and power supply set-up. Voltage is measured across the wire

junction, and the current is measured across the precision resistor.

Measured voltages were in the range of 25-50 volts, and currents were in the range of

0.8-3.5 amps. Table 3-3 shows a sample of the power settings for the following rib

configuration: P/e=10, AR = 4:1, e/H=0.125, square ribs on two walls. Most of the heat

generated went into the flow; however, some losses were associated with the test section.

Table 3-3 Summary of Power Settings for P/e=10, AR=4:1, e/H=0.125

Reynolds Voltage Current Power

V A W

14038 2.3 29.6 66.6

20876 2.8 36.1 99.3

25064 3.0 39.5 118.5

30954 3.0 39.4 118.2

39175 3.5 46.1 161.4

Figure 3-14 shows a schematic of the two heat loss pathways. The first pathway went

through the solid wall where heat flux flowed from the heater surface through the MDF wall

through the insulation, ultimately being exposed to ambient room conditions. The second

pathway went from the surface of the heater through an air gap through the ZnSe window, finally

35

being exposed to ambient room conditions. In order to image the backside of the heater, a

barrier was needed that would allow IR radiation to pass through for imaging while still

insulating the heater to prevent excess losses. When the viewing area was not in use, the ZnSe

window was covered with insulation to prevent further losses. When the insulation was removed

from the ZnSe window to take a picture, the temperature decreased by up to 0.4 °C. The actual

temperatures recorded during the IR picture taking were used in the data reduction process,

which is explained in Appendix B. The effect was minimized by removing the insulation over

the window for the least amount of time possible, and it was replaced while the IR camera was

reset between images.

1.3 cm

1.9 cmMDF

Insulation

ZnSe

Air Gap

q"loss,wall q"loss,window

Loss thermocouples

Heaterq"flowFLOW

2.5 cm

0.6 cm

0.03 cm

Figure 3-14. Schematic of the heat loss pathways in the test section. Heat that does not enter

the flow is lost to the surroundings and modeled with a 1-D conduction analysis.

Losses were calculated by placing thermocouples on the outer surface of the channel,

between the MDF and insulation, equidistantly, at 12.2 cm apart, in the streamwise direction.

This placement created a streamwise temperature profile used to calculate spatial losses. With a

constant heat flux boundary condition, the losses increased with increasing streamwise direction.

The surface of the ZnSe window was susceptible to scratches, so no thermocouple measurements

could be obtained on the window surface to calculate the actual losses occurring through the

window. If the window surface had blemishes, it would affect the quality of the IR images.

36

In order to determine if the losses calculated through the MDF walls of the channel were

an accurate representation of the losses occurring in the IR window area, a thermal resistance

analysis was conducted. A one-dimensional conduction analysis was used because the test rig

walls could be treated like a composite wall where each layer had an individual thermal

resistance. Table 3-4 shows the values for thermal conductivity and length of the various

materials in the loss pathways.

Table 3-4 Thermal Conductivity and Thickness of Materials in the Loss Analysis

MDF Insulation Air Gap ZnSe

Thermal Conductivity, k W/m-K 0.124 0.026 0.026 18.0

Thickness, L m 0.019 0.025 0.006 0.013

For the wall pathway, the thermal resistance is shown by Equation 3-2.

(3-2)

For the window pathway, the thermal resistance is shown by Equation 3-3.

(3-3)

The thermal resistances were found to be Rwall= 1.42 m2-K/W and Rwindow=1.33 m

2-K/W.

The difference of 6.6% is small enough that the losses through the IR window could be

calculated by using the spatially developed losses through the MDF walls of the channel.

The actual losses used in the data reduction were found by using the thermal resistance

and the temperature gradient of the MDF wall. Recall, the loss thermocouples were located

between the MDF and the insulation. These calculations are shown by Equations 3-4 and 3-5,

respectively.

(3-4)

(3-5)

ambins

ins

MDF

MDFwall

hk

L

k

LR

1++=

ambins

ins

ZnSe

ZnSe

air

airwindow

hk

L

k

L

k

LR

1+++=

MDF

MDFMDF

k

LR =

MDF

oendwallloss

R

TTq

−="

37

The value of RMDF was calculated to be 0.154 m2-K/W. At the lowest Reynolds number

of 12,000, the losses ranged from 2-10% depending on the configuration. For the highest

Reynolds number of 40,000, the losses decreased to a range of 1-8%. Losses on the ribbed side

were expected to be lower than losses on the unribbed side as a result of the increased heat

transfer caused by the turbulators. Table 3-5 shows each configuration and the respective losses

for high and low Reynolds numbers, in addition to the ribbed versus unribbed losses. Because of

the enhanced heat transfer on the ribbed side of the channel, the loss on the ribbed endwall was

found to be approximately half the loss of the unribbed endwall.

Table 3-5 Losses for Rib Configurations

Re=40,000

Heat Flux

[W/m2]

Ribbed Side

Loss [W/m2]

Ribbed Percent

Loss [W/m2]

Unribbed Side

Loss [W/m2]

Unribbed Percent

Loss [W/m2]

P/e=10, AR=5, e/H=0.2 1415 17.1 1% 34.2 2%

P/e=5, AR=5, e/H=0.2 1610 17.5 1% 36.0 2%

P/e=10, AR=2.86, e/H=0.2 1156 27.5 2% 51.9 4%

P/e=5, AR=2.86, e/H=0.2 1156 23.1 2% 62.3 5%

P/e=10, AR=4, e/H=0.125 Parallel Two Ribbed Walls 1194 7.2 1% - -

Smooth Channel No Ribs 240 12 5% 18 8%

Re=12,000

Heat Flux

[W/m2]

Ribbed Side

Loss [W/m2]

Ribbed Percent

Loss [W/m2]

Unribbed Side

Loss [W/m2]

Unribbed Percent

Loss [W/m2]

P/e=10, AR=5, e/H=0.2 509 13.7 3% 19.9 4%

P/e=5, AR=5, e/H=0.2 881 17.8 2% 23.6 3%

P/e=10, AR=2.86, e/H=0.2 517 25.5 5% 42.8 8%

P/e=5, AR=2.86, e/H=0.2 408 20.6 5% 40.1 10%

P/e=10, AR=4, e/H=0.125 Parallel Two Ribbed Walls 495 7.8 2% - -

Smooth Channel No Ribs 118 11 9% 12 10%

Discrete

V-Shaped

One Ribbed

Wall

Configuration

Discrete

V-Shaped

One Ribbed

Wall

Configuration

The 0.6 cm air gap between heater surface and ZnSe window was designed to minimize

losses and also to prevent natural convection from occurring (see Figure 3-14). To check that

instabilities did not develop into natural convection cells, the Rayleigh number had to be less

than the critical value of 1708.

(3-6)

In Equation 3-6, the Rayleigh equation, g is the acceleration due to gravity, β is the

volume expansion coefficient, Tendwall is the endwall heater temperature, Tairgap is the temperature

in the air gap, d is the depth of the air gap, α is the thermal diffusivity, and ν is the kinematic

( )να

β

⋅

⋅−⋅⋅=

4dTTgRa

airgapendwall

t

38

viscosity. A conservative temperature difference of 30 K was used in the analysis. For the ZnSe

window air gap, the Rayleigh number was approximately 680. Therefore, a 1D conduction

analysis was determined to be a valid approximation for the heat loss calculations, and no

instabilities in the air gap would result in natural convection cells.

3.3.2 Pressure Penalty

To calculate friction factor, the pressure drop across the ribbed portion of the test was

needed. Pressure taps were installed in the sidewall, 1 hydraulic diameter upstream of the start

of the ribs. Downstream of the ribbed portion, there were two sets of three pressure taps located

3.5 and 4 hydraulic diameters aft of the heater. All pressure taps were installed and

manufactured by using the same method described in Section 3.2. The smooth channel between

the taps and ribs was subtracted in order to obtain the true friction factor of just the ribbed

region. The Blasius equations, for a smooth channel, were used to calculate the friction factor in

the smooth portions of the channel. The pressure losses due to the smooth portion of the channel

then were subtracted from the overall measured value as shown in Equation 3-7.

(3-7)

Figure 3-15 shows the how the ∆x length was calculated in the previous equation. The

pressure drop, dPflow, was further reduced to a friction, which will be described in detail in

Section 3.4.2.

∆

⋅⋅⋅−=

H

omeasuredD

xVfdPdP

2

2

1ρ

39

∆xL1 L2

Pressure taps Ribbed section

∆x = L1+L2

FLOW

Figure 3-15. Pressure taps are located upstream and downstream of the ribbed section of the

channel; the extra length of channel is accounted for in the friction factor

calculations. The upstream and downstream lengths are summed in ∆x.

Prior to running the rounded rib configurations, the test section underwent benchmarking

to ensure the channel construction and data reduction were accurate. In the next section, the data

reduction for heat transfer and friction factor is covered.

3.4 Data Reduction

For each rib configuration, the experiment was run at various Reynolds numbers ranging

from 12000 to 40000. To obtain the different flow conditions, the mass flow rate was adjusted

while the remaining parameters were held constant. An orifice plate flow meter was used to

calculate volumetric flow rate through the orifice, and then the value was converted to a test

section volumetric flow rate. Reynolds number was then calculated from the flow velocity in the

test section. The volumetric flow rate through the orifice was found by using the line flow

conditions and correlations provided by the manufacturer. The detailed calculations for

determining volumetric flow rate are shown in Appendix A. Once the volumetric flow rate, Qstd,

though the orifice was determined, the mass flow rate for the experimental facility was

calculated by using Equation 3-8.

(3-8)

stdstdQm ρ⋅=&

40

The standard density of air, ρstd=1.223 kg/m3, was found by using Equation 3-9, the ideal

gas law, where Pamb was 101325.9 Pa and Tamb was 15.6 °C. The base ambient conditions were

provided by the orifice plate flow meter specifications [Lamba Square, Inc.].

(3-9)

Once the mass flow rate of the test facility was known, the volumetric flow rate of the

test section was found by using Equation 3-10. Mass flow rate was constant throughout the

entire test facility, so it could be used to find the volumetric flow rate, Q, in the test section.

(3-10)

The density of the flow, ρ, in the test section was found by using the ideal gas law with

the inlet pressure and temperature of the test section. Finally, the area-dependent velocity of the

flow in the test section, V, was calculated by using Equation 3-11, where Ac is the cross sectional

area of the test section.

(3-11)

The Reynolds number based on hydraulic diameter was finally calculated by using

Equation 3-12.

(3-12)

The dynamic viscosity of air, µ, was interpolated from tables in Incropera and DeWitt

[2002] using the mean temperature of the flow defined in Equation 3-13.

(3-13)

Heat transfer and friction factor augmentation values varied with Reynolds number; thus,

it was the central calculation in the data reduction process.

amb

ambstd

TR

P

⋅=ρ

mQ

&

ρ=

cA

QV =

µ

ρ⋅⋅=

VDHRe

2

outinmean

TTT

+=

41

3.4.1 Heat Transfer Augmentation

Temperature and pressure measurements were continuously recorded throughout the

duration of a test, but only data collected during steady state was used in the final reduction

process. Typically, a test starting at ambient conditions would require three hours to come to

steady state. When the temperature values leveled and began to alternate around a mean reading,

the thermocouple standard deviation was checked to ensure it was approximately 0.2 °C. At this

point the test section was assumed to be at steady state, and measurements were collected.

Heat transfer calculations were obtained in two different manners. First, thermocouples

were embedded along the centerline of the test section. Second, infared (IR) camera images

were used to calculate spatially averaged heat transfer coefficients. Regardless of the method by

which temperature data was collected, the heat transfer reduction began by calculating the

amount of heat entering the flow. The heater power, Q, was found by measuring the current and

voltage across the heater with a digital multimeter. The heat flux of each heater, shown in

Equation 3-14, was calculated by using the planform surface area of the heater, Ap.

(3-14)

The total heat flux entering the flow took into account the heat loss out of the channel. In

Section 3.3 a detailed analysis of the heat loss is presented. From this analysis, it was possible to

conclude that the total heat entering the flow, q"conv, is defined as follows:

(3-15)

The bulk temperature was calculated by using a first law analysis shown in Equation 3-

16.

(3-16)

The heat transfer coefficient, shown in Equation 3-17, was calculated at each

thermocouple location.

