AERODYNAMICS AND THERMAL PHYSICS OF HELICOPTER ICE …

The Pennsylvania State University

The Graduate School

College of Engineering

AERODYNAMICS AND THERMAL PHYSICS OF

HELICOPTER ICE ACCRETION

A Dissertation in

Aerospace Engineering

by

Yiqiang Han

2016 Yiqiang Han

Submitted in Partial Fulfillment

of the Requirements

for the Degree of

Doctor of Philosophy

May 2016

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The dissertation of Yiqiang Han was reviewed and approved* by the following:

Jose L. Palacios

Assistant Professor of Aerospace Engineering

Dissertation Advisor

Chair of Committee

Kenneth S. Brentner

Professor of Aerospace Engineering

Robert F. Kunz

Senior Scientist and Head of the Computational Mechanics Division,

Applied Research Laboratory, and Professor of Aerospace Engineering

Namiko Yamamoto

Assistant Professor of Aerospace Engineering

John M. Cimbala

Professor of Mechanical Engineering

George A. Lesieutre

Professor of Aerospace Engineering

Head of the Department of Aerospace Engineering

*Signatures are on file in the Graduate School

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ABSTRACT

Ice accretion on aircraft introduces significant loss in airfoil performance. Reduced lift-to-

drag ratio reduces the vehicle capability to maintain altitude and also limits its maneuverability.

Current ice accretion performance degradation modeling approaches are calibrated only to a limited

envelope of liquid water content, impact velocity, temperature, and water droplet size; consequently

inaccurate aerodynamic performance degradations are estimated. The reduced ice accretion

prediction capabilities in the glaze ice regime are primarily due to a lack of knowledge of surface

roughness induced by ice accretion. A comprehensive understanding of the ice roughness effects

on airfoil heat transfer, ice accretion shapes, and ultimately aerodynamics performance is critical

for the design of ice protection systems.

Surface roughness effects on both heat transfer and aerodynamic performance degradation

on airfoils have been experimentally evaluated. Novel techniques, such as ice molding and casting

methods and transient heat transfer measurement using non-intrusive thermal imaging methods,

were developed at the Adverse Environment Rotor Test Stand (AERTS) facility at Penn State. A

novel heat transfer scaling method specifically for turbulent flow regime was also conceived. A

heat transfer scaling parameter, labeled as Coefficient of Stanton and Reynolds Number (𝐶𝑆𝑅 =

𝑆𝑡𝑥 𝑅𝑒𝑥−0.2⁄ ), has been validated against reference data found in the literature for rough flat plates

with Reynolds number (Re) up to 1×107, for rough cylinders with Re ranging from 3×104 to 4×106,

and for turbine blades with Re from 7.5×105 to 7×106. This is the first time that the effect of

Reynolds number is shown to be successfully eliminated on heat transfer magnitudes measured on

rough surfaces.

Analytical models for ice roughness distribution, heat transfer prediction, and

aerodynamics performance degradation due to ice accretion have also been developed. The ice

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roughness prediction model was developed based on a set of 82 experimental measurements and

also compared to existing predictions tools. Two reference predictions found in the literature

yielded 76% and 54% discrepancy with respect to experimental testing, whereas the proposed ice

roughness prediction model resulted in a 31% minimum accuracy in prediction. It must be noted

that the accuracy of the proposed model is within the ice shape reproduction uncertainty of icing

facilities. Based on the new ice roughness prediction model and the CSR heat transfer scaling

method, an icing heat transfer model was developed. The approach achieved high accuracy in heat

transfer prediction compared to experiments conducted at the AERTS facility. The discrepancy

between predictions and experimental results was within ±15%, which was within the measurement

uncertainty range of the facility. By combining both the ice roughness and heat transfer predictions,

and incorporating the modules into an existing ice prediction tool (LEWICE), improved prediction

capability was obtained, especially for the glaze regime.

With the available ice shapes accreted at the AERTS facility and additional experiments

found in the literature, 490 sets of experimental ice shapes and corresponding aerodynamics testing

data were available. A physics-based performance degradation empirical tool was developed and

achieved a mean absolute deviation of 33% when compared to the entire experimental dataset,

whereas 60% to 243% discrepancies were observed using legacy drag penalty prediction tools.

Rotor torque predictions coupling Blade Element Momentum Theory and the proposed drag

performance degradation tool was conducted on a total of 17 validation cases. The coupled

prediction tool achieved a 10% predicting error for clean rotor conditions, and 16% error for iced

rotor conditions. It was shown that additional roughness element could affect the measured drag by

up to 25% during experimental testing, emphasizing the need of realistic ice structures during

aerodynamics modeling and testing for ice accretion.

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TABLE OF CONTENTS

LIST OF FIGURES ................................................................................................................. viii

LIST OF TABLES ................................................................................................................... xiv

ACKNOWLEDGEMENTS ..................................................................................................... xv

Chapter 1 Introduction ............................................................................................................. 1

1.1 Background and Motivation ....................................................................................... 1 1.2 Effect of Surface Roughness ...................................................................................... 7

1.2.1 Heat Transfer Enhancement ............................................................................ 11 1.2.2 Performance Degradation ................................................................................ 33

1.3 Dissertation Objectives .............................................................................................. 36 1.4 Dissertation Overview ................................................................................................ 38

Chapter 2 Experiment Configurations ..................................................................................... 41

2.1 Rotor Ice Accretion Experiment ................................................................................ 41 2.2 Icing Condition .......................................................................................................... 44

2.2.1 Icing Parameters .............................................................................................. 44 2.2.2 Icing Scaling Parameters ................................................................................. 48

2.3 Test Blade Designs ..................................................................................................... 50 2.3.1 Design of 21-inch-chord NACA 0012 Rotor Blade ........................................ 50 2.3.2 Design of 1-inch & 4.5-inch-Diameter Cylinder Rotor Blades ....................... 51

2.4 Test Matrices .............................................................................................................. 52 2.4.1 Cylinder Ice Roughness Experiment ............................................................... 52 2.4.2 Airfoil Ice Roughness Experiment .................................................................. 53 2.4.3 Airfoil Ice Shape Accretion Experiment ......................................................... 54

2.5 Ice Shape Molding and Casting Techniques .............................................................. 56 2.6 Wind Tunnel Experiment Setup ................................................................................. 61

2.6.1 Wind Tunnel Heat Transfer Test Setup ........................................................... 61 2.6.2 Wind Tunnel Aerodynamics Test Setup ......................................................... 73

Chapter 3 Ice Roughness Measurement and Prediction ........................................................... 76

3.1 Experimental Ice Roughness Measurements.............................................................. 76 3.2 Ice Roughness Prediction ........................................................................................... 80

3.2.1 Ice Roughness Prediction on an Airfoil .......................................................... 84 3.2.2 Ice Roughness Prediction on a Cylinder ......................................................... 89

Chapter 4 Transient Heat Transfer Measurements .................................................................. 93

4.1 Theory ........................................................................................................................ 93 4.2 Technique Validation ................................................................................................. 97

4.2.1 Technique Validation on a Flat Plate .............................................................. 97 4.2.2 Technique Validation on a Circular Cylinder ................................................. 99 4.2.3 Technique Validation on an Airfoil ................................................................. 104

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4.3 Transient Heat Transfer Measurement Results on Ice-Roughened Surfaces ............. 105 4.3.1 Ice-Roughened Cylinder ................................................................................. 106 4.3.2 Ice-Roughened Airfoil ..................................................................................... 109

Chapter 5 Heat Transfer Model Development ......................................................................... 122

5.1 Scaling Method for Heat Transfer Measurements ..................................................... 123 5.1.1 Existing Dimensionless Parameters for Heat Transfer Scaling ....................... 124 5.1.2 Development of a new heat transfer scaling parameter - CSR ........................ 130 5.1.3 Validation of CSR on flat plates ...................................................................... 132 5.1.4 Validation of CSR on cylinders ....................................................................... 133 5.1.5 Validation of CSR on airfoils .......................................................................... 138 5.1.6 Recommendation for Use of Heat Transfer Scaling Parameters ..................... 140

5.2 AERTS Empirical Correlation for Heat Transfer on Ice Roughened Surface ........... 141 5.3 AERTS Analytical Prediction for Heat Transfer on an Ice Roughened Surface ....... 143

5.3.1 Model Overview .............................................................................................. 144 5.3.2 Laminar Flow Regime ..................................................................................... 146 5.3.3 Turbulent Flow Regime .................................................................................. 147 5.3.4 Transition / Separation Criteria ....................................................................... 151 5.3.5 Post-roughness Region Treatment ................................................................... 152 5.3.6 Final Heat Transfer Model Comparison .......................................................... 153

Chapter 6 Improved Ice Accretion Predicting Tool ................................................................. 154

6.1 Ice Shape Prediction for Cold, Rime Ice Regime ...................................................... 157 6.2 Ice Shape Prediction for Rime-to-Glaze Transition Regime...................................... 159 6.3 Ice Shape Prediction for Warm, Glaze Ice Regime ................................................... 161 6.4 Ice Shape Prediction Compared to Experimental Ice Shapes .................................... 164 6.5 Summary of Ice Shape Prediction Comparison ......................................................... 167

Chapter 7 Aerodynamics Testing and Modeling with Accreted Ice Structures ....................... 168

7.1 Analytical Correlation between Drag Increase and Icing Conditions ........................ 169 7.1.1 Existing Database for Correlation Development ............................................. 169 7.1.2 Performance Degradation Correlation Development ...................................... 170 7.1.3 Correlation Compared to Experimental Database ........................................... 176 7.1.4 Correlation Compared to Existing Models ...................................................... 178 7.1.5 Correlation Applied to Cambered Airfoils ...................................................... 181 7.1.6 Correlation for Varying Angles of Attack ....................................................... 182

7.2 Experimental Validation ............................................................................................ 185 7.2.1 Experimental Polar Data ................................................................................. 185 7.2.2 Experimental Performance Degradation Comparison ..................................... 188 7.2.3 Effect of Additional Ice Roughness Element .................................................. 190

7.3 Comparison between Correlation and AERTS Experimental Results ....................... 194

Chapter 8 Conclusions ............................................................................................................. 200

References ................................................................................................................................ 209

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Appendix A Experimental Measurements - Ice Roughness on Airfoil .................................... 223

Appendix B Experimental Measurements – Aerodynamics Testing ....................................... 225

Appendix C Scaling Methods for Ice Accretion Testing ......................................................... 228

Appendix D Angular Variation of Thermal Infrared Emissivity ............................................. 234

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LIST OF FIGURES

Figure 1-1. Distribution of icing related LOC-I aircraft incidents ........................................... 2

Figure 1-2. Aircraft accidents involved with icing .................................................................. 3

Figure 1-3. A rescue helicopter waiting to be rescued ............................................................. 5

Figure 1-4. Sample aircraft ice roughness ............................................................................... 8

Figure 1-5. Reference ice accretion time sequence photograph (1) ......................................... 9

Figure 1-6. Reference ice accretion time sequence photograph (2) ......................................... 10

Figure 1-7. Reference wind tunnel setup for artificially roughened flat plate test ................... 13

Figure 1-8. Reference rough flat plate skin friction without virtual origin correction............. 16

Figure 1-9. Reference rough flat plate skin friction with virtual origin correction .................. 16

Figure 1-10. Reference artificially roughened flat plate heat transfer ..................................... 17

Figure 1-11. Reference heat transfer measurements on clean cylinder ................................... 19

Figure 1-12. Reference heat transfer on artificially roughened cylinders at Re = 2.2×105 ...... 22

Figure 1-13. Reference heat transfer on artificially roughened cylinders at Re = 4×106 ......... 23

Figure 1-14. Example of LEWICE heat transfer over-prediction ............................................ 25

Figure 1-15. Reference heat transfer coefficients from flight test ........................................... 28

Figure 1-16. Reference heat transfer on artificially roughened airfoils at zero AOA ............... 30

Figure 1-17. Reference surface roughness effect on aerodynamics ......................................... 34

Figure 1-18. Work path for this research ................................................................................. 38

Figure 2-1. AERTS test chamber schematic ............................................................................ 41

Figure 2-2. AERTS rotor test stand with the test blade mounted ............................................ 42

Figure 2-3. AERTS current test stand schematics, renovated in Spring 2015 ......................... 43

Figure 2-4. Ice shape categorization ........................................................................................ 45

Figure 2-5. Icing condition envelop suggested by FAA .......................................................... 47

Figure 2-6. AERTS 21-inch-chord “Paddle Blade” ................................................................. 50

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Figure 2-7. AERTS cylinder test rotor ..................................................................................... 52

Figure 2-8. Ice shape comparison with reference literature ..................................................... 56

Figure 2-9. Test rotor blade mounted on molding stand inside cold chamber ......................... 57

Figure 2-10. Example ice mold and casting models ................................................................ 57

Figure 2-11. Sample ice casting model comparison ................................................................ 58

Figure 2-12. Sample ice roughness casting model ................................................................... 59

Figure 2-13. Laser scan of ice wrap surface ............................................................................ 60

Figure 2-14. CAT scan of 3D ice shape ................................................................................... 60

Figure 2-15. Penn State Hammond Building wind tunnel CAD model ................................... 61

Figure 2-16. Cylinder heat transfer evaluation test setup in wind tunnel ................................ 62

Figure 2-17. Test airfoil with sandpaper in the wind tunnel for flow sensitivity check .......... 62

Figure 2-18. Schematics of transient heat transfer testing in the wind tunnel ......................... 63

Figure 2-19. Wind tunnel airfoil model ................................................................................... 64

Figure 2-20. Temperature time history inside casting model .................................................. 65

Figure 2-21. Example heat transfer time history data .............................................................. 66

Figure 2-22. Paddle blade mounted in wind tunnel for direct heat transfer measurement ...... 67

Figure 2-23. Signal conditioning circuits designed for thin-film sensors ................................ 68

Figure 2-24. Direct heat transfer measurements in wind tunnel and on rotor stand ................ 69

Figure 2-25. Top view from IR camera (greyscale) and temperature mapping (color) ........... 72

Figure 2-26. Wind tunnel test section with airfoil mounted .................................................... 73

Figure 3-1. AERTS example ice roughness categorization ..................................................... 76

Figure 3-2. Digital dial indicator on an optical bench ............................................................. 77

Figure 3-3. Ice roughness measurement using casted natural ice roughness shape ................. 79

Figure 3-4. Categorization of cylinder surface roughness distribution .................................... 79

Figure 3-5. Schematic of roughness distribution ..................................................................... 80

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Figure 3-6. Sample roughness measurement and comparison to LEWICE prediction ............ 84

Figure 3-7. AERTS roughness height correlation .................................................................... 85

Figure 3-8. AERTS smooth zone width correlation ................................................................ 86

Figure 3-9. Correlation results comparison - roughness height ............................................... 86

Figure 3-10. Comparison of ice roughness prediction using LEWICE ver1 equation ............ 87

Figure 3-11. Comparison of ice roughness prediction using LEWICE ver3.2 equation ......... 87

Figure 3-12. Correlation results comparison - smooth zone width .......................................... 88

Figure 3-13. Sample roughness measurement and prediction comparison .............................. 89

Figure 3-14. AERTS cylinder roughness height correlation .................................................... 90

Figure 3-15. AERTS smooth zone width correlation .............................................................. 91

Figure 3-16. Comparison of predicted ice roughness and experimental measurements .......... 92

Figure 4-1. Wind tunnel flat plate model setup ....................................................................... 98

Figure 4-2. Heat transfer measurement on a turbulent flat plate .............................................. 99

Figure 4-3. Clean cylinder heat transfer - ReD = 1×105 ........................................................... 100



Figure 4-6. Frossling number on a clean airfoil ....................................................................... 104

Figure 4-7. Comparison of heat transfer on ice roughened cylinder surface - ReD = 1×105 .... 106



Figure 4-10. Typical ice roughness: case R2 (left) and R1 (right) ........................................... 110

Figure 4-11. Effect of temperature ........................................................................................... 111

Figure 4-12. Effect of velocity ................................................................................................. 112

Figure 4-13. Effect of droplet size ........................................................................................... 115

Figure 4-14. Effect of LWC (1) ................................................................................................ 116

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Figure 4-15. Effect of LWC (2) ................................................................................................ 117

Figure 4-16. Effect of time (1) ................................................................................................. 118



Figure 4-19. Flow transition location vs. icing time ................................................................ 120

Figure 5-1. Example heat transfer comparison – htc ............................................................... 123

Figure 5-2. Reference rough flat plate heat transfer in St ........................................................ 125

Figure 5-3. Reference rough cylinder heat trasnfer in Fr – 0.45 mm roughness ..................... 127

Figure 5-4. Reference rough cylinder heat trasnfer in Fr – 0.9 mm roughness ....................... 127

Figure 5-5. Example scaled heat transfer comparison – Fr ..................................................... 128

Figure 5-6. Frossling number used for heat transfer scaling .................................................... 129

Figure 5-7. Reference rough flat plate skin friction as a function of Rex-0.2 ............................. 131

Figure 5-8. Reference rough flat plate heat trasnfer in CSR .................................................... 132

Figure 5-9. Reference rough cylinder heat trasnfer in CSR – 0.45 mm ................................... 133

Figure 5-10. Reference rough cylinder heat trasnfer in CSR – 0.9 mm ................................... 134

Figure 5-11. CSR applied to AERTS ice-roughened cylinder – C3 ......................................... 136

Figure 5-12. CSR applied to AERTS ice-roughened cylinder – C7 ......................................... 137

Figure 5-13. Reference turbine blade heat trasnfer in CSR ...................................................... 138

Figure 5-14. Example scaled heat transfer measurement comparison – CSR .......................... 139

Figure 5-15. Example heat transfer (CSR) and roughness distribution comparison ................ 141

Figure 5-16. Example heat transfer (CSR) and proposed correlation comparison ................... 142

Figure 5-17. Validation of the laminar flow field and heat transfer prediction ....................... 147

Figure 5-18. Comparison of empirical equations for skin friction coefficient......................... 149

Figure 5-19. Schematics of the definition of effective roughness, ks ...................................... 149

Figure 5-20. AERTS heat transfer correlation and model comparison .................................... 153

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Figure 6-1. Example improvement of ice prediction (1).......................................................... 154

Figure 6-2. Example improvement of ice shapes and heat transfer predictions (2) ................. 155

Figure 6-3. LEWICE coupling schematic ................................................................................ 156

Figure 6-4. Reference ice shapes from Shin & Bond’s Experiment ........................................ 158

Figure 6-5. Reference ice shapes from Olsen’s Experiment (cold regime) ............................. 159

Figure 6-6. Reference ice shapes from Olsen’s Experiment (warm regime) ........................... 162

Figure 6-7. Example ice shape matching comparisons ............................................................ 164

Figure 6-8. Improved ice prediction compared to AERTS ICE1-4 ice shapes ........................ 166

Figure 7-1. Comparison of performance database used for different correlations................... 174

Figure 7-2. Comparison of Cd from HPC and measured Cd from three ref. experiments ...... 176

Figure 7-3. Comparison of ∆Cd predictions against Olsen's experiments ............................... 179

Figure 7-4. Comparison of ∆CdError predictions against Flemming's experiments .................. 180

Figure 7-5. HPC model applied to cambered airfoil cases ...................................................... 181

Figure 7-6. Comparison between Exp. Cd at various AOA and HPC prediction ..................... 184

Figure 7-7. Summary of aerodynamics polar results (ice shapes ICE 1 - 4)............................ 185

Figure 7-8. Cl vs Cd comparison among the testing airfoils.................................................... 189

Figure 7-9. Ice feathers Removed from ICE3 .......................................................................... 191

Figure 7-10. Cl and Cd comparisons between ICE3 and ICE3-FR (Feather Removed) ......... 192

Figure 7-11. Cm comparison between ICE3 and ICE3-FR (Feather Removed) ...................... 193

Figure 7-12. Comparison between AERTS experiments and HPC calculation ....................... 194

Figure 7-13. Angle of Attack variation along a rotor blade ..................................................... 196

Figure 7-14. Sample torque calculation – clean NACA 0012 rotor, pitch angle 8°................. 197

Figure 7-15. Sample torque calculation – iced rotor, pitch angle 10° ...................................... 198

Figure 7-16. Summary of torque calculation – clean rotor ...................................................... 198

Figure 7-17. Summary of torque calculation – iced rotor ........................................................ 199

xiii

Figure C-1. Flow Chart of Icing Condition Scaling Method ................................................... 229

Figure D-1. Angular emissivity of different materials ............................................................. 234

Figure D-2. Wind tunnel camera setup schematics – cylinder test .......................................... 235

Figure D-3. Wind tunnel camera setup schematics – airfoil test ............................................. 236

Figure D-4. (a) Angle of incidence, and (b) Emissivity vs. Azimuth angle on cylinder ......... 236

xiv

LIST OF TABLES

Table 1-1. Reference Virtual Origin Length Measured on Rough Flat Plate .......................... 15

Table 2-1. AERTS Facility Specifications ............................................................................... 43

Table 2-2. AERTS Cylinder Ice Roughness Test Matrix ........................................................ 53

Table 2-3. AERTS Airfoil Ice Roughness Testing Matrix ...................................................... 54

Table 2-4 AERTS Ice Shape Accretion Testing Matrix .......................................................... 55

Table 4-1. Measured Thermal Properties of Ice Casting Models ............................................ 95

Table 4-2. Summary of Ice-Roughened Cylinder Heat Transfer Behavior ............................. 109

Table 7-1. Summary of Experimental Icing Aerodynamic Degradation Database .................. 170

Table A-1. Roughness Zone Transition Location and Ice Limit on Airfoil ............................. 223

Table A-2. Measured Roughness Heights (R1-R5) ................................................................. 223

Table A-3. Measured Roughness Heights (R6-R10) ............................................................... 224

Table B-1. AERTS ICE1 Iced Airfoil Polar Data .................................................................... 225



Table B-4. AERTS ICE3-FR Iced Airfoil Polar Data ............................................................. 227


xv

ACKNOWLEDGEMENTS

I would like to acknowledge the enormous help and guidance from my dissertation advisor,

Dr. Jose Palacios. His insightful advice and enthusiasm in icing research inspired and motivated

me throughout my doctoral study at Penn State. During various projects working with him, I learned

not only from his academic expertise, but also from his passionate attitude toward the research.

Without his brilliant guidance, my research could never have been completed.

I would like to thank my committee members, including Dr. Robert Kunz, Dr. Namiko

Yamamoto, Dr. Kenneth Brentner, and Dr. John Cimbala, for their helpful comments during every

meeting. My sincere gratitude also goes to Dr. Cengiz Camci who generously provided technical

guidance on heat transfer measurement experiments and gave me access to equipment. I am also

grateful to the help and advice on wind tunnel testing from Mr. Richard Auhl and Mr. Mark

Catalano. The research is impossible without their valuable suggestions and guidance.

I am indebted to many of my colleagues at the AERTS lab. Without their dedicated

contribution to the facility, a lot of the research ideas could not have been fully implemented. Help

from Edward Rocco, Matthew Drury, Ahmad Haidar, and Belen Veras-Alba on proofreading this

dissertation is cordially appreciated.

It is my honor to thank the U.S. Army for sponsoring this research and also Mr. Eric

Kreeger at NASA Glenn Research Center as our VLRCOE task monitor POC. This research is

partially funded by the National Rotorcraft Technology Center (NRTC) under the Vertical Lift

Research Center of Excellence (VLRCOE) Agreement No. W911W6-11-2-0011.

Finally, I owe my deepest gratitude to my parents. They are my source of energy that kept

me going through every stage of my life. I also want to specially thank my girlfriend Lily for her

support, patience, and encouragement. I would like to dedicate this dissertation as a small token in

return to their endless love.

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Chapter 1

Introduction

1.1 Background and Motivation

Ice accretion on airfoils has a severe impact on the safety of aircraft. After ice accretes on

the airfoil, the outer aerodynamic surface is greatly changed. The flight capability is considerably

degraded, with increases in profile drag and loss of lift. Following the early onset of ice accretion,

airfoil performance is degraded because of the increased surface roughness, which results in a

premature flow separation, promoting pre-stall at low angle of attack. As water droplets

continuously impact and freeze onto the airfoil, the accreted ice shape modifies the airfoil profile,

which results in severe penalties in aerodynamic performance. An aircraft cannot maintain its

altitude with the degraded performance, which is extremely dangerous during climbing / landing

approach.

As reported in a recent issue of Annual Safety Review published by European Aviation

Safety Agency (EASA) (European Aviation Safety Agency, 2015), there were 16 fatal accidents

and 648 fatalities in 2014, compared to 14 fatal accidents in 2013 with only 185 fatalities. The

sharp increase in fatality numbers resulted from three major fatal accidents, two of which were

related to icing. In an accident involving 116 fatalities, Air Algerie Flight 5017 crashed during a

climbing and leveling procedure in thunderstorm conditions. These conditions led to an icing

problem. It has been officially confirmed by French Bureau d'Enquêtes et d'Analyses pour la

Sécurité de l'Aviation Civile (BEA) that the accident was directly related to icing induced plane

stall and loss of control in-flight (BEA, 2015). A similar accident occurred to Indonesia AirAsia

Flight 8501 causing 162 fatalities. This event was also believed to be caused by atmospheric icing,

2

as indicated by Indonesia’s meteorological agency (The Guardian, 2015). Overall, the icing

problem was regarded as one of the most significant contributors of “Loss of Control In-flight

(LOC-I)” accident category, as stated by EASA (European Aviation Safety Agency, 2015):

“LOC-I remains the top risk area leading to the largest number of fatal accidents

and fatalities in the CAT fixed wing. LOC-I involves the momentary or total loss

of control of the aircraft, usually involving a significant deviation from the

intended flight path. This might be the result of reduced aircraft performance or

because the aircraft was flown outside its capabilities for control…The top five

issues are: … 5. Management of adverse weather conditions.”

Based on a study from 2009 to 2014, 65 aircraft incidents were categorized as LOC-I, as

illustrated in Figure 1-1. Icing conditions were found to be related to six (6) accidents (most severe

scenario), two (2) serious incidents, and not related to incidents (least severe scenario). Icing

problems are among the top contributing factors for most severe accidents jeopardizing aircraft

safety.

Figure 1-1. Distribution of icing related LOC-I aircraft incidents

Data source: Annual Safety Review 2014 (European Aviation Safety Agency, 2015)

In another study of icing related accidents, Jones et al. analyzed 663 aircraft incident reports

from 1988 to 2007 and found that icing is a significant factor affecting subsonic aircraft safety

(Jones, Reveley, Evans, & Barrientos, 2008). Judging from statistical analysis, the number of icing

3

incidents was very small (<1% for total incidents, 10%-23% for annual weather related incidents)

compared to other types of incidents. However, the icing problem is more likely to be involved

with fatal accidents. Out of the 663 reports studied by Jones et al., 141 resulted in the crew declaring

an emergency. Several severe aircraft accidents involving fatalities, including Roselawn, IN (1994),

Monroe, MI (1997), Pueblo, CO (2005), San Luis, CA (2006) and Lubbock, TX (2009) etc., have

been identified to be caused by ice accretion on airfoil (Weener, 2011).

A third statistical study of aircraft accidents involved with icing is shown in Figure 1-2.

These statistics again confirm the severity of ice accretion incidents. Icing accidents account for

12% of total weather accidents, where 27% of accidents involved fatalities. The NTSB (National

Transportation Safety Board) has safety recommendations on aircraft icing dating back to 1981 and

it has been on the NTSB’s most wanted list of safety improvements since 1997 (Weener, 2011).