(3-17)

pA

Qq ="

lossconv qqq """ −=

( )bulkendwallsidesideendwall

conv

TTAAA

Qh

−⋅

++

=

2

1

2

1

p

pconv

inbulkcm

AqTT

⋅

⋅+=

&

"

42

The area used in the heat transfer coefficient calculation did not account for the added

surface area of the ribs in the channel; instead, it was accounted for later in the Nusselt number

weighting. Planform area was the smooth surface area of the heaters, while the total, or wetted,

area represented the actual surface area the flow encountered. Therefore, the total area included

the heater surface between the ribs and the exposed top and side surfaces of the ribs. In Equation

3-17, a planform area representing the endwall and half of each sidewall was used.

Depending on the specific configuration, ribs were installed on one or two endwalls in

the channel, leaving the sidewalls smooth in all cases. The ribbed endwall had a higher total

surface area compared to a smooth wall and, by using the planform area in the data reduction, the

analysis remained consistent regardless of the configuration under consideration. Using the

planform area also allowed for uniform comparison between ribbed and smooth walls. It was

important to calculate a heat transfer coefficient for each wall because of the difference in the

magnitude between a turbulated and a smooth wall.

Finally, the channel Nusselt number was calculated by using Equation 3-18; this number

represents the temperature gradient at the wall.

(3-18)

Augmentation is a nondimensional number that characterizes the heat transfer caused by

the addition of turbulators. The measured channel Nusselt number is divided by a smooth

circular tube correlation. For this study, the fully developed turbulent correlation used was

Dittus-Boelter [Incropera], shown in Equation 3-19.

(3-19)

Any augmentation value above 1.0 means the heat transfer was enhanced by the

turbulator feature. The augmentation was calculated for the ribbed channel walls, the unribbed

channel walls, and finally a global channel area-averaged value, given in Equation 3-20.

(3-20)

air

H

k

DhNu

⋅=

4.08.0 PrRe023.0 ⋅⋅=oNu

( ) 4.08.0 PrRe023.0 ⋅⋅⋅+++

+++⋅=

sideunribbedribendwall

sideunribbedunribbedunribbedribribendwallendwall

o AAAA

ANuANuANuANu

Nu

Nu

43

Figure 3-16 is a schematic defining the areas Aendwall, Arib, Aunribbed, and Aside used in the

area weighted augmentation. The Aendwall did not include the heater surface covered by the ribs,

only the exposed area between the ribs. Arib was the surface area of the rib not including the

bottom surface that was in contact with the heater. Aunribbed was the viewable area on the smooth

side of the channel. Finally, Aside was the smooth sidewall area consistent with the length of the

IR window viewing area.

50 100 150 200

20

40

60

80

100

120

Augmentation Cropped

50 100 150 200

20

40

60

80

100

120

Aendwall

Rib

Arib

Aunribbed

Aside

W

H

Figure 3-16. Schematic defining the various areas used in the area-weighted Nusselt number

augmentation.

The thermocouple values along the centerline of the channel provided only streamwise

dependent point values. In order to obtain spatial averages, temperature maps were collected at a

specified location in the channel. Each pixel in the image represented a temperature at that

coordinate location. Using all the pixels, a full map of the heat transfer was provided, and

spatially averaged values were calculated. For each test, five IR images of the backside of the

heater were collected at each of the two viewing locations. Multiple images were captured to

44

reduce the pixel-to-pixel noise and the measurement uncertainty. A full description of the image

capture process, calibration, and reduction are provided in Appendix B.

In addition to heat transfer data, pressure measurements were made across the test section

to determine friction factors.

3.4.2 Friction Factor Augmentation

Darcy friction factor across a ribbed channel is shown in Equation 3-21.

(3-21)

The pressure drop across the ribbed portion of the test section was calculated by

measuring the pressure drop from the plenum to the pressure taps downstream of the ribs and

then subtracting the pressure drop from the plenum to pressure taps upstream of the ribs. The

difference between the measurements was the pressure drop across the ribbed section only. The

measurement was verified by directly measuring the pressure drop across the ribbed section,

from the upstream to downstream taps, during the test channel development. During testing, the

pressure drop across the ribbed portion of the channel was not directly measured because the

data-acquisition system had a limited number of channels available for use. In order to

accurately resolve the pressure drops at various Reynolds numbers, various pressure transducers

with the appropriate differential ranges were used. The number of measurements needed,

however, exceeded the available channels on the data-acquisition system. Therefore, a pressure

manifold was designed to accommodate multiple measurements on one pressure transducer. The

pressure transducers used are described in detail in Section 3.2.

Because the pressure taps were not located immediately upstream and downstream of the

ribs, there were some smooth wall contributions to the pressure drop, as explained in Section 3.3.

The pressure drop across the smooth endwalls was calculated by using the Blasius correlations

for a smooth surface tube and then subtracting them from the measured pressure drop. Detailed

explanations of the rig set-up and pressure measurement methods are presented in Section 3.2.

Blasius correlations are Reynolds dependent, with different equations for flow conditions above

or below Re=20,000. Both correlations are shown in Equations 3-22 and 3-23.

⋅⋅

=

2

2

1V

D

L

dPf

H

ρ

45

(3-22)

(3-23)

The friction factor augmentation is a nondimensional way to characterize the effects of

the turbulators on the pressure drop across each unique rib configuration, and it is given by f/fo.

3.5 Uncertainty Analysis

Uncertainty analyses were calculated for heat transfer and friction factor calculations in

order to quantify how well the experimental data represented the actual physics of the flow.

Because a range of Reynolds numbers was tested, the analysis was carried out for the highest and

lowest values in order to obtain a range of uncertainties. Equation 3-24 is the method described

by Kline and McKintock [1953] and Moffat [1985] for single sample measurement uncertainty.

(3-24)

The uncertainty in measurement R is given by the square root of the sum of the squares

of the partial derivative of R with respect to variable xi multiplied by the uncertainty in variable

xi. With many different measured quantities used to calculate one variable of interest, this

equation accounts for the propagation of experimental error due to the uncertainty present in the

various measured quantities.

For the heat transfer results, the uncertainty was calculated for the Reynolds number, the

heat transfer coefficient, the Nusselt number, and the Nusselt number augmentation.

Furthermore, the calculations were broken down into a high and low Reynolds number, as well

as ribbed and unribbed values. Table 3-6 summarizes the ribbed uncertainty values, and Table 3-

7 summarizes the unribbed uncertainty values. Detailed calculations for heat transfer uncertainty

are presented in Appendix C. For the ribbed Nusselt augmentation, the uncertainty ranged from

3.3–4.4%, while the unribbed uncertainty ranged from 2.9–3.9%. Because the range of Reynolds

numbers tested was only 12,000 to 40,000, little variation in uncertainty existed over the entire

spectrum of Reynolds numbers tested.

000,20ReRe316.0 25.0 ≥⋅= −of

000,20ReRe184.0 2.0 <⋅= −of

2

1

∑=

∂

∂±=

N

i

x

i

R iu

x

Ru

46

Table 3-6 Uncertainty in Ribbed Heat Transfer

Variable Target Reynolds Value Uncertainty Uncertainty (%)

13,000 13295 849 6.4%

40,000 40122 2230 5.6%

13,000 48.8 1.0 2.0%

40,000 102.5 1.5 1.5%

13,000 127.9 5.7 4.5%

40,000 267.3 11.4 4.3%

13,000 39.9 2.0 5.0%

40,000 96.6 4.3 4.5%

13,000 3.19 0.22 6.9%

40,000 2.72 0.17 6.3%Nu/Nuo

Re

h

Nu

Nuo

Table 3-7 Uncertainty in Unribbed Heat Transfer


13,000 13295 849 6.4%

40,000 40122 2230 5.6%

13,000 22.7 0.2 0.9%

40,000 48.3 0.4 0.8%

13,000 58.3 2.4 4.1%

40,000 123.3 5.0 4.1%

13,000 39.9 2.0 5.0%

40,000 96.6 4.3 4.5%

13,000 1.52 0.1 6.6%

40,000 1.36 0.08 5.9%Nu/Nuo

Re

h

Nu

Nuo

Similarly, the friction factor uncertainties were broken down into four components:

Reynolds number, channel friction factor, smooth channel friction factor, and friction factor

augmentation. The uncertainty calculated for these values is shown in Table 3-8, and detailed

calculations are presented in Appendix D. Both heat transfer and friction factor augmentations

are Reynolds dependent, and the range of uncertainty in Reynolds was 2.8–4.2% for values of

12,000 to 40,000, respectively. Uncertainty in the friction factor augmentation was 4.6–10.3%

over the range of Reynolds numbers tested.

One of the highest contributors to the uncertainty in the heat transfer augmentation was

the use of the Dittus-Boelter correlation. To reduce this contribution, smooth channel

benchmark testing was conducted. Smooth channel testing not only verified the rig was

operational, but proved that any additional heat transfer was due to the addition of the ribs in the

channel.

47

Table 3-8 Uncertainty in Friction Factor Measurements


13,000 13295 849 6.4%

40,000 40122 2230 5.6%

13,000 0.24 3.0E-02 12.5%

40,000 0.21 1.8E-02 8.6%

13,000 0.029 4.7E-04 1.6%

40,000 0.022 3.1E-04 1.4%

13,000 8.24 1.1 13.3%

40,000 9.44 0.8 8.5%

Re

f

fo

f/fo

One final evaluation was completed in order to reduce the uncertainty in the

measurements, and that was repeatability testing. On the first ribbed configuration tested (P/e=5,

AR=2.86:1, e/H=0.2, and one ribbed wall), repeatability cases were run at the highest and lowest

Reynolds numbers. Two cases were run under the exact same conditions, and a third case was

run with 25% higher heat flux on each heater. Heat transfer coefficients are independent of the

amount of power put into the heater under a constant heat flux boundary condition; therefore, it

was expected that this increase in heat flux would not affect the heat transfer results.

The first repeatability test, run under the exact same conditions, yielded the same

augmentations for the ribbed wall, smooth wall, and channel average. At a Re=29500, the ribbed

side augmentation varied 0.6% between the two tests, 1.3% for the smooth wall, and 0.4% for

the channel average. When the heat flux was increased by 5% from 918 W/m2 to 1164 W/m

2,

the percent difference on the ribbed wall increased slightly to 2.1%. The percent difference from

the original case to the higher heat flux case for the smooth wall was 0% and 1.1% for the

channel average. Table 3-9 summarizes the augmentation values and the percent difference for

the repeatability testing.

48

Table 3-9 Summary of the Repeatability testing

ReynoldsRib

Augmenation

Percent

Difference

Average

Augmentation

Percent

Difference

Smooth

Augmentation

Percent

DifferenceCondition

29806 3.29 2.1% 2.76 1.1% 2.29 0.0%5% more

heat flux

29563 3.38 0.6% 2.80 0.4% 2.26 1.3% Exact repeat

29394 3.36 - 2.79 - 2.29 - Original

12871 3.84 1.3% 3.15 0.6% 2.51 0.0% Exact repeat

12822 3.79 - 3.13 - 2.51 - Original

12647 3.74 1.3% 3.15 0.6% 2.59 3.1%5% more

heat flux

49

Chapter 4

EXPERIMENTAL RESULTS

This chapter presents the experimental heat transfer and friction factor results for the

benchmarking and the rounded rib configurations over a Reynolds number range of 12,000 < Re

< 40,000. As established in the previous chapter, thermal measurements were taken with

thermocouples and also infared camera thermography. The friction factor was determined from

the pressure drop inside the channel. Section 4.1 presents the smooth channel and characteristic

geometry benchmarking. Section 4.2 summarizes the heat transfers results and the effects of rib

spacing and aspect ratio. Finally, Section 4.3 shows similar effects of rib spacing and aspect

ratio on the friction factor results.

4.1 Benchmarking

Two methods of benchmarking were completed: a smooth channel and a characteristic

open literature rib geometry [Wright, 2004]. The first benchmark case was heat transfer and

friction factor tests in a smooth channel. No ribs were installed in the channel, but the data

acquisition occurred in the same manner.

Heat transfer coefficients and friction factor measurements were obtained and then

compared with correlations published in open literature. The heat transfer results for the baseline

testing of a 4:1 aspect ratio channel are presented in Figure 4-1 with various turbulent, fully

developed correlations for a smooth channel. The maximum percent difference between the

Dittus-Boelter (2) correlation, shown in Equation 4-1, and the current study’s channel averaged

Nusselt number was 9.2% at the lowest Reynolds number. Then as Reynolds numbers increased,

the deviation from Dittus-Boelter (2) decreased to 0.3%.

(4-1)

The Dittus-Boelter (1), found in Incropera [2002] and shown in Equation 3-19, is a

modified version of the original correlation Dittus-Boelter (2), found in Kakaç [1987]. For the

smooth channel benchmarking, the Nusselt number at the lowest Reynolds was 4.0% different

relative to the Dittus-Boelter (1) correlations. At the highest Reynolds number, the Nusselt

4.08.0 PrRe024.0 ⋅⋅=oNu

50

number deviated by 13.5%. In open literature, Dittus-Boelter (1) is used commonly to define

augmentation, and in the current study it was used to calculate the heat transfer augmentation for

all the configurations. In a smooth, rectangular duct with symmetric heating, the channel Nusselt

number is insensitive to aspect ratio, including very wide channels [Kakaç, 1987].

Benchmarking at an aspect ratio of 4:1 was thereby inconsequential. Kakaç also concluded that

with a smooth channel and symmetric heating, the Nusselt number can be determined to within

±10% of the smooth, circular correlations. The use of the Dittus-Boelter correlations was

significant source of uncertainty. By conducting the smooth channel testing, any heat transfer

enhancements can be attributed to the addition of the rib turbulators.

0

20

40

60

80

100

0 5 10 15 20 25 30 35 40

Current StudyDittus-Boelter (1) [Incropera]Dittus-Boelter (2) [Kakac]Nusselt [Kakac]Drexel & McAdams [Kakac]Gnielinski [Incropera]

Nu

Re [103]

Figure 4-1. Channel average Nusselt number results for a smooth channel plotted with

smooth, turbulent, fully developed heat transfer correlations.

In addition to heat transfer data, friction factor was calculated and compared with open

literature correlations. In Figure 4-2, the channel friction factor is plotted with various turbulent,

fully developed correlations for a smooth channel. The maximum percent difference between

the channel friction factor and Blasius correlation, shown in Equations 3-22 and 3-23, was 12.4%

at the highest Reynolds number. At the lowest Reynolds number, the percent difference was

2.7%. Unlike the Nusselt comparison, the percent difference in friction factor increased with

51

increasing Reynolds. Correlations indicated that as the aspect ratio of the smooth channel

increased, the friction factor would increase [Kakac, 1987]. This trend was also observed once

ribs were introduced to the channel.

0

0.01

0.02

0.03

0.04

0.05

0 5 10 15 20 25 30 35 40

Current StudyBlasius [Incropera]Colebrook [Kakac]Drew et al. [Kakac]Kakac [Kakac]

f

Re [103]

Figure 4-2. Channel friction factor results plotted with smooth, turbulent, fully developed

correlations.

To ensure that the ribbed channel measurements would be characterized accurately in the

experiments, benchmarking was done against a study published by Wright et al. [2004]. To

quantitatively compare the Wright results with those obtained in the current study, the non-

dimensional parameters of the test section and ribs were matched. Both studies had an aspect

ratio of 4:1 with ribs on two opposing walls. The ribs were square in cross-section with a rib

height-to-channel height ratio of e/H = 0.125. All ribs were parallel spanning the width of the

channel and placed at a 45° angle to the flow. Figure 3-3, in the previous chapter, showed the

benchmark rib configuration in the channel. Only the ribbed walls were heated, and the sidewall

remained unheated consistent with Wright’s test facility. Testing was done to ensure the heat

transfer remained independent of the sidewall heating. In Figure 4-3, the heat transfer

augmentation along the centerline of the channel is plotted for a test run with heated sidewalls

and a test run with unheated sidewalls. There is a negligible difference in the heat transfer

52

augmentation, and the remaining cases were run without the sidewalls heated consistent with

Wright.

0

1

2

3

4

5

0 2 4 6 8 10 12

Heated Sidewalls: Top Endwall

Heated Sidewalls: Bottom Endwall

Unheated Sidewalls: Top Endwall

Unheated Sidewalls: Bottom Endwall

Nu

Nuo

x

DH

Figure 4-3. For the benchmark square rib case, two tests were run at Re=30000 to verify

heating the sidewalls did not effect the heat transfer augmentation. The

augmentation development along the centerline of the channel was the same

regardless of whether the sidewalls were heated.

The current study was scaled up four times from the Wright experiment for ease of

manufacturing the components and overall test facility compatibility. In addition to the physical

non-dimensional parameters, the flow conditions were also matched. Both studies had unheated

entrance lengths and a heated test section that was 7.5DH long. This heated length corresponded

to testing over nine rib pitches.

Wright et al. used a constant surface temperature boundary condition on the two ribbed

walls. This boundary condition was achieved by using 0.32 cm thick copper plates with heaters

on the backside. Each copper plate had an embedded thermocouple, which measured the block

temperature. From each thermocouple reading, an average augmentation value was calculated

for that copper block. Prior to testing, Wright et al. conducted a Biot analysis to ensure the

lumped capacitance model was accurate. There were 24 blocks in the channel, and all the

individual copper block augmentations were averaged to obtain a channel-averaged

augmentation.

53

The current study used a constant surface heat flux boundary condition, which was

achieved with the foil heaters. The thermocouple readings in a constant surface heat flux

boundary condition experiment are not spatial averages but rather represent only a point value.

Therefore, the thermocouple reading was sensitive to its placement relative to the rib, which is

not the case with a constant surface temperature boundary condition. To have an accurate

comparison with Wright et al.’s results, the IR spatially averaged values were used from the fully

developed region. Spatially averaged augmentations are an average of the entire channel

endwall and thus are directly comparable with Wright et al.’s results.

In addition to the Wright study, Mahmood et al. [2002] used nearly the same

configuration, but collected the temperature data using infared camera thermography instead of

the lumped capacitance method. The difference between the current study and Mahmood et al. is

the rib orientation. Instead of parallel in the case of the current study, where the ribs are angled

the same direction on each endwall, the Mahmood configuration had crossed ribs of

perpendicular angles on each endwall. Figure 4-4 illustrates the difference between a parallel

and crossed rib orientation. Because the remaining rib configuration parameters are the same,

the results of the Mahmood et al., Wright et al., and the current study are compared for

benchmarking. Table 4-1 shows a summary of the parameters in the current study, Wright et al.,

and Mahmood et al.

Figure 4-4. Difference between crossed (Mahmood [2003]) and parallel (current study) rib

orientation is the angle of attack of each side of the channel.

Crossed Orientation Parallel Orientation

Ribs on top wall Ribs on bottom wall

54

Table 4-1 Summary of Ribbed Benchmark Configurations

Current

Study

Wright

et al.

Mahmood

et al.

Rib Profile

Rib Shape Angled Angled Angled

Orientation Parallel Parallel Crossed

No. Ribbed Walls 2 2 2

P/e 10 10 10

e/H 0.125 0.125 0.125

AR 4:1 4:1 4:1

α 45° 45° 45°

Measurement

MethodIR Camera

Lumped

CapacitanceIR Camera

The heat transfer augmentations were calculated and compared with the open literature

studies, shown in Figure 4-5. The agreement is within the uncertainty reported by Wright and

the uncertainty calculated for this experiment, but the values were consistently higher for the

current study. The range of Reynolds numbers was defined by the data available in the Wright et

al. study. At the highest Reynolds number of 40,000, the augmentation was 2.8, and Wright

reported an augmentation of 2.3. Both the current study and Mahmood et al. found an

augmentation of 2.9 at a Reynolds number of 26,000. For the low Reynolds number of 12,000,

the augmentation was 3.3, while Wright and Mahmood both reported augmentations for

Reynolds as low as 10,000, with augmentations 2.7 and 3.4, respectively. Between Wright and

the current study the trend seen was similar, and the actual values were within the 10%

uncertainty of the augmentation value, although consistently higher. However, Mahmood and

the current study reported similar trends and similar augmentation levels.

55

0

1

2

3

4

5

0 10 20 30 40

Current Study

Wright [2004]

Mahmood [2002]

Nu

Nuo

Re [10-3

]

Figure 4-5. Heat transfer augmentation for the benchmark case compared with Wright et al.


Heat transfer augmentation contours for the benchmark study are shown in Figure 4-6a

and Figure 4-6b. Immediately downstream of the rib, the heat transfer augmentation decreased

due to the presence of a recirculating flow. Moving further downstream from the rib, the

augmentation increases due to the reattachment of the boundary layer. Mahmood et al. [2002]

reported a small area of recirculation just upstream of the rib. This was not easily observed in

the current study because of the resolution of the images. In Mahmood et al.’s study, the

viewing area was concentrated on one rib, not several rib pitches; therefore, they were able to

finely resolve the near-rib area of the endwall.

56

Figure 4-6a. Augmentation contours show the endwall heat transfer for the benchmarking

configuration.

Re=307831

2

3

4

5

6

7

Top Endwall Bottom Endwall

Re=25064

Re=30954

Re=39175

Nu

Nuo

Nu

Nuo

57

Figure 4-6b. Augmentation contours show the endwall heat transfer for the benchmarking

configuration.

A heat transfer augmentation contour from Mahmood’s study is shown in Figure 4-7.

Behind the rib, the flow formed a vortex that travelled up the length of the angled rib and

impinged on the sidewall. For the current study, the area of highest heat transfer was directly

Re=20876

Re=12892

Re=14038

1

2

3

4

5

6

7

Nu

Nuo

Nu

Nuo

Top Endwall Bottom Endwall

58

downstream of the streamwise leading end of the rib. Here, the rib caused the most disruption of

the flow, and the boundary layer was the least developed. Moving along the angle of the rib, the

boundary layer is free to redevelop until it impinges on the sidewall. The nature of the rib

orientation generated a warmer and cooler side to the channel, shown as lower augmentation and

higher augmentation in the contours of Figure 4-6.

Figure 4-7. Heat transfer augmentation contour, for Re=10,000, from Mahmood et al. [2002],

where the region immediately upstream and downstream of the rib was resolved.

In addition to heat transfer augmentation, friction factor augmentation was compared

with the Wright and Mahmood results shown in Figure 4-8. The variation between the current

study and both the open literature studies was within the uncertainty in the experiment, and the

results in the current study were consistent with findings in open literature. Friction factor

agreement between the current study and the Wright study was very good, with only minimal

deviation at the highest Reynolds number. For Re=40,000, the friction factor was 8.8, and

Wright’s value was 9.0. At the lowest Reynolds number of 12,000, both studies found friction

factors of 7.0. Between Mahmood and the current study, the friction factor augmentation did not

agree as well as the heat transfer data; however, this can be attributed to the difference in rib

59

orientation, crossed versus parallel. From the review of relevant literature, it can be concluded

that rib orientation has a more prominent effect on friction factor than heat transfer. Wright et al.

[2004] reported a heat transfer augmentation change of 0.5 for an orientation change from

parallel to V-shape; however, the friction factor augmentation changed by 1.25. Similarly, Park

et al. [1992] found a greater effect on friction factor augmentation compared with heat transfer

augmentation when the rib angle of attack is changed. For an angle of attack change from 30° to

45°, they reported the friction factor augmentation changed from 6.0 to 11.0, while the heat

transfer augmentation changed only by 0.1.

0

5

10

15

0 10 20 30 40

Current Study

Wright [2004]

Mahmood [2002]

f

fo

Re [10-3

]

Figure 4-8. Friction factor augmentation for the benchmark case compared with Wright et al.


With acceptable agreement between the current experiment and data found in open

literature, the channel and data reduction methods were assumed accurate. Therefore, the

experimentation on the rounded ribs of interest could be conducted.

4.2 Heat Transfer Results with Rounded Ribs

For the rounded rib configurations, the ribs were present on only one side of the channel.

Therefore, the heat transfer results were calculated for the ribbed side, smooth side, and a global

60

channel averaged value. Table 4-2 is a test matrix of all the cases run for the various

configurations. Data from open literature studies was used to validate the trends found in the

current study, and the rib parameters from each are summarized in Table 4-3.

Table 4-2 Test Matrix for All Configurations

Table 4-3 Summary of the Geometries Tested and Compared with Literature for Results

Current

Study

Rhee

et al.

Viswanathan

et al.

Liu

et al.

Kunstmann

et al.