Figure 1-2. Aircraft accidents involved with icing

(Source: Air Safety Foundation, AOPA)

In particular, compared to fixed-wing vehicles, helicopters are more prone to be affected

by ice accretion due to their operational envelope and mission requirements. During most of the

mission time, helicopters usually fly at low altitude where super-cooled water droplets exist in

4

liquid form while the ambient temperature is below freezing. As soon as a helicopter enters an icing

cloud, incoming water droplets impact and freeze on the rotating blade and other components of

the helicopter. The performance of the blade is greatly degraded by the ice accretion phenomena.

With ice on the blade, the required torque to maintain flight typically increases by 10% to 25%.

Rotor icing can also introduce excessive vibration due to blade imbalance after asymmetric ice

shedding. These effects contribute to loss of control of the vehicle and degrade maneuverability,

such as autorotation capability (Heinrich, et al., 1991).

Due to the inherent risks of ice accretion on the rotor system, helicopter pilots are directed

to exit the icing cloud or land as soon as possible. A 20% torque increase indicates that normal

autorotation rotor RPM requirements may not be satisfied. Therefore, the performance-degraded

rotor system may not be able to keep the vehicle operating in the safe landing altitude and airspeed

combination envelope. As a result of failure to maintain altitude, the sharply accelerated descent

velocity may prohibit safe landing. To avoid this danger, a helicopter must escape from the adverse

environment immediately, often by way of emergency landing.

A RAF Sea King helicopter trapped on a mountain is shown in Figure 1-3. The helicopter

was performing a rescue mission on a mountain in the North Scotland area, UK. Soon after it took-

off, the helicopter encountered a blizzard. An emergency landing was necessary because the vehicle

was not equipped with a deicing system. The helicopter remained on the ground for one day until

the ground rescue troop could carry a de-icing system to the mountain top, even though the nearest

airport is only 4 minutes away by flight.

5

Figure 1-3. A rescue helicopter waiting to be rescued

(Notice: ice accretion at the leading edge of the rotor blade, indicating this is an in-flight icing

case rather than ground icing or snow cover case; Source: BBC NEWS, Mar 2nd 2006)

To eliminate the risks of icing problems, anti-icing or de-icing systems are required for

helicopters operating in adverse icing environment. For the current world-wide fleet, few

helicopters are equipped with ice protection systems. Most equipped helicopters are for military or

specialized usage (such as oil rig transportation helicopters in North Sea oil drilling area). Only

helicopters with anti-icing / de-icing certifications are allowed to be released for flight in known

icing conditions. For instance, although only 0.5% of U.S. Army aircraft accidents are icing related,

this number is still of concern since it occurs in spite of the Army’s strict regulations forbidding

flight into known icing conditions (Peck, Ryerson, & Martel, 2002). Other helicopters, which are

mostly civil helicopters, simply avoid flying in adverse icing environments. The mission capability

of helicopters is significantly affected by icing. A general guideline for several utility helicopters

is quoted from Aircraft Icing Handbook published by FAA (Heinrich, et al., 1991):

“For example, the US Army UH-60A BLACK HAWK, which has a bleed air engine

inlet anti-ice system and an electro-thermal rotor deice system, is qualified for

flight in super-cooled 20 micron droplet clouds with liquid water contents that do

not exceed 1.0 grams per cubic meter and temperatures that are not below -4 °F

(-20 °C). Earlier versions of the UH-60A were not equipped with blade de-icing

6

systems. For these helicopters an envelope limited to liquid water contents of 0.3

grams per cubic meter has been recommended. Similarly the Marine CH-53E

helicopter, which does not have blade de-icing capability, has received a

recommendation that it be cleared for flight in icing conditions up to 0.5 grams

per cubic meter, with flight at temperatures below 14 °F (-10 °C) limited to

operational necessities only. Bell 214ST and Sikorsky S-61N helicopters have been

granted limited CAA clearances for North Sea operations, where an escape route

to the warmer ocean surface is available. For these aircraft the maximum liquid

water content is 0.20 and the minimum temperature is 23 °F (-5 °C). A release to

fly the RAF HC-Mk1 Chinook in icing at temperatures above 21 °F (-6 °C) (liquid

water content = .56 grams per cubic meter) was recommended.”

Recently, there has been an increased necessity for robust and efficient ice protection

systems (IPS) for both civil and military helicopters. To facilitate the design and test of novel IPS

devices, a comprehensive knowledge of the fundamental aerodynamics and thermal physics that

involved in ice accretion phenomena is necessary. The fundamental icing physics related to rotor

icing, such as the effect of surface roughness on both heat transfer coefficients and airfoil

performance in different icing regimes, are not well understood and require further investigation.

At the onset of ice accretion on an airfoil, the surface roughness and its associated surface

energy exchange can vary significantly as a function of liquid water content (LWC), water droplet

median volume diameter (MVD), impact velocity and temperature. Several investigations of

helicopter icing exist in the literature regarding ice shapes (Flemming & Lednicer, 1985), ice

protection system design (Gent, Markiewicz, & Cansdale, 1987) (Overmeyer, Palacios, Smith, &

Roger, 2011) (Overmeyer, Palacios, & Smith, 2013), ice shedding phenomenon (Brouwers,

Palacios, Smith, & Peterson, 2010) and helicopter blade ice protection coating evaluation

(Brouwers, Peterson, Palacios, & Centolanza, 2011) (Soltis, Palacios, Wolfe, & Eden, 2013).

However, the surface energy exchange on the iced surface has not been systematically studied and

modeled. The heat transfer due to the altered surface shape and roughness must be measured

experimentally to assist in the physical interpretation and development of existing empirical

relationships. The impact of the loss of aerodynamic shape due to onset of ice also needs to be

7

evaluated. A systematic database for airfoil performance degradation of helicopter blade is crucial

for the development of helicopter rotor performance prediction tools and eventually the design of

efficient ice protection system.

Due to the unique operational mechanism and environment, the fundamental physics

involved with rotorcraft icing needs special attention. Existing experimental and analytical

databases for ice accretion are not only scattered, but also primarily focus on fixed-wing aircraft

representative structures. The constant free-stream condition experienced in fixed wing aircraft is

very different from the locally varying conditions experienced by a helicopter rotor in forward

flight with varying angle of attack (AOA) at different azimuthal positions. These complexities in

helicopters drive the need of improved modeling as a potential path to develop the correlation

between ice accretion effects and icing conditions, which will eventually provide improved ice

protection systems and simplified icing certification procedures.

Currently, the certification for vehicles flying under icing condition is critical and also

costly. Natural icing conditions are available only at certain regions across the globe and within a

certain time frame. In an effort to reduce the cost of “chasing the weather”, ice prediction tools

have been developed since late 20th century to help understand the ice accretion phenomenon. The

validation of such predicting tools requires a comprehensive database of ice accretion testing under

extensive icing conditions. A comprehensive investigation of heat transfer and aerodynamics on

ice-roughened airfoils is of interest to improve heat transfer predictions and will be covered in later

sections.

1.2 Effect of Surface Roughness

As mentioned in the previous section, misinterpretation of surface roughness is a major

contributor to the inaccurate prediction of ice accretion and aerodynamic performance degradation.

8

During an icing event, the impinging water droplets may form beads or rivulets before they freeze

on the surface. This is called the running water phenomenon which introduces a great amount of

surface roughness. The roughness will then change the interfacial shear stress between the airfoil

and the incoming flow, consequently changing the friction coefficient, and eventually, the heat

transfer coefficient. It is known that even a small amount of ice roughness protruding into the local

flow boundary layer (from micrometer scale to several millimeters) will change the flow behavior

thereafter significantly. A typical surface roughness introduced by ice accretion is shown in Figure

1-4.

Figure 1-4. Sample aircraft ice roughness

Source: Ref. (Vargas & Tsao, 2007)

The importance of surface roughness was recognized in the early 20th century.

Experimental investigations of the effects of surface roughness have been conducted by numerous

researchers, but most of the roughness databases were based on simple geometry such as flat plates

or cylinders, which are not representative of ice-roughened airfoil. Two examples of pioneering

work in the field of surface roughness effects can be found in the literature (Nikuradse, 1933) and

(Schlichting, 1936). Based on their experimental database, several researchers (Dvorak, 1969)

(Simpson, 1973) (Cebeci & Chang, 1978) (Lin & Bywater, 1980) attempted to correlate the skin

friction and associated local heat transfer rate with the roughness and specific type of surface

geometry. All these calculations rely heavily on the previous experiments by Schlichting and focus

9

on simple geometries. The surface roughness on an iced airfoil, on the other hand, requires different

sets of experimental data and analysis given the unique geometry and physics.

Compared to artificial roughness with constant height and distribution, it has been

experimentally observed that there are both spatial (chordwise / spanwise locations) and temporal

(icing time) dependencies in ice roughness growth (Tsao & Anderson, 2005) (Vargas & Tsao,

2007). Few photographic data exist in literature to illustrate this unique feature of natural ice

roughness. A sample time sequence photograph obtained from a Super-cooled Large Droplet (SLD)

ice accretion test on a swept wing configuration at NASA IRT is shown in Figure 1-5. The set of

SLD roughness images represents a severe icing condition that could be encountered by fixed-wing

aircraft. The roughness in Figure 1-6 was accreted under regular aircraft icing conditions,

representative of a general trend of roughness growth on generic airfoils. As mentioned before,

there is no experimental ice roughness database specifically tested for helicopter icing

phenomenon. Limited data for various ice roughness types on different aircrafts prohibited detailed

understanding of ice accretion physics.

Figure 1-5. Reference ice accretion time sequence photograph (1)

45° swept wing, tst = -15.2°C, V = 77 m/s, MVD = 200μm, LWC = 0.75 g/m3, time = 15, 30, 50 s

Source: Ref. (Vargas & Tsao, 2007)

Judging from the pictures in Figure 1-5, it can be seen that there was a clear development

of a three-dimensional ice shape (“scallop” ice shape) built on a swept wing, both in chordwise and

spanwise condition. The test airfoil was setup with a 45° tilting angle in icing wind tunnel to

10

simulate the icing phenomenon on commercial transportation aircraft. The initial ice roughness

turned into a highly 3D ice shape within 50 seconds under such a severe icing condition as listed

below the Figure 1-5.

A similar but gradual procedure of ice roughness growth eventually turning into a major

ice shape can be seen in Figure 1-6. As can be observed from photo taken at 73s, the accreted ice

structure still followed the airfoil shape, whereas the roughness distribution was noticeable at 241

seconds of ice spay. At 881 s and 1381 s in Figure 1-6, the macro ice shape took over the dominant

role in aerodynamics and thermal physics. The time and location dependent roughness inevitably

introduced an unsteady flow field on the airfoil and thus affected the ice accretion process.

Figure 1-6. Reference ice accretion time sequence photograph (2)

chord=91.4 cm, tst=-9°C, V=51 m/s, MVD=30μm, LWC=0.8 g/m3, 28 min

Source: Ref. (Tsao & Anderson, 2005)

During the initial 241 s of the test in Figure 1-6, the surface heat transfer curve still follows

the clean airfoil trend, with limited enhancement due to local roughness. However, the distribution

of roughness imposes critical impact on future ice shape build-up, as can be seen in Figure 1-6 and

later sections of this research. This ice roughness growth phenomenon was also observed by Shin

(Shin, 1994). It was found that there was a rapid roughness growth in the first two minutes, whereas

First Impingement 241 sec

881 sec 1381 sec

73 sec

11

the roughness height stayed at the same level or even decreased at time beyond two minutes. The

trend of roughness growth and associated heat transfer for early ice onset are the primary focuses

of this research.

The unique roughness growth feature of ice accretion poses difficulty for analytical

modeling efforts. The prediction of ice accretion and its associated effects have been attempted by

researchers since 1980s. One of the most widely used tools is LEWICE, developed at the NASA

Glenn (formerly Lewis) Research Center. One of the main factors still affecting prediction codes

25 years after they were first introduced is the empirically determined (based on limited testing

points) surface roughness, which dominates ice accretion during the entire icing event in terms of

heat transfer and aerodynamic shape.

As suggested in the title of this research, the following sections are divided into two parts

to individually describe the effect of roughness on local heat transfer rate (thermal physics) and

airfoil performance (aerodynamics).

1.2.1 Heat Transfer Enhancement

A fundamental understanding of the energy exchange on the airfoil surface is critical for

both ice protection system development and aircraft certification in severe icing conditions. A

comprehensive literature survey was conducted focusing on heat transfer studies in relation to ice

accretion. Ice accretion on generic shapes, such as flat plates or cylinders, have been thoroughly

studied and can shed light on the airfoil heat transfer analysis. Before reviewing the enhanced heat

transfer on airfoils due to roughness, the literature review of heat transfer evaluation on flat plates

and cylinders is presented in the upcoming subsections.

The literature study in this subsection covers the heat transfer enhancement due to

natural/artificial surface roughness on flat plates, cylinders, and airfoils.

12

1.2.1.1 Heat Transfer on Flat Plates

There are numerous research papers on the effect of surface roughness on the heat transfer

of flat plates. One of the most pioneering and widely referenced efforts was done by Schlichting

(Schlichting, 1936), which established the foundation of surface roughness research. Data from a

total of 79 test cases on 14 rough surfaces with various roughness element shapes, sizes, and

distribution were studied to determine skin frictions. Different combinations of roughness element

features were attempted and correlated to the classic sand grain roughness size data reported in a

previous pipe flow experiment by Nikuradse (Nikuradse, 1933). Schlichting proposed a term called

“equivalent sand grain roughness” for those roughness that exhibited the same flow resistance

compared to Nikuradse’s work, which was later widely adopted by other researchers. Prediction of

skin friction factor on rough surfaces were also attempted by Prandtl and Schlichting (Prandtl &

Schlichting, 1934), and also von Karman (von Karman, 1934) using Nikuradse’s results. Since

1936, these pioneering efforts to determine skin friction have been extensively re-evaluated (e.g.

(Coleman, Hodge, & Taylor, 1984)) and extended (e.g. (Bergstrom, Kotey, & Tachie, 2002)

(Bergstrom, Akinlade, & Tachie, 2005)).

Among experimental efforts on artificially roughened flat plates, a series of studies done

at Stanford University in the 1970’s (Blackwell, Kays, & Moffat, 1972) (Healzer, Moffat, & Kays,

1974) (Pimenta, Moffat, & Kays, 1975) (Ligrani, Moffat, & Kays, 1979) were particularly helpful

for understanding heat transfer physics and will be discussed in this section and later in Chapter 4

and Chapter 5. A schematic of the wind tunnel setup used in Healzer (Healzer, Moffat, & Kays,

1974) and Pimenta’s (Pimenta, Moffat, & Kays, 1975) artificially roughened flat plate test is shown

in Figure 1-7. Some of the detailed test data were summarized in Appendix E of a textbook by Kays

and Crawford (Kays & Crawford, 1993).

13

Figure 1-7. Reference wind tunnel setup for artificially roughened flat plate test

The test setup was intended to study heat transfer with transpiration (air suction/blowing),

but also provided comprehensive measurements on an artificially roughened surface without

blowing effects as baseline. For this series of experiments, the flat plates with smooth, transitional

rough, and fully rough conditions were tested, across wide range of Reynolds numbers. The tunnel

speeds used in Healzer’s test were 11, 28, 43, 58, and 74 m/s which corresponded to a maximum

Reynolds number of 10 million (max. Rex=1×107). Similarly, the test speeds used by Pimenta were

9, 16, 27, and 40 m/s, which provided a maximum Reynolds number of 8×106. For the artificially

roughened flat plate testing, twenty-four (24) roughness test strips were installed to form the rough

plate, which resulted in a total test-section-length of 2.4384 m (8 feet). Densely packed 1.27 mm

(0.05 inch) spherical roughness elements were used on each of the 24 monitoring stations. The

elements were made from copper balls which were closely arranged to provide a uniform porosity

for the transpiration experiments. By following Schlichting’s suggested conversion method

(Schlichting, 1968), the roughness was correlated to equivalent sand grain roughness (ks) by a

factor of 0.625, resulting in a ks value of 0.787 mm (0.031 inch). The different rough regimes were

categorized according to the roughness Reynolds number, Rek, as defined in Equation (1-1)

𝑅𝑒𝑘 =𝑘𝑠 ∙ 𝑢𝜏

𝜈 (1-1)

where, ks is the sand-grain roughness, and 𝑢𝜏 = √𝜏𝑤𝑎𝑙𝑙 𝜌⁄ is the shear velocity. The different rough

regimes were categorized as follows:

Start Vel.

Profile:

Length = 3 m

Height

2 m

Tunnel Flow

End Vel.

Profile:

24 monitoring stations

Each station: 0.1016 m (4 inch) length test strip

Roughness: 1.27 mm diameter, packed spheres

14

𝑅𝑒𝑘 ≤ 5 Hydraulically (aerodynamic) smooth

5 ≤ 𝑅𝑒𝑘 ≤ 65 Transitionally rough

𝑅𝑒𝑘 ≥ 65 Fully rough

The range of roughness Reynolds number for Healzer’s test was from 24 to 200. Most cases

reported in the series studies were fully rough cases, even over some surface area in the lowest

testing speed case (9 to 11 m/s case). In fact, based on Pimenta’s experimental observation, heat

transfer data were found exhibiting fully-rough characteristics even with sufficient low free stream

velocities, which brought the roughness Reynolds number down to 14.

In the reported data sets, boundary layer velocity profile close to the leading edge and the

end of the flat plat were recorded together with temperature measurements. Twenty-four roughness

element plates were placed in the test section with heaters for heat flux monitoring. Each boundary

layer profile data set contained velocity and temperature measurements at 24 locations through the

boundary layer thickness direction. Multiple monitoring stations were set up along the surface of

flat plate, between the two profile measurement stations. At each monitoring station, detailed flow

characteristics, such as: boundary layer edge velocity, wall temperature, dimensionless heat transfer

rate (Stanton number, St), Reynolds numbers based on enthalpy thickness (ReΔ2) and momentum

thickness (Reδ2), and skin friction coefficient (cf) measurements were reported. The boundary layer

velocity profiles were measured using hot wire probes. Temperatures were monitored using

thermocouples. Heat transfer rate was calculated from control volume energy balance, based on

heater output power and temperature data. Skin friction factors were deduced from a two-

dimensional boundary layer momentum integral equation, based on experimentally measured

momentum thickness, as shown in Equation (1-2):

𝑐𝑓

2=

𝑑𝛿2

𝑑𝑥− 𝐹 (1-2)

15

where, δ2 is the momentum thickness and F is the blowing fraction (0 for the cases cited in this

dissertation). The derivative of δ2 was obtained by least-square curve fitting the experimental

measured discrete δ2 as a function based on local distance (x) and flat plate virtual origin (x0), as

shown in Equation (1-3):

𝛿2 = 𝑎(𝑥 − 𝑥0)𝑏 (1-3)

where the virtual origin was extrapolated from the plots of momentum thickness to the 5/4th power

as a function of local distance. This term was used to address the curve slope shifting between

turbulent boundary layer and its preceding laminar boundary layer. Healzer’s experimental

measured virtual origin length on artificially roughened flat plate (Healzer, Moffat, & Kays, 1974)

were listed in Table 1-1.

Table 1-1. Reference Virtual Origin Length Measured on Rough Flat Plate

Test

Speed, m/s

Rex at last

roughness

station

Virtual origin

(x0), m

% of plate

length

11 1.6×106 0.48 16%

28 4.2×106 0.09 3%

43 6.5×106 -0.02 -1%

58 8.9×106 -0.07 -2%

74 1.0×107 -0.06 -2%

In Table 1-1, the experimentally obtained virtual origin lengths are presented together with

test speed and maximum Reynolds number. The Rex is shown solely as a reference magnitude for

each case. The effect of the virtual origin was usually observed in tests with no pressure gradient

and low testing Reynolds numbers. For most other circumstances, this virtual origin was considered

to be overlapped with the leading edge point, i.e., the distance from leading edge could be directly

used for distance in turbulent boundary layer. Notice that the negative value of virtual origin

indicates that the virtual start of the turbulent boundary layer profile was in front of the leading

16

edge of the flat plate. The skin friction coefficient distribution without virtual origin correction is

shown in Figure 1-8.

Figure 1-8. Reference rough flat plate skin friction without virtual origin correction

Data source: Ref. (Healzer, Moffat, & Kays, 1974)

Judging from Figure 1-8, it can be observed that the representation of skin friction under

the lowest testing speed (11 m/s) exhibited a different slope compared to other cases. The virtual

origin effect gradually diminished when moving to higher testing speeds. After applying the virtual

origin correction in Table 1-1, a consistent distribution of the cf over the test Rex based on local

distance from virtual origin, ranging from 1×105 to 1×107, was obtained and shown in Figure 1-9.

Figure 1-9. Reference rough flat plate skin friction with virtual origin correction


0.0000

0.0005

0.0010

0.0015

0.0020

0.0025

0.0030

0.0035

1.E+04 1.E+05 1.E+06 1.E+07 1.E+08

Skin

Fri

ctio

n C

oef

f., C

f/2

Rex

7458432811Smooth

Tunnel Vel.(m/s)

0.0000

0.0005

0.0010

0.0015

0.0020

0.0025

0.0030

0.0035

1.E+04 1.E+05 1.E+06 1.E+07 1.E+08

Skin

Fri

ctio

n C

oef

f., C

f/2

Rex

7458432811smoothEmp. Corr.

17%

69%

89%

110%130%

Avg. IncreasaeTunnel Vel.(m/s)

17

An empirical correlation for smooth flat plate skin friction was also shown in solid grey

line for reference. The correlation defined in Equation (1-4) indicated the proportionality between

skin friction and Reynolds number with -0.2 power for the turbulent flow regime over smooth flat

plate. Its counterparts on roughened surfaces on bodies other than flat plate will be examined later

in Chapter 5.

𝑐𝑓

2= 0.0287𝑅𝑒𝑥

−0.2 (1-4)

It can be observed from the comparison between skin friction on rough and smooth flat

plates that increased testing speeds resulted in increased skin friction due to roughness, ranging

from 17% to 130%.This increase in skin friction is also reflected in the measured heat transfer

curve, as shown in Figure 1-10.

Figure 1-10. Reference artificially roughened flat plate heat transfer


In Figure 1-10, the heat transfer rate data were reported in terms of Stanton number,

defined as the ratio between the thermal energy transferred into a fluid through convection and the

thermal capacity of fluid, as shown in Equation (1-5):

𝑆𝑡 =ℎ

𝜌 ∙ 𝑢 ∙ 𝑐𝑝=

𝑁𝑢

𝑅𝑒 ∙ 𝑃𝑟 (1-5)

0

0.002

0.004

0.006

1.E+04 1.E+05 1.E+06 1.E+07 1.E+08

Stan

ton

Nu

mb

er

Rex

7458432811Smooth

Tunnel Vel. (m/s)

18

where, h is convective heat transfer coefficient, ρ and cp are density and specific heat of the fluid,

and u is the free stream velocity. Nusselt number (𝑁𝑢𝑥 = ℎ ∙ 𝑥 𝑘⁄ ) measures the ratio between

convective heat transfer and conductive heat transfer of fluid over a characteristic length of x,

whereas Reynolds number (𝑅𝑒𝑥 = 𝑢 ∙ 𝑥 𝜈⁄ ) deals with the ratio between inertial forces and viscous

forces. Therefore, by combining these two dimensionless factors, Stanton number can also

represent a relationship between the shear force at the wall (viscous drag due to skin friction) and

the total heat transfer at the wall (due to thermal diffusivity).

Similar behaviors of the heat transfer curves at varying test speeds were observed in Figure

1-10, especially for the cases with higher tunnel velocities (43, 58, and 74 m/s). The heat transfer

measured on the rough surface rendered a higher initial magnitude at the beginning of the flat plate,

when compared to the smooth plate case. The curves slowly decreased as the distance increased

along the plate and tend to follow the smooth plate curve. Flow over a rough plate tended to reach

the smooth behavior after a long distance. It was concluded by Healzer that the boundary layer on

the tested rough surfaces seemed to be completely turbulent, with no discernible molecular effect.

No viscous sublayer was identified for the fully rough state. Transition on the rough surface began

at approximately the same momentum thickness Reynolds number (350-450) for all of the

conditions tested, similar to the smooth plate cases. Stanton number appeared entirely independent

of velocity, only a function of enthalpy thickness, whereas skin friction may be independent, or at

most has a small dependence, on velocity (Healzer, Moffat, & Kays, 1974).

Similar observations were made in Pimenta’s results. Friction factor and Stanton number

in the fully rough state (tunnel speed > 27 m/s or 89 ft/s) both showed non-dependency on Reynolds

number being functions of only local momentum and enthalpy thickness, respectively.

Additionally, with respect to the smooth wall, it was concluded that a turbulent boundary layer on

a smooth wall forgets its previous history within a few boundary-layer thicknesses (two or three)

(Pimenta, Moffat, & Kays, 1975).

19

1.2.1.2 Heat Transfer on Cylinders

The heat transfer on smooth circular cylinders has been extensively explored under a wide

span of Reynolds number (Re), as found in the literature. Given the large amount of data available

for cylinders, experimental measurements and analytical prediction models are available and can

shed light on the physics of heat transfer due to ice accretion. Smooth cylinders under various

Reynolds number regimes have been extensively tested by Achenbach (Achenbach, 1975). Heat

transfer measurements were reported together with static pressure and skin friction for half of the

cylinder surface. Measurements were conducted on a 0.15-meter-diameter cylinder within a wide

range of Re = 3×104 to 4×106 to serve as benchmark database. The flow transition behavior was

found to pose a significant effect on the heat transfer curve. Different transition behaviors on a

clean cylinders under various Reynolds numbers (Achenbach, 1975) were digitized and compared

in Figure 1-11.

Figure 1-11. Reference heat transfer measurements on clean cylinder

Data source: Ref. (Achenbach, 1975)

0

1

2

3

0 30 60 90 120 150 180

Fr =

Nu

/sq

rt(R

e)

Azimuth Angle, deg

1.0E5

2.2E5

3.1E5

4.0E5

1.3E6

1.9E6

2.8E6

4.0E6

Re

20

The measured heat transfer rate was reported by Achenbach in form of a non-

dimensionalized factor called the Frossling number (Fr) (Frossling, 1958), which is defined as a

ratio between Nusselt number and Reynolds number as shown in Equation (1-6).

𝐹𝑟 =𝑁𝑢

√𝑅𝑒 (1-6)

Through implementation of the Frossling number, the heat transfer rate could be properly

scaled in the laminar regime prior to separation, as indicated in the good matching region between

0° to 60° over the wide range of Reynolds number in Figure 1-11.

As can be seen in Figure 1-11, different transitional Re regimes, such as subcritical

(Re<3×105), critical (3×105<Re<1.5×106), and supercritical (Re>1.5×106) flows were

experimentally identified. The flow at low Re range (subcritical) remained fully laminar before it

separated from the cylinder surface. The separation point was often found between 82° and 85°. As

Reynolds number increased to the critical regime, there was usually a laminar separation bubble

starting approximately at 110°. Flow reattachment was observed for this range as depicted by a

sudden rise in heat transfer coefficient. As the tunnel speed increased to the supercritical regime

(Re>1.5×106), the laminar flow was found to naturally transition to turbulent flow at the front half

of the cylinder. The transition angle was clearly spotted as a function of the Reynolds number based

on cylinder diameter. All three regimes have been experimentally observed during this research

and will be shown in later chapters. This is one of the advantages of the cylinder tests. It is very

rare to observe turbulent behavior at a clean airfoil leading edge due to the favorable pressure

gradient in that region. For instance, the typical transition location on a clean NACA 0012 airfoil

is usually at 60% chordwise location. It requires high speed, large chord, and large monitoring area

to observe the natural transition on airfoils. The full coverage of Reynolds number over the flow

transition regimes obtained during heat transfer measurements of cylinders would have been

impossible using airfoil shapes given the capabilities of the available facilities. Achenbach’s set of

21

clean cylinder heat transfer data is also later used as a baseline for validation of testing techniques

implemented in this research prior measurement of heat transfer due to natural ice roughness.

Besides heat transfer measured from clean cylinder surfaces, roughness effects have also

been studied on artificially roughened cylinders. The roughness effect was initially studied by

Nikuradse for pipe internal flow with sand grains (Nikuradse, 1933). The focus for that research

was on flow deficit due to skin friction. Nikuradse applied circular pipes with packed sand grains

as densely as possible. Unfortunately, for many real world applications, such as ice roughness, the

roughness density is significantly smaller than what was used by Nikuradse. Many analytical heat

transfer correlations developed by other authors adopted the term of equivalent sand roughness

(ks), but there was no universal conversion rule for converting real roughness to equivalent

roughness.

Heat transfer on a rough cylinder in cross flow was also studied by Achenbach. Achenbach

reported heat transfer enhancement with the presence of surface roughness for cross-flow

configurations (Achenbach, 1977). The roughness element was a pyramid shape and was

manufactured by knurling the surface of a copper cylinder. Achenbach measured the mean value

of the peak-to-valley roughness heights and reported the value both in dimensional form (k, mm)

and non-dimensionalized form (equivalent sand roughness with respect to cylinder diameter, ks/d).

Three different roughness sizes (k) were tested: 0.11 mm, 0.45 mm, and 0.9 mm, with

corresponding equivalent sand roughness height (ks) to be: 0.11 mm (ks/d = 75×10-5), 0.45 mm

(ks/d = 300×10-5), and 1.35 mm (ks/d = 900×10-5). Since there was no universal conversion rule

from the experimentally measured roughness height (k) to equivalent sand roughness height (ks)

(and Achenbach did not specify the method he used), the value k was used throughout this

dissertation, rather than the value of ks. The roughness was machined on the entire cylinder surface.

Although not representative of natural ice roughness, these data are still the most comprehensive

and systematic data in the literature related to the topic of heat transfer with surface roughness. It

22

was later found extremely valuable in heat transfer scaling law development in Chapter 5. The heat

transfer measurements on three types of artificially roughened cylindrical surfaces at Re = 2.2×105

are shown in Figure 1-12 and used as reference comparison cases in later experiments and analytical

model development.

Figure 1-12. Reference heat transfer on artificially roughened cylinders at Re = 2.2×105


Notice that the three different types of flow behaviors found on a clean cylinder under a

large range of Re (as already shown in Figure 1-11) were also identified on artificially roughened

cylinders at a single Reynolds number. In Figure 1-12, the clean cylinder operating at Re = 2.2×105

still exhibits the laminar separation behavior around 82°, whereas the 0.11 mm roughness cases

shows a clear spike indicating a strong flow reattachment after a prolonged laminar flow separation,

as denoted by the red circles. The two larger-size roughness cases (0.45 mm and 0.9 mm) follow a

similar early transition due to local roughness trend, especially after the two curves reach their peak

values around 50°-60°. The transition angle for the higher roughness element (0.9 mm) case was

found to be at the leading edge stagnation location, compared to the lower roughness (0.45 mm)

0

1

2

3

4

0 30 60 90 120 150 180

Fr =

Nu

/sq

rt(R

e)

Azimuth Angle, deg

Clean

0.11 mm

0.45 mm

0.9 mm

23

transitioning at 20.3°. Achenbach also published smooth and rough cylinders tested under a very

high Reynolds number of 4×106 as shown in Figure 1-13.

Figure 1-13. Reference heat transfer on artificially roughened cylinders at Re = 4×106


As can be seen from Figure 1-13, the two higher roughness element cases still exhibit

similar fully turbulent behavior with a transition immedietely at the stangnation region. Notice that

the overall magnitude of Frossling numbers is shifted up for these two cases. The lowest rough case

(0.11 mm) and the clean case did not transition at the stanagtion location. All four curves behaved

in a similar trend after their peak value, and also all separated from the surface at location around

110°. This was the highest Reynolds number tested in Achebach’s pressurized wind tunnel, which

is beyond the scope of this research. Figure 1-13 was shown to demonstrate the effect of Reynolds

number on the measured heat transfer magnitude. This Reynolds number effect on fully turbulent

cylinder heat transfer has been successfully eliminated using a proposed heat transfer scaling

parameter that will be shown in Chapter 5.

Makkonen proposed a modeling approaching based on integral boundary layer equations

(Makkonen, 1985) to model Achenbach’s artificially roughened cylinder tests. Results for three

0

2

4

6

8

0 30 60 90 120 150 180

Fr =

Nu

/sq

rt(R

e)

Azimuth Angle, deg

Clean

0.11 mm

0.45 mm

0.9 mm

24

example Reynolds numbers on the roughest cylinder were shown to correlate well in terms of the

overall magnitude. Inaccuracy in predicting transition angle was observed. Curvature effects were

ignored since the ratio of the boundary layer thickness to the cylinder diameter was considered to

be small enough. One observation based on the model was that the maximum predicted Nusselt

number was always found at 58°, independent of cylinder sizes and types of roughness. This

corresponds to a local velocity peak in the prescribed velocity distribution over azimuth angles. A

detailed discussion of the model can be found in the heat transfer model development section in

Chapter 5.

In addition to cylinder cases with surface roughness, direct heat transfer measurements on

artificially simulated irregular ice shapes on cylinders were attempted by researchers from 1984 to

1988. Identical ice shape models based on a 0.066 m (2.6 inch) diameter cylinder have been tested

at three facilities: NASA IRT (Van Fossen, Simoneau, Olsen, & Shaw, 1984), University of

Kentucky (Arimilli, Keshock, & Smith, 1984), and University of Tennessee (Pais & Singh, 1985).

The ice shapes were accreted to represent a time sequence of ice accretion for 2, 5, and 15 minutes

on the test cylinder. Two types of rough conditions were tested. One type used densely packed sand

grains as roughness elements, which featured an average height of 0.33 mm; whereas the other

condition was triggered using trip wires with roughness height of 0.508 mm. Two turbulent

intensities (0.5% and 3.5%) were tested in addition to surface roughness. The Nusselt numbers (Nu)

obtained within a range of Reynolds number (Re from 1×105 to 1.5×105) were found to agree well

across the three sets of data. The boundary layer transition from laminar to transitional or even

turbulent was found to be triggered and dominated by surface roughness. The presence of surface

roughness enhanced the heat transfer especially in the glaze ice horn region prior to separation. The

surface roughness was observed to account for an approximately 100% increase in maximum Nu,

whereas the minimum Nu values were virtually unchanged. In contrast, the free stream turbulence

uniformly raised the overall heat transfer level while the heat transfer rate distribution remained

25

unchanged. The measured Nu on rough surface were found to be a strong function of Re. Power-

law curve fittings were used to correlate Nu at different monitoring angles in the form of AReB.

Unfortunately, the curve fitting results for cylinder tests were case sensitive and deemed to be not

useful for natural ice-roughened surface modeling.

The experimental measurements on the previously mentioned four simulated ice shapes

were compared to heat transfer predictions by LEWICE 2D, version 1 (Ruff & Berkowitz, 1990).

LEWICE was developed at NASA Glenn (formerly Lewis) Research Center, and was regarded as

one of the most widely used industrial standard ice prediction codes. The code was developed based

on a 2D panel method rather than a 3D grid-based solution. Therefore, the code can be executed

very fast and was found to be very robust. Later in this dissertation, certain improvements of the

prediction on ice roughness and heat transfer were also based on LEWICE’s support. The outcome

of this research resulted in an improved ice prediction capability, as will be shown in Chapter 6.

One sample comparison of the LEWICE predicted heat transfer (code version 1) against

experimental measurement is shown in Figure 1-14.

Figure 1-14. Example of LEWICE heat transfer over-prediction

Data source: Ref. (Van Fossen, Simoneau, Olsen, & Shaw, 1984) and (Ruff & Berkowitz, 1990)

-2.1 -1.26 -0.84 0 0.84 1.26 2.1

Dimensionless Location on cylinder, s/D

0

300

600

900

1200

1500

Heat T

ransfe

r C

oeff., W

/m2K

26

Experimentally measured results on a 5-minute simulated cylinder ice shape with 8 flux

sensors (top-left corner, sensors denoted by red circles) were compared to LEWICE heat transfer

predictions as shown in Figure 1-14. Close to the stagnation area, the prediction was at the same

level as the experiments. LEWICE also predicted the general trend for heat transfer distribution on

the cylinder ice shape. However, the heat transfer rate at the edge of the ice shape (“horn” like

shape) was significantly over-predicted, as shown by the solid black line in the heat transfer chart.

This over-prediction was also observed during the experimental measurement in this study, as will

be shown later in Chapter 4. This phenomenon was also one of the motivations for this study, which

was to improve the current heat transfer module for ice prediction.

Compared to the limited experiments conducted on artificially simulated surfaces

mentioned above, even less data exist for cylinder heat transfer related to natural ice roughness. In

the late 1980s, Hansman et al. (Hansman, Yamaguchi, Berkowitz, & Potapczuk, 1989) categorized

natural ice roughness distribution on cylinders in three icing wind tunnels (NASA IRT, B.F.

Goodrich Ice Protection Research Facility, and the Data Products of New England six inch test

facility). Multiple zones of roughness were identified during the study. Typically, a smooth zone

at the leading edge was observed close to the cylinder stagnation line, followed by a rough zone

and later merged to clean surface. Transition locations were also recorded (Hansman & Turnock,

1988) with respect to icing spray time at two different ambient temperatures (-4.5°C vs. -9°C), two

different materials of substrates (copper vs. Plexiglas), and two different surface finishes (knurled

vs. polished). Unfortunately, no tabulated test matrix (missing information such as roughness

height, smooth zone width, complete icing conditions, and test cylinder diameter etc.) was found

for this study. Therefore, no quantitative analysis can be completed for the roughness distribution

on ice roughened cylinders found in the literature. A detailed measurement of both natural ice

roughness distribution on the cylinder and associated heat transfer needs to be conducted to fill in

this research gap.

27

1.2.1.3 Heat Transfer on Airfoils

Although there have been numerous heat transfer models of surface roughness effects on

flat plates, cylinders, and other simple geometries, there are still limited experimental databases on

airfoils with surface roughness.

Early studies of heat transfer on iced airfoils can be dated back to the 1940s, at which time

the importance of understanding ice protection system efficiency was recognized by aircraft

engineers. Between the years 1946 and 1951, comparison of heat transfer data taken both in-flight

and in NASA Glenn Research Center (formerly Lewis Research Center) Icing Research Tunnel

(IRT) has been carried out on clean and iced airfoils. In-flight data of seven cases for NACA 0012

airfoil and fifteen cases for NACA 65,2-016 airfoil were obtained by Neel et al (Neel, Bergrun,

Jukoof, & Schlaff, 1947). Five of the NACA 65,2-016 data sets were later compared to nine IRT

wind tunnel results conducted by Gelder and Lewis (Gelder & Lewis, 1951) using a 2.44 m (8 ft.

chord) by 1.83 m (6 ft. span) test model. When comparing IRT experiments to the flight measured

data, the heat transfer rates at the stagnation region were inconsistent and case sensitive. An average

of 35% deviation was observed in the IRT measured data. The discrepancy was attributed to the

high turbulence intensity in the tunnel. No further comparisons between IRT data and flight tests

were made due to this discrepancy.

The flight tests by Neel et al (Neel, Bergrun, Jukoof, & Schlaff, 1947) were designed to

provide heat transfer data so as to predict the power requirement of thermal de-icing system.

Electric heaters were used at the leading edge area of test airfoils. It was found that extension of

the heated area to 18% s/c was adequate to ensure evaporation of all of the water intercepted. An

increase in heat requirement to de-ice was found corresponding to a decrease in altitude. This was

caused by the rate of evaporation of water increasing as altitude decreased. Therefore, it was

recommended that airfoil thermal ice protection system with a fixed power supply (such as

28

electrical systems) be designed for the minimum altitude at which the airplane was expected to

encounter icing. In addition, to make a more realistic estimation of power requirement, the

predicted transition location was shifted from experimentally measured smooth airfoil heat transfer

curve to an estimated early transition location (5% s/c). This shift was determined to be necessary

to account for the premature transition at the wetted leading edge area due to residual ice roughness

when using an electrical de-icing system. The early laminar to turbulent transition enhanced local

convective heat loss, for which the lost power was supposed to be used for de-icing purposes.

Therefore, additional thermal heating power was required to overcome the convective heat due to

the early transition induced by the de-icing procedure. By assuming a premature transition at 5%

chord length, it was estimated that the de-icing system required 10% more power to de-ice,

compared to an ideal laminar flow condition during flight test. This early flow transition concern

due to residual ice roughness for ice protection design is illustrated in Figure 1-15. Notice that the

estimation of 5% premature flow transition was used for all the tests reported in Neel’s work. There

was no discussion about whether the 5% transition location was a safe assumption for all different

icing conditions. A more systematic examination of the surface heat transfer behavior was required

to ensure an accurate power requirement estimation for an ice protection system.

Figure 1-15. Reference heat transfer coefficients from flight test

Chart from Figure 30 of Ref. (Neel, Bergrun, Jukoof, & Schlaff, 1947)

29

No systematic experiments on iced airfoils had been conducted for the three decades since

the 1950s. At the late 1980s, by following the same attempt to relate the local Nu to Re as mentioned

above in cylinder heat transfer research, Pais and Singh conducted heat transfer measurements of

artificially simulated ice shapes on both a cylinder (Pais & Singh, 1985) and a NACA 0012 airfoil

with varying angles of attack (AOA) up to 8° (Pais, Singh, & Zou, 1988). The leading edge nose

region of the clean airfoil yielded similar heat transfer results to those of the cylinder, which were

found to be independent of the angle of attack. Therefore the Frossling number (𝐹𝑟 = 𝑁𝑢 √𝑅𝑒⁄ )

which was introduced in previous cylinder studies was also used for airfoil heat transfer

measurement. The Frossling number was originally defined for low Re, laminar boundary layer,

cylinder-in-cross-flow heat transfer analysis, but was found to be also effective to non-

dimensionalize heat transfer for airfoil cases. The use of Frossling number as a measure of heat

transfer in place of the Nusselt number was also adopted for a series of testing conducted at NASA

IRT for heat transfer studies on airfoils with artificial roughness. The series of tests involved both

in-flight testing (Newton, Van Fossen, Poinsatte, & DeWitt, 1988) and experiments in NASA IRT

(Poinsatte & Van Fossen, 1990) (Poinsatte, Van Fossen, & Newton, 1991). A total of 46 sets of

data for both clean and artificially roughened airfoils was reported. A total of 28 copper heat flux

gauges was applied to the airfoil, but only 12 discrete locations (ranging from -3.6% to 9.5% of the

surface wrap distance with respect to the airfoil chord, s/c) were monitored due to the gauge size

limitation and complexity of the accompanied guard heater system (Newton, Van Fossen, Poinsatte,

& DeWitt, 1988). The surface roughness was simulated using a 2-mm diameter hemisphere

roughness element in three patterns: leading edge, sparse, and dense packed. The addition of

artificial roughness drastically increased the heat transfer downstream of the stagnation. From the

comparison of the effect between the sparse and dense roughness, it was found that the effect of

the increased density of the roughness dramatically disturbed the local boundary layer and

30

immediately downstream. In contrast, as the flow passed the dense roughness area, the heat transfer

recovered to a level that was consistent with the sparse roughness pattern, as shown in Figure 1-16.

Figure 1-16. Reference heat transfer on artificially roughened airfoils at zero AOA

Chart from Figure 15 of Ref. (Newton, Van Fossen, Poinsatte, & DeWitt, 1988)

The symbols were measurements on artificially roughened airfoil under different Reynolds

numbers, whereas the solid line was clean airfoil measurement. The clean airfoil heat transfer data

were also used for comparison with the AERTS measurements in later chapters. As indicated by

Figure 1-16, the heat transfer rate measured across various Reynolds number correlated well in

terms of Frossling number. The heat transfer curves initially followed the clean airfoil trend as

depicted using a solid black line. The sudden jump in the curves suggested that a flow transition

due to local roughness elements took place in all the test cases at the same location. After flow

passed 4.8% s/c where the dense roughness pattern ended, the curves relaxed to a lower level,

following the smooth airfoil trend. This trend was also observed in the study outlined in this

dissertation and will be shown in later experimental result section. The NASA testing results also

suggested that the modeling method of using an inscribed cylinder and flat plate approximation

substantially over-predicted heat transfer for the NACA 0012 airfoil. Early transition from laminar

2% 4% 6% 8% 10%

Fro

sslin

g#,

Fr=

Nu

/Re

0.5

0Dimensionless Surface Distance, s/c

0

6

2

8

4

Dense roughness pattern ends here

31

to turbulent flow due to roughness elements protruding outside of the boundary layer was also

observed.

The shortcoming of the previously mentioned testing was that artificial roughness is not

representative of real ice roughness. Shin (Shin, 1994) conducted a series of parametric studies on

surface roughness on a 0.5334 m (21 inch) chord NACA 0012 airfoil. The roughness height was

evaluated from photographic processing of photos taken from side views of iced airfoils. The

roughness base diameter and spacing were calculated from the top view, assuming the element was

a uniform hemispherical shape. The results indicated that a uniformly distributed artificial

roughness model was valid only at the very early stage of ice onset. The roughness height ranged

from 0.28 to 0.79 mm. The element base diameters varied from 0.56 mm to 1.56 mm with a spacing

of 1 to 1.3 times of element diameters. Further research that analyzed a total of 76 surface roughness

measurements on three different chords of NACA 0012 airfoils was conducted by Anderson et al.

(Anderson, Hentschel, & Ruff, 1998). It was suggested that roughness element diameter increased

with the accumulation parameter until it reached a plateau of about 0.06 d/2R, which was 1.01 mm

in this test case. Judging from these two independent research results, the previously mentioned

heat transfer measurements on 2-mm-diameter, equally-spaced artificial roughness elements were

not representative of the natural convective heat transfer related to aircraft ice accretion. In addition,

roughness height data were obtained from two-dimensional photographic images that inherently

came with large uncertainty. Anderson et al. (Anderson, Hentschel, & Ruff, 1998) did a human

factor study to determine the measurement consistency. It was concluded that the image processing

technique was subject to significant user interpretation. The authors suggested two alternative

techniques: three-dimensional scanning, and ice shape molding and casting. The 3D scanning

technique, such as the one used in Reference tests at NASA IRT (Lee, Broeren, Addy, Sills, &

Pifer, 2012) (Kreeger & Tsao, 2014), is considerably expensive and it is time-consuming to post-

process the scanned surface before it can be imported into computational fluid dynamics (CFD)

32

codes. The latter technique, the ice casting model, has been recognized for its capability of retaining

fine ice features and can be tested outside icing wind tunnel environments (Reehorst & Richter,

1987). Both techniques have been adopted for this research and will be compared in detail in

Chapter 3.

Due to the complexity of the ice accretion and molding procedure, scattered data exist in

literature for heat transfer on ice casting models. From 1995 to 1999, Dukhan et al. (Dukhan,

Masiulaniec, & DeWitt, 1999) studied seven flat plate test strips with ice shape castings on the

surface. Correlation development between flat plate Stanton number (St) and Reynolds number

(Re) was attempted. Some dependencies of St magnitude on the roughness element height were

observed, but could not be applied to all models for the entire range of Re tested. Two years later,

the same research group (Dukhan, DeWitt, Masiulaniec, & Van Fossen, 2003) conducted wind

tunnel testing on two ice-roughened casting models of NACA 0012 airfoils. The results were

compared to those of clean airfoils and artificially roughened airfoils with hemispherical elements

used in previous testing (Newton, Van Fossen, Poinsatte, & DeWitt, 1988). The authors identified

a 306% maximum increase in heat transfer coefficient on actual ice roughness compared to results

measured on clean airfoil surfaces, and a 192% increase compared to the artificial dense

hemispherical element results. Flow transition very close to the leading edge (less than 4% s/c) was

also observed for the two cases. So far, only two ice-roughened airfoil heat transfer measurements

have been identified from the literature. Heat transfer data from representative ice shape castings

with actual surface roughness continues to be desired. The experimental gap will be addressed in

this research.

Apart from the lack of experimental measurements of the surface roughness effects on ice

roughened airfoils, the accuracy of the analytical prediction of ice accretion on airfoils depends

heavily on the surface energy balance, where the convective heat transfer plays a dominant role.

For instance, the widely used LEWICE 2D ice prediction code utilizes integral boundary layer

33

equations to calculate heat transfer coefficients. As mentioned, the surface roughness height is

estimated by empirical correlations. It had also been mentioned in several editions of user manuals

(Ruff & Berkowitz, 1990) (Wright, 1993) that LEWICE tends to over-predict the magnitude of the

maximum heat transfer coefficient, which was part of the reason for the failure to predict glaze ice

accretion shapes. A detailed comparison of the proposed heat transfer prediction tools developed

in this research and the LEWICE heat transfer prediction module can be found in Chapter 5 and

Chapter 6.

1.2.2 Performance Degradation

Airfoil performance can be significantly altered by ice accretion during adverse weather

encounters. Aircrafts have difficulty maintaining altitude under icing conditions due to significantly

reduced lift-to-drag ratios of iced lifting surfaces. Specifically for helicopters, ice accretion

increases drag and may cause a rise in required torque to maintain a desired operational rotation

speed. Ice accretion on rotor blades increases power consumption, confines the maneuverability of

the helicopter, limits autorotation envelopes, and may even result in engine failure. Airfoil

performance degradation due to ice accretion must be fully understood to address these safety

concerns.

As mentioned in the previous sub-sections, after the surface roughness changes the local

heat transfer mapping on an airfoil, the ice starts to build towards a fish-tail shape (in glaze icing

regimes) at the leading edge stagnation region. An inaccurate prediction of ice shape due to heat

transfer overestimation is likely to occur using current prediction models and thus result in incorrect

performance degradation predictions. The effect of additional surface roughness on iced airfoil has

been studied by Bragg (Bragg, 1982). The test airfoil was a NACA 65A413 airfoil with a 0.1524

m (6 inch) chord and 0.1524 m (6 inch) span. A total of 42 pressure taps was used to provide lift

34

and pitching moment data. The drag coefficient was calculated using the wake deficit method. The

ice thickness accounted for 2.5% of the chord length, protruding into the incoming flow stream.

The roughness elements were Carborundum grits with an average size of 0.381 mm (0.015 inch),

which resulted in a roughness-to-chord ratio (k/c) of 0.0025. A comparison of lift and drag polar

data is shown in Figure 1-17

Figure 1-17. Reference surface roughness effect on aerodynamics

Source: Figure A-10 and A-11 of Ref. (Bragg, 1982)

Bragg’s wind tunnel aerodynamics testing of simulated ice shape with and without artificial

roughness revealed that a clean airfoil (no ice) with artificial leading edge roughness had the same

drag penalty compared to an airfoil with smooth rime ice shape. The most severe case occurred

when combining the simulated rime ice shape together with artificial surface roughness. At Angle

of Attack of 4°, a 100% increase in drag on the iced airfoil with roughness was measured compared

to clean airfoil. The additional roughness on rime ice accounted for more than 50% increase in

drag. In addition, there was no effect from either rime ice shape or leading edge roughness on the

pitching moment. There was an approximate 20% reduction in lift for all cases, independent of

35

roughness, smooth ice shape, or rough ice shape model. The overall magnitude of the lift curve fell

in to same range. Reductions in stall angle and maximum lift coefficient (Clmax) were also observed.

Notice that the primary goal of Bragg’s test was to differentiate the surface roughness effect on

aerodynamics. The ice shape studied in this case was a simulated ice shape without any icing

condition tabulated. The simulated ice shape was not representative for natural aircraft ice

accretion. Additional experimental work was needed to analyze the aerodynamics impact of surface

roughness on natural aircraft ice shapes.

Despite the concerns due to inaccurate ice accretion, data from experimental testing is still

limited to validate the current ice shape prediction tools and performance degradation prediction

models. Gray et al. conducted a series of tests on several airfoils under icing condition in the late

1950’s (Gray, 1958) (Gray & Von Glahn, 1958). Flemming and Lednicer investigated high-speed

ice accretion on various rotorcraft airfoils (Flemming & Lednicer, 1985). Wind tunnel airfoil drag

measurements with ice shapes obtained under different icing conditions have been carried out by

Shaw et al. (Shaw, Sotos, & Solano, 1982), Olsen et al. (Olsen, Shaw, & Newton, 1984), Shin &

Bond (Shin & Bond, 1992), and (Addy, Potapczuk, & Sheldon, 1997). Simulated ice shapes have

also been used for dry air wind tunnel aerodynamics testing (Papadakis, Alansatan, & Seltmann,

1999) (Broeren, et al., 2010).

Experimental ice accretion databases are limited mainly due to the limited number of icing

facilities available and the relatively high cost of testing. Compared to icing experiments, numerical

ice accretion simulation tools have been recognized to be capable of reducing the cost to evaluate

ice accretion effects. Two-dimensional and three-dimensional ice prediction codes, such as

LEWICE 2D (Wright, 2008) and FENSAP (Bourgault, Boutanios, & Habashi, 2000) have been

developed and implemented for airfoil performance evaluation under icing conditions. Even with

these modeling advances, the fidelity of these numerical tools for ice shape prediction and

36

performance evaluation cannot be fully validated due to limited documented ice shapes and related

aerodynamic data.

Empirical correlations between test conditions and the resultant aerodynamic coefficients

are most prevalently used as engineering tools during the design of airfoils and ice protection

systems. The commonly used empirical performance degradation correlations were established by

Gray (Gray, 1964), Bragg (Bragg, 1982) and Flemming (Flemming & Lednicer, 1985). Due to the

limited database available, the three existing drag correlations are validated only to their own

experimental datasets which were obtained when the empirical prediction tools were developed.

The three correlations have limitations when applied to a more comprehensive icing condition

range (Miller, Korkan, & Shaw, 1987).

To understand the performance degradation due to icing on helicopters rotor blades, both

analytical and experimental determination methods based on rotor ice accretion experimental

measurements are desirable. Miller et al. demonstrated the feasibility of statistical analysis as a

powerful instrument in empirical ice performance degradation tool development (Miller, Korkan,

& Shaw, 1983). Due to the scattered data available at the time when Miller’s paper was written, the

prediction developed using statistical methods was not satisfactory in terms of accuracy, as stated

by the author in one of his later publications (Miller, 1986). Given the potential benefits of statistical

methods to provide ice degradation prediction tools and the current lack of experimental ice shape

and performance datasets, a novel, icing-physics-based correlation tool to predict drag increases

due to icing conditions was developed in this research using available experimental icing databases

and new rotor testing ice shapes.

1.3 Dissertation Objectives

The following objectives are identified in this dissertation:

37

1. To obtain representative natural ice shapes with different surface roughness regimes on an

airfoil to expand the existing icing roughness database.

2. To develop a method to capture the delicate ice roughness so that the preserved shape can

be used for warm air wind tunnel testing. To fabricate detailed accreted ice structure models

and obtain quantified roughness data.

3. To develop a measuring technique for high-resolution heat transfer acquisition without

damaging the delicate ice structures. To compare the experimental measured heat transfer

to existing reference data. To develop a scaling method to eliminate Reynolds number

effects when comparing results conducted at different conditions.