Rib Profile

Rib Shape V-Shape V-Shape Parallel Parallel W-Shape

Continuous No Yes Yes Yes Yes

No. Ribbed Walls 1 2 2 2 1

P/e 5, 10 10 10 5, 10 10

e/H 0.20 0.06 0.10 0.125 0.4 - 0.12

AR 2.86:1, 5:1 3:1 1:1 1:2 2:1 - 8:1

α 45° 60° 45° 45° 45°

The testing focused on investigating the effect of changing pitch between 5 and 10 and

also changing aspect ratio between 2.86 and 5. The result in Figure 4-9 shows that an increase in

pitch from 5 to 10 caused decreases in heat transfer. As the spacing between the ribs varied, the

boundary layer redevelopment changed. With a large space between ribs (higher P/e), the

boundary layer is able to reattach to the endwall and grow. It is then disturbed again by the next

rib. As that spacing is decreased, the boundary layer does not have the necessary length to

redevelop. High heat transfer is associated with a thin boundary layer; therefore, smaller pitches

yield the best heat transfer. If the rib spacing becomes too small, however, the boundary does

not reattach between the ribs, causing a significant reduction in the heat transfer benefit. Ribs

Rib

Orientation

Rib

Shape

Aspect

Ratio

Pitch-to-Height

Ratio

Blockage

Ratio

No. of

Heated Ribs

Entry Length-

to-Hydrualic Diameter

w/H P/e e/H Lentry/DH





parallel square 4.0 10 0.13 9 17.7

61

not only alter the flow to enhance heat transfer, they also conduct heat away from the endwall.

With a smaller pitch, there are more ribs in a channel and thus more surface area available to pull

heat away from the endwall.

0

1

2

3

4

5

0 10 20 30 40

Current Study: P/e=10, AR=2.86:1, e/H=0.2Current Study: P/e=5, AR=2.86:1, e/H=0.2Current Study: P/e=10, AR=5:1, e/H=0.2Current Study: P/e=5, AR=5:1, e/H=0.2Liu: P/e=10, AR=1:2, e/H=0.125Liu: P/e=5, AR=1:2, e/H=0.125

Nu

Nuo

Re [10-3

]

Figure 4-9. The effect of increasing the pitch is an increase in heat transfer. This increase is

more prominent at lower Reynolds numbers, as shown by the current study ribbed

results (AR=5:1, e/H=0.2) and a Liu et al. [2006] study.

Liu et al. [2006] showed for the same pitch change, 5 to 10, at Re=10,000 the effect was a

decrease in ribbed side augmentation of 0.8, while at Re=40,000 the ribbed side augmentation

decrease was 0.3. Similar magnitudes and trends were observed in the current study: as

Reynolds increased, the effect of pitch on augmentation decreased. In the current study, for the

aspect ratio 2.86:1 configuration, at Re=12,000, the pitch change on augmentation was 0.6 and

decreased to a change on augmentation of 0.2 at Re=40,000. Figure 4-9 shows the agreement

between the current study and Liu et al.’s results with the magnitude of augmentation change

associated with a pitch change of P/e=10 to P/e=5 being very similar. For the aspect ratio case

5:1, at Re=12,000, the change in augmentation was 0.8, and the change at Re=40,000 was 0.4.

For ribbed side data, the pitch effect was similar regardless of aspect ratio.

62

Immediately behind the rib there is a region of recirculation and consequently lower heat

transfer. The contours of the ribbed endwall in Figure 4-10 show the flow encountered the V-

shaped rib, and the area of highest heat transfer occurred at the tip of the V. Here the greatest

disturbance to the flow occured. The rib-induced secondary flow generated a vortex moving

along the rib and impinged on the sidewall. Flow then moved up the sidewall and curled back

done toward the center of the channel. That large vortex entrained cooler fluid from the center of

the channel and brought it back down to the endwall. Figures 4-11 through 4-14 show the ribbed

side heat transfer augmentation contours for all the cases run. Figures 4-15 through 4-18 show

the unribbed side heat transfer augmentation contours for each case. The number of ribs visible

for each case varied because the window was a fixed size, and as the pitch increased or

decreased, the number of visible ribs changed. Because the rounded rib configurations had ribs

on only one side, an interesting effect of aspect ratio was discovered.

1 1.5 2 2.5 3 3.5 4 4.5 5

Re=24000 Re=12000

Figure 4-10. Contours from AR=5:1, e/H=0.2, P/e=5 show the secondary flow induced by the

V-shape ribs.

Open literature work suggests that aspect ratio has no effect on heat transfer

augmentation; however, nearly all the relevant studies used a two ribbed wall configuration

including [Han and Park, 1988], [Rhee et al., 2003], [Kim et al., 2007], and [Huh et al., 2008].

63

With the blockage ratio held constant at e/H=0.2, the aspect ratio was varied from 2.86 to 5.

This was accomplished by having two sets of ribs because as the channel height changed, the

blockage ratio changed if the physical rib was not also changed. In the current study, changing

the aspect ratio had no effect on the ribbed wall augmentation, which is consistent with previous

study’s ribbed wall results. However, an aspect ratio effect was observed on the unribbed, or

smooth side, of the channel. Kunstmann et al. [2009] showed that in a one-ribbed wall channel,

the effects of channel aspect ratio variation were apparent on the unribbed wall of the channel.

They found as the aspect ratio decreased, the heat transfer augmentation decreased, which is

consistent with the findings in the current study.

Re=24000

Nu

Nuo

Nu

Nuo

Re=18000

Re=35000 Re=30000

Re=13000

Re=40000

1

1.5

2

2.5

3

3.5

4

4.5

5


64

Nu

Nuo

Nu

Nuo

Re=38000

Re=24000

Re=34000

Re=18000

Re=30000

Re=12000 1

1.5

2

2.5

3

3.5

4

4.5

5


Re=40000 Re=35000 Re=30000

Re=24000 Re=12000Re=17000

Nu

Nuo

Nu

Nuo

1

1.5

2

2.5

3

3.5

4

4.5

5


65

Re=35000

Re=17000

Re=40000

Re=24000

Nu

Nuo

Nu

Nuo

1

1.5

2

2.5

3

3.5

4

4.5

5

Re=30000

Re=12000



66



67


For the same pitch, changing the aspect ratio from 2.86 to 5 did not produce a change in

the ribbed side heat transfer augmentation, as seen in Figure 4-19. Rhee et al.’s data is also

shown, which also found the aspect ratio had minimal effect on heat transfer for the ribbed side

of the channel.

68

0

1

2

3

4

5

0 10 20 30 40

Current Study: AR=2.86:1, P/e=10, e/H=0.2

Current Study: AR=5:1, P/e=10, e/H=0.2

Current Study: AR=2.86:1, P/e=5, e/H=0.2

Current Study: AR=5:1, P/e=5, e/H=0.2

Rhee: AR=3:1, P/e=10, e/H=0.06

Rhee: AR=5:1, P/e=10, e/H=0.1

Rhee: AR 6.82:1, P/e=10, e/H=0.14

Nu

Nuo

Re [10-3

]

Figure 4-19. Comparing Rhee et al. [2003] with the current study confirms that no aspect ratio

effect was expected on the ribbed side heat transfer augmentation; however, an

increase in pitch from 5 to 10 decreased heat transfer.

In Figure 4-20, the current study smooth side augmentation is shown, and a difference in

augmentation appeared when the aspect ratio was varied. Kunstmann et al.’s [2009] unribbed

side augmentation results are in Figure 4-21, and a similar trend is identified; the highest

augmentation occurred at the highest aspect ratio.

69

0

1

2

3

4

5

0 10 20 30 40

P/e=5, AR=2.86, e/H=0.2P/e=10, AR=2.86, e/H=0.2P/e=5, AR=5, e/H=0.2P/e=10, AR=5, e/H=0.2

Nu

Nuo

Re [10-3

]

Figure 4-20. The smooth side augmentation shows that when only one-wall of the channel was

ribbed, the aspect ratio had an effect of the augmentation. As the aspect ratio

increased, the smooth wall heat transfer decreased.

0

1

2

3

4

5

0 100 200 300 400 500

Kunstmann: AR=8:1, P/e=10, e/H=0.12



Nu

Nuo

Re [10-3

]

Figure 4-21. Kunstmann et al. [2009] tested W-shape ribs in a one-ribbed wall channel; the

unribbed side heat transfer augmentation reflected an aspect ratio effect where the

largest aspect ratio has the highest augmentation.

70

This finding was expected given that aspect ratio defines the distance between the two

endwalls. As the aspect ratio decreased the endwalls became further apart. So, as the sidewall

height increased, the impinging flow had more length to develop a boundary layer on the

sidewall and also to entrain cooler core fluid from the center of the channel. In Figure 4-22, the

smooth wall contours show higher augmentation levels near the sidewall. Centerline

augmentation was the same for both aspect ratios, approximately 1.9. For the 5:1 aspect ratio,

however, the near wall augmentation peaked at 2.5, while the 2.86:1 aspect ratio case peaked at

3.0. The grey ribs in the image indicate where the ribs were on the opposite endwall. The cell

downstream of the rib is an area of higher augmentation, the result of the large vortex caused by

the flow travelling along the rib and along the sidewall.

Figure 4-22. Smooth wall contours for Re=30,000, P/e=10, e/H=0.2 show the lower aspect

ratio had higher heat transfer near the sidewall.

Because the global channel average was an area-weighted average of the ribbed side,

smooth side, and sidewalls, the global average reflected an aspect ratio effect. The Nusselt

number was not measured on the sidewalls. To calculate the channel average the Nusselt

number, the unribbed wall Nusselt number was applied to the sidewall areas. Figure 4-23 shows

the augmentation for the ribbed side, global average, and unribbed side for the aspect ratio 2.86

cases.

71

0

1

2

3

4

5

0 10 20 30 40

Ribbed: P/e=10, AR=2.86:1, e/H=0.2Global Average: P/e=10, AR=2.86:1, e/H=0.2Unribbed: P/e=10, AR=2.86:1, e/H=0.2Ribbed: P/e=5, AR=2.86:1, e/H=0.2Global Average: P/e=5, AR=2.86:1, e/H=0.2Unribbed: P/e=5, AR=2.86:1, e/H=0.2

Nu

Nuo

Re [10-3

]

Figure 4-23. The ribbed side, unribbed side, and channel average augmentation for the 2.86:1

aspect ratio cased.

Likewise, Figure 4-24 shows the 5:1 aspect ratio cases. The global channel averaged

augmentation shown in Figure 4-25 indicated there was a decrease in heat transfer as the aspect

ratio increased, due to the smooth wall contribution.

72

0

1

2

3

4

5

0 10 20 30 40

Ribbed: P/e=10, AR=5:1, e/H=0.2Global Average: P/e=10, AR=5:1, e/H=0.2Unribbed: P/e=10, AR=5:1, e/H=0.2Ribbed: P/e=5, AR=5:1, e/H=0.2Global Average: P/e=5, AR=5:1, e/H=0.2Unribbed: P/e=10, AR=5:1, e/H=0.2

Nu

Nuo

Re [10-3

]

Figure 4-24. The ribbed side, unribbed side, and channel averaged augmentation for the 5:1

aspect ratio cases.

0

1

2

3

4

5

0 10 20 30 40

P/e=5, AR=2.86, e/H=0.2

P/e=10, AR=2.86, e/H=0.2

P/e=5, AR=5, e/H=0.2

P/e=10, AR=5, e/H=0.2

Nu

Nuo

Re [10-3

]

Figure 4-25. Channel-averaged heat transfer augmentation reflects the smooth wall

contribution; therefore, the channel average does showed aspect ratio effect for

this rib orientation.

73

The heat flux typically is calculated by using the planform area of the heater; when used

in the heat transfer data reduction, this calculation shows the heat transfer enhancement relative

to a smooth channel. However, if the data is reduced with the total wetted surface area, then the

results indicate the true heat transfer enhancement of the channel because the advantage of the

additional surface area is removed. Using the total wetted surface areas caused a reduction in the

augmentation seen in Figures 4-26 and 4-27, which are the results for the ribbed side of the

channel with a pitch of 10 and 5, respectively.

0

1

2

3

4

5

0 10 20 30 40

Wetted Area: P/e=10, AR=5, e/H=0.2

Planform Area: P/e=10, AR=5, e/H=0.2

Wetted Area: P/e=10, AR=2.86, e/H=0.2

Planform Area: P/e=10, AR=2.86, e/H=0.2

Nu

Nuo

Re [10-3

]



74

0

1

2

3

4

5

0 10 20 30 40





Nu

Nuo

Re [10-3

]



Figure 4-28 shows the augmentation for the unribbed side of the channel for all

configurations, and there is no variation between the total wetted area and planform area results.

This result was expected because the wetted area equaled the planform area on the smooth side

of the channel. Finally, Figures 4-29 and 4-30 show the global average results for configurations

with pitch of 10 and 5, respectively. Liu et al.’s [2006] results indicated that when the total

wetted area was used, configurations of different aspect ratio would converge to one heat transfer

augmentation value. Because the smooth side results in the current study did not shift with the

area change, but the ribbed side results decreased, the global channel average also decreased.

The magnitude of the decrease in the average results was less than the shift on the ribbed side of

the channel. The smooth wall contribution affected the global results in a manner that is not

typically observed in the relevant literature studies due to the one-ribbed wall rib orientation of

the current study but does agree with Liu et al..

75

0

1

2

3

4

5

0 10 20 30 40









Nu

Nuo

Re [10-3

]

Figure 4-28. Unribbed side heat transfer results for all cases show minimal change in


As the Reynolds number increased, heat transfer augmentation decreased, as seen in

Figures 4-29 and 4-30. This outcome occurred because at lower Reynolds numbers, the ribs

significantly altered the turbulent mixing. As Reynolds number increased, the effect of the rib

on convective transport was less prominent; hence, the increase resulted in lower augmentation

as Reynolds number increased. In the next section the friction factor augmentation results are

examined.

76

0

1

2

3

4

5

0 10 20 30 40





Nu

Nuo

Re [10-3

]



0

1

2

3

4

5

0 10 20 30 40





Nu

Nuo

Re [10-3

]



77

4.3 Friction Factor Results for Rounded Ribs

Friction factor augmentation increased as Reynolds increased, as shown in Figure 4-31.

As the separation region behind the rib grew with increasing Reynolds number, so did the

pressure drop and, consequently, the friction factor.

0

5

10

15

0 10 20 30 40

P/e=5, AR=2.86, e/H=0.2

P/e=10, AR=2.86, e/H=0.2

P/e=5, AR=5, e/H=0.2

P/e=10, AR=5, e/H=0.2

f

fo

Re [10-3

]

Figure 4-31. Friction factor results for the current study show friction factor increased with

increasing Reynolds. Also, the highest pressure penalty occurred for the P/e=5

and AR=5 configuration.

The conclusion to note is that as aspect ratio increased, with a constant blockage ratio, the

friction factor increased as well. Rhee et al. [2003] also concluded that aspect ratio and friction

factor increased together. Figure 4-32 summarizes the P/e=10 results from the current study and

similar findings from Rhee et al., with respect to change in aspect ratio. While the current study

found that for an aspect ratio change from 2.86 to 5, the friction factor increased by an average of

1.3, Rhee et al. observed a larger increase of 3.5. One reason the Rhee et al. study saw a greater

magnitude change of aspect ratio could be that a different rib shape was used. Rounded ribs are

expected to have a lower pressure drop than square ribs because they reduce the size of the

separation region around the rib. Also, Rhee et al. increased the aspect ratio and the blockage

ratio simultaneously, which is expected to cause higher friction factors.

78

0

2

4

6

8

10

12

0 10 20 30 40

Current Study: P/e=10, AR=2.86:1, e/H=0.2


Liu: P/e=10, AR=1:2, e/H=0.125

Liu: P/e=5, AR=1:2, e/H=0.125

f

fo

Re [10-3

]

Figure 4-32. Comparing the current study with the Rhee et al. [2003] showed similar aspect

ratio trends; as AR was changed from 5 to 2.86, the friction factor decreased.

Measurements indicated as pitch increased, the friction factor decreased. This is the

same trend observed in the heat transfer results. Comparing Liu et al. [2006] results with the

current study in Figure 4-33 showed a similar effect of pitch. The effect of pitch was consistent

as Reynolds number changed. The pressure drop increased with decreasing pitch (more ribs in

the channel), causing an increase in friction factor augmentation. While the magnitude of the

Liu et al.’s results was not consistent with the current study, the same rib configuration was not

tested. The literature suggests pressure drop is more sensitive to rib and channel orientation than

heat transfer, so it is not expected that the friction factor augmentation would agree.

Viswanathan and Tafti’s [2005] computational study found the rounded rib friction factor was

33% different than square ribs for the same configuration; however, no noticeable effect on heat

transfer was noted.

79

0

2

4

6

8

10

12

0 10 20 30 40



Liu: P/e=10, AR=1:2, e/H=0.125

Liu: P/e=5, AR=1:2, e/H=0.125

f

fo

Re [10-3

]

Figure 4-33. A comparison of friction factor augmentation for the current study with Liu et

al.’s [2006] study shows that as pitch increased, friction factor decreased.

80

Chapter 5

CONCLUSIONS

The results collected during this study contribute to the improved development of rib

turbulated channels for turbine blade cooling. Ribbed channels are the standard method of

internal cooling in the mid-portion of the turbine blade. The goal was to maximize the heat

transfer while minimizing the pressure loss. Endwall heat transfer measurements were reduced

from thermocouples and infared camera images to augmentation levels. The friction factor was

also calculated from the pressure drop in the channel. The pitch-to-rib heights studied were 5

and 10, and the aspect ratios of interest were 2.86:1 and 5:1. For all the cases, the rib height-to-

channel height was kept constant at 0.2. All the rounded rib configurations were 45°,

discontinuous V-shapes on one-wall of the channel.

A test section was designed specifically for this study, and it was compatible with an

existing test facility in the lab. The channel width was constant, but to accommodate various

aspect ratios, the height of the channel walls changed. Two set of ribs were milled so that as the

channel height changed, the blockage ratio remained constant.

Infared camera thermography was used to collect temperature measurements in the fully

developed region of the channel. Temperature maps were calibrated and reduced to

augmentation contours. The rib spacing results are summarized in Section 5.1. Section 5.2

presents the aspect ratio results. The effect of using planform versus total wetted area in the data

reduction is reviewed in Section 5.3. Finally, the recommendations for future work are made in

Section 5.4.

5.1 Rib Spacing Effects

Heat transfer augmentation with a P/e=5 was higher than that of P/e=10. For the ribbed

wall and the unribbed wall, a smaller pitch consistently yielded higher heat transfer

augmentation. The ribbed wall contours showed that the highest heat transfer occurred

immediately behind the break in the V-shape. As the flow moved downstream from the rib

toward the next rib, the heat transfer augmentation gradually decreased. With a smaller P/e ratio,

the distance between the ribs was small enough that the next rib was able to disturb the boundary

layer before it fully redeveloped. Also, with more ribs present in a given length, there was more

surface area to conduct heat away from the metal.

81

Regarding friction factor augmentation, the P/e=5 cases had higher values than the

P/e=10. For the same reason a smaller pitch has higher conduction, the friction factor was higher

because there were more obstacles in the path of the flow.

5.2 Aspect Ratio Effects

No aspect ratio effect was found on the ribbed side augmentation as aspect ratio changed

from 2.86:1 to 5:1. The unribbed side of the channel had higher augmentation for the 2.86:1

cases relative to the 5:1 cases. Because of definition of the global average, it also reflected an

aspect ratio change similar to the unribbed wall. This finding was not typically observed in the

literature; however, most studies had two-ribbed wall orientations. If the current study had two-

ribbed walls, there would be no aspect ratio effect present. Cooler core fluid was entrained as

the boundary layer developed along the channel sidewalls. For a smaller aspect ratio, the

channel sidewall was longer. Contour data supports this theory: the unribbed contours showed a

cell of higher augmentation on the unribbed side of the channel. For the 2.86:1 aspect ratio

cases, this cell had higher augmentation than the 5:1 cases. When there were ribs present on

both of the walls, this subtle effect of aspect ratio was overcome by the presence of the additional

rib turbulators.

Aspect ratio also had an effect on friction factor augmentation. The aspect ratio of 5:1

had a higher friction factor augmentation than the 2.86:1 case. This is because the channel

height is lower for AR=5. Even with the same blockage ratio, the flow is more constricted,

causing greater pressure loss.

5.3 Area Effects

When the planform area was used in determining heat flux, the results indicated how well

the rib orientation improved heat transfer relative to a smooth channel. If the total wetted area

was used, the results were independent of the additional surface area each orientation adds.

Generally, most studies use the planform area in order to quantitatively compare different rib

orientations. When the rib configuration is changed, the benefit of that increase or decrease in

surface area is what the researchers are investigating.

Using the total wetted area reduced the heat transfer augmentation when compared with

the planform area results. Previous work has shown that for a given configuration, when the

82

aspect ratio of the channel was changed, the results collapsed on a single value. This study did

not observe this effect because the configuration had only one-ribbed wall; therefore, the percent

increase in area between planform and wetted was much less than in a two-ribbed wall study.

5.4 Recommendations for Future Work

Internal cooling methods, in particular rib turbulated channels, are of increased

importance in advancing gas turbine efficiency and power output. Much work has been and will

continually be done to improve the heat transfer in these channels, while minimizing the pressure

loss.

Many researchers have studied the combined effect of varying blockage and aspect ratio

together. There is limited data available on the isolated effects of one or the other, on heat

transfer and friction factor. Manufacturing multiple sets of ribs or multiple sidewalls would be

required to accomplish this work. That becomes material, time, and cost intensive, but it would

be valuable information for rib turbulated channel designers. Furthermore, the effect of one

versus two ribbed walls in a channel needs further investigation. Aspect ratio effects were

discovered unexpectedly because of the one-ribbed wall orientation used in this study.

Future work also needs to focus on the use of infared thermography for temperature

mapping. The current work images the back side of the heater; however, imaging the top side of

the heater would provide heat transfer data on the rib surface. By imagine the backside of the

heater, researchers are assuming the rib is at a uniform temperature. Imaging the top side of the

heater and ribs would eliminate that assumption. Another useful piece of information would be

augmentation data, in the form of contours, in the thermally and hydrodynamically developing

region of the channel. This could be accomplished by creating several areas where the zinc s

elenide window could be installed and temperature maps collected.

83

References

Abdel-Wahab, S., Tafti, D., 2004, “Large Eddy Simulation of Flow and Heat Transfer in a

Staggered 45 degree Ribbed Duct,” GT2004-53800.

Ames, F.E., Nordquist, C.A., and Klennert, L.A., 2007, “Endwall Heat Transfer Measurements

in a Staggered Pin Fin Array with an Adiabatic Pin,” GT2007-27432.

Bunker, R.S., 2008, “The Effects of Manufacturing Tolerance on Gas Turbine Cooling,”

GT2008-50124.

Chanteloup, D., Juaneda, Y., Bolcs, A., 2002, “Combined 3D Flow and Heat Transfer

Measurements in a 2-pass Internal Coolant Passage of Gas Turbine Airfoils,” GT2002-30214.

Cho, H.H., Kim, Y.Y., Kim, K.M., Rhee, D.H, 2003, “Effects of Rib Arrangements and Rotation

Speed on Heat Transfer in a Two-Pass Duct,” GT2003-38609.

Cotronics, 2008, “DURALCO 132 - 500ºF Thermally Conductive Adhesive,”

http://www.cotronics.com/vo/cotr/pdf/132.pdf (Brooklyn, New York: Cotronics 2008).

Diette, C., Arts, T., Sgarzi, O., Laroche, E., 2004, “Investigation of a High Aspect Ratio

Rectangular Channel with High Blockage Ratio Round-Corner Ribs,” GT2004-53163.

Graham, A., Sewall, E., Thole, K., 2004, “Flowfield Measurements in a Ribbed Channel

Relevant to Internal Turbine Blade Cooling,” GT2004-53361.

Han, J.C., Park, J.S., 1988, “Developing heat transfer in rectangular channels with rib

turbulators,” Int. J. Heat Mass Transfer, Vol. 31, No. 1, pp. 183-195.

Han S., Goldstein R.J., 2005, “Influence of Blade Leading Edge Geometry on Turbine

Endwall Heat(Mass) Transfer,” GT2005-68590.

Hill, P.G., and Peterson, C.R., 1992, “Mechanics and Thermodynamics of Propulsion,”

2nd Edition. Reading, Massachusetts: Addison-Wesley Publishing Company Inc.