4. To develop a novel physics-based modeling tool to predict ice roughness distribution and

associated heat transfer coefficient. To implement the proposed roughness and heat transfer

models to improve current ice shape prediction model.

5. To validate the ice prediction tool by conducting ice shape accretion tests and use the

accreted ice shape for wind tunnel aerodynamics testing to evaluate the airfoil performance

penalty in terms of lift, drag and pitching moment.

6. To develop a physics-based correlation between icing condition and resultant drag penalty.

To implement the performance degradation correlation coupled with a rotor aerodynamics

code to predict torque along the entire span of rotor and compare to the rotor test stand

torque measurements, so as to validate the proposed aerodynamics model.

38

1.4 Dissertation Overview

Based on the above proposed objectives of this study, both experimental and analytical

approaches have been determined to be carried out. A work path was established to achieve these

objectives, as shown in Figure 1-18.

Figure 1-18. Work path for this research

The previously mentioned research objectives are addressed following each step in Figure

1-18. Accordingly, this dissertation has been subdivided into following chapters:

An Improved Ice Accretion Prediction Tool

for Helicopter Icing Research

Generate Ice Shapes

(Rotor Test Stand)

Icing Condition Scaling

Icing Cloud Calibration

Airfoil Cylinder Flow Field Simulation

Molding and Casting3D Laser Scan Mesh

for CFD Analysis

Surface Roughness

MeasurementRoughness Prediction

Heat Transfer Testing

(Wind Tunnel)

Heat Transfer Modeling

Coupled w/ LEWICE

Aerodynamics Testing

(Wind Tunnel)

Performance Correlation

Coupled w/ BEMT

Experimental Analytical

39

Chapter 2: Experiment Configurations

Experimental configurations for testing are presented in this chapter. A rotor testing stand

for ice accretion and a wind tunnel for 2D heat transfer and aerodynamics data analysis are first

introduced. Parameters for ice accretion tests are explained. Airfoil design and associated test

matrices are then listed for different tasks. Testing techniques such as molding and casting

techniques, temperature monitoring techniques, and force and moment measurement techniques

are described in details in subsections.

Chapter 3: Ice Roughness Measurement and Prediction

In this chapter, the experimental method for ice roughness measurement is introduced.

Roughness can be categorized and compared to existing correlations. A novel correlation based on

icing-physics between icing conditions and roughness features are then developed for cylinders and

airfoils. The roughness prediction results are compared to both existing databases and the

experimental measurements in this study.

Chapter 4: Transient Heat Transfer Measurements

A non-intrusive experimental method for heat transfer measurement on surfaces with

roughness is described in this chapter. The technique was validated against various reference data

on simple geometries. Heat transfer measurements on ice-roughened cylinders and airfoils are then

discussed in detail. The flow transition behaviors associated with heat transfer under extensive

Reynolds number regimes are deliberated. A parametric study of effects of individual icing

condition on heat transfer is presented and shed light on the model development in Chapter 5.

Chapter 5: Heat Transfer Model Development

Scaling methods for heat transfer over both laminar and turbulent regimes are examined in

this chapter. A novel heat transfer scaling method designed for fully turbulent flow regime was

applied to reference heat transfer measurements on generic testing surfaces. A correlation and an

40

analytical heat transfer modeling tool applicable to aircraft icing heat transfer phenomenon are

developed.

Chapter 6: Improved Ice Accretion Predicting Tool

This chapter serves as a bridge between the aerodynamics and thermal physics study in this

research. The previous approaches for ice roughness prediction and heat transfer modeling are

coupled with an ice shape predicting tool (LEWICE 2D) to obtain an improved ice shape prediction

capability. Predicted ice shapes were compared to both literature and experimental measured shapes

for validation. The accreted ice shapes were then used in study in Chapter 7 for airfoil performance

degradation analysis.

Chapter 7: Aerodynamics Testing and Modeling with Accreted Ice Structures

Aerodynamics testing of representative natural ice shapes was conducted. An extensive

survey of existing aerodynamic performance degradation correlation is provided. Based on the

literature survey and experimental measurements, a comprehensive correlation for aerodynamics

performance prediction on iced airfoils was developed and coupled with a rotor aerodynamics code

to predict rotor torque penalty. The proposed correlation is then compared to databases on various

types of airfoils at varying Angles of Attack found in literature and experimental measurements in

this study.

Chapter 8: Conclusions

This chapter gives a review of the previous chapters. The analytical and experimental

efforts in aerodynamics and thermal physics study of aircraft ice accretion are summarized.

Concluding remarks on the findings together with recommendations for future research are

presented.

41

Chapter 2

Experiment Configurations

2.1 Rotor Ice Accretion Experiment

All ice accretion experiments are conducted at the Adverse Environment Rotor Test Stand

(AERTS) laboratory at the Pennsylvania State University. A schematic three-dimensional model

of the test stand inside a cold chamber is shown in Figure 2-1.

Figure 2-1. AERTS test chamber schematic

CAD model: courtesy of Ed Brouwers (Brouwers, 2010)

The test stand is inside a cold chamber that is capable of maintaining constant temperatures

ranging from 0 to -25 °C during icing tests. Ballistic walls are placed surrounding the test stand for

protection. The chamber has dimensions of 6 m (length) × 6 m (width) × 3.5 m (height). The test

rotor blades can be mounted onto a rotor head, which was originally designed and manufactured

42

for QH-50 DASH unmanned helicopter in 1960’s. A slip ring is located in the center of the test

chamber to couple the electric signals between the rotating test stand and the static data/power

transmission cables. A total of 48 channels for data communication and 48 channels for power

supply is available to transmit signal/power between the rotor test stand and the control room.

Fifteen (15) standard icing nozzles were donated by the NASA Icing Research Tunnel (IRT) and

placed in the ceiling of the chamber. The nozzles are used to spray icing clouds representative of

natural icing conditions by controlling the size and cloud density of water particles. The icing

clouds are generated by following the standard calibration procedure at NASA IRT (Ide &

Oldenburg, 2001). The first test stand motor was donated by the Boeing Company and was

originally used on a tilting engine prototype research. It was capable of delivering 120 hp of power

with tilting capability, but locked in place for all the previous research. A picture of the rotor test

stand with a set of testing rotor blades is shown in Figure 2-2.

Figure 2-2. AERTS rotor test stand with the test blade mounted

In Spring 2015, the facility went through a major renovation. A new test stand that houses

a Torque Master 125 Hp, 1800 RPM (Revolution per Minute) motor was designed and installed by

the author of this dissertation, as shown in Figure 2-3. The new rotating plane was set approximately

at the same height of the previous configuration (only 3 inches higher), thus minimizing the flow

43

field changes between two configurations. With the introduction of the new 1800 RPM motor, the

testing capability has been significantly improved.

Figure 2-3. AERTS current test stand schematics, renovated in Spring 2015

The test facility is capable of accommodating full-scale-chord rotor blades for various

testing purposes, such as rotor ice accretion tests, rotor shedding tests for coating evaluation, high-

speed impact tests, etc. Specific information regarding the facility’s capabilities is summarized in

Table 2-1.

Table 2-1. AERTS Facility Specifications

Chamber Dimensions [m] 6 × 6 × 3.5

Rotor Speed [RPM] 0 to 1800

Blade Diameter [m] 2.743

Driving Motor Power [Hp] 125

Collective Pitch Range [deg] -2 to 12

LWC [g/m3] 0.2 to 5

MVD [μm] 10 to 50 (standard), 50 to 500 (Mod-1 nozzle)

Signal and Power Transmission 48 signal channel / 48 power channel slip ring

Measurement Instrument Shaft torque sensor / 6-axis load cell

44

2.2 Icing Condition

In previous icing conditions measurements and ice shape reproduction efforts in the

facility, the capability to measure and control icing cloud parameters such as Median Volume

Diameter (MVD) and Liquid Water Content (LWC) has been demonstrated (Palacios, Brouwers,

Han, & Smith, 2010) (Palacios, Han, Brouwers, & Smith, 2012). During the facility calibration

procedure, one important lesson was learned when comparing ice shapes accreted in different

facilities with different test airfoil dimensions. To obtain the same non-dimensionalized ice shapes,

it was necessary to apply an icing condition scaling method to match the non-dimensionalized icing

scaling parameters (Anderson, 2004). Before introducing the test matrices for experimental efforts

in this study, an overview of conventional icing parameters and non-dimensionalized icing scaling

parameters from icing conditions scaling methods are presented in this section.

2.2.1 Icing Parameters

In a natural icing condition, even at very low temperature, there are super-cooled water

droplets suspended in the air, with droplet temperature below the freezing point. When an aircraft

impacts the water droplets, the water freezes onto the aircraft frame, wings, and helicopter blades.

To characterize different icing clouds, three icing parameters are described here to categorize

different icing regimes, namely: ambient temperature, Median Volume Diameter (MVD) and

Liquid Water Content (LWC). Depending on the icing conditions, different ice shapes will occur,

which could be generally categorized into three groups: rime ice, glaze ice, and mixed ice which is

a mixture of rime ice and glaze ice. Ice shapes obtained from previous facility validation efforts

(Han, Palacios, & Smith, 2011) are shown in Figure 2-4 to represent the proposed ice shape

categorization.

45

Figure 2-4. Ice shape categorization

Glaze ice is usually obtained at warm temperatures when high water content is found inside

an icing cloud. At warm temperatures, super-cooled water droplets may not freeze upon

impingement; rather, it generates a thin water film on the surface, allowing the water to move to a

position farther back from the leading edge and then freeze. As can be seen in Figure 2-4, it features

a wet growth due to the existence of a water layer on top of the ice structure. The accreted ice shape

has peak thickness at an angle from the airfoil chord centerline. The ice structure protruding into

the incoming free stream is often called an ice horn and the overall ice shape is usually called a

“fish tail” shape. In contrast, rime ice is usually found to be smooth in shape and opaque. In cold

temperatures, the water particles are likely to freeze upon impact. The accreted ice shapes are then

likely to follow the airfoil aerodynamic shape. The direct freezing procedure introduces particle

deposition with air trapped in the ice structure, therefore rendering the opaque white ice shape. The

mixed ice shape has characteristics of the two major ice shape categories. It has a dry growth at the

leading edge stagnation area, where some irregular ice structure suggests surface running water

effect is dominating this region away from the stagnation area. Some ice structures that are isolated

from the main ice shape can also be seen from the mixed ice. These structures are called ice feathers,

which will be shown to affect the aerodynamics in Chapter 7.

In a natural icing environment, the ambient temperature usually ranges from -30 °C to the

freezing point of water as stated in the FAA Aircraft Icing Handbook (Heinrich, et al., 1991). The

46

temperature has a primary effect on the final ice shape type. Typically, rime ice occurs at

temperatures lower than -10 °C; whereas glaze ice usually is found at relatively warmer

temperatures, from 0 °C to -10 °C.

Liquid Water Content (LWC) and Median Volume Diameter (MVD) are two parameters

that are typically used to describe an icing cloud. LWC is the characteristic water-to-air

concentration in a two-phase flow (liquid and gas). The unit is g/m3 which denotes the liquid water

content per unit volume of the incoming air. Higher water concentration in an icing cloud increases

the likelihood of ice accretion and therefore is more likely to jeopardize the flight safety.

The MVD of a cluster of water droplets denotes the average water droplet size in

micrometers. The MVD in the AERTS facility is controlled by the input air-to-water pressure ratio

of the spraying nozzles. The air and water pressures are monitored by gauge sensors mounted on

the nozzles. The particle size is then determined by the input air pressure according to NASA Glenn

IRT calibration tables (Ide & Oldenburg, 2001). From previous understanding of fixed wing

aircraft, the Super-cooled Large Droplet (SLD, 50 – 500 μm) in the air also has large effect on

aircraft safety. Well-known aircraft accidents raised attention of the SLD icing issues, such as

aircraft accidents at Roselawn, IN (1994), Monroe, MI (1997), Pueblo, CO (2005), San Luis, CA

(2006) and Lubbock, TX (2009) etc. (Weener, 2011). For this research, the regular MVD range

between 10 μm and 50 μm are studied primarily for helicopter icing.

The distribution of LWC and MVD inside of a natural icing cloud is summarized in Figure

2-5. The two shaded areas are icing envelopes defined by FAA in Appendix C of FAR Part 25

(Transport category airplanes) / Part 29 (Transport category rotorcraft) (Federal Aviation

Administration, 2001). The two groups are separated based on the extended range of different

clouds. From meteorology studies, the icing clouds can be categorized into two forms: stratiform

clouds and cumuliform clouds. The former is an evenly distributed cloud with continuous

characteristics; the latter is based on convective clouds that only exist in intermittent form. The

47

stratiform has a range of 17.4 nmi (nautical mile), while the cumuliform only lasts 2.6 nmi as

recorded in Aircraft Icing Handbook (Heinrich, et al., 1991).

Figure 2-5. Icing condition envelop suggested by FAA

Compared to the FAR Appendix C icing envelopes in the shaded areas, the dashed lines in

Figure 2-5 provide a different representation of the icing cloud measurements. The three dashed

lines are the outer envelopes of around 1000 measured LWC-MVD data combinations under

different temperature ranges recorded in Aircraft Icing Handbook (Heinrich, et al., 1991).

A particular icing cloud should be considered as a system of icing parameters. LWC and

MVD combinations need to be analyzed to characterize an icing cloud. As can be seen in Figure

2-5, the MVD and LWC in an icing cloud both drop sharply as the temperature decreases. This

phenomenon shows a contrast between extreme ambient temperature and extreme icing clouds.

-30°C

0°C

0°C

-10°C

-20°C

-10°C

-20°C

-30°C

48

When designing an icing protection system, the icing severity needs to be weighted according to

different icing parameter combinations. For most of the cases, larger LWC-MVD combinations at

warmer temperatures are usually more severe than lower LWC-MVD combinations at colder

temperatures. This is because water, as a heat transfer medium, has a large specific heat capacity.

More water frozen on the surface means more energy consumption to eliminate it. For a hot air de-

icing or electro-thermal de-icing system, low energy consumption is always desired.

2.2.2 Icing Scaling Parameters

The icing scaling method is considered in the context that a given icing facility may only

be able to achieve a certain range of test conditions in terms of velocity, temperature, geometry, or

icing cloud (LWC and MVD). An icing scaling method has to be implemented to obtain scaled icing

conditions due to dimension changes between a reference model and a scaled-down model. A

detailed discussion of the scaling method for ice accretion testing is presented in Appendix C.

Validation of this scaling method at the AERTS laboratory has also been demonstrated in a previous

Master thesis (Han, 2011). In this section, only the non-dimensionalized icing scaling parameters

that will be used later in icing physics model development are introduced.

The first dimensionless parameter, collection efficiency, β, was introduced by Langmuir

and Blodgett to define the fraction of incoming water content that actually impacts the monitoring

control volume (Langmuir & Blodgett, 1946), where the subscript, 0, denotes that it is calculated

at the stagnation line. It is assumed that there is no incoming interfering water into the control

volume at this location. The expression for β0 is given by:

𝛽0 =1.40 (𝐾0 −

18)

.84

1 + 1.40 (𝐾0 −18)

.84 (2-1)

49

where K0 is Langmuir and Blodgett’s expression for the modified inertia parameter. The numerical

expression of this parameter can be found in Appendix C as a function of impact velocity and

droplet size.

An accumulation parameter, Ac, is defined in Equation (2-2) to show normalized maximum

local ice thickness to represent the non-dimensionalized incoming water mass flux caught in the

local surface control volume.

𝐴𝑐 =𝑉 ∙ 𝐿𝑊𝐶 ∙ 𝜏

𝑐 ∙ 𝜌𝑖=

𝑖𝑛𝑐𝑜𝑚𝑖𝑛𝑔 𝑖𝑐𝑒 𝑚𝑎𝑠𝑠

𝑟𝑒𝑓. 𝑖𝑐𝑒 𝑚𝑎𝑠𝑠 𝑏𝑎𝑠𝑒𝑑 𝑜𝑛 𝑐ℎ𝑜𝑟𝑑∙

𝑝𝑒𝑟 𝑢𝑛𝑖𝑡 𝑣𝑜𝑙.

𝑝𝑒𝑟 𝑢𝑛𝑖𝑡 𝑣𝑜𝑙. (2-2)

where, τ is the icing time and d is the characteristic model dimension, which is usually the diameter

of the test cylinder and twice the leading edge radius for symmetric airfoils. The leading edge radius

is defined as the radius of airfoil nose circle centered on a line tangent to the leading-edge camber

(chord line of a symmetrical airfoil) and connecting the tangency points of the upper and lower

surfaces of the leading edge. Typical leading-edge radii are zero to 1 or 2 percent of the chord (e.g.

1.58% for NACA 0012 airfoil).

Last but not least, the freezing fraction, n, is introduced to denote the ratio of impinging

water that freezes within a control volume. This term was first introduced by Messinger (Messinger,

1953) and later developed by Ruff (Ruff, 1986) as shown in Equation (2-3):

𝑛0 = (𝑐𝑝,𝑤𝑠

Λ𝑓) (𝜙 +

𝜃

𝑏) (2-3)

where the subscript, 0, denotes this freezing fraction is calculated at the stagnation line. The exact

definitions for ϕ, θ, and b can be found in Appendix C of this dissertation.

This validity of this scaling method has been demonstrated in several research papers (Han,

Palacios, & Smith, 2011) (Han, 2011). The previously mentioned icing scaling parameters, i.e.,

collection efficiency (β0), accumulation parameter (Ac) and freezing fraction (n0), will be valuable

during the development of icing aerodynamics and thermal physics prediction models.

50

2.3 Test Blade Designs

The facility can accommodate test blades with dimensions up to 0.813 m chord (32 inch)

and 2.743 m diameter (9 ft). Two rotor blades have been used during this research to generate

experimental ice shapes on cylinders and airfoils. A brief introduction of the test rotor blade design

is shown in this subsection.

2.3.1 Design of 21-inch-chord NACA 0012 Rotor Blade

A CAD model of the test blade used for the majority of ice shape experiments is shown in

Figure 2-6.

Figure 2-6. AERTS 21-inch-chord “Paddle Blade”

This is the same model that has already been shown in Figure 2-2 in the facility

introduction. The blade radius is 1.372 m (54 inch). The designed rotational speed of the blade is

between 300 and 600 RPM. The tip velocity ranges from 43 to 86 m/s. This speed range provides

Reynolds numbers between 1.5×106 and 3.5×106 at the outboard tip area. The outboard part is the

ice shape monitoring area, labeled as “Paddle Blade”. This paddle blade is designed to have a

51

NACA 0012 cross-sectional profile. The spanwise length of the paddle blade is 30.48 cm (12 inch).

The chord of the test section is 53.34 cm (21 inch), which is of the same magnitude of a full-scale

helicopter rotor blade, such as the Bell UH-1H helicopter. This NACA 0012 airfoil with the same

chord has also been used in several icing experiments at the NASA IRT (Olsen, Shaw, & Newton,

1984) (Shin & Bond, 1992) (Anderson & Tsao, 2003). A direct match of the airfoil chord avoids

the need of scaling for icing conditions between the two different facilities when comparing ice

shapes. The inboard part of the blade features a NACA 0015 profile and has a chord of 17.27 cm

(6.8 inch). This inboard carrier blade is designed to carry the outboard test blade section and to

minimize the influence of the blade to the inflow pattern in the test chamber. The 12.7-cm (5-inch),

non-lifting adapter is designed to minimize the disturbance of chord size transition, which is from

17.27 cm (6.8 inch) to 53.34 cm (21 inch).

2.3.2 Design of 1-inch & 4.5-inch-Diameter Cylinder Rotor Blades

The facility and pictures of the test cylinder are shown in Figure 2-7. The top picture is the

rotor test stand with a 1-inch-diameter (0.0254 m) cylinder rotor blade used in previous facility

calibration efforts (Palacios, Han, Brouwers, & Smith, 2012). A new test cylinder rotor based on

this configuration is shown in the bottom two pictures. The original 1-inch-diameter blades were

modified to carry a larger diameter cylindrical structure at the tip of the rotor. The rotor total length

stayed the same, measuring 1.27 m (50 inch) from rotor tip to the rotation center (hub). The test

cylinder was made from a 12-inch-length (0.3048 m) Schedule 40 PVC pipe. The cross-sectional

profile of the pipe was 0.1016 m (4 inch) Nominal Pipe Size (NPS), which resulted in a 0.1143 m

(4.5 inch) Outer Diameter (OD). The monitoring area was selected at the outboard of the test

cylinder rotor, 0.9652 m – 1.27 m (38 inch – 50 inch) from the hub, i.e., outboard 24% area from

the rotor tip.

52

Figure 2-7. AERTS cylinder test rotor

2.4 Test Matrices

The test conditions for rotor ice accretion experiments are listed in this section. As

mentioned in Chapter 1, several ice roughness and ice shape experiments were planned to generate

databases to develop ice roughness, heat transfer, and aerodynamics models. Each test database

required different test matrices, as shown in the next three subsections.

2.4.1 Cylinder Ice Roughness Experiment

To study the roughness effect on heat transfer on generic shapes, a set of eight (8) test cases

were conducted on a 4.5-inch-diameter (0.1143 m) cylinder. The test matrix is shown in Table 2-2.

Two ice roughness families were generated according to different LWC. As mentioned in the

53

objectives section, ice roughness experiments were scheduled for conducting parametric studies.

Within each ice roughness family, four cases of ice roughness were made with four different icing

spray durations (30, 60, 90, and 120s). The time series of the ice roughness are suitable to provide

systematic data for the proposed parametric study. The controlled test conditions can be used for

correlation development within a comprehensive range.

Table 2-2. AERTS Cylinder Ice Roughness Test Matrix

AERTS

Casting #

LWC

g/m3

Spray

Time, s

Tstatic

°C

MVD

µm

Local

Vel., m/s

Rotor

RPM

C3

0.5

120

-5.85 20 30 256

C4 90

C5 60

C6 30

C7

0.25

120

C8 90

C9 60

C10 30

2.4.2 Airfoil Ice Roughness Experiment

The test matrix to generate the ice roughness database on a 21-inch-chord (0.5334 m)

“paddle blade” NACA 0012 airfoil is listed in Table 2-3. Test cases labeled from R0 to R10 are 11

ice casting models made during this study. Test icing conditions were focused on the glaze ice

conditions since the initial roughness and heat transfer are much more critical for glaze ice

modeling than rime ice. In an ice roughness observation study (Shin, 1994), Shin found that the

roughness height grew very rapidly during the first two minutes, whereas there would be a very

slow or even possibly a zero-rate growth during the later stage of ice accretion process. Following

this guideline, the ice accretion times were all within two minutes to focus on early stage ice

roughness. All the ice roughness cases were accreted at 0° angle of attack for simplicity of analysis.

54

Table 2-3. AERTS Airfoil Ice Roughness Testing Matrix

AERTS

Casting #

LWC

g/m3

Spray

Time, s

Tstatic

°C

MVD

µm

Local Vel., m/s

Rotor

RPM

R0 0.6 60 -10.20 20 44.5 300

R1 1.7 94 -3.60 30 66.7 450

R2 1.7 94 -5.54 30 66.7 450

R3 1 94 -5.86 30 66.7 450

R4 1 75 -5.78 30 66.7 450

R5 0.6 94 -9.90 20 66.7 450

R6 0.25 94 -5.58 20 66.7 450

R7 1 120 -5.90 20 66.7 450

R8 1 45 -5.80 30 66.7 450

R9 1 94 -5.76 20 66.7 450

R10 0.6 94 -9.84 20 44.5 300

2.4.3 Airfoil Ice Shape Accretion Experiment

As discussed in Chapter 1, the available reference ice shapes and corresponding

aerodynamics measurements from published data were usually scattered with results for very few

AOAs. Also, most of the tests only recorded Cd data (or even only Δ Cd based on the authors own

clean airfoil data), whereas the associated Cl and Cm were not documented. To expand the current

data matrix, ice shape accretion experiments under representative, long-spray-time durations were

conducted. Ice shapes were properly retained in solid model form by using a molding and casting

technique that will be introduced in Section 2.5. Ice shape castings obtained at the AERTS facility

were tested in a dry-air warm temperature wind tunnel to obtain aerodynamic data for a full range

of AOA.

As shown in Table 2-4, four (4) ice shapes obtained at the NASA IRT (Olsen, Shaw, &

Newton, 1984) were reproduced experimentally at the AERTS facility and corresponding ice shape

55

casting models were fabricated. The test rotor blade was the 21-inch-chord (0.5334 m) “paddle

blade” NACA 0012 airfoil.

Table 2-4 AERTS Ice Shape Accretion Testing Matrix

AERTS

Casting #

LWC

g/m3

Time

s

Tstatic

°C

MVD

µm

Vel.

m/s

AOA

deg Ref. Cd

Ref.

Run #

AERTS

ICE1 1 360 -13.3 20 67.1 4 0.02767 O-10

AERTS

ICE2 1.3 480 -16.6 20 58.1 4 0.02105 S-69

AERTS

ICE3 2.1 300 -9.7 20 58.1 0 0.02294 O-8

AERTS

ICE4 1.3 480 -8.9 20 41.4 4 0.01622 S-33

The four digitized ice shapes are shown in Figure 2-8, with comparisons to both

experimental results by Olsen et al. and LEWICE 2D ice predictions. Good agreements between

the AERTS experimental ice shapes and the NASA IRT experimental shapes have been achieved,

in terms of general ice shapes and stagnation line ice thickness, further validating the capability of

the facility to generate representative icing conditions. The LEWICE predictions compared with

both experimental results less favorably, with general under-predicted total ice volume. The ice

limit prediction correlated to experimental results well, except for AERTS ICE 3, which was

accreted at zero angle of attack. The protruding rime ice feathers behind the main ice shape were

not captured by LEWICE predictions. For the Olsen et al.’s experimentally accreted reference ice

shapes, the ice frost and ice feathers did accrete on the airfoil, but were intentionally removed after

every test (Olsen, Shaw, & Newton, 1984), therefore they were not shown in this comparison. The

effect of these missing feathers will be discussed in more detail later in this study.

56

Figure 2-8. Ice shape comparison with reference literature

2.5 Ice Shape Molding and Casting Techniques

To capture the three-dimensional ice shape and to retain its delicate ice features, an ice

molding and casting technique, first introduced at the NASA IRT (Reehorst & Richter, 1987), was

applied at the AERTS facility. In this section, the molding and casting process for airfoil ice shape

accretion experiments is used as an example to illustrate the experimental techniques. Detailed

roughness measurements and comparisons for casting models of both airfoils and cylinders will be

discussed in Chapter 3.

After an ice accretion experiment, the rotor blade was taken off from the rotor hub and

mounted on a molding stand inside the cold chamber. Mold bath boxes were designed specifically

for cylinder molding and airfoil molding tasks respectively. The airfoil mold bath box had

dimensions of 0.1016 m width (4 inch) × 0.1524 m height (6 inch) × 0.3048 m length (12 inch);

whereas its counterpart for the cylinder mold bath container was made from two concentric pipes

57

which formed an annulus with ID = 0.06033 m (2.375 inch) and OD = 0.1532 m (6.031 inch).

Taking airfoil ice molding as an example, the box was attached to both sides of the paddle blade,

so that molding material only covered the top and bottom surfaces of the airfoil, excluding the

sides. A photograph of the molding stand setup is shown in Figure 2-9.

Figure 2-9. Test rotor blade mounted on molding stand inside cold chamber

A sample ice shape casting model section is shown in Figure 2-10, where the pink material

is the molding material and the white material is the example casting model.

Figure 2-10. Example ice mold and casting models

During the process, the molding material (RTV silicone rubber) was pre-cooled in a freezer

before its application to ice. The liquid rubber was poured into the mold box and then left at the

same icing temperature for 24 hours for curing. The cured mold was then taken out of the cold

58

chamber and relieved from the rotor blade under room temperature. Ice was allowed to melt since

the shape had already been retained. Then the urethane liquid plastic casting material could be

applied to the mold. The cure time for the liquid plastic was 15 minutes.

Multiple ice shape duplications could be fabricated from one mold. The advantage of the

ice shape molding is that it does not require physically removing the ice shape from the airfoil,

which ensures that the full 3D features of the ice shape and ice roughness could be properly

retained.

An example ice casting model is shown in Figure 2-11. The ice casting model was 0.1143

m (4.5 inch) in height, which corresponds to 21.4% of the chord. Based on literature and past

experience on ice accretion experiments, the ice limit on a test airfoil is usually less than 20% for

the finite AOA range tested at the AERTS. It can be observed that the ice model obtained from the

molding and casting techniques properly retained fine details of the 3D ice shape on the test blade,

in terms of ice thickness, main ice shape, ice feathers, ice limit, and surface roughness.

Figure 2-11. Sample ice casting model comparison

59

The surface-finish (thickness) resolution capability of the molding material has been

evaluated using a profilometer. The roughness on the smoothest surface zone on the model was

measured to be 0.127 to 0.305 µm (5 to 12 micro inch), thus it can capture very small ice feathers

and roughness elements. Therefore, this technique was also suitable for capturing the micro features

(ice roughness casting) along with the macro structure (ice shape casting). A sample ice roughness

casting model is shown in Figure 2-12. Hansman and Turnock (Hansman & Turnock, 1989)

suggested that early-stage ice roughness distribution can be segmented into smooth zone and rough

zone, as denoted in Figure 2-12. For the sample ice casting model, the smooth zone width was

measured to be 2% of chord length, the rough zone started at 2% and ended at the ice roughness

limit of 7.5% of the chord. The detailed roughness measurement is discussed in Chapter 3.

Figure 2-12. Sample ice roughness casting model

A direct application of the casting model is that it can be readily scanned into a three-

dimensional model using either a table-top laser scanner (Figure 2-13) or a more advanced CAT

scan machine (Figure 2-14). AERTS ice shapes have been scanned (Han, Palacios, & Smith, 2011)

both on the rotor (direct scan, without casting) and also on a table top (casting model, 360° surface

wrap scan). Both scanning methods were validated with ice shapes and proved to be useful for CFD

code application. While it is possible to scan the ice directly, it is time consuming and potentially

less accurate. Scanning a model is easier and can be done over a longer period of time in a much

larger range of facilities.

60

Figure 2-13. Laser scan of ice wrap surface

As can be seen in Figure 2-14, a 3D CAT scan offered a much better improvement in scan

resolution. It could provide a complete 3D body mesh, rather than a surface mesh, which was very

favorable for CFD flow analysis.

Figure 2-14. CAT scan of 3D ice shape

A detailed CFD analysis for a CAT scan model was done by a collaborating group at Penn

State (Brown, et al., 2014). The trade-off of using such detailed scanned model was a much higher

cost and longer post-processing time, therefore it was not used in this experimental study. Direct

measurement of the roughness using a surface profilometer and a digital dial indicator will be

introduced in Chapter 3.

61

2.6 Wind Tunnel Experiment Setup

The ice roughness effects on both heat transfer and airfoil performance were evaluated in

the Penn State low-speed wind tunnel. It is a closed-circuit, single-return atmospheric tunnel. The

cross-sectional test area is rectangular. The dimensions of the test section are 0.9144 m (36 inch,

height) × 0.6096 m (24 inch, width), with filleted corners. The maximum test section speed is 46

m/s (150 ft/s). The tunnel dimensions are denoted on a CAD model, as shown in Figure 2-15. The

testing setup for two different kinds of tests inside the tunnel will be described in detail in the

following subsections.

Figure 2-15. Penn State Hammond Building wind tunnel CAD model

2.6.1 Wind Tunnel Heat Transfer Test Setup

After completing the ice roughness experiments, the ice casting models were put into the

wind tunnel for heat transfer evaluation. To accurately capture the heat transfer procedure on the

ice casting models, proper thermal measurement including surface temperature and heat flux

measurements must be implemented. In this subsection, the wind tunnel configurations for heat

transfer testing on both airfoils and cylinders are first presented. Two different thermal

62

measurement techniques are then introduced. Lessons learned from experimental results measured

at the rotor test stand and the wind tunnel are presented along with discussion.

2.6.1.1 Model Setup

The heat transfer model setups for cylinder roughness testing and airfoil roughness testing

are shown in Figure 2-16 and Figure 2-17, respectively.

Figure 2-16. Cylinder heat transfer evaluation test setup in wind tunnel

Figure 2-17. Test airfoil with sandpaper in the wind tunnel for flow sensitivity check

63

Taking the heat transfer evaluation test on ice-roughened airfoil as an example, the heat

transfer testing airfoil model was a NACA 0012 airfoil with dimensions of 0.6096 m (24 inch) in

span, and 0.5334 m (21 inch) in chord (matching the chord of the paddle blade used for rotor ice

accretion tests). The airfoil is comprised of two parts: removable leading edge ice shape casting

models and a trailing edge base. The black sandpaper attached at the leading edge was used for

flow sensitivity shake down and testing technique development before the testing of ice casting

models. Different grits of sandpaper were tested to represent different severities of the ice

roughness accretion. The tunnel turbulence intensity was identified to be 0.22% during

aerodynamic tests (Han & Palacios, 2013). The laminar tunnel flow has been observed to be fully

turbulent as the air passes the sandpaper region during the flow sensitivity testing.

The ice shape casting models were mounted on two rails, allowing it to travel in the

spanwise direction inside/outside of the wind tunnel. The reason for this rail design was to quickly

transport the airfoil from steady heated conditions (outside tunnel) to a transient cooling

environment (inside tunnel). A schematic block diagram and an actual wind tunnel model are

shown in Figure 2-18 and Figure 2-19, respectively, to illustrate this testing procedure.

Figure 2-18. Schematics of transient heat transfer testing in the wind tunnel

Wind Tunnel~22°C

TOP VIEW

Heating Chamber~40°C

Heated Leading EdgeOutside Tunnel

Leading Edge Cooled by Tunnel Flow

Inside Tunnel

Trailing Edge

64

Figure 2-19. Wind tunnel airfoil model

The tunnel wall was cut in the shape of an airfoil so that the airfoil could pass through. The

constant heating environment outside the tunnel was provided by a convective heating chamber

placed outside of the tunnel. An electric cartridge heater was also used for auxiliary heating, as can

be seen by the rod with cords inside the leading edge model in Figure 2-19. The chamber was

directly connected to the wind tunnel wall. Before every test, the tunnel was turned on and

maintained at a constant testing speed under room temperature (typically 22°C). In the meantime,

the airfoil leading edge section was heated until it reached a uniform temperature distribution

(typically 40°C) outside the tunnel. Then, the airfoil could be inserted into the tunnel to be cooled

down by the tunnel air. A transient heat transfer procedure was created, and the temperature

variations recorded were used to calculate heat transfer coefficients. The detailed theoretical

background used during the calculation and experimental results will be discussed in Chapter 4.

This same technique was used with the cylindrical structures.

2.6.1.2 Thermal Measurement - Thin Film Sensors

As previously denoted in Figure 2-16 and Figure 2-17, four (4) surface-mount thin-film

thermocouples and five (5) internal thermistors (not visible, inside the model) were used for

temperature monitoring. A LabVIEW code employing a PID control algorithm was developed to

65

provide uniform heating conditions for the test models prior to insertion into the tunnel. The internal

thermistors were placed at 0.5x, 1x, 2x, 3x, and 4x length of leading edge radius from the leading

edge stagnation to determine the heat condition by monitoring internal temperature distribution of

the casting model. A typical temperature time history of the internal temperature can be seen in

Figure 2-20. The internal temperature started at the same level at the beginning of the test for all

temperature sensing locations. During the test, the model experienced a forced convective cooling

procedure. The internal temperatures tended to decrease over time. It can be clearly seen that only

the location closest to the leading edge of the casting model (0.5x length of leading edge radius

from the stagnation line) dropped temperature over the monitoring time history. To ensure a

uniform temperature distribution inside the model (needed for accurate calculation of heat transfer),

transient data were taken within the steady internal temperature range, as indicated using the two

vertical blue lines. The detailed calculation procedure will be shown in Section 4.1.

Figure 2-20. Temperature time history inside casting model

Two heat flux sensors were also applied to serve as an external data check to quantify the

transient status of the testing. A direct heat transfer coefficient calculation could be applied based

on the surface heat flux, surface temperature, and tunnel temperature. A time history of the heat

Inte

rnal

Tem

per

atu

re (

°C)

Test Time (s)

45

40

35

30

0 10 20 30 40 50

66

transfer on two monitoring positions were then obtained. A sample plot of time-history monitoring

data obtained at 13% chordwise location from AERTS case R2 is shown in Figure 2-21.

Figure 2-21. Example heat transfer time history data

The chart on the top of Figure 2-21 is the time history of the heat flux sensor and the two

temperatures read from embedded thermocouples and infrared camera readings, which will be

discussed in detail in next subsection. The output from the heat flux sensor was the heat flux

measurement per unit area at the sensor location with a unit of W/m2. The two temperatures are

shown in dashed lines and a good correlation between the two temperatures was observed. The

chart on the bottom is the calculated heat transfer coefficient comparison from Equation (2-4).

ℎ =�̇�

𝑇𝑠 − 𝑇∞ (2-4)

It can be seen that the two calculated heat transfer coefficient curves based on two different

surface temperature readings ramped up gradually within the first 8s (the curve section between

two vertical lines) and then tended to level after arriving at a steady value. The initial transient

calculation was then applied for the initial period only (i.e. before reaching steady state values).

0 10 20 30 40 50 600

200

400

600

800

He

at

Flu

x,(

W/m

2)

20

25

30

35

40

45

Te

mp

era

ture

,(d

eg

C)

Heat flux through the surface

Temperature, embeded TC

Temperature, IR Camera

0 10 20 30 40 50 600

50

100

150

Time,(s)

He

at

Tra

nsfe

r C

oe

ff.,

(W/(

m2*K

))

HTC based on embeded TC

HTC based on IR Camera

67

The pre-heating condition varied for different cases. The transient times for all the cases were

therefore determined experimentally according to the heat flux and temperature history

measurement. In this way, the correct behavior needed for the implementation of the 1D heat

transfer equations applicable to semi-infinite bodies could be captured.

The direct measurement technique (utilizing heat flux sensors) has been applied to a clean

airfoil both on the rotor stand and also in the tunnel, as shown in Figure 2-22. The motivation of

this implementation was to demonstrate the heat transfer measurement on a rotor stand and its

potential applicability for measuring heat transfer on real natural ice roughness surfaces.

Figure 2-22. Paddle blade mounted in wind tunnel for direct heat transfer measurement

Significant difficulties were encountered on this rotor heat transfer measurement task. To

apply the sensors on a rotating frame, the slip ring introduced in Chapter 1 was used to transmit

signals between the rotating blade and static electric cables that connected to a data acquisition

system for thermal measurements. Due to the delicate heat flux sensor, very low voltage signals

(micro-volts level) were output and a signal amplifier had to be designed to provide low-voltage

signal conditioning. On the other hand, thermocouples measure temperature through a differential

voltage signal from two special types of metal. By using a slip ring, the voltages were transmitted

on cables that had different impedances, which resulted in error of measured temperature.

68

Therefore, a voltage converter was designed to first convert the thermocouple readings into regular

proportional voltage signals and then sent to the data acquisition system. The two signal

conditioning devices were designed using ExpressPCB software and have been implemented onto

both rotor and wind tunnel testing. The casing of the electronics was waterproof and has a one-

square-inch silicone rubber heater inside to control the temperature in the electronics casing during

icing testing.

Figure 2-23. Signal conditioning circuits designed for thin-film sensors

After applying the signal conditioning devices, heat transfer data from both the rotor test

stand and the wind tunnel have been obtained and compared to the reference experiment (Newton,

Van Fossen, Poinsatte, & DeWitt, 1988) mentioned in Figure 1-16 in Chapter 1. A comparison of

the directly measured heat transfer coefficients is shown in Figure 2-24.

During this comparison, all the clean airfoil test data obtained in the wind tunnel (red

square) correlated very well with both reference experimental results (black circle) and analytical

prediction by LEWICE (solid green line). This proves that the direct measurement can provide

accurate readings of heat transfer on clean airfoil surfaces. However, when comparing the data from

the rotor stand with the reference data, it can be seen that the first two points matched the trend,

whereas the last two points showed deep drop from the reference curve. Later, it was found that the

two deviations were from local surface deformation. This was also observed in the last three data

69

points in NASA reference data, which were at the same level of the rotor test stand values. The

reason was found in a separate reference paper (Feiler, 2001), where it was commented by the

experimentalist that the reduction in measured heat transfer coefficient was due to local surface

deformation on the reference airfoil model.

Figure 2-24. Direct heat transfer measurements in wind tunnel and on rotor stand

The conclusions after these efforts on direct measurement were that the thin-film sensors

can measure accurate heat transfer coefficients on smooth surfaces. However, it was also found that

the sensors were very fragile and came with instrumentation difficulties on a rotating frame. A low-

voltage signal conditioning circuit and a voltage converter for thin-film thermocouples to transmit

signal through slip-ring configuration were designed to overcome this challenge. The major

limitations of this technique were that the thin-film heat flux sensor could not be applied to highly

curved surfaces, especially those with surface roughness presence. Also, each of the sensor strips

took up a surface area of 0.0119 m (0.47 inch, chordwise length) × 0.0254 m (1 inch, spanwise

width), which determined the maximum number of sensors that can be applied to the surface. The

limited coverage and low data resolution was not appropriate for heat transfer mapping over the

wide range of the leading edge area for this study. The criteria to choose the next thermal

measurement tools was set to identify a system that was non-intrusive so that it can be applied to

0

50

100

150

200

250

300

0% 4% 8% 12% 16% 20%Dimensionless Surface Wrap Distance (s/c)

Analytical Prediction

NASA Ref. Exp.

AERTS - Wind Tunnel

AERTS - Rotor Test

70

rough surfaces without modifying the local geometry. The measurement technique also had to be

able to provide a higher resolution to quantify the thermal variations within the scale of the

roughness element sizes. Based on these lessons learned from the direct measurement technique

development, an infrared thermal measurement technique was proposed. The technique is discussed

in the next section.

2.6.1.3 Thermal Measurement - Infrared Measurement

The temperature and heat flux measurements from thermocouple and heat flux sensors

mentioned above were only able to provide localized information rather than a complete surface

mapping information. To obtain the temperature mapping data on the entire test specimen

throughout the transient heat transfer procedure, a FLIR T620 Infra-Red (IR) Camera was used.

The camera provided 640×480 resolution, which meant 307200 measured temperature data can be

read from camera pixels from a single IR picture. For the test runs conducted, the averaged pixel

size was 0.3175 mm (0.0125 inch) in length, which was at the same level or even finer resolution

than a typical ice roughness element size. This camera resulted in better resolution than traditional

temperature mapping tools, such as those using liquid crystal techniques.

The IR camera was placed 0.5334 m (21 inch), one-chord-length upstream of the model

and outside of the ceiling of the wind tunnel. The emissivity setting of the camera for the casting

material was 0.95, similar to that of plastic, acrylic, and PVC material. The tunnel walls were

painted in a flat black color to eliminate radiant interference. The test specimens were not painted,

with the intention of preventing the paint from bridging the gaps between small roughness elements,

which could potentially affect the heat transfer measurements. A viewing circle was cut into the

tunnel ceiling wall so that the test specimen can be directly exposed to the camera. No IR

transparent window was used to seal the tunnel. The same camera setup had been used in B.F.

71

Goodrich Ice Protection Research Facility for surface roughness growth monitoring on cylinders

(Hansman, Yamaguchi, Berkowitz, & Potapczuk, 1989). The IR photographic data had also been

compared to those obtained with standard CCD camera in sealed wind tunnels at the Data Products

of New England six-inch test facility and the NASA IRT at the Glenn Research Center. For the

testing at the Goodrich facility, the absolute calibration of the IR system was found to drift because

of the cold air from the icing wind tunnel blowing out of the viewing slot. For the setup of the

current study, the advantage is that the tunnel was running under constant room temperature for

which the IR camera was calibrated. IR system calibration drift due to cold air was inherently

avoided due to this setup. During the testing, special attention was given to the thermal infrared

emissivity on the testing surfaces, since the temperatures are calculated from measured thermal

radiant power which is a strong function of emissivity. A technique developed during the study to

estimate the angular dependency of emissivity on curved surfaces is reported in Appendix D.

A LabVIEW code was developed to acquire the stream of video data from the camera and

to interpolate the temperature on the pixel grayscale value at the real-time processing speed. The

code was able to save both video and high definition photographs of the transient procedure. The

video saved eight (8) frames per second with 640×480 resolution. The temperature can be

interpolated in real-time from pictures and results were saved every 0.5 sec. The temperature data

were then post-processed to solve for the mapping of the heat transfer coefficient over the

monitoring area. The advantage of this technique was that it was a non-intrusive technique and

therefore, no damage was made to surface. In this way, the roughness structure and pattern could

be properly retained, which was impossible by using other sensor techniques. A set of sample

output results is shown in Figure 2-25.

72

Figure 2-25. Top view from IR camera (greyscale) and temperature mapping (color)

In Figure 2-25, all images are from the top view of the airfoil leading edge upper surface.

The tunnel flow was coming from the bottom-to-top direction of the image. The two images in the

left column denoted the grayscale IR image and the corresponding digitized surface temperature

mapping at the initial time of the test. The two pictures on the right are an end-time IR image and

a temperature mapping image, respectively. The horizontal and vertical axes were pixel numbers

from the IR camera. The four red squares with labels from the top-left picture are used to indicate

the locations of the surface-mounted thermocouples used in the test. It can be noted that the uniform

color in the initial temperature mapping image indicates a good steady pre-heating condition when

the airfoil was pushed into the tunnel. The much larger color gradient at the leading edge area of

the end-time temperature mapping image illustrates a local high gradient of heat transfer rate in

that area due to the presence of local roughness elements. This heat transfer enhancement due to

roughness will be discussed in detail in Chapter 4.

Flo

w D

ire

ctio

n

Span Width: 6 inch

Chordwise Length: 4.5 inch, 21.4% chord

Top View from IR Camera

Embedded Thermocouple

Top View from Thermal Mapping

Note: Leading Edge High Thermal Gradient

73

2.6.2 Wind Tunnel Aerodynamics Test Setup

The aerodynamics test airfoil was a NACA 0012 airfoil with dimensions of 0.6096 m span

(24 inch) and 0.5334 m chord (21 inch), which matched the chord of the rotor paddles used for

rotor ice accretion. The airfoil was comprised of two parts: a removable leading edge ice shape

casting model and a trailing edge base. The test airfoil mounted in the wind tunnel can be seen in

Figure 2-26.

Figure 2-26. Wind tunnel test section with airfoil mounted

2.6.2.1 Aerodynamic Force and Moment Measurements

During the aerodynamics test, the wind tunnel motor was kept running at a constant power

output ratio of 80%. The test speed was measured to be 40 m/s. The turbulence intensity (Ti) was

determined to be 0.22%. The corresponding Reynolds number was 1.4×106. Although the wind

tunnel test speed and associated Re were relatively lower than the rotor icing test Re (V = 41-67

74

m/s, Re = 1.4-2.4 ×106), it has been observed by other researchers (Korkan, Cross, & Cornell, 1984)

(Papadakis, Alansatan, & Seltmann, 1999) (Broeren, et al., 2010), that both Reynolds number and

Mach number have little effect on the iced airfoil performance. The airfoil performance degradation

evaluation could be compared as long as the Re values had the same order of magnitude

To measure the drag force and corresponding drag coefficient of the model, a wake survey

rig and a force balance were used to calculate the 2D/3D drag coefficient. The hot-wire probe wake

survey rig was mounted at two-chord lengths (1.0668 m) downstream of the airfoil model. The

wake probe traverse route was aligned to the spanwise centerline of the model. The heated hot wire

measured the velocity profile downstream of the airfoil with a sampling rate of 1000 Hz. A wake

momentum deficit method was used to calculate the 2D sectional drag coefficient. For different

cases, spatial sampling step increments varied from 0.05 to 0.1 inch across the vertical tunnel span

to ensure capturing of the wake profile with sufficient data points. A wake deficit profile was

typically described by 100 to 200 data points per test. A 6-axis external force balance was also used

to measure the 3D drag, lift, and pitching moment coefficients (Cd, Cl, and Cm). The force balance

sampled at a rate of 1000 Hz, taking 5000 samples per reading. The reason for using an external

force balance rather than pressure taps to measure Cl and Cm is that the 3D vortex shedding on the

upper surface of the airfoil with ice accretion was very unsteady and vigorous. This unsteady feature

of the flow was difficult to interpret using surface-attached pressure taps (Broeren, et al., 2010);

whereas by using proper signal filter and averaging methods, the measurements from the external

force balance can generate meaningful results. The force and moment measurements on both clean

and ice-roughened airfoils will be compared.in Chapter 7. The drag coefficient measured from the

3D force balance and wake survey probe will also be compared and presented together with

reference data for clean airfoils at various angles of attack.

75

2.6.2.2 Tunnel blockage

By mass flow continuity and Bernoulli’s equation, the presence of the test model reduced

the wind tunnel test section cross-sectional area and therefore the tunnel air speed was higher in the

vicinity of the model than the free-air no-blockage setup. In this subsection, the tunnel blockage

issued was studied using the test cylinder model as an example.

For a 2D simplified condition, a cylinder can be modeled as a doublet recommended by

Barlow et al (Barlow, Rae, & Pope, 1999). The solid blockage was then determined from Equation

(2-5):

휀𝑠𝑏 =𝜋2

3

𝑅2

ℎ2 (2-5)

where, for this case, the R was cylinder radius, 0.0572 m (2.25 inch), and h was wind tunnel test

section height, 0.9144 m (36 inch). The calculated solid blockage was then determined to be 1.28%,

i.e., the tunnel local speed around the test cylinder was increased by 1.28%.

Apart from the local velocity change around the test body, the wake blockage should also

be considered, since it had an effect on the increase in measured uncorrected drag coefficient. The

2D wake was modeled as a line source starting from the trailing edge. The blockage coefficient

was defined in Equation (2-6):

휀𝑤𝑏 = 𝜏𝐶𝑑,𝑢 ≈𝑐/ℎ

4 (2-6)

where, for this case, c was the chord (diameter) of the test cylinder (0.1143 m, 4.5 inch), and

therefore the increased calculated drag coefficient due to wake blockage was determined to be

3.125%.

The total blockage was defined as the sum of the two sources of the blockage, thus only

4.405%. By convention, a blockage ratio lower than 7.5% can be safely ignored. The tunnel flow

velocity was still corrected using the solid blockage assumption for this study.

76

Chapter 3

Ice Roughness Measurement and Prediction

3.1 Experimental Ice Roughness Measurements

Hansman and Turnock (Hansman & Turnock, 1989) suggested that most early stage ice

roughness distribution can be divided into a smooth zone and a rough zone, as already indicated in

Figure 2-12. The smooth zone features a thin water film at the surface during growth, hence, it is

also referred to as the smooth wet zone. On the other hand, the rough zone is a result of dry growth

of droplet deposit and has a rougher surface than the smooth zone. A third zone, called the runback

zone, features surface water rivulets, and although not frequent, may also be possible in warm icing

cases. These different categories of ice roughness have also been identified during tests at the

AERTS facility on both iced airfoils and cylinders. For instance, distinctive smooth zone and rough

zone can be clearly identified on accreted airfoil ice roughness as depicted in Figure 3-1.

Figure 3-1. AERTS example ice roughness categorization

By applying the molding and casting techniques introduced in the previous chapter, the ice

shape and roughness elements could be captured into a solid casting model. The roughness

77

measurements were then conducted using a profilometer and a digital dial indicator. A photograph

of the digital dial indicator taking measurements on an optical bench is shown in Figure 3-2.

For the example ice casting model shown in Figure 3-2, the smooth zone width was

measured to be 1.6% of chord length, while the rough zone started from 1.6% and ended at the ice

roughness limit of 7.5% of the chord. A first attempt on measuring roughness height was conducted

using a portable lab profilometer. The clean surface roughness height was determined to be 0.305

µm (12 micro inch). On the surfaces where ice accreted, the roughness increases significantly. The

smooth zone roughness height was measured to be 6.350 µm (250 micro inch), whereas the rough

zone had a roughness height larger than 7.620 µm (300 micro inch) which exceeded the limit of

the profilometer. For a majority of the AERTS icing cases, the ice roughness elements were usually

at the 10 – 1000 µm order of magnitude which was beyond the measurement limit of a profilometer.

A digital dial indicator was then introduced to measure the surface roughness height of the ice

casting models.

Figure 3-2. Digital dial indicator on an optical bench

The digital dial indicator shown in Figure 3-2 has a resolution of 10µm (equivalent to

0.0005 inch, for reference, width of cotton fiber). The diameter of indicator tip is 100 µm (0.004

inch, for reference, is the average diameter of a strand of human hair), which is one order of

78

magnitude smaller than that of the ice roughness element spacing according to measurements by

Shin (Shin, 1994). Eight chordwise locations were selected to monitor for ice casting models R1-

R10, namely: 0% (stagnation line), 1%, 2%, 3%, 4%, 6%, and 8% of dimensionless surface distance

(s/c). Ten (10) spanwise stations with half-inch (0.0127 m) intervals were measured for each of the

chordwise locations. Arithmetic averages of absolute values of peak-to-valley roughness height

(Ra) were recorded and are reported in Appendix A of this dissertation (including standard

deviations for the measured data). The medians of each data group were also recorded and

compared to the arithmetic averages. The difference between medians and means for each

measurement set ranged from -2% to 10%. Good agreement between the averages (Ra) and medians

proved the feasibility of using statistical Gaussian distribution and standard deviation to describe

the data. The ice limit and the transition location from smooth zone to rough zone are also provided.

The average smooth zone range was determined to be 0-1.5% s/c, whereas the average rough zone

range was 1.5-7.6% s/c. The effect of surface roughness will be discussed in the following sections.

The experimentally measured ice roughness dimension data are listed in Appendix A of

this dissertation. The smooth zone to rough zone transition location and the ice limit can be found

in Table A-1. The measured roughness heights for the 10 casting models are summarized in Table

A-2 and Table A-3.

Similar to the measurement technique described above for airfoil ice roughness, casted ice

roughness models for cylinder ice roughness studies are also measured with a digital dial indicator.

The casting model measurement process for cylinder tests is shown in Figure 3-3.

79

Figure 3-3. Ice roughness measurement using casted natural ice roughness shape

The cylinder roughness measurement took place on 10 different azimuth angles (0-90°,

green lines on the cylinder body). Repeat measurements of at least 11 times were conducted across

the spanwise direction (11 monitoring locations as denoted by the cross of green and red lines in

Figure 3-3). A zoom-in picture of a detailed natural ice roughness distribution is shown in Figure

3-4.