Huh, M., Liu, Y.H., Han, J.C., Chopra, S., 2008, “Effect of Rib Spacing on Heat Transfer in a

Two-Pass Rectangular Channel (AR=1:4) with a Sharp Entrance at High Rotation Numbers,”

GT2008-50311.

Incropera, F.P., DeWitt, D.P., 2002, “Fundamentals of Heat and Mass Transfer,” 5th Edition,

New York, New York: John Wiley & Sons, Inc.

Jang, Y.J., Chen, H.C., Han, J.C., 2001, “Flow and Heat Transfer in a Rotating Square Channel

With 45 deg Angled Ribs by Reynolds Stress Turbulence Model,” Transactions of ASME, Vol.

123, pp. 124-132.

84

Johnson, B.V., Wagner, J.H., Steuber, G.D., Yeh, F.C., 1994, “Heat Transfer in Rotating

Serpentine Passages With Trips Skewed to the Flow,” J. Turbomachinery, Vol. 116, pp. 113-

123.

Kim, K.M., Park, S.H, Jeon, Y.H., Lee, D.H., Cho, H.H., 2007, “Heat/Mass Transfer

Characteristics in Angled Ribbed Channels with Various Bleed Ratios and Rotation Numbers,”

GT2007-27166.

Kakaç, S., Shah, R.K., Aung, W., 1987, Handbook of Single-Phase Convective Heat Transfer,

New York, New York: John Wiley & Sons, Inc.

Kline, S.J., McKlintock, F.A., 1953, “Describing Uncertainties in Single-Sample

Experiments,” Mech. Eng., Vol. 75, pp. 3-8.

Kunstmann, S., von Wolfersdorf, J., Ruedel, U., 2009, “Heat Transfer and Pressure Loss in

Rectangular One-Side-Ribbed Channels with Different Aspect Ratios,” GT2009-59333.

Lambda Square Inc., 2008, “Oripac Model 4150-P Specification Sheet,”

http://www.lambdasquare.com/oripac/4150p_spec.asp (Babylon, New York: Lambda Square

Inc. 2008).

Lee, E., Wright, L.M., Han, J.C., 2005, “Heat Transfer in Rotating Rectangular Channels with V-

Shaped and Angled Ribs,” J. Thermophysics and Heat Transfer, Vol. 19, No. 1, pp. 48- 56.

Liou, T.M., and Hwang, J.J., 1993, “Effect of ridge shapes on turbulent heat transfer and friction

factor in a rectangular channel,” Int. J. Heat Mass Transfer, Vol. 36, No. 4, pp. 931-940.

Liu, Y.H., Wright, L.M., Fu, W.L., Han, J.C., 2006, “Rib Spacing Effect on Heat Transfer and

Pressure Loss in a Rotating Two-Pass Rectangular Channel (AR=1:2) with 45-Degree Angled

Ribs,” GT2006-90368.

Lyall, M.E., 2006, “Heat Transfer from Low Aspect Ratio Pin Fins,” Master’s Thesis,

Department of Mechanical Engineering, Virginia Polytechnic Institute and State University.

Mahmood, G.I., Ligrani, P.M., Won, S.Y., 2002, “Spatially-Resolved Heat Transfer and Flow

Structure in a Rectangular Channel with 45° Angled Rib Turbulators,” GT2002-30215.

Maurer, M., von Wolfersdorf, J., 2006, “An Experimental and Numerical Study of Heat Transfer

and Pressure Loss in a Rectangular Channel with V-shaped Ribs,” GT2006-90006.

Meriam Instruments, 2008, “2100 Series Smart Gauge,”

http://www.meriam.com/downloads/pdf/DataSheets/smartgauges_datasheet.pdf (Cleveland,

Ohio: Meriam Process Technologies, 2008).

Moffat, R.J., 1985, “Uncertainty Analysis in the Planning of an Experiment,” J. of Fluids

Engineering, Vol. 107, pp. 173-181.

85

Ostanek, J.O., 2008, “Establishing a Methodology for Resolving Convective Heat Transfer from

Complex Geometries,” Master’s Thesis, Department of Mechanical and Nuclear Engineering,

The Pennsylvania State University.

Papa, M., Goldstein, R.J., Gori, F., 2002, “Effects of Tip Geometry and Tip Clearance on the

Heat/Mass Transfer From a Large-Scale Gas Turbine Blade,” GT2002-30192.

Park, J.S., Han, J.C., Huang, Y., Ou, S., 1992, “Heat transfer performance comparisons of five

different rectangular channels with parallel angled ribs,” Int. J. Heat Mass Transfer, Vol. 35, No.

11, pp. 2891-2903.

Rallabandi, A.P., Alkhamis, N., Han, J.C., 2009, “Heat Transfer and Pressure Drop

Measurements for a Square Channel 45DEG Round Edged Ribs at High Reynolds Numbers,”

GT2009-59546.

Rhee, D.H., Lee, D.H., Cho, H.H., Moon, H.K., 2003, “Effects of Duct Aspect Ratio on

Heat/Mass Transfer with Discrete V-Shaped Ribs,” GT2003-38622.

Setra Systems, 2008, “Model 264 Very Low Differential Pressure Transducer,”

http://www.setra.com/tra/pro/pdf/264.pdf (Boxborough, Massachusetts: Setra Systems 2008a).

Setra Systems, 2008, “Model 370 Ultra-High Accuracy Setraceram™ Digital Barometric

Pressure Gauge,” http://www.setra.com/tra/pro/p_ba_370.htm (Boxborough, Massachusetts:

Setra Systems 2008b).

Stephens, M.A., Shih, T. I-P., 1995, “Computation of Flow and Heat Transfer in a Rectangular

Channel with Ribs,” AIAA 95-0180.

Webb, R.L., and Eckert, E.G., 1972, “Application of Rough Surfaces to Heat Exchangers,” Int. J.

Heat Mass Transfer, Vol. 15, pp. 1647-1658.

Wright, L.M., Fu, W.L., Han, J.C., 2004, “Thermal Performance of Angled, V-shaped,

and W-shaped Rib Turbulators in Rotating Rectangular Cooling Channels (AR=4:1),” J.

Heat Transfer. Vol. 126, pp. 604-614.

Viswanathan, A.K., Tafti, D.K., “Large Eddy Simulation in a Duct with Rounded Skewed Ribs,”

GT2005-68117.

86

Appendix A

Flowrate Calculations

Nomenclature

C = discharge coefficient

Dbore = diameter of the bore [in]

dPori = pressure drop across the orifice [in H2O]

K = flow coefficient

Patm = atmospheric pressure [psi]

PL = pressure on the high side of the orifice [psi]

Qori = volumetric flowrate in the orifice [SCFM]

SG = specific gravity entering the orifice [1 = air]

TB = baseline temperature at standard conditions [60 °F]

TL = temperature on the high side of the orifice [°F]

Y = expansion factor

Greek

β = bore / hydraulic diameter

The volumetric flowrate was measured by using an Oripac model 4150-P calibrated

orifice plate flow meter manufactured by Lambda Square Inc. Of the available flow meters, the

orifice was selected over the venturi tube flow meter because of the low flow rates needed for the

study. The orifice resolved a smaller pressure drop; hence, lower volumetric flow rates. Figure

A-1 shows a sample performance curve for the orifice and venturi. To calculate the volumetric

flow rate through the orifice, Equation A-1 was used.

(A-1)

+

⋅⋅

+

⋅⋅⋅⋅⋅⋅

=

B

atm

L

Loribore

ori

T

SGP

T

PdPYKD

Q

460

703.2

460

703.29816.5

2

87

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0 100 200 300 400 500 600

Orifice

Venturi

Pressure Drop

[in H20]

Qori

[SCFM]

Figure A-1. Sample performance curve for the orifice and venturi flow meters shows the

orifice was better suited for resolving low-flow conditions.

In the equation, PL [psia] and TL [°F] represent the absolute line pressure and temperature

of the flow, respectively. The absolute pressure was measured directly at the high side of the

orifice plate flow meter with a Setra model 264 pressure transducer. A Type E thermocouple

was positioned in the center of the PVC pipe upstream of the orifice to obtain an accurate inlet

temperature. The remaining parameters are as follows: Dbore [m] is the diameter of the orifice, K

is the flow coefficient, Y is the expansion coefficient, dPori [in H2O] is the pressure drop across

the orifice, Patm is the standard atmospheric pressure (14.7 psi), SG is the specific gravity (air =

1), and TB [°F] is the baseline temperature at standard conditions (60 °F). The flow coefficient,

K, is defined in Equation A-2, where C and β are parameters specific to the orifice. Table A-1

offers a summary.

(A-2)

41 β−=

CK

88

The value of K was constant for orifice calculations and was found to be 0.617377.

Finally, the expansion coefficient, Y, is given in Equation A-3.

(A-3)

Table A-1 Parameters for the Orifice and Venturi Flow Meters

Orifice Venturi

bore Dbore 2.50 3.58

discharge coefficient C 0.6084 0.9950

Dbore / Dpipe β 0.4122 0.5903

ValueVariableParameter

( )L

ori

P

dPY

⋅

⋅⋅⋅+−=

4.1

0361.035.041.01 4β

89

Appendix B

Infared Image Data Reduction

Nomenclature

As = surface area [m2]

Bi = Biot number

E = total radiation generated [W/m2]

G = irradiated heat flux [W/m2]


kCu = thermal conductivity of copper, [400 W/mK]

Lc = characteristic length, equivalent to V/As [m]

q"rad = radiative heat flux [W/m2]

Tw = heater temperature [°C]

Tex = background temperature [°C]

V = volume [m3]

Greek

ε = emissivity

ρ = reflectivity

σ = Stefan-Boltzmann constant, 8107.5 −× [W/m2]

Infrared images of the back side of the heater were collected while the test section was at

steady state conditions, as described in Section 3.1. The two 20.3 cm endwalls both had

openings for the Zinc Selenide (ZnSe) window; however, only one window was available for

use. Therefore, the window had to be moved from one side of the channel to the other in order to

image both back sides of the heaters. When the window was not installed in the channel, MDF

inserts were secured in the opening, and then a piece of insulation covered the wooden insert.

When the window was installed but no data was being collected, a piece of insulation was used

to cover the ZnSe window to prevent losses.

For imaging, the insulation was removed, and a picture was saved to the camera. After

one image was taken, the insulation was replaced while the camera processed the saved image;

when the camera was able to take the next image, the insulation was removed and the process

repeated. Five images were collected in order to reduce the precision uncertainty in the

measurements, as is consistent with standard operating procedure in the lab. A ThermaCam P20

Infrared (IR) camera manufactured by FLIR Systems, Inc. was used to capture the images. All

five images were collected over the course of approximately 45 seconds; this time was dictated

by the speed at which the camera was able to reset between saving images.

90

When the IR camera was oriented directly across from the window, a reflection was

generated between the ZnSe surface and the camera lens. However, with the ZnSe window tilted

45° to the flow, the camera could be placed directly across from the window, and the reflection

would have appeared where the MDF endwall was present. Thus, the reflection did not obscure

the viewing area of interest.

In order to properly calculate heat transfer coefficients from the raw IR images, four

calibration thermocouples were placed on the heater surface. The thermocouples were secured to

the back side of the heater with Omegabond thermally conductive cement. Temperatures from

the calibration thermocouples were recorded during the image capture process, and those values

were used to calibrate the images. Figure B-1 shows a raw IR image and the locations of the

calibration thermocouples, identified by the red circles. Accurate calibration required capturing

nearly the entire span of temperatures in the image; therefore, the four calibration thermocouples

were placed in the highest and lowest temperature zones. Placement of the thermocouple was

important not only to capture the full temperature span, but also to ensure that the thermocouple

bead was placed in the middle of an Inconel strip on the heater. If the thermocouple had been

placed between the Inconel strips on the Kapton, it would not have given accurate measurements.

Figure B-1. Raw infared image captured with the Flir camera, for square cross-section ribs,

45° parallel to the flow, P/e=10, e/H=0.125, AR=4:1. The thermocouple

locations, window frame, and ribs are identified.

Thermocouple

Locations

ZnSe Window

Frame

Rib

91

After the images were captured, they were imported to ThermaCam Researcher 2002

(ThermaCam) software from Flir Systems, Inc. In the software various image parameters were

adjusted to match the image readings with the calibration thermocouple readings. Prior to

testing, the Cartesian coordinate location of each calibration thermocouple was identified relative

to the window frame. So regardless of which rib configuration was being tested, the location of

the thermocouples was always known.