Figure 3-4. Categorization of cylinder surface roughness distribution

Similar to the findings on a reference cylinder roughness experiment (Hansman,

Yamaguchi, Berkowitz, & Potapczuk, 1989), three distinctive zones were identified in all 10 test

cases on cylinder specimens, namely: smooth zone, rough zone, and clean surface zone. Based on

experimental observation of the ice roughness in Figure 3-4, a simple parabolic distribution was

80

considered to correlate icing conditions to the roughness size distribution. As mentioned, the ice

roughness measured for cylinders and airfoils did not start at the stagnation area. Under common

icing condition (except extreme cold cases), a smooth zone region featured a wet growth

phenomenon starting at the stagnation of the structures, resulting in a smooth surface area. Past the

smooth zone, the roughness was observed to be growing in a parabolic shape that featured a dry

growth. The schematic of the roughness distribution and modeling parameters are shown in Figure

3-5.

Figure 3-5. Schematic of roughness distribution

Using the parabolic distribution of cylinder roughness, predictions for such distribution on

both cylinders and airfoils are developed as functions of icing conditions as will be shown in next

section.

3.2 Ice Roughness Prediction

The pioneering work on correlating the effect of surface roughness to aerodynamic

performance has been conducted by Von Doenhoff and Horton (von Doenhoff & Horton, 1958) in

1958. A simple flow transition criterion was proposed and used as a guideline for flow transition

with surface roughness after a long period of time, as shown in Equation (3-1):

𝑅𝑒𝑐,𝑐𝑟 = 600 (3-1)

xk

w Ice limit

81

Early versions of LEWICE used this correlation, but found a constant critical Reynolds

number of 600 often gave premature transition. In addition, the surface roughness by ice accretion

was assumed to be with constant roughness height over the entire surface. Sand papers were used

as artificial roughness to study the flow transition which was deemed not to be fully representative

of the natural ice roughness distribution.

As mentioned in Chapter 1, in late 1980s, Hansman et al. (Hansman, Yamaguchi,

Berkowitz, & Potapczuk, 1989) categorized natural ice roughness distribution on cylinders in an

icing wind tunnel. Multiple zones of roughness were identified during the study. Typically, a

smooth zone at the leading edge was usually observed close to the airfoil stagnation line, then

followed by a rough zone, and later transitioned to clean surface. Other rough zones such as the

horn zone, runback zone, or rime feather zone can also be found during ice accretion, but with less

likelihood. There were no tabulated test matrix (e.g., roughness height, smooth zone width, detailed

icing conditions, test cylinder diameter etc.) for this study. Therefore no quantitative correlation

can be established and applied to other different icing conditions or different airfoils.

Although there was no quantitative data points available for an iced cylinder, there are still

some limited experiments available for airfoil natural ice roughness measurements. In 1987, Gent

et al. (Gent, Markiewicz, & Cansdale, 1987) compared 11 cases of roughness height against

Velocity, LWC, and Temperature. Later, an empirical correlation as shown in Equation (3-2) was

developed based on these data. This correlation was adopted by the first version of NASA

LEWICE, which has been recognized as an industry-standard ice prediction tool since then. The

correlation assumed a linear relationship between the roughness height and the velocity and

temperature, whereas a parabolic relationship was found with respect to the LWC. The predicted

roughness element height was defined as a product of three non-dimensionalilzed sub-functions.

The height estimation was validated based on experimental test baseline data and test airfoil chord.

The overall equation is shown in Equation (3-2).

82

𝑥𝑘 = [𝑥𝑘 𝑐⁄

𝑥𝑘 𝑐⁄ 𝑏𝑎𝑠𝑒

]𝑉∞

[𝑥𝑘 𝑐⁄


]𝐿𝑊𝐶

[𝑥𝑘 𝑐⁄


]𝑇𝑠

𝑥𝑘 𝑐⁄ 𝑏𝑎𝑠𝑒 ∙ 𝑐 (3-2)

where, the three sub-functions of roughness are also included in Equation (3-3), (3-4), and (3-5) for

completeness:

[𝑥𝑘 𝑐⁄


]𝑉∞

= 0.4286 + 0.0044139 ∙ 𝑉∞ (3-3)

[𝑥𝑘 𝑐⁄


]𝐿𝑊𝐶

= 0.5714 + 0.2457 ∙ 𝐿𝑊𝐶 + 1.2571 ∙ 𝐿𝑊𝐶2 (3-4)

[𝑥𝑘 𝑐⁄


]𝑇𝑆

=46.8384 ∙𝑇𝑆

1000− 11.2037 (3-5)

A more systematic parametric study was conducted by Shin in 1994. A total of 22 cases of

glaze/rime ice shapes was generated at NASA Icing Research Tunnel (IRT). The tests were used

to study the effect of temperature, time, velocity, LWC on roughness distribution on the early stage

of airfoil ice accretion. Smooth/rough zones, as mentioned previously, were confirmed also exist

for airfoil ice accretion. Test measurements such as: roughness height, equivalent bead diameter,

roughness element spacing, and width of smooth zone were tabulated in detail for each individual

case. Rapid roughness growth was observed in first 2 minutes, and then became constant height or

even decreased with extended icing time. The flow transition trigger was attributed to roughness

extruding the boundary layer thickness. Temperature, time, and LWC were all found to be the

primary factors affecting the roughness growth. Therefore, a parameter that can summarize the

effects of all the three parameters should be used for correlation development. Although velocity

was found having little effect on the roughness height growth, the boundary layer thickness is a

strong function of the Reynolds number. In this way, the velocity was also found affecting flow

transition and thus affecting heat transfer. Later in 1997, based on Shin’s experimental work,

Anderson and Shin (Anderson & Shin, 1997) introduced scaling parameters for development of

83

correlation for both smooth zone width and roughness height. The smooth zone width (w) was

shown as a linear function of Accumulation Parameter (Ac), as already defined as a non-

dimensionalized ice accretion rate indicator in Section 2.2.

An attempt to correlate the roughness height (xk) to a single function of another icing

scaling parameter, known as freezing fraction (n0, also abbreviated as ff in some other references),

was conducted. The freezing fraction is a water freeze ratio within a control volume at stagnation

line which was previously discussed in Section 2.2.

The exact equation of xk as a function of n0 based on Shin’s 22 ice shapes was not shown

with the correlated curve (Anderson & Shin, 1997), but can be found in the later versions of

LEWICE user manual (Wright, 2008), as shown in Equation (3-6).

𝑥𝑘 =1

2√0.15 +

0.3

𝑛0 (3-6)

This equation was later widely used by LEWICE and other ice prediction codes for

maximum roughness height prediction. LEWICE reported both the overall maximum roughness

height, as well as local roughness height based on local freezing fraction along the chordwise

direction using this same equation. The determination of local roughness used a different definition

of freezing fraction, as it was calculated from control volume mass and energy equilibrium

equations.

Anderson et al. (Anderson, Hentschel, & Ruff, 1998) in 1998 further developed a more

comprehensive test matrix for a roughness correlation database. A total of 76 cases was conducted

to study the effect of chord, Ac and n0 on roughness distribution. The roughness was suggested to

be normalized against airfoil leading edge diameter (xk/2R). This document also follows this

suggestion in later correlation development sections. Contrary to their findings in the previous

reference, Anderson et al. found there was no effect of freezing fraction in the range of 0.2 – 0.4

observed for either smooth zone width (w) or roughness height (xk). This result implied that

84

modeling roughness height and smooth zone width as single functions of Ac or n0 was not enough.

A new, more comprehensive correlation that is based on all the previously mentioned databases are

then developed based on the database found during the literature survey and also from the AERTS

experiments. Detailed development procedures and comparison with the above two existing

correlations are discussed in the following sub-sections.

3.2.1 Ice Roughness Prediction on an Airfoil

A sample of measured experimental roughness on airfoil is shown in Figure 3-6. The

measured roughness height was also compared to the LEWICE roughness prediction using

Equation (3-6). The peak experimental roughness height was 0.705 mm for this case where the

LEWICE prediction was 1 mm, which resulted in a discrepancy of 42%.

Figure 3-6. Sample roughness measurement and comparison to LEWICE prediction

In Figure 3-6, the roughness height recorded at the AERTS facility was arithmetic

roughness height (Ra, arithmetic average of peak-to-valley roughness height), which later was

denoted as k(x) in the heat transfer prediction tool development effort. The proposed modeling

approach for the roughness is also shown to the right of the comparison chart. The most generalized

85

curve fit for such a distribution required inputs of maximum roughness height (xk), smooth zone

width (w), and ice limit (l) to construct the parabolic distribution in Equation (3-7):

𝑘(𝑥) =−4 𝑥𝑘

(𝑙 − 𝑤)2(𝑠(𝑥) −

𝑙 + 𝑤

2)

2

+ 𝑥𝑘 (3-7)

By combining the previously mentioned reference test databases together, ice roughness

data from a total of 74 cases (11 [Gent] + 22 [Shin] +31 [Anderson] + 10 [AERTS]) was used to

develop a new correlation for ice roughness height on airfoil. For roughness height, instead of the

1 √𝑛0⁄ term used in Equation (3-6), a new term of √𝐴𝑐 𝑛0⁄ was used for correlation of roughness

height normalized with respect to twice of the leading edge radius, xk/2R, as shown in Equation (3-

8):

𝑥𝑘

2𝑅= −0.008246 ∙

𝐴𝑐

𝑛0+ 0.03752 ∙ √

𝐴𝑐

𝑛0 (3-8)

The comparison chart of the correlation with the four different sets of data is shown in

Figure 3-7:

Figure 3-7. AERTS roughness height correlation

Similarly, the smooth zone width could be obtained from 63 cases (22 [Shin] +31

[Anderson] + 10 [AERTS]). The correlation is shown in Equation (3-9) and in Figure 3-8.

86

𝑤

2𝑅= 0.07254 ∙ (𝐴𝑐 ∙ 𝑛0)−0.6952 (3-9)

Figure 3-8. AERTS smooth zone width correlation

The correlation results compared favorably for both roughness height and smooth zone

width prediction as indicated in Figure 3-9 and Figure 3-12. Although there were several data

outliers (e.g. 416% difference in xk/2R) in roughness height prediction, the mean absolute deviation

was 31% for the entire 74-case database for xk/2R.

Figure 3-9. Correlation results comparison - roughness height

In contrast, if using the existing correlations shown in Equation (3-2) and Equation (3-6)

for estimation of the maximum roughness height, it would result in a mean absolute deviation of

76% and 54% for the entire set of data, respectively. The results obtained from Equation (3-2) and

Equation (3-6) are also compared to the reference experimental dataset, and are shown in Figure

3-10 and Figure 3-11 separately.

-100%

-50%

0%

50%

100%

Roughness Height Prediction Mean Absolute Deviation = 31%

128% 157% 416%

0

0.02

0.04

0.06

0.08

0.1

Ro

ugh

nes

s H

eigh

t, x

k/2

R

Roughness Height Prediction

Exp. Roughness Height AERTS Prediction

87

Figure 3-10. Comparison of ice roughness prediction using LEWICE ver1 equation

Figure 3-11. Comparison of ice roughness prediction using LEWICE ver3.2 equation

As can be seen from both Figure 3-10 and Figure 3-11, the two prediction models achieved

less accuracy in predicting the roughness element height. Also, due to the limitations of the

databases when the two correlations were developed, the two curves are significantly biased to their

own datasets. For instance, as mentioned previously, Anderson et al. (Anderson, Hentschel, & Ruff,

1998) found that there was no effect of freezing fraction in the range of 0.2 – 0.4 observed in their

experimental measurements for either smooth zone width (w) or roughness height (xk). This is

88

reflected in Figure 3-11 as denoted by the over-prediction of the LEWICE ver3.2 (orange diamond

symbols) compared to the blue circles.

With respect to the smooth zone width (w/2R) prediction, there was no reference prediction

equation found in the literature for external comparison. Only the comparison between the proposed

smooth zone prediction and the reference experimental database is shown here, as depicted in

Figure 3-12.

Figure 3-12. Correlation results comparison - smooth zone width

A mean absolute deviation of 30% in the internal comparison between the AERTS

correlation and reference experimental measurements was found, which is considered satisfactory

since the reproduction of surface roughness in different icing facilities could deviate as much as

30% (Hansman, Yamaguchi, Berkowitz, & Potapczuk, 1989).

With respect to the third term, ice limit (l) in Equation (3-7), reference measurements of

the ice limit were not available in the literature. It was also found that this ice limit did not change

within the extensive icing envelope tested in the AERTS facility. Therefore, the current AERTS

roughness correlation used a constant of 7.5% s/c for ice limit, based on the AERTS’s own

experimental observations for the tested airfoil shapes and angles of attack. For the roughness

heights that were outside the rough zone (smooth zone & clean surface zone), the minimum

roughness height was set to be a very small constant, 0.05 mm, as recommended by LEWICE user

0

1

2

3

Smo

oth

Zo

ne

Wid

th, w

/2R Smooth Zone Width Prediction

Exp Smooth Zone Width AERTS Prediciton-100%

-50%

0%

50%

100%

Smooth Zone Width PredictionMean Absolute Deviation = 30%

89

manual (Wright, 2008). This treatment was solely for numerical considerations to keep the

roughness equations working for smooth surface calculation.

The previously mentioned AERTS roughness distribution correlation was then applied to

all AERTS roughness datasets for validation. A sample correlation was plotted against the

experimental ice distribution and LEWICE prediction (initially shown in Figure 3-6) for

comparison in Figure 3-13.

Figure 3-13. Sample roughness measurement and prediction comparison

The ice roughness distribution could be successfully captured using the proposed

prediction model. The match in parabolic shape resulted in an average of ±12% error in prediction,

compared to LEWICE’s up to 400% over-prediction at very small roughness region (s/c<1% and

s/c>1%) and 42% discrepancy in predicting the maximum roughness height. Based on these

validation efforts, this improved roughness distribution prediction was then implemented into

developing the physics-based heat transfer model, as will be shown in later chapters.

3.2.2 Ice Roughness Prediction on a Cylinder

Similar approaches were also implemented in development of ice roughness prediction for

a cylinder. As mentioned in the literature survey of this chapter, there were no tabulated cylinder

90

ice roughness measurement data to serve as reference database for correlation development. In this

study, 8 test cases from the AERTS facility were used to generate a simple correlation for the

parameters in Equation (3-9). The maximum roughness height (xk) was non-dimensionalized with

respect to the cylinder diameter (2R) and was plotted against the accumulation parameter (Ac) in

Figure 3-14. A clear linear correlation could be readily developed.

Figure 3-14. AERTS cylinder roughness height correlation

As can be seen in Figure 3-14, by introducing the non-dimensionalized scaling factor, the

two sets of time series data can be grouped to fit on one single line, prescribed by Equation (3-10).

By using this correlation for maximum roughness height prediction, the mean absolute deviation

for eight cases was 15%, whereas this number was 86% if using LEWICE ver3.2 equations.

𝑥𝑘

2𝑅= 0.3224 ∙ 𝐴𝑐 (3-10)

Similarly, correlation for the smooth zone width on the cylinder was also attempted. The

dimensionless surface location was denoted using azimuth angle, therefore smooth zone width (w)

was defined in unit of degree.

During correlation development, the experimental smooth zone widths for two sets of time

series could not be grouped into a single line. In fact, the smooth zone width was found to be a

function of both icing time and Ac. The icing time affected the overall growth trend (i.e. slope) of

C6

C5

C4

C3

C10

C9

C8C7

y = 0.3224xR² = 0.9042

0

0.002

0.004

0.006

0.008

0 0.005 0.01 0.015 0.02

Hei

ght,

xk/

2R

AERTS ExperimentAERTS Correlation

𝐴𝑐

91

the roughness migrating towards the stagnation line, i.e., the longer icing time, the less smooth zone

width. The LWC effect was inherent in the accumulation parameter, and that was the reason that

separated the two lines. The difference was represented as an almost constant shift in the two curves

in Figure 3-15.

Figure 3-15. AERTS smooth zone width correlation

The negative value of the smooth zone widths (time series C3 – C6 in Figure 3-15) did not

hold any physical meanings. The negative value only indicated there was no smooth zone at the

cylinder stagnation, and the curve of the roughness distribution was shifting towards the stagnation

line. Eventually, the location of maximum roughness (xk) would coalesce with the stagnation line

which indicates a direct ice roughness deposition happened on the entire cylinder surface (no run-

back of the surface water, highest roughness at the stagnation). The proposed equation for the

smooth zone width is shown in Equation (3-11). The mean absolute deviation between predictions

using this correlation and experimental measurements for the eight cases was 7%.

𝑤 = −0.0649 ∗ 𝑡𝑖𝑚𝑒 −𝐴𝑐

𝑡𝑖𝑚𝑒∗ 260000 + 32 (3-11)

With respect to the third term in Equation (3-7), the ice limit (l) was found to be almost

constant during all the AERTS test runs. Again, similar to the roughness prediction for airfoil

section, there was no measurement of such parameter available in the literature for comparison.

92

Therefore, current AERTS cylinder roughness correlation used a constant of 65° for l. For the

roughness heights that were outside the rough zone, the minimum roughness height was again set

to be 0.05 mm, as recommended by LEWICE user manual (Wright, 2008).

The previously mentioned AERTS correlation was then applied to all AERTS roughness

datasets for comparison. The prediction for two ice roughness families are shown in Figure 3-16.

The symbols with dashed lines are experimental measurements, whereas the solid lines with

corresponding colors are predicted ice roughness distributions for each case.

Figure 3-16. Comparison of predicted ice roughness and experimental measurements

The correlation for ice roughness on ice-roughened cylinders achieved good agreements

with experimental measurements, especially for the higher LWC cases (C3 – C6). There were

underestimations for C7 and C8, due to the deviation in xk prediction as can be seen in Figure 3-14.

Overall, the correlation could capture the global growth trend and has potential to be integrated into

other numerical heat transfer or ice accretion predicting tools.

0

0.1

0.2

0.3

0.4

0.5

0 30 60 90

Ro

ugh

ne

ss H

eig

ht

(mm

)

Azimuth Angle (deg)

C7 - Exp

C8 - Exp

C9 - Exp

C10 - Exp

Prediction

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 30 60 90

Ro

ugh

ne

ss H

eig

ht

(mm

)

Azimuth Angle (deg)

C3 - Exp

C4 - Exp

C5 - Exp

C6 - Exp

Prediction

93

Chapter 4

Transient Heat Transfer Measurements

The experimental studies of heat transfer on various surfaces with varying roughness are

presented in this chapter. The rationale behind the experimental setup, introduced in Chapter 2, is

described first. Validation of the heat transfer measurement technique on flat plates, cylinders, and

clean airfoils are presented to prove the feasibility of the proposed experimental approach.

Observations and discussions on the experimentally measured heat transfer on both ice-roughened

cylinders and ice-roughened airfoils is then provided. A parametric study is finally conducted to

assist with the development of a semi-empirical model to predict heat transfer due to ice-roughened

surfaces.

4.1 Theory

After the roughness height was measured on ice casting models, the heat transfer on ice-

roughened surfaces was evaluated using a transient heat transfer analysis approach. The theory of

the transient heat transfer measurement procedure is introduced in this section.

The theory is based on transient heat conduction analysis on a semi-infinite flat plate. The

heat transfer coefficient is obtained by solving the energy balance at the interface between a solid

body and a fluid. A solid body subject to a transient change of temperature can be regarded as being

infinitely large in comparison with the initial region of the temperature change. If this is a cooling

procedure between the incoming fluid and the isothermal surface body, this problem can be

approximated as a transient heat conduction in a semi-infinite solid body with convective boundary

conditions. An exact solution exists for such a transient cooling problem (Carslaw & Jaeger, 1959).

94

If a constant heat convection condition at the boundary is applied, the convective heat transfer

coefficient can be obtained by solving the heat balance between heat conduction in the solid and

the convective cooling at the interface of the solid and the fluid. This analytical method has been

applied to curved surfaces combined with temperature-sensitive liquid crystals, as described by the

techniques used by Camci et al. (Camci C. , Kim, Hippensteele, & Poinsatte, 1991) (Camci C. ,

Kim, Hippensteele, & Poinsatte, 1993). The validation of this method can be found in the literature

conducted by the same group of researchers (Kim, Wiedner, & Camci, 1992) (Kim, Wiedner, &

Camci, 1992). Although the technique has been applied to turbine heat transfer measurements, this

is the first time that a transient heat transfer evaluation approach is applied to ice-roughened

surfaces.

In this study, the heat transfer coefficient was evaluated at the interface between the solid

airfoil and the incoming tunnel flow. During the test, the airfoil was preheated to a temperature

higher than the wind tunnel flow. The surface temperature was monitored using thermocouples and

thermistors. The average temperature difference between the wind tunnel flow and the testing

model was approximately 20°C. After an isothermal surface was achieved, the cooling procedure

started abruptly when the model was inserted into the flow. This abrupt cooling problem can be

considered to be a 1-D transient heat conduction problem on a semi-infinite region. The governing

equation for the problem is shown in Equation (4-1):

∇2T =1

α

∂T

∂t (4-1)

where, the term α is defined as thermal diffusivity as shown in Equation (4-2). It is a measure of

how quickly a material can carry heat away from a hot source. In its definition, k is the thermal

conductivity, ρ is density, and c is specific heat. The product of ρc is also called volume heat

capacity. These three thermal properties of the test specimen were determined experimentally by

using a combination of thermocouples, heat flux sensors and silicone rubber heaters.

95

𝛼 =𝑘

ρc (4-2)

A summary of the measured casting model material thermal properties is shown in Table

4-1, with comparison to those of Plexiglas.

Table 4-1. Measured Thermal Properties of Ice Casting Models

Test Specimen Property

Casting

Material

(Polyurethane)

Plexiglas

Density, ρ [kg/m3] 1046 1180

Specific Heat, c [J/(kg·K)] 4792 1470

Thermal Conductivity, k [W/(m·K)] 0.22 0.19

Thermal Diffusivity, α [m2/s] 4.39×10-8 10.95×10-8

To solve the governing partial differential equation with explicit solution, the position and

time needed to be collapsed into one independent variable. By using dimensional analysis, a new

variable, ζ, can be introduced to transfer the partial differential equation (PDE) into an ordinary

differential equation (ODE). The dimensionless term ζ is defined as:

휁 =𝑥

√ατ (4-3)

Correspondingly, the temperature T is normalized with respect to free stream temperature,

T∞, and initial temperature, Ti. The new variable θ is defined as:

𝜃 =𝑇 − 𝑇∞

𝑇𝑖 − 𝑇∞ (4-4)

Following the definitions of ζ and θ in Equation (4-3) and (4-4), the governing PDE of the

1-D semi-infinite heat conduction is converted into a new ODE, as shown in Equation (4-5).

𝑑2𝜃

𝑑휁2 = −휁

2

𝑑𝜃

𝑑휁 (4-5)

96

The relationship can be considered as 1-D transient heat conduction problem subject to

boundary conditions of the third kind, i.e. at the boundary, transient heat conduction is balanced by

convective heat transfer:

−𝑘𝜕𝑇

𝜕𝑥|

𝑥=0= ℎ(𝑇 − 𝑇∞)|𝑥=0 (4-6)

For the specific problem governed by Equation (4-5) with boundary conditions, Equation

(4-6), θ is both a function of ζ and the combination of conductive and convective heat transfer

coefficients. To solve this governing equation, the latter part is then organized into a new variable,

β, as described in Equation (4-7). The term,√𝛼𝑡, has units of distance (m) and thus can be regarded

as a pseudo characteristic length. This dimensionless number, β, has a similar format as the Biot

number in transient heat conduction analysis, but has no physical meaning:

𝛽 =ℎ√𝛼𝑡

𝑘 (4-7)

With all the analytical terms defined, the surface temperature during the transient procedure

can be expressed in its normalized form by Equation (4-8):

𝑇 − 𝑇∞

T𝑖 − 𝑇∞= 𝑒𝛽2

[1 − 𝑒𝑟𝑓(𝛽)] at x=0 (4-8)

where erf is the error function, which is defined as:

𝑒𝑟𝑓(𝑥)=2

√𝜋∫ 𝑒−𝑡2

𝑑𝑡𝑥

0

(4-9)

During wind tunnel testing, the surface temperature, T, can be monitored using different

sensors. The only unknown term in Equation (4-8) is β. With a power series approximation of the

error function (Abramowitz & Stegun, 1965), as shown in Equation (4-10), β can be solved readily

using numerical methods.

𝑒𝑟𝑓(𝑥)≈1-(𝑎1𝜆 + 𝑎2𝜆2 + 𝑎3𝜆3)𝑒−𝑥2 (4-10)

97

where λ = 1/(1+px), p = 0.47047, a1 = 0.3480242, a2 = −0.0958798, a3 = 0.7478556. The maximum

error from this approximation is 2.5×10-5. Once the value of β is obtained, the convective heat

transfer coefficient h can be found directly from Equation (4-7).

4.2 Technique Validation

The proposed experimental technique has been applied to three geometries in this study,

namely: a flat plate, a cylinder, and airfoils. The feasibility of the proposed approach has been

examined by comparing experimental measurements conducted in this study to those referenced in

the literature (see Chapter 1). Validation cases on these generic test models are presented in the

following subsections.

4.2.1 Technique Validation on a Flat Plate

To validate the analytical calculation method and the surface temperature mapping

technique using an infrared (IR) camera, a flat plate heat transfer measurement was conducted and

compared to reference data from the literature. The flat plate was made out of Plexiglas and covered

with flat black paint. The plate had a dimension of 0.406 m (16 inch) in length and 0.610 m (24

inch) in span. The flat plate also featured a 30° wedge shape leading edge to precondition the flow.

A photograph of the flat plate model is shown in Figure 4-1. Various grit grades of roughness were

used as turbulators to study the flow sensitivity to varying roughness heights. A similar setup was

used for the airfoils tested, as already shown in Figure 2-17.

98

Figure 4-1. Wind tunnel flat plate model setup

Due to the rough surface finish of the test model and tunnel turbulence intensity,

transitional flow was observed during the attempt to experimentally reproduce pure laminar flow

over the flat plate, eliminating the possibility to generate laminar flow on the available plate.

Instead, a turbulent flat plate was tested and compared to empirical equations. The maximum

Reynolds number based on distance for the test was 1.2×106, well above the rule-of-thumb

transition criterion of Rex = 5×105 used for smooth flat plates.

Based on the previously mentioned experimental approach, the transient surface

temperature change was monitored using the IR camera. The measured temperature data were used

together with Equation (4-1) to (4-10) to calculate heat transfer coefficients. The monitoring region

of the IR camera covered a rectangular area with dimensions of 0.20 m (7.8 inch) width, and 0.15

m (5.9 inch) length. The pixel size was 0.318 mm (0.0125 inch). The experimental measured data

used for calculating two-dimensional heat transfer curve was taken from the mean of 10 pixel

values at the center span location of the plate. To compare with the experimental results, established

empirical correlations between heat transfer coefficient (h) and Reynolds number based on distance

(Rex) were used. The empirical equations are shown in Equation (4-11) as below:

ℎ𝑡𝑢𝑟𝑏=0.0296𝑅𝑒𝑥4 5⁄

𝑃𝑟1 3⁄

ℎ𝑙𝑎𝑚=0.332𝑅𝑒𝑥1 2⁄

𝑃𝑟1 3⁄

(4-11)

99

The measured turbulent heat transfer coefficients are shown in Figure 4-2 and they are

compared against empirical correlations for both laminar and turbulent flow.

Figure 4-2. Heat transfer measurement on a turbulent flat plate

The experimental measurements are shown in dark solid line, whereas the two empirical

correlations are plotted in dashed gray color lines. Excellent agreement between the AERTS flat

plate experimental data and empirical equation for turbulent regime was obtained. The transient

heat transfer measurement technique was validated against empirical predictions for the turbulent

region of a plate.

4.2.2 Technique Validation on a Circular Cylinder

The technique was also validated on clean cylinders by comparing experimental results

against reference measurements by Achenbach (Achenbach, 1975), which were already shown in

Figure 1-11. Three Re regimes were reproduced experimentally in the wind tunnel, namely: Re =

1×105, 2×105, and 3×105. Detailed comparisons of the surface temperature history, as well as the

calculated heat transfer rate, are presented in Figure 4-3, Figure 4-4, and Figure 4-5.

100

Taking the case with Re = 1×105 shown in Figure 4-3 as an example, the top chart was used

to show the transient temperature change between the monitoring time intervals, denoted by the red

and blue line. The temperatures readings were obtained from the two images shown on the right of

figures. The two pictures were surface temperature greyscale images acquired by the IR camera.

They are shown here to visualize the staring and final temperature recordings. The red squares and

texts (TC1, TC2, TC3, and TC4) were locations of surface-mounted thermocouples used for

validation of the IR measurements. The thermocouple readings were also denoted as red and blue

dots in the top chart for reference.

Figure 4-3. Clean cylinder heat transfer - ReD = 1×105

In Figure 4-3, the heat transfer rate was presented in terms of Frossling number (Fr), as

shown in the bottom chart by a solid blue line. This non-dimensionalized number was defined in

the introduction section of Chapter 1, but is shown here again for convenience in Equation (4-12).

It was named after Frossling’s work (Frossling, 1958). The relationship was usually used to scale

heat transfer measurements in a laminar flow regime and it is suitable for cylinder testing in cross-

flow conditions.

101

𝐹𝑟 =𝑁𝑢𝐷

√𝑅𝑒𝐷

(4-12)

As can be seen in all three comparison figures, Fr curves shown in solid lines (blue, yellow,

and green, in Figure 4-3, Figure 4-4, and Figure 4-5 respectively) matched the experimental data,

shown by discrete dots, very well. In cylinder laminar flow regimes, the highest heat transfer was

always observed at the stagnation line, and it was followed with a gradual decrease when moving

away from the leading edge area. The sudden recovery in the curves was due to laminar separation,

rather than laminar-to-turbulent transition under the relatively low test Reynolds numbers. The heat

transfer for the clean cylinders tested in this study were all within the transitional Re region. Most

part of the curves (before 80°) were still in a laminar region until they reached the separation point

around azimuth angles of 83° for Re = 1×105 and 2×105, or 101° for Re = 3×105. These separation

regions matched the experimental results very accurately. At a separation location, the lowest value

in heat transfer rate also corresponded to the least change between the start and end temperature

profiles. Accordingly, there was a bright band across the spanwise direction shown on the IR

camera pictures, indicating a local higher temperature that occurred during the transient cooling

process in the wind tunnel. This IR visualization technique was proven to assist with the monitoring

of the flow separation/transition behavior.

Similar conclusions can be drawn from tests with higher Reynolds number as shown in

Figure 4-4. Notice that the separation location in Figure 4-4 shifted with Re and again matched the

transient heat transfer evaluation technique.

102


One interesting observation in Figure 4-4 is that there were two dark steak-shaped lines in

the vertical direction from the IR camera pictures. These two lines indicated turbulence

propagations due to local surface roughness disturbance. At lower Re regime (Figure 4-3), viscous

effect dominated the inertial effect, the boundary layer was thick, and thus the roughness effect was

not “felt” by the flow, i.e., the surface was aerodynamically smooth at low Re. When the Re

increased, the local boundary layer thickness decreased below the surface roughness height. The

flow was locally energized due to the presence of the surface debris. The dark line indicated an

enhanced heat transfer rate behind the roughness element. Due to the effect of the favorable

pressure gradient, the overall flow still remained laminar at the location of the roughness.

Therefore, there was only vertical lines of local heat transfer enhancement, corresponding to

“streaks” generated by the local boundary layer perturbation. Once past the separation point, the

disturbance became “wedge” shape, and also extended the separation further downstream of the

cylinder surface, as indicated by the movement of the bright band in the diagonal direction. Similar

effects of the separation line movement was more obvious in Figure 4-5. As the Re increased to

103

3×105, a shift in the separation angle can be clearly observed from both temperature measurement

and the heat transfer curve. This delay in separation indicated that the boundary layer was stable at

higher Re. As already mentioned in discussion of Figure 1-11, this delay resulted from a laminar

separation bubble. Under this Reynolds number, the flow regime was still within the critical regime.

If the Re kept increasing, laminar separation bubble will disappear and the flow will be able to

transition to turbulent flow before it left the cylinder surface.


The dark region on the left of the IR pictures were due to heat transfer enhancement after

flow passed the surface-mount sensors. This phenomenon actually suggested that temperature

measurements from sensors were still valid since the grey-scaled color from IR output was still

with the same color on the sensor location, compared to that of nearby regions. The dark color was

only observed behind the sensor wires. It must be noted that the heat transfer curve was only

evaluated at the right edge of the picture, where the flow was not affected by the sensor wires.

104

4.2.3 Technique Validation on an Airfoil

As indicated in Chapter 1, clean airfoil heat transfer data obtained at other facilities, such

as at the NASA IRT (Newton, Van Fossen, Poinsatte, & DeWitt, 1988) were available and was

used as validation datasets in this study.

Similarly to the technique validation conducted on smooth cylinders, the validation data

were presented in terms of Frossling number. Although it was first introduced for cylinder-in-

crossflow with low Re, the Frossling number has been demonstrated its applicability over a large

range of Re at the leading edge nose area of an airfoil (where the flow is laminar). Yeh et al. (Yeh,

Hippensteele, Van Fossen, & Poinsatte, 1993), implemented the Frossling number in their heat

transfer study on turbine airfoils in cascade flow configurations. It was shown that for a given

turbulence intensity level (1.8%-15.1%), heat transfer at the leading edge area for all Reynolds

numbers tested (0.75-7.0×106) can be correlated in to a single curve using the Frossling number.

The Fr was also a standard output parameter provided by the LEWICE heat transfer prediction

module. Therefore, Fr measured in this study for clean airfoil was able to be compared to both

NASA experiments (Newton, Van Fossen, Poinsatte, & DeWitt, 1988) and LEWICE predictions,

as shown in Figure 4-6.

Figure 4-6. Frossling number on a clean airfoil

105

The black solid line is the experimental Fr obtained at the AERTS facility. The LEWICE

prediction is shown in grey color. The LEWICE input condition was set to a nominal zero-icing

condition, where LWC and MVD were set sufficiently low to render no effect on heat transfer. The

discrete data shown in diamond markers were the experimental data taken at the NASA IRT. The

two experimental clean airfoil data correlated very well at the leading edge, except the sharp drops

of the NASA experiment data between 6% to 8% chordwise location. This irregular change in curve

had also been noticed by other researchers, as mentioned by Feiler who wrote: “Poinsatte comments

on this unsteadiness (the data drop between 6% and 8%) as probably being caused by a local surface

deformation” (Feiler, 2001). The NASA experimental results are also plotted in the following

section of ice roughened airfoil heat transfer comparison to provide a reference of Fr magnitude of

clean airfoil. The good match between experimental results and predictions for this clean airfoil,

shown in Figure 4-6, further validated the wide applicability of the proposed transient heat transfer

measurement techniques.

4.3 Transient Heat Transfer Measurement Results on Ice-Roughened Surfaces

After the proposed techniques were validated against reference experiments at extensive

Re regimes on various smooth surfaces, the experimental observations of heat transfer due to

natural ice roughness are examined in this section. The experimental results from both ice-

roughened cylinders and ice-roughened airfoils are shown in the following sections. The

corresponding ice accretion test matrices are listed in Table 2-2 and Table 2-3 respectively.

106

4.3.1 Ice-Roughened Cylinder

The experimental measured heat transfer rates on ice-roughened cylinders were presented

in terms of Frossling number. The comparison was conducted for the two ice roughness families

with four different icing times. Results from the two icing families were placed in the same figure

side by side for comparison. The two sets of data were compared in three test Re regimes (Re =

1×105, 2×105, and 3×105), as shown in Figure 4-7, Figure 4-8, and Figure 4-9. In general, the lower

LWC cases (C7-C10), shown at the left chart of each figure, featured lower roughness height and

less overall heat transfer amplitude, compared to cases with higher LWC (C3-C6). The following

heat transfer measurements will be discussed according to different Reynolds numbers.

Figure 4-7. Comparison of heat transfer on ice roughened cylinder surface - ReD = 1×105

At low Re = 1×105, as shown in Figure 4-7, the less rough cases (left chart) followed the

clean cylinder trend (taken from Figure 1-11), as denoted by the blue circles. All cases except C7

ended up with a laminar separation at the regular separation location (83°) as seen on the clean

cylinder case. The case C7 in red line in the left chart can be seen to be more locally energized as

the flow passed the rough zone of ice roughness, and later resulted in a laminar separation and

reattachment flow behavior. On the right chart, the fluctuation in the rough zone area implied a

higher heat exchange rate. Flow started to behave differently according to different roughness level.

The roughest case (C3 in red) started a local flow transition process due to the roughness accreted

0

0.5

1

1.5

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0 30 60 90 120 150

Fr =

Nu

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rt(R

e)

Azimuth Angle, deg

Ref CleanC7 - 120 sC8 - 90 sC9 - 60 sC10 - 30 s

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Ref CleanC3 - 120sC4 - 90sC5 - 60sC6 - 30s

107

to the cylinder. The less rough case (C4 in blue), although not initially transitioning to a turbulent

regime, was also observed to have a delayed separation due to the upstream energized flow

boundary layer. The rest of the two less rough cases (C5 in green and C6 in yellow) were observed

to still behave like the clean cylinder case. The local fluctuations at the rough zone of C5 and C6

did not generate changes in flow transition/separation.

As flow Re was increased to Re = 2×105, as illustrated in Figure 4-8, the least rough cases

in both sets of data (C10 in yellow and C6 in yellow) still behaved like the clean cylinder trend.

The separation locations were found to be the same as the clean case as denoted by the yellow lines

with triangles. As for the rest of cases with higher roughness, the heat transfer differences were

even apparent.


In Figure 4-8, by comparing the two charts, it is seen that the two families behaved

differently due to the difference in overall roughness level and roughness distribution. The missing

smooth zone in the higher LWC group (C3-C6 in Figure 3-16) clearly contributed in the higher heat

transfer level and related to turbulent flow behavior.

The highest Reynolds number test for this study was Re = 3×105, as shown in Figure 4-9.

Based on Achenbach’s clean cylinder test results (Achenbach, 1975), this Reynolds number was

on the boarder of subcritical and critical flow regime, as indicated by the green cross marker on

0

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108

both charts. The flow on the clean cylinder still did not transition to a turbulent flow until it

separated and reattached onto the surface. The higher Reynolds number only shifted the separation

location further downstream on the clean cylinder surface when compared to results obtained for

lower Re cases for clean cylinder (discussed in technique validation section). However, with the

presence of ice roughness, most of the cases started early transition at the rough zone, except the

least rough case (C10 in yellow in the left chart), which clearly indicated a laminar separation with

reattachment flow behavior. At the reattachment location after the creation of a laminar separation

bubble, case C10 in yellow, exhibited a sudden transition to turbulent flow and a significant

increase in heat transfer, which was much higher than other turbulent cases with early transition

due to roughness.


For the rest of the 7 cases except case C10, the flow behavior in both charts showed a

similar trend which can be used for further turbulent model development studies.

To summarize the experimental observations, a comparison of the separation/transition

behavior was quantified and tabulated in Table 4-2.

0

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109

Table 4-2. Summary of Ice-Roughened Cylinder Heat Transfer Behavior

4.3.2 Ice-Roughened Airfoil

The effects of temperature, velocity, droplet size (MVD), liquid water content (LWC), and

icing time on the measured surface roughness heights and heat transfer are examined in this section.

Each of the figures in the subsections shows comparisons of both heat transfer measurement (chart

on the left) and roughness height (chart on the right). The roughness data are shown together with

the heat transfer experimental measurements to provide a reference on the correlation between the

two key parameters. This correlation between roughness and heat transfer also provided insight for

heat transfer model development as a function of surface roughness distribution (to be described in

upcoming sections). The experimental data measured are presented in solid lines with gray and

case #Separation / Transition Location (unit: azimuth angle, deg)

ReD = 1E+05 ReD = 2E+05 ReD = 3E+05begin end length begin end length begin end length

3 87.9 102.4 14.5

4 97.6 112.3 14.7

5 86.6 102 15.4 101.3 114 12.7

6 84.07 98.5 14.43 82.8 99.2 16.4 94.61 112.9 18.29

7 85.5 100 14.5 94.4 110 15.6

8 85.71 101.7 15.99 107 122 15 87.5 105 17.5

9 84.2 99.6 15.4 106.3 121.5 15.2 94.2 112 17.8

10 84.8 100.9 16.1 83.1 101.4 18.3 104.3 120 15.7

Laminar separationLaminar separation w/ reattachment

Heat transfer amplified at rough zone,

separation / transition at post-rough region

Fully turbulent flowat rough zone

110

black color, while the corresponding LEWICE predictions are shown in dashed lines with

associated case colors accordingly. The roughness height data are plotted in terms of Ra with ±1

standard deviation. The experimental heat transfer data of a clean NACA 0012 airfoil from NASA

are also shown (discrete diamond symbols) as a reference of magnitude and for comparison.

4.3.2.1 Effect of temperature

The effect of temperature on heat transfer measured on ice-roughened surfaces was found

to primarily result from the ice roughness distributions. In this sub-section, roughness distributions

and associated heat transfer for AERTS case R2 and R3 are presented. The testing temperature for

case R1 (see Section 2.4.2 for description of the test matrix) was -3.60°C, whereas it was -5.54°C

for case R2. All other icing conditions remained the same for both cases. A photographic

comparison of the roughness distribution between case R1 and R2 is shown in Figure 4-10.

Figure 4-10. Typical ice roughness: case R2 (left) and R1 (right)

Case R1 (right) was designed to represent a fully glaze ice condition. Under the warm

temperature, a run-back zone was found mixed with roughness elements at the back part of the

rough zone. The run-back water effect was so high that water beads tended to be driven by

combined effects of centrifugal forces and aerodynamic forces. Clear water traces of spanwise and

Run-Back Zone:Water Rivulets formed in Diagonal Direction

Rough Zone

No Smooth Zone Detected:Fully Rough at Leading Edge

Smooth (Wet) Zone

Case R1

Case R2

Ice Limit

111

chordwise movement had been observed on the ice castings. Instead of direct depositing at the

leading edge area, the impact water droplets tended to form streaks and rivulets and moved in

diagonal direction.

The corresponding effects of temperature on the heat transfer coefficients and surface

roughness are shown in Figure 4-11. The saw-teeth shape heat transfer curve of case R1 (grey solid

line on the left) indicated it was resulted from the unsteadiness of surface running water effects that

froze on the surface of the airfoil. From the heat transfer comparisons between experiments and

predictions, the LEWICE predictions featured abrupt transition at 1% s/c, and over-predicted the

heat transfer for both two cases.

Figure 4-11. Effect of temperature

With respect to the roughness height comparison, the results seemed to be counter-intuitive

at first sight. At the region of 2%-6%, the roughness height of the more glaze-like case, R1, was

measured to be lower than R2. The possible reason for this phenomenon is that the surface tension

of the water film cannot sustain a local large-size water bead to freeze up at a warm temperature,

whereas under a colder temperature, the water beads can be more sufficiently cooled and form ice

roughness at the impact location. This hypothesis has also been validated by comparing the ice

limits of the two cases. The ice element ended at 7.6% s/c in case R2 whereas the ice roughness of

R1 extended all the way to 15.2% of the surface. Also, the error bars (standard deviation) of R1

was much higher than R2. The ratio of standard deviation over the average (SD/Ra) for case R1

0

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0% 2% 4% 6% 8% 10% 12% 14% 16% 18% 20%

Fro

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mb

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Dimensionless Surface Distance, s/c

NASA Clean

LEWICE R1

LEWICE R2

AERTS R1

AERTS R2

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0.2

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LEWICE R1

LEWICE R2

AERTS R1

AERTS R2

112

fluctuated with locations due to the flowing and freezing rivulets of water. The range of this ratio

was 23%-50% from 0% to 6% s/c and it was 50%-100% between 8% and 10%, which meant these

regions belonged to the run-back zone where most ice roughness was frozen water rivulets rather

than evenly distributed ice roughness elements. In contrast, the ratio of SD over Ra had a maximum

of only 26% for case R2 which indicated a much smaller fluctuation across the spanwise

distribution. These facts added together suggested the large spanwise variation were caused by

surface water rivulets. One last point worth noticing is that although the general roughness height

of R1 was lower than R2, the measured heat transfer of R1 was still higher than R2. This might be

attributed to the much higher leading edge roughness of R1 than the colder case R2. There was no

smooth zone for case R1. The flow boundary layer of R1 was energized by the initial flow mixing

at the fully rough leading edge. Consequently, the measured heat transfer level of R1 was higher

although the roughness height measured at the back of leading edge nose area was lower than that

of case R2.

4.3.2.2 Effect of velocity

Cases R10 and R5 are two cases differing only in the velocity used during testing, while

other icing conditions were held the same. The effect of velocity on heat transfer and surface

roughness height is shown in Figure 4-12.

Figure 4-12. Effect of velocity

0

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0% 2% 4% 6% 8% 10% 12% 14% 16% 18% 20%

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NASA Clean

LEWICE R10

LEWICE R5

AERTS R10

AERTS R5

0

0.1

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LEWICE R10

LEWICE R5

AERTS R10

AERTS R5

113

For these two example cases, the rotating speed of the R10 case was 300 RPM (Vtip = 44.5

m/s), whereas that for case R5 the RPM was 450 RPM (Vtip = 66.7 m/s). From heat transfer

comparisons (on the left graph of Figure 4-12), the two cases shared the exact same trend of heat

transfer up to 2% s/c. The same trend can be found in both the LEWICE prediction and the NASA

clean airfoil measurements, which indicated the existence of a laminar flow region despite the ice

accretion, and therefore not affecting the heat transfer coefficient. On the right comparison chart,

the experimental roughness heights also overlapped on each other in this region. The location for

smooth zone to rough zone transition was determined to be at 1.4% s/c, being the same for both

cases. This good agreement denoted that the roughness height at the smooth zone of these two cases

was very similar. The flow passing through the smooth zone at the leading edge area remained

laminar and was not affected by the ice roughness. One of the possible reasons for this insensitivity

to roughness is that at the high curvature of the leading edge region, the favorable pressure gradient

helps to keep the flow stable. As long as the roughness height does not exceed the flow transition

critical height, the heat transfer will not be altered by the additional small roughness induced by

accreted ice at higher velocities.

For both heat transfer and roughness height measurements, after 2% s/c, the four data sets

shown so far (Figure 4-12) started to show different trends. On the roughness height side,

experimental results shared a similar general trend with LEWICE predictions. The experimental

R5 roughness results reached its peak around 4% s/c. The LEWICE prediction was 238% that of

the experimental peak-to-peak experimental measurements. The LEWICE prediction for R10

showed a sharp drop to its minimum value after passing its peak at 2% s/c, whereas the roughness

measured for case R10 kept a gradual growth for another 2% s/c before the height started to

decrease, which also resulted in an extension of the ice limit by 2% when compared to LEWICE

predictions.

114

The comparison of LEWICE predictions for cases R5 and R10 shows a discrepancy in

roughness height and extent predictions, introducing a propagating effect in the heat transfer. The

black dash line (LEWICE R5) in heat transfer comparison chart bounced up at the location where

the R5 roughness prediction reached its peak value, which indicted a sudden flow transition in the

LEWICE prediction. The LEWICE R5 prediction then followed the clean airfoil trend but with a

large constant shift of Fr = 5. The gray dashed line (LEWICE R10) followed the clean airfoil heat

transfer curve, which indicated that the flow remained laminar for the entire 20% portion of the

leading edge region. The 0.6 mm LEWICE predicted roughness height under the R10 icing

condition did not exceed the flow transition critical height.

For the comparison between experimental cases R5 and R10, although there was a clear

difference in roughness height between the two cases in the 2% to 8% s/c rough zone region, the

measured Frossling number remained at the same level. The additional roughness of R5 only

contributed to the unsteadiness of the Fr curve. The effect of velocity on the roughness height is

evident, whereas it is not equivalently large enough to make a distinction in heat transfer.

In the comparisons shown between experimental data and LEWICE heat transfer, the over-

prediction provided by the predictions can be clearly spotted. The abrupt jump of the heat transfer

was not observed in experimental results. The highest Frossling values of the two experimental

cases were also obtained at a location 4% back with respect to the peak location of the LEWICE

prediction. This means transition to fully turbulent has been delayed compared to predictions. There

is a transitional region before the flow became fully turbulent. A transition model is desirable to

describe the difference between the experimentally obtained smooth transition and the abrupt heat

transfer coefficient jump obtained in LEWICE predictions.

115

4.3.2.3 Effect of droplet size

The effect of droplet size in terms of MVD is shown in Figure 4-13. The only difference

between the two cases was that the MVD of case R9 was 20 µm and for case R3 it was 30 µm.

Figure 4-13. Effect of droplet size

The effect of MVD on both heat transfer and roughness height was as expected: the larger

the droplet size, the higher roughness height, and consequently, the higher heat transfer rate. It is

worth noticing that there was a delay of flow transition for case R3. Although the ice limit based

on the span of R9 was measured to be 7.2%, the majority of the roughness elements resided within

the s/c range between 1% and 4%. The flow did not transition until it passed the majority of the

roughness elements of case R9. On the contrary, the heat transfer of case R3 indicated a flow

transition much closer to the leading edge, where the roughness height level was the same as that

of case R9. This phenomenon meant that the larger droplet size may introduce more spanwise

unsteadiness to the roughness distribution, which helped the flow mixing and enhanced flow

transition.

4.3.2.4 Effect of liquid water content (LWC)

The LWC has a unit of g/m3 and therefore is a measure of droplet mass density in an icing

cloud. Its effect on heat transfer and roughness height is illustrated in Figure 4-14 and Figure 4-15.

0

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0% 2% 4% 6% 8% 10% 12% 14% 16% 18% 20%

Fro

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NASA Clean

LEWICE R9

LEWICE R3

AERTS R9

AERTS R3

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LEWICE R9

LEWICE R3

AERTS R9

AERTS R3

116

In Figure 4-14, the LWC comparison is between 0.25 g/m3 (R6) and 1 g/m3 (R9). When comparing

experimental results and predictions, LEWICE over-predicted both the roughness height and heat

transfer rate. Although the overall predicted roughness trends for the two cases matched with the

experiments, the magnitude of the peak value ranged between 200% and 391% of the measured

values.

For the comparison between experimental results R6 and R9, the effect of LWC was very

clear. The roughness of the lower LWC case (R6) resembled a similar trend seen in case R9, i.e.

similar roughness spatial distribution, similar ice limit, but with much smaller amplitude. For peak

value comparison, the highest roughness of case R6 was only 28.2% of that of case R9 at the same

location. The small amplitude of the surface roughness height of R6 did not sufficiently trigger

flow to transition. The gray curve in the heat transfer comparison chart showed a trend more

representative of a clean airfoil trend.

Figure 4-14. Effect of LWC (1)

It is shown in Figure 4-15 a comparison of LWC for a different LWC range. The LWCs

considered in these two cases were 1 g/m3 (R3) and 1.7 g/m3 (R2). For the comparison of cases R3

and R2, the effect of LWC showed clear difference in roughness height but did not show equally

significant changes in heat transfer. The effect of LWC on roughness height in Figure 4-15 was

similar to Figure 4-14. The roughness trends were very similar with difference in magnitude. The

LWC effect in heat transfer for these two cases was not discernable compared to that of Figure 4-14.

0

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NASA Clean

LEWICE R6

LEWICE R9

AERTS R6

AERTS R9

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LEWICE R9

AERTS R6

AERTS R9

117

Figure 4-15. Effect of LWC (2)

The phenomenon that explains why different roughness heights did not cause significant

heat transfer changes has already been shown in the comparison of velocity effects. The limit range

of the LWC effect that dominate the heat transfer needs to be further examined with more

experimental inputs.

4.3.2.5 Effect of icing time

Three comparison charts are shown in this subsection to illustrate the effect of icing time.

The first comparison is between a 60 s ice accretion case (R0) and 94 s ice accretion case (R10), as

shown in Figure 4-16. When comparing heat transfer between experimental results and LEWICE

predictions, the LEWICE prediction contradicted the measurements. The R10 case, which was

accreted for longer time (94 s), was predicted to follow a clean airfoil heat transfer curve, whereas

the R0 with less icing time (60 s) was predicted to have a flow transition around 3% s/c location.

The LEWICE predictions for these two cases were questionable. Unfortunately, for the case R0,

the roughness height was not recorded and therefore not shown for comparison to R10. No

corresponding roughness comparison was available to provide further explanation for the different

heat transfer trends.

0

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0% 2% 4% 6% 8% 10% 12% 14% 16% 18% 20%

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NASA Clean

LEWICE R3

LEWICE R2

AERTS R3

AERTS R2

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LEWICE R3

LEWICE R2

AERTS R3

AERTS R2

118

Figure 4-16. Effect of time (1)

Another comparison between 94 s (R9) and 120 s (R7) icing time is shown in Figure 4-17.

The predicted roughness height of R7 matched with measurements, but the predicted heat transfer

was still around twice of the experimental results in magnitude. For the comparison between

AERTS cases R9 and R7, the difference in roughness height was very large, which indicated that

the last 26 s of accretion in R7 accounted for significant increase of roughness height. The

corresponding difference in heat transfer was also evident. The saw-teeth shape curve of the solid

black line (R7) between 1.5% and 6% s/c confirmed the roughness height ramped up in rough zone

and also the large spanwise variation (large error bar value) of roughness.


The last icing time comparison is among three cases, namely: case R8 (45 s), R4 (75 s) and

R3 (94 s), as shown in Figure 4-18. Again, it can be seen that the roughness grows with time as

expected and same trend can also be observed from heat transfer data.

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NASA Clean

LEWICE R0

LEWICE R10

AERTS R0

AERTS R10

0

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LEWICE R0

LEWICE R10

AERTS R10

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NASA Clean

LEWICE R9

LEWICE R7

AERTS R9

AERTS R7

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LEWICE R9

LEWICE R7

AERTS R9

AERTS R7

119

The case R8 was the shortest icing test conducted during this study, and the roughness

height was almost one order of magnitude lower than those measured for the other two cases. The

heat transfer of R8 followed the clean airfoil trend as expected. The cases R4 and R3 were tests

with only 19 s of icing time difference. It can be seen that the roughness growth in this last 19 s of

R3 was noticeably smaller than in the last 26 s of R7 in Figure 4-17. The heat transfer also

confirmed that the levels of heat transfer rate of the two cases were similar, whereas the case with

longer icing time (R3) exhibited a 1% s/c earlier flow transition.


Overall, the roughness height build-up rate was not linear with respect to time. The slope

of growth rate increased with time. Also, the effect of icing time in the above three comparisons

showed that the flow transition tended to migrate with time towards the stagnation point (0% s/c),

as shown in Figure 4-19. The transition locations of the six cases discussed in the effect of icing

time are categorized into three groups as summarized in the chart shown in Figure 4-19. Case R8

was not shown in the chart since there was no transition detected in the monitored area. Clear trends

of the transition location marching towards the stagnation line have been observed.