The IR camera saved the images in the default color palette of iron, which is an orange

(hot) to purple (cold) color map. In the software the color palette of the images was adjusted to

rain 900, which is a standard red (hot) to blue (cold) color map. Next, the drawing tool was used

to create small circles on the image, placing them at the proper coordinates to emulate the

thermocouples. The readings from the circles then were matched to the actual thermocouple

readings by varying the image parameters.

Infared cameras recorded the radiation heat flux emitted by a surface, and the value can

be determined by Equation B-1:

(B-1)

where E is the total radiation generated, ρ is the reflectivity of the surface, and G is the heat flux

irradiated onto the surface of the heater from the surroundings. In order to understand how the

image parameters affected the recorded surface temperatures, the equation needed to be

manipulated to contain the proper parameters. The Stefan-Boltzmann Law was used to substitute

temperatures for blackbody emittance for E and G, assuming the surroundings acted as

blackbody. Because the heater surface was opaque, the reflectivity was equal to 1 minus the

emissivity, ε, of the surface. Equation B-1 then can be rewritten as Equation B-2:

(B-2)

where σ is the Stefan-Boltzmann constant, Tw is the heater temperature, and Tex is the

background temperature. Finally, the wall temperature was found by rearranging Equation B-2

to Equation B-3:

GEqrad ⋅+= ρ"

( ) 44" 1 exwrad TTq ⋅⋅−+⋅⋅= σεσε

92

(B-3)

This relationship shows how manipulating the image parameters - emissivity and external

temperature - altered the wall temperature. The remaining image parameters - ambient

temperature, transmissivity, and distance - affected how the ThermaCam calculated the radiative

heat flux term [Lyall, 2006].

Some parameters were set to a fixed value based on the ZnSe window properties and the

test section dimensions. Emissivity was set to 0.96, transmissivity was set to 0.7, and the

distance the camera was located from the window was set to 0.8 m. Typically, the ambient

temperature is set to 22 °C; however, for some tests this value needed to be adjusted between

22–30 °C. The main parameter adjusted for calibration was the external (or background)

temperature, which ranged between 18–26 °C. The two temperatures were adjusted until the

image calibration readings were all within 0.2 °C of the thermocouple readings, which was a

value selected based on the precision uncertainty of the thermocouple measurements. Tables B-1

and B-2 show sample calibration results for the case Re=40,000, P/e=5, e/H=0.125, and AR=5:1

(ribbed side and unribbed side, respectively).

( )( )4

1

"" 11

⋅⋅−+⋅= exradw TqT σε

εσ

93


AR=5:1, Ribbed Side

1 2 3 4 5

Transmissivity, τ 0.7 0.7 0.7 0.7 0.7

External Temperature, °C 20.0 20.4 21.2 21.6 21.8

Emissivisty, ε 0.96 0.96 0.96 0.96 0.96

Distance, m 0.8 0.8 0.8 0.8 0.8

Ambient Temperature, °C 22 22 22 22 22

Thermocouple Reading, °C

TA 33.2 33.2 33.2 33.2 33.2

TB 31.1 31.1 31.1 31.1 31.1

TC 34.0 34.0 34.0 34.0 34.0

TD 34.7 34.7 34.7 34.7 34.7

Image Calibration Result, °C

TA,cal 33.2 33.3 33.3 33.3 33.3

TB,cal 31.1 31.2 31.2 31.0 31.1

TC,cal 33.9 34.0 34.0 33.9 33.9

TD,cal 34.5 34.7 34.7 34.7 34.7

Temperature Difference, °C

|TA-TA,cal| 0.03 0.13 0.13 0.13 0.13

|TB-TB,cal| 0.05 0.05 0.05 0.15 0.05

|TC-TC,cal| 0.09 0.01 0.01 0.09 0.09

|TD-TD,cal| 0.18 0.02 0.02 0.02 0.02

Image

94


AR=5:1, Smooth Side

6 7 8 9 10

Transmissivity, τ 0.7 0.7 0.7 0.7 0.7

External Temperature, °C 24.8 21.4 21.4 22.5 23.0

Emissivisty, ε 0.96 0.96 0.96 0.96 0.96

Distance, m 0.8 0.8 0.8 0.8 0.8

Ambient Temperature, °C 30 24 24 24 24

Thermocouple Reading, °C

TE 39.7 39.7 39.7 39.7 39.7

TF 49.2 49.2 49.2 49.2 49.2

TG 49.0 49.0 49.0 49.0 49.0

TH 44.9 44.9 44.9 44.9 44.9

Image Calibration Result, °C

TE,cal 39.7 39.6 39.8 39.8 39.8

TF,cal 49.3 49.1 49.3 49.3 49.3

TG,cal 48.7 49.1 49.1 48.9 48.8

TH,cal 45 44.8 45.0 44.8 44.8

Temperature Difference, °C

|TE-TE,cal| 0.03 0.07 0.13 0.13 0.13

|TF-TF,cal| 0.11 0.09 0.11 0.11 0.11

|TG-TG,cal| 0.20 0.12 0.12 0.08 0.18

|TH-TH,cal| 0.11 0.09 0.11 0.09 0.09

Image

Each image was saved as a Matlab data file, .mat, and imported to Matlab. In order to

reduce the uncertainty, the five images were compiled into one average image. A Matlab code

was written for additional post processing. The code reduced the data by using the same

equations outlined in Section 3.1, at this point each pixel represented a temperature, and from

that temperature a Nusselt number was calculated for each location. Spatial averages were

calculated for either the endwall region or the underside of the rib region, and augmentation

contour maps were generated.

Because the ribs were copper, the temperature profile along the centerline of the bottom

of the rib was assumed to be the lengthwise temperature profile of the rib with a constant

temperature across the span of the rib. In order to assume the rib was a uniform temperature

spanwise, a Biot calculation was performed. Equation B-4 shows the definition of the Biot

number:

(B-4)

Cuk

LchBi

⋅=

95

where h is heat transfer coefficient, Lc is the characteristic length defined as the volume of rib

divided by the surface area of the rib (Lc=V/As), and k is thermal conductivity of the rib

material. The heat transfer coefficient used was an average value representative of the centerline

average of the rib. The Biot number was calculated for highest and lowest Reynolds for each

different size rib. Table B-3 shows the characteristic length and the Biot number calculations for

the three different ribs. Biot values significantly less than 1 validated the assumption that the

copper ribs were at uniform temperature at any time during a transient process. In all cases, the

Biot numbers for both the rounded ribs and the square ribs were much less than 1.

Table B-3 Biot Calculations for Each Rib at High and Low Re Numbers

Rib Re Bi Lc

12,000 2.2E-04

40,000 4.6E-04

12,000 2.4E-05

40,000 5.7E-05

12,000 2.5E-04

40,000 5.4E-04

Rounded Rib

AR = 2.86:1

Square Rib

AR = 4:1

1.5E-03

2.7E-03

1.6E-03

Rounded Rib

AR = 5:1

96

Appendix C

Heat Transfer Uncertainty Calculations

Nomenclature

Aheater = surface area of heater [m2]



H = height [m]

I = current [A]

kair = thermal conductivity of air [W/mK]

Nu = Nusselt number

Nuo = smooth channel Nusselt number, Dittus-Boelter

Pr = Prandtl number

Qori = volumetric flowrate [SCFM or m3/s]


∆T = change in temperature between endwall and flow [K]

ux = uncertainty in the measurement of parameter x

V = velocity [m/s] or voltage [V]

W = width [m]

Greek

µ = dynamic viscosity [kg/m-s]


This appendix shows sample calculations for the heat transfer augmentation uncertainty

calculations. Uncertainty propagates through the calculations; therefore, it was necessary to

account for all the measured values factoring into the final uncertainty value. The uncertainty

associated with the fluid properties was neglected because of the relatively small changes in

temperature and pressure over the length of the test section. Each uncertainty was found by

using the Kline and McKintock [1953] method outlined in Section 3.3.

Reynolds Number

The Reynolds number for this work was based on channel hydraulic diameter and can be

written as:

(C-1)

µ

ρ⋅⋅= HDV

Re

97

where the channel dimensions can be substituted for hydraulic diameter and volumetric flow rate

for velocity. Therefore, the Reynolds number can be rewritten as Equation C-2:

(C-2)

The detailed calculations of volumetric flowrate are presented in Appendix A. Using the

root-sum-square uncertainty method, the uncertainty in Reynolds number is given by Equations

C-3 and C-4.

(C-3)

(C-4)

(C-4)

Table C-1 shows the results for the highest and lowest Reynolds numbers tested.

Table C-1 Uncertainty in Reynolds Number

VariableTarget

ReynoldsValue

Precision

Uncertainty

Bias

Uncertainty

Total

Uncertainty

12,000 13295 - - 564 (4.3%)

40,000 40122 - - 1137 (2.8%)

12,000 49.9 - - 1.6

40,000 150.5 - - 0.6

12,000 14.1 2E-02

40,000 14.1 2E-02

12,000 529.1 4E-01

40,000 527.3 4E-01

12,000 0.4 3E-02

40,000 3.4 3E-02

12,000 2.0E-01 - 7.9E-04

40,000 2.0E-01 - 7.9E-04

12,000 4.1E-02 - 7.9E-04

40,000 4.1E-02 - 7.9E-04

1.6E-03

3.4E-05

0.13.4E-05

7.9E-04

7.9E-04

0.4

2.5E-02

Re

Qstd [m3/s]

PL [psia]

H [m]

TL [°R]

∆P [in H20]

W [m]

( )HW

Q stdori

+⋅

⋅⋅=

µ

ρ2Re

222

Re

ReReRe

⋅

∂

∂+

⋅

∂

∂+

⋅

∂

∂= HWQ

ori

uH

uW

uQ

uori

( ) ( )

( )

2

2

2

2

2

Re

2

22

⋅

+⋅

⋅⋅−

+

⋅

+⋅

⋅⋅−+

⋅

+⋅

⋅

=

Hstdori

Wstdori

Qstd

uHW

Q

uHW

Qu

HWu

ori

µ

ρ

µ

ρ

µ

ρK

98

Heat Transfer Coefficient

The heat transfer coefficient is given by:

(C-5)

Again, the root-sum-square method was used to calculate the uncertainty, given in C-6

and C-7:

(C-6)

(C-7)

The calculations for uncertainty in heat transfer coefficient are presented in Tables C-2

and C-3 for the ribbed and unribbed side of the channel, respectively.

Table C-2 Uncertainty in Heat Transfer Coefficient for the Ribbed Channel Wall

VariableTarget

ReynoldsValue

Precision

Uncertainty

Bias

Uncertainty

Total

Uncertainty

12,000 48.8 - - 0.99 (2.0%)

40,000 105.2 - - 1.51 (1.5%)

12,000 44.2 - 5.0E-03

40,000 73.9 - 5.0E-03

12,000 2.3 - 5.0E-03

40,000 3.8 - 5.0E-03

12,000 0.2 - - 2.0E-04

40,000 0.2 - - 2.0E-04

12,000 10.1 0.2

40,000 13.6 0.21.6E-03 0.2

5.0E-03

Aheater [m2]

∆T [K]

h [W/m2K]

V [V] 5.0E-03

I [A]

( )TA

IVh

heater ∆⋅

⋅=

2222

⋅

∆∂

∂+

⋅

∂

∂+

⋅

∂

∂+

⋅

∂

∂= ∆TA

heater

IVh uT

hu

A

hu

I

hu

V

hu

heater

2

2

2

2

22

⋅

∆⋅

⋅−+

⋅

∆⋅

⋅−

+

⋅

∆⋅+

⋅

∆⋅=

∆T

heater

A

heater

I

heater

V

heater

h

uTA

IVu

TA

IV

uTA

Vu

TA

I

u

heater

K

99

Table C-3 Uncertainty in Heat Transfer Coefficient for the Smooth Channel Wall

VariableTarget

ReynoldsValue

Precision

Uncertainty

Bias

Uncertainty

Total

Uncertainty

12,000 22.7 0.22 (1.0%)

40,000 48.3 0.35 (0.7%)

12,000 44.2 - 5.0E-03

40,000 73.9 - 5.0E-03

12,000 2.3 - 5.0E-03

40,000 3.8 - 5.0E-03

12,000 0.2 - - 2.0E-04

40,000 0.2 - - 2.0E-04

12,000 22.7 0.2

40,000 28.6 0.2

h [W/m2K]

V [V]

∆T [K]

5.0E-03

1.6E-03 0.2

5.0E-03

I [A]

Aheater [m2]

Nusselt Number

Next, the Nusselt number is defined in Equation C-8.

(C-8)

The root-sum-square method yields the following equations for the uncertainty in Nusselt

number:

(C-9)

(C-10)

The uncertainty results for the Nusselt number calculations are summarized in Tables C-4

and C-5 for the ribbed and unribbed side of the channel, respectively.

( )HWk

HWh

k

DhNu

airair

H

+⋅

⋅⋅⋅=

⋅=

2

222

⋅

∂

∂

⋅

∂

∂+

⋅

∂

∂=

hHWNuu

H

Nuu

W

Nuu

h

Nuu

( ) ( )

( ) ( ) ( )

22

2

2

2

222

22

⋅

+⋅

⋅⋅+

⋅

+⋅

⋅⋅+

+⋅

⋅⋅⋅−

+

⋅

+⋅

⋅⋅+

+⋅

⋅⋅⋅−

=

H

air

H

airair

W

airair

Nu

uHWk

WHu

HWk

Wh

HWk

HWh

uHWk

Hh

HWk

HWh

u

K

100

Table C-4 Uncertainty in Nusselt Number for the Ribbed Channel Wall

VariableTarget

ReynoldsValue

Precision

Uncertainty

Bias

Uncertainty

Total

Uncertainty

12,000 127.9 - - 3.7 (2.9%)

40,000 267.3 - - 6.7 (2.5%)

12,000 48.8 - - 0.99

40,000 105.2 - - 1.51

12,000 2.0E-01 - 7.9E-04

40,000 2.0E-01 - 7.9E-04

12,000 4.1E-02 - 7.9E-04

40,000 4.1E-02 - 7.9E-04

h [W/m2K]

Nu

H [m] 7.9E-04

W [m] 7.9E-04

Table C-5 Uncertainty in Nusselt Number for the Smooth Channel Wall

VariableTarget

ReynoldsValue

Precision

Uncertainty

Bias

Uncertainty

Total

Uncertainty

12,000 58.3 - - 1.3 (2.3%)

40,000 123.3 - - 2.7 (2.2%)

12,000 22.7 - - 0.22

40,000 48.3 - - 0.35

12,000 2.0E-01 - 7.9E-04

40,000 2.0E-01 - 7.9E-04

12,000 4.1E-02 - 7.9E-04

40,000 4.1E-02 - 7.9E-04

7.9E-04

H [m] 7.9E-04

W [m]

h [W/m2K]

Nu

Dittus-Boelter Smooth Channel Nusselt Number

The smooth channel Nusselt number can be written as:

(C-11)

The uncertainty is written as:

(C-12)

(C-13)

Table C-6 shows the results for the smooth channel Nusselt number calculations.

4.08.0 PrRe023.0 ⋅⋅=oNu

2

ReRe

⋅

∂

∂= u

Nuu o

Nuo

2

Re2.0

4.0

Re

Pr0184.0

⋅

⋅= uuNu

101

Table C-6 Uncertainty in the Smooth Channel Nusselt Number

VariableTarget

ReynoldsValue

Precision

Uncertainty

Bias

Uncertainty

Total

Uncertainty

12,000 39.9 - - 1.4 (3.4%)

40,000 96.6 - - 2.2 (2.3%)

12,000 13295 - - 564

40,000 40122 - - 1137Re

Nuo

Nusselt Number Augmentation

The heat transfer augmentation was given by Nu / Nuo, and the uncertainty is given by:

(C-14)

(C-15)

Finally, the results for the augmentation uncertainty are presented in Tables C-7 and C-8

for the ribbed and unribbed sides of the channel, respectively.

Table C-7 Uncertainty in Nusselt Number Augmentation for the Ribbed Channel Wall

VariableTarget

ReynoldsValue

Precision

Uncertainty

Bias

Uncertainty

Total

Uncertainty

12,000 3.19 - - 0.14 (4.5%)

40,000 2.72 - - 0.09 (3.5%)

12,000 127.9 - - 3.7

40,000 267.3 - - 6.7

12,000 39.9 - - 1.4

40,000 96.6 - - 2.2

Nu/Nuo

Nuo

Nu

22

⋅∂

∂+

⋅∂

∂= Nu

oNu

o

o

Nu

Nu uNu

NuNu

uNu

NuNu

uo

o

2

2

2

1

⋅

−+

⋅=

o

o

Nu

o

Nu

oNu

Nu uNu

Nuu

Nuu

102

Table C-8 Uncertainty in Nusselt Number Augmentation for the Smooth Channel Wall

VariableTarget

ReynoldsValue

Precision

Uncertainty

Bias

Uncertainty

Total

Uncertainty

12,000 1.52 - - 0.06 (3.9%)

40,000 1.36 - - 0.04 (2.9%)

12,000 58.3 - - 1.3

40,000 123.3 - - 2.7

12,000 39.9 - - 1.4

40,000 96.6 - - 2.2

Nu/Nuo

Nuo

Nu

103

Appendix D

Friction Factor Calculations

Nomenclature

dP = pressure drop [in H20 or Pa]


f = Darcy friction factor

fo = Blasius smooth channel friction factor

H = height [m]

L = length [m]

Qori = volumetric flowrate [SCFM or m3/s]


ux = uncertainty in the measurement of parameter x

V = velocity [m/s]

W = width [m]

Greek

µ = dynamic viscosity [kg/m-s]


This appendix shows sample calculations for the friction factor augmentation uncertainty

calculations. Uncertainty propagates through the calculations; therefore, it was necessary to

account for all the measured values factoring into the final uncertainty value. The uncertainty

associated with the fluid properties was neglected because of the relatively small changes in

temperature and pressure over the length of the test section. Each uncertainty was found by

using the Kline and McKintock [1953] method outlined in Section 3.3.

Reynolds Number

The Reynolds number for this work was based on channel hydraulic diameter and can be

written as:

(D-1)

where the channel dimensions can be substituted for hydraulic diameter and volumetric flow rate

for velocity. Therefore, the Reynolds number can be rewritten as Equation D-2:

(D-2)

µ

ρ⋅⋅= HDV

Re

( )HW

Q stdori

+⋅

⋅⋅=

µ

ρ2Re

104

The detailed calculations of volumetric flowrate are presented in Appendix A. Using the

root-sum-square uncertainty method, the uncertainty in Reynolds number is given by Equations

D-3 and D-4.

(D-3)

(D-4)

Table D-1 shows the results for the highest and lowest Reynolds numbers tested.

Table D-1 Uncertainty in Reynolds Number

VariableTarget

ReynoldsValue

Precision

Uncertainty

Bias

Uncertainty

Total

Uncertainty

12,000 13295 - - 564 (4.3%)

40,000 40122 - - 1137 (2.8%)

12,000 49.9 - - 1.6

40,000 150.5 - - 0.6

12,000 14.1 2E-02

40,000 14.1 2E-02

12,000 529.1 4E-01

40,000 527.3 4E-01

12,000 0.4 3E-02

40,000 3.4 3E-02

12,000 0.2007 - 7.9E-04

40,000 0.2007 - 7.9E-04

12,000 0.0406 - 7.9E-04

40,000 0.0406 - 7.9E-04

Re

Qstd [m3/s]

PL [psia]

H [m]

TL [°R]

∆P [in H20]

W [m] 7.9E-04

7.9E-04

0.4

2.5E-02

1.6E-03

3.4E-05

0.13.4E-05

Darcy Friction Factor

The Darcy friction is given in Equation D-5.

(D-5)

222

Re

ReReRe

⋅

∂

∂+

⋅

∂

∂+

⋅

∂

∂=

HWQ

ori

uH

uW

uQ

uori

( ) ( )

( )

2

2

2

2

2

Re

2

22

⋅

+⋅

⋅⋅−

+

⋅

+⋅

⋅⋅−+

⋅

+⋅

⋅

=

Hstdori

Wstdori

Qstd

uHW

Q

uHW

Qu

HWu

ori

µ

ρ

µ

ρ

µ

ρK

2

2

1V

D

L

dPf

H

⋅⋅

=

ρ

105

000,20ReRe316.0 25.0 ≥⋅= −of

000,20ReRe184.0 2.0 <⋅= −of

Again, the root-sum-square method was used to calculate the uncertainty in friction factor

given in Equations D-6 and D-7:

(D-6)

(D-7)

The calculations for uncertainty in friction factor are presented in Table D-2.

Table D-2 Uncertainty in Friction Factor

VariableTarget

ReynoldsValue

Precision

Uncertainty

Bias

Uncertainty

Total

Uncertainty

12,000 2.4E-01 - - 2.5E-02 (10.2%)

40,000 2.1E-01 - - 9.0E-3 (4.5%)

12,000 6.8E-02 - - 1.4E-03

40,000 6.8E-02 - - 1.4E-03

12,000 18.4 1.2

40,000 144.7 1.2

12,000 1.0 7.9E-04

40,000 1.0 7.9E-04

12,000 1.2 - - 2.8E-07

40,000 1.2 - - 2.8E-07

12,000 3.0 - - 1.1E-01

40,000 8.9 - - 1.8E-01

8.5E-03 1.2

- 7.9E-04

f

DH [m]

dP [Pa]

L [m]

ρ [kg/m3]

V [m/s]

Blasius Smooth Channel Friction Factor

The smooth channel friction factor varied depending on the Reynolds number. Equation

D-8 is for Re ≥ 20,000, and Equation D-9 is for Re < 20,000.

(D-8)

(D-9)

The uncertainty in fo is shown in Equation D-10. For Re ≥ 20,000, the specific

uncertainty equation is depicted in Equation D-11; for Re < 20,000, the specific uncertainty is

given in Equation D-12.

22222

⋅

∂

∂+

⋅

∂

∂+

⋅

∂

∂+

⋅

∂

∂+

⋅

∂

∂= VD

H

LdPf uV

fu

fu

D

fu

L

fu

dP

fu

H ρρ

2

3

2

22

2

2

2

22

2

2

42

222

⋅

⋅⋅

⋅⋅−+

⋅

⋅⋅

⋅⋅−

+

⋅

⋅⋅

⋅+

⋅

⋅⋅

⋅⋅−+

⋅

⋅⋅

⋅

=

VHH

DLH

dPH

f

uVL

dPDu

VL

dPD

uVL

dPu

VL

dPDu

VL

D

u

H

ρρ

ρρρ

ρ

K

106

(D-10)

(D-11)

(D-12)

Table D-3 shows the results for the smooth channel friction factor uncertainty.

Table D-3 Uncertainty in Smooth Channel Friction Factor

VariableTarget

ReynoldsValue

Precision

Uncertainty

Bias

Uncertainty

Total

Uncertainty

12,000 2.9E-02 - - 3.1E-04 (0.7%)

40,000 2.2E-02 - - 1.6E-04 (1.1%)

12,000 13295 - - 564

40,000 40122 - - 1137

fo

Re

Friction Factor Augmentation

The friction factor augmentation was given by f / fo, and the uncertainty is given by:

(D-13)

(D-14)

Finally, the results for the augmentation uncertainty are presented in Table D-4.

2

Re25.1Re

079.0

⋅

−= uu

of

2

Re2.1Re

037.0

⋅

−= uu

of

22

⋅∂

∂+

⋅∂

∂=

o

o

f

o

of

o

f

f uf

ff

uf

ff

u

2

2

2

1

⋅

−+

⋅=

o

o

f

o

f

of

f uf

fu

fu

2

Re

∂

∂= o

f

fu

o

107

Table D-4 Uncertainty in Friction Factor Augmentation

VariableTarget

ReynoldsValue

Precision

Uncertainty

Bias

Uncertainty

Total

Uncertainty

12,000 8.24 - - 0.9 (10.3%)

40,000 9.44 - - 0.4 (4.6%)

12,000 2.4E-01 - - 2.5E-02

40,000 2.1E-01 - - 9.0E-03

12,000 2.9E-02 - - 3.1E-04

40,000 2.2E-02 - - 1.6E-04fo

f

f/fo

Documents

HEAT TRANSFER AND FRICTION FACTOR AUGMENTATION IN …