0

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0% 2% 4% 6% 8% 10% 12% 14% 16% 18% 20%

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NASA Clean

LEWICE R8

LEWICE R4

LEWICE R3

AERTS R8

AERTS R4

AERTS R3

0

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LEWICE R8

LEWICE R4

LEWICE R3

AERTS R8

AERTS R4

AERTS R3

120

Figure 4-19. Flow transition location vs. icing time

4.3.2.6 Summary of parametric study on ice-roughened airfoil testing

1. Experimental measured heat transfer and roughness heights were compared to LEWICE

predictions. For all the experimental cases, except for case R10, LEWICE over-predicted the

roughness heights and consequently over-predicted the heat transfer rate, supporting the need

for an improved heat transfer model (described in upcoming chapters).

2. Test results were used during a parametric study investigating the effects of temperature,

droplet size, cloud density, impact velocity and accretion time. Although the comparisons are

far from being comprehensive, the results shed insight and guidance for heat transfer modeling

development that will be discussed in the following chapter.

3. A surface running water phenomenon was observed during a temperature comparison tests.

The warm temperature of one of the cases (R1) resulted in water steaks growing in both

chordwise and spanwise locations. There was an additional run-back zone of roughness,

whereas no smooth roughness zone found for this case. Roughness at the leading edge area was

R101.3%

R02.2%

R32.1%

R43.05%

R71.05%

R93.4%

0%

1%

2%

3%

4%

40 60 80 100 120 140

Tran

siti

on

Lo

cati

on

, s/c

Icing Time, s

R10 vs. R0 R3 vs. R4 R7 vs. R9

121

fully-grown and caused the heat transfer to fluctuate starting from the stagnation line and all the

way to the ice limit area.

4. Larger droplet size caused a larger roughness size and also a spanwise unsteadiness, which

was believe to trigger an early flow transition.

5. Two comparisons on the effect of liquid water content indicated that variation in lower

region (0.25 g/m3 vs. 1 g/m3) caused noticeable changes in both roughness height and heat

transfer. The liquid water content comparison at higher densities (1g/m3 vs 1.7 g/m3) showed

noticeable change in roughness but no significant change in heat transfer.

6. The overall icing time effect was seen to introduce a flow transition point migration towards

the stagnation point. The growth rate of the roughness element was not a linear function of the

icing time. The rate increased with time as it approached the upper limit of the tested maximum

time.

122

Chapter 5

Heat Transfer Model Development

In the previous chapter, experimental heat transfer measurements were conducted on both

clean and rough surfaces. Heat transfer in terms of Frossling number for both cylinders and airfoils

were validated and examined. Notice that all the experimental comparisons of different roughness

levels were evaluated under the same Reynolds number. However, during model development, to

predict heat transfers at different Reynolds number levels, a good understanding of the effect of

Reynolds number on heat transfer, especially turbulent heat transfer regime is critical.

Heat transfer enhancement due to surface roughness have been studied in the literature on

flat plates (Pimenta, Moffat, & Kays, 1975), cylinders (Achenbach, 1977) (Van Fossen, Simoneau,

Olsen, & Shaw, 1984) and airfoils (Poinsatte & Van Fossen, 1990). To incorporate the reference

database into current model development, heat transfer must be evaluated using an effective non-

dimensionalized parameter. During the comparison of experimental results across different

facilities, it was found that the scaling of the convective heat transfer magnitude was not well

understood, especially in the turbulent regime. Therefore, further studies were conducted to develop

a scaling parameter for heat transfer in the turbulent regime. Based on the proposed scaling method

for heat transfer, a correlation was found that relates the surface heat transfer with experimentally

measured surface roughness distributions. Motivated by the possible correlation between the icing

conditions and experimentally measured heat transfer, the development of an analytical heat

transfer predicting model was carried out. In this chapter, a new heat transfer scaling method is

proposed. The associated heat transfer correlation to experimental roughness measurements is then

123

presented. Based on the knowledge learned in these efforts, a novel icing-physics-based analytical

model for heat transfer on ice-roughened airfoils was developed.

5.1 Scaling Method for Heat Transfer Measurements

Scaling difficulties for turbulent heat transfer measurements were encountered when

comparing heat transfer coefficients (htc) measured at various Reynolds numbers with predictions

obtained under a different condition (different in ice accretion velocity and/or airfoil chord). An

example of heat transfer coefficients measured on an ice-roughened airfoil without any heat transfer

scaling is shown in Figure 5-1, together with comparison from LEWICE predictions. AERTS

experimental measurements are shown as a black line with grey shaded area representing ±1

standard deviation (std). Each of the AERTS testing conditions was repeated three times. For each

run, the standard deviations were calculated from the spatial difference over the monitoring area of

10 pixels’ width from images obtained with the IR camera. Standard deviations were displayed

based on the mean of the local heat transfer coefficient, to illustrate the 3D spatial variation on the

surface. The LEWICE prediction using same icing conditions as the AERTS ice accretion

experiment is shown with a grey dashed line for comparison.

Figure 5-1. Example heat transfer comparison – htc

124

In Figure 5-1, a noticeable amplitude difference can be observed between the AERTS

experimental measurement and the LEWICE prediction. This amplitude variance resulted from the

different Reynolds number used in testing and prediction. In an experimental environment,

measured local heat transfer coefficient is a function of local flow speed. To simulate the natural

aircraft icing encounter, the ice accretion test speed at the AERTS facility was 66.7 m/s; LEWICE

used the same icing condition for both roughness and heat transfer predictions. On the other hand,

the low-speed, warm-air wind tunnel where the AERTS heat transfer measurement testing was

conducted could not reproduce such high velocity. The heat transfer coefficient was measured at a

tunnel velocity of 30 m/s, 45% of the speed where the roughness was accreted.

This scaling issue related to Reynolds number effect also showed up when comparing the

AERTS experimental results with those from other testing facilities that used different model

dimensions and/or different tunnel speeds. A proper scaling method must be developed before any

meaningful comparison can be made for heat transfer modeling and validation.

5.1.1 Existing Dimensionless Parameters for Heat Transfer Scaling

In the literature, multiple dimensionless coefficients related to convective heat transfer

were available, such as: Stanton number, Nusselt number, and Frossling number, for different

purposes of comparison. In this section, these three dimensionless coefficients are examined based

on reference experimental studies of heat transfer on various surfaces, with a focus on eliminating

the Reynolds number effects on heat transfer magnitudes.

125

5.1.1.1 Stanton number for Flat Plate

The Stanton number (𝑆𝑡 = 𝑁𝑢 𝑅𝑒𝑃𝑟⁄ ) has been shown to be capable of representing flat

plate heat transfer, as already demonstrated in Figure 1-10. This figure is repeated from Chapter 1

and shown here in Figure 5-2 for the convenience of the discussion.

Figure 5-2. Reference rough flat plate heat transfer in St

Duplicated from Figure 1-10 for convenience in comparison

In Figure 5-2, the curves measured under different Reynolds numbers on artificially

roughened flat plate behaved in a similar trend, but scattered in space. For the higher speed range

cases (43, 58, and 74 m/s), the three curves tended to collapse into a single curve. Research on

artificially roughened flat plates with accelerating flow also supported the use of this Stanton

number for both smooth and artificially roughened flat plates inclined at various angles, as can be

observed in Figure 10 and 14 in a reference paper by Masiulaniec et al. (Masiulaniec, DeWitt,

Dukhan, & Van Fossen, 1995). This same group of researchers later examined seven (7) aluminum

casting models of ice-roughened surfaces on a flat plate for Rex ranging from 5.3×104 to 1.3×106

(Dukhan, Masiulaniec, & DeWitt, 1999). The unique trend found in the previous study no longer

existed on the more realistic ice-roughened surfaces. The authors concluded that “Some

0

0.002

0.004

0.006

1.E+04 1.E+05 1.E+06 1.E+07 1.E+08

Stan

ton

Nu

mb

er

Rex

7458432811Smooth

Tunnel Vel. (m/s)

126

dependence of Stanton-number magnitude on the roughness element height was noticed, but it was

not universal for all models for the whole range of local Reynolds numbers.”

5.1.1.2 Nusselt number for cylinder

The Nusselt number (𝑁𝑢 = ℎ𝑥 𝑘⁄ ) has been used in several references for heat transfer

comparison, such as the reference work by Van Fossen et al. (Van Fossen, Simoneau, Olsen, &

Shaw, 1984), where heat transfer on four (4) simulated ice accretion shapes on cylinder were

studied. However, as already stated in the introduction of this dissertation, the authors of this

reference paper found that, although each case could be curve-fitted into a form of 𝑁𝑢 = 𝐴𝑅𝑒𝐵,

the correlations were case sensitive and a unique scaled curve cannot be found for all the test cases.

In spite of its important thermal-physical meanings, Nusselt number is not suitable for comparing

heat transfer measured at different Reynolds number scales.

5.1.1.3 Frossling number for cylinder

The last and most promising heat transfer scaling factor used in the literature was Frossling

number (𝐹𝑟 = 𝑁𝑢𝐷 √𝑅𝑒𝐷⁄ ). As already introduced in Chapter 1, it was initially and primarily used

in heat transfer study for cylinders. It has been proven that Fr is suitable for scaling of laminar flow

on both cylinders and airfoils. For cylinder heat transfer, Frossling number can be mathematically

shown to be equal to one (Fr = 1) at the cylinder stagnation line. The Frossling number at the

cylinder leading edge was found to be independent of a large range of Reynolds number and model

dimensions (Schlichting, 1968). Heat transfer in terms of Frossling number has also been

extensively measured over a large range of Reynolds number (3×104 to 4×106) on a clean cylinder

by Achenbach (Achenbach, 1975), as already demonstrated in Figure 1-11 and Figure 1-12. The

127

Fr curves were shown to follow the same trend until transition from laminar to turbulent flow, or

separation from surface. Two of the artificially roughened cylinder tests with roughness element

heights of 0.45 mm and 0.9 mm were digitized from Achenbach’s paper (Achenbach, 1977) and

shown in Figure 5-3 and Figure 5-4 respectively. The two test series were conducted under seven

(7) Reynolds number conditions, and therefore are suitable for heat transfer scaling method

development that will be shown in a later section of this chapter.

Figure 5-3. Reference rough cylinder heat transfer in Fr – 0.45 mm roughness


Figure 5-4. Reference rough cylinder heat transfer in Fr – 0.9 mm roughness


0

1

2

3

4

5

6

7

8

0 30 60 90 120 150 180

Fr =

Nu

/sq

rt(R

e)

Angle, deg

7.2E4

1.27E5

1.46E5

2.26E5

8.6E5

4E6

ReD

0

1

2

3

4

5

6

7

8

0 30 60 90 120 150 180

Fr =

Nu

/sq

rt(R

e)

Angle, deg

4.8E4

7.3E4

2.8E5

3.8E5

8.8E5

1.9E6

4.1E6

ReD

128

5.1.1.4 Frossling number for airfoil

Similar trends as those observed on cylinders have also been observed on airfoils.

Reference heat transfer measurements on both clean and ice roughened airfoils under different

Angles of Attack (AOA) have been published in terms of Frossling number (Newton, Van Fossen,

Poinsatte, & DeWitt, 1988). Scattered Fr values on artificially roughened surfaces obtained under

five Reynolds numbers have been compared to clean Fr values. One example has already been

shown in Figure 1-16. Measurements on the front portion of the airfoil (10% s/c) collapsed onto a

single curve for all test Reynolds numbers. Frossling number has also been used as a standard heat

transfer parameter in LEWICE 2D prediction output. Besides reference data, previous AERTS

measurements of heat transfer in laminar regime also agreed well with findings in literature, as

already seen in both ice-roughened cylinder and airfoil experimental results in Chapter 4. Figure

5-1 was then modified and presented in terms of Frossling number, as seen in Figure 5-5.

Figure 5-5. Example scaled heat transfer comparison – Fr

As can be observed from Figure 5-5, the AERTS experimental measurement and LEWICE

prediction are in good agreement in the laminar region, before the two curves deviate when

transition due to roughness occurs. The curves after passing the rough zone (>~8% s/c) followed

the same trend again, but with an almost constant magnitude shift. The effects of different Reynolds

129

numbers are still distinctive in the turbulent region. Nonetheless, the similar behaviors in

experimental measurements and analytical prediction results proved the adequacy of the Frossling

number in comparing the heat transfer in laminar regime. It was for this reason that all of the

experimental measurements shown in prior chapters were presented and compared in terms of the

Frossling number. In addition, all of the previous comparisons for the AERTS experimental

measurements were evaluated under the same Reynolds number, where the scaling issue was not a

concern. However, for the ultimate goal of this research, a model of heat transfer on ice-roughened

surfaces required a successful correlation for heat transfer curves under an extensive range of

Reynolds numbers. In this regard, a new scaling parameter that can eliminate the Reynolds number

effect in the turbulent region must be developed.

This argument was supported from a reference on turbine blade heat transfer analysis by

Yeh et al. (Yeh, Hippensteele, Van Fossen, & Poinsatte, 1993). Experimentally measured heat

transfer coefficients were used to study the effects of Reynolds number and turbulence intensity.

The test Reynolds numbers ranged from 7.5×105 to 7×106. An example of the experimental

measurements is shown in Figure 5-6.

Figure 5-6. Frossling number used for heat transfer scaling

Modified from Figure 9 & 10 from Ref. (Yeh, Hippensteele, Van Fossen, & Poinsatte, 1993)

Again, it was found that through applying Frossling number, the htc curves close to the

stagnation area can be successfully characterized using a single Fr curve, as shown in Figure 5-6.

130

However, the rest of the heat transfer curves (turbulent regime) were scattered in space, which have

already been seen in Figure 5-3, Figure 5-4, and Figure 5-5. No correlation can be developed based

on this Frossling parameter for turbulent regime, where the most practical interest is focused.

5.1.2 Development of a new heat transfer scaling parameter - CSR

To fill in the research gap, a new scaling parameter was designed specifically for turbulent

heat transfer scaling on generic shapes. Unlike laminar flow, the heat and mass transportation

mechanism of turbulent flow is almost independent of boundary layer viscosity. The viscous

sublayer only accounts for approximately 5% of the total boundary layer thickness. One of the most

simple and popular assumption in turbulent flow is that the heat flux is transported by turbulent

motion of the same mass element that conducts the shear stress, known as Reynolds Analogy (Kays

& Crawford, 1993) (White, 2006). If assuming equal mass and thermal diffusivity for air (Prturb ≈

1, i.e. same amount of mass and thermal energy by diffusion), under the simplified condition that

incoming flow has constant velocity, no pressure gradient, and no temperature gradient, the non-

dimensionalized heat transfer coefficient in terms of Stanton number (St) can be proportionally

correlated to the coefficient of skin friction:

𝑆𝑡 ≡𝑁𝑢

𝑅𝑒𝑃𝑟∝ 𝑐𝑓/2 (5-1)

where for several elementary cases, such as flat plate cases, the skin friction coefficient (𝑐𝑓 2⁄ ) can

be expressed as a function of Reynolds number based on surface distance as described in Equation

(5-2). The potential correlation between skin friction coefficient and the Reynolds number based

on surface distance has been illustrated using flat plate as an example in Figure 1-9 and Equation

(1-4). The Figure 1-9 was then modified and shown in Figure 5-7 to illustrate the linear correlation.

131

The horizontal axis was changed from Rex (Figure 1-9) to Rex-0.2 (Figure 5-7), while other properties

remained the same.

Figure 5-7. Reference rough flat plate skin friction as a function of Rex-0.2


As suggested by the linear curve fittings in Figure 5-7, a simple linear correlation can be

found for each individual data series, as summarized in Equation (5-2):

𝑆𝑡 ∝ 𝑐𝑓/2 ≈ 𝐶𝑜𝑛𝑠𝑡 ∙ 𝑅𝑒𝑥−0.2 (5-2)

The correlation shown in Equation (5-2) was a simplified assumption. The skin friction

coefficient can be expressed in other forms with higher accuracy, such as a function of momentum

thickness. Still, the goal of this part of the research was to find a generalized correlation to bridge

the heat transfer and local Reynolds number based on model dimension, rather than boundary layer

properties that varied case by case. The correlation in Equation (5-2) was still used for scaling

method development purposes. The rationale of this scaling method development was then to take

the ratio between Stanton number and Reynolds number based on surface distance, so as to

eliminate the magnitude change due to Reynolds number. A scaling parameter called Coefficient

of St and Re (CSR) was therefore proposed for this study and defined as follows:

𝐶𝑆𝑅 ≡ 𝑆𝑡𝑥 𝑅𝑒𝑥−0.2⁄ (5-3)

132

where the subscript, x, was used as a generalized coordinate index; it was later substituted by the

surface wrap distance, s, in heat transfer modeling efforts. Notice that the definition was based on

local Reynolds number, rather than the Reynolds number based on the total airfoil chord (diameter

for cylinder) used in Frossling number definitions presented in Equation (4-12), Chapter 4. In the

following three sections, the validity of proposed CSR will be examined on reference experimental

heat transfer measurements identified during the literature survey in previous section.

5.1.3 Validation of CSR on flat plates

To examine the effectiveness of the proposed CSR scaling parameter, the reference

experimental measurements of Stanton number from rough flat plates and Frossling number from

rough cylinders and airfoils were converted into CSR for comparison. The artificially roughened

flat plate results previously shown in Figure 5-2 were first studied and can be found in Figure 5-8.

Figure 5-8. Reference rough flat plate heat transfer in CSR

As expected, the smooth flat plate heat transfer (red circles) could be characterized by CSR

as a constant over the entire Reynolds number range. However, the curves for the rough flat plate

under different test velocities were still scattered with different magnitudes. Heat transfer on

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

1.E+04 1.E+05 1.E+06 1.E+07 1.E+08

CSR

Rex

7458432811Smooth

Tunnel Velocity

(m/s)

133

roughened flat plates were not grouped into similar trend lines. In this example case, CSR did not

exhibit advantages compared to the original Stanton number representation. But unlike the

cascaded trend lines in St domain, the trend between different test cases can be presented more

clearly in terms of CSR. All cases behaved as a straight line with same slope before transition; after

transition, all rough cases gradually dropped magnitude as Rex increased.

5.1.4 Validation of CSR on cylinders

Next, the CSR was applied to rough cylinder reference experimental measurements, with

even better scaling results, as can be seen in Figure 5-9 and Figure 5-10. For comparison, the

reference experimental measured heat transfer rates were reported in Frossling number, originally

shown in Figure 5-3 and Figure 5-4.

Figure 5-9. Reference rough cylinder heat transfer in CSR – 0.45 mm

As can be seen in Figure 5-9, distinctive differences were found between a complete

laminar heat transfer trend line (blue shaded line, comprised by blue triangles) and a unique

turbulent trend line (yellow shaded line) independent of Re. Turbulent heat transfer curves that used

0

0.02

0.04

0.06

0.08

0 30 60 90 120 150 180

CSR

= S

t/R

e^

-0.2

Angle, deg

7.2E4

1.27E5

1.46E5

2.26E5

8.6E5

4E6

ReD

Laminar

Turbulent

134

to be scattered due to Reynolds number now can be compared under the same scale. The Reynolds

number effect in scaling was successfully eliminated.

For the smaller roughness case (0.45 mm) in Figure 5-9, the transition happened at multiple

azimuth angles. Besides the two highest Re cases (solid triangles and solid squares) that transitioned

immediately at the stagnation region, there were three (3) curves (open squares, crossings, and open

circles) that crossed in between the laminar curve and the turbulent curve. After transition, the heat

transfer curve merged onto the turbulent trend line smoothly. Similar transition behavior at different

positions on the cylinder surface was clearly indicated by the sudden shifting from blue trend line

to yellow trend line. This representation for fully / transitional turbulent flow could be valuable for

correlation development.

For the larger roughness case (0.9 mm) in Figure 5-10, the same trend was found in the

higher-roughness-height cases, especially for the turbulent trend line. The yellow shaded trend line

was exact the same as the one found in 0.45 mm case. There was a virtual “ceiling” of the heat

transfer curve represented using CSR, independent of the roughness size, once it transitions to fully

turbulent regime.

Figure 5-10. Reference rough cylinder heat transfer in CSR – 0.9 mm

0

0.02

0.04

0.06

0.08

0 30 60 90 120 150 180

CSR

= S

t/R

e^-

0.2

Angle, deg

4.8E4

7.3E4

2.8E5

3.8E5

8.8E5

1.9E6

4.1E6

ReD

Laminar

Turbulent

135

In Figure 5-10, the difference between the laminar and turbulent trend lines were even more

distinguishable. With the roughness height doubled from last case, only the lowest Re case in this

set of data still exhibited a pure laminar trend and only one case under Re = 7.3×104 showed a

transition away from the leading edge region. Again, before transition, it followed the blade-

triangle-curve, after transition, it immediately followed the turbulent trend line. The curves

measured from Re = 2.8×105 to 4.1×106 could be grouped into a unique turbulent trend line, which

means the measurement taken at low Reynolds number could be scaled and applied to higher

Reynolds number (more than 10 times for this case) applications. Considering that the reference

test data was conducted in a compressed air wind tunnel which required additional processes and

cost for testing, this scaling method could potentially help simplify the testing procedure. For

example, in Achenbach’s experiments, a tunnel static pressure of 40 bar was used to achieve the

additional high Reynolds number capability.

After excellent application of CSR on reference rough cylinder measurements was

observed, the CSR was also applied to the AERTS experimental measurements on ice-roughened

cylinders as introduced in Chapter 4. Recall that the cylinder test results in Chapter 4 were grouped

by the same Reynolds number with varying roughness conditions. This time, the cylinder heat

transfer measurements are compared at three Reynolds numbers for the same roughness. Cases C3

and C7 were selected since the CSR works best in fully-turbulent flow, and cases C3 and C7 are

the two roughest cases in the two time series as indicated in test matrix in Table 2-2. Case C3 heat

transfer measured in terms of both Frossling number (left) and the new scaling parameter CSR

(right), for Reynolds number ranging from 1×105 to 3×105 are shown in Figure 5-11.

136

Figure 5-11. CSR applied to AERTS ice-roughened cylinder – C3

The same scaling trend on reference artificially roughened cylinders as shown in Figure

5-9 and Figure 5-10 were also observed from the AERTS ice-roughened cylinder measurements.

The Frossling number plot demonstrated that the scattered heat transfer curves resulted from

Reynolds number difference. This effect was eliminated by presenting heat transfer data in CSR.

AERTS measurements may seem more irregular when compared to the reference artificially

roughened cylinder tests, as indicated by the fluctuating dotted red line at leading edge area. This

is, again, the uniqueness of the natural ice-roughened testing due to the irregular ice roughness

distribution. Also, due to the fact that the roughness was not on an entire surface, although the

overall trend is similar to reference artificial roughened cylinders, the AERTS experimentally

measured CSR values are with lower amplitude due to a less energized boundary layer. The

maximum heat transfer was again obtained around 58°, as already observed from previous

reference experiments.

0

0.02

0.04

0.06

0.08

0 20 40 60 80 100 120 140

CSR

= S

t s/R

e s-0

.2

Angle, deg

0

0.01

0.02

0.03

0.04

0.05

0.06

0 20 40 60 80 100 120 140

CSR

= S

t/R

e^-0

.2

Angle, deg

Re = 1E5Re = 2E5Re = 3E5ReD = 3×105

ReD = 1×105

ReD = 2×105

0

1

2

3

0 20 40 60 80 100 120 140

Fr =

Nu

D/s

qrt

(Re D

)

Angle, deg

0

0.01

0.02

0.03

0.04

0.05

0.06

0 20 40 60 80 100 120 140

CSR

= S

t/R

e^-0

.2

Angle, deg

Re = 1E5Re = 2E5Re = 3E5ReD = 3×105

ReD = 1×105

ReD = 2×105

137

Figure 5-12. CSR applied to AERTS ice-roughened cylinder – C7

The heat transfer curves for another ice-roughened cylinder, case C7, are shown in Figure

5-12. The surface roughness height in this case was less than that of case C3. Therefore, similar

trends but with lower magnitudes were observed for this case, under Re = 1×105 to 3×105. The

curve for lowest testing Reynolds number (red dotted line) indicated a laminar separation occurred

approximately at 88° azimuth angle with a reattachment at 102°. It is worth noticing that this trend

in red dotted line was even more apparent in CSR plot on the right of Figure 5-12. The red line

initially overlapped with the other two curves, indicating a transition due to local roughness at the

leading edge rough zone area. Then, the curve reverted back to a clean cylinder laminar heat transfer

behavior and also later showed evidence of laminar separation near the aft portion of the cylinder.

This is another important finding of the AERTS tests, i.e., the flow has a relaxation effect after

passing the rough zone. The heat transfer may drop down again following the clean surface trend

with less magnitude than turbulent curves. This phenomenon has also been found in ice-roughened

airfoil testing, as will be shown in modeling section of this chapter.

0

0.02

0.04

0.06

0.08

0 20 40 60 80 100 120 140

CSR

= S

t s/R

e s-0

.2

Angle, deg

0

0.01

0.02

0.03

0.04

0.05

0.06

0 20 40 60 80 100 120 140

CSR

= S

t/R

e^-0

.2

Angle, deg

Re = 1E5Re = 2E5Re = 3E5ReD = 3×105

ReD = 1×105

ReD = 2×105

0

1

2

3

0 20 40 60 80 100 120 140

Fr =

Nu

D/s

qrt

(Re D

)

Angle, deg

0

0.01

0.02

0.03

0.04

0.05

0.06

0 20 40 60 80 100 120 140

CSR

= S

t/R

e^-0

.2

Angle, deg

Re = 1E5Re = 2E5Re = 3E5ReD = 3×105

ReD = 1×105

ReD = 2×105

138

5.1.5 Validation of CSR on airfoils

After validating the capability of the proposed scaling parameter (CSR) on rough flat plates

and rough cylinders. Heat transfer measurements on airfoils were transformed to CSR values for

validation of the proposed scaling method. Since there was limited data found in literature, Yeh’s

heat transfer coefficient measurements on turbine blades (Yeh, Hippensteele, Van Fossen, &

Poinsatte, 1993) (originally shown in Figure 5-6) were digitized from the literature and transformed

into CSR, as shown in Figure 5-13. Since the test turbine blade was a highly curved structure, the

suction surface and pressure surface exhibited different trends under different Reynolds numbers.

Figure 5-13. Reference turbine blade heat transfer in CSR

As can be seen in the blue dashed circle at the leading edge region (close to s/c = 0) in

Figure 5-13, curves were not grouped into a single line in the laminar regime close to that region.

This was expected, since CSR was designed to be primarily used in the fully turbulent regime,

which in this case was the area where s/c>0.4 or s/c<-0.4. For the higher speed cases (Rec = 5×106

and 7×106), the transition of the flow happened very close to leading edge. These two curves for

high Reynolds numbers behaved very similar and could be used for describing the fully turbulent

heat transfer trend. The other three lines illustrated transitions later on the airfoil surface away from

leading edge. Transitions from laminar to turbulent trend line for these cases were very similar to

0

0.005

0.01

0.015

0.02

0.025

0.03

-1.2 -0.8 -0.4 0 0.4 0.8 1.2

CSR

= S

ts/R

es-0

.2

Surface Wrap Distance, s/c

7.5E5

1.5E6

3.0E6

5.0E6

7.0E6

ReSuction Surface Pressure Surface

C

139

the behaviors seen on cylinder tests, as already shown in Figure 5-9 and Figure 5-10. Also,

compared to the original reported curves in heat transfer coefficient (Figure 5-6), the CSR curves

under different Reynolds numbers were properly scaled and could be compared at the same

magnitude. The behaviors during transition could be clearly spotted and correlation could be readily

developed if desired. By comparing heat transfer coefficients for turbine blades in terms of Fr in

Figure 5-6 and CSR in Figure 5-13, it was again proven that Fr could be used for the laminar

regime, whereas CSR was capable to be used for heat transfer scaling in fully turbulent regime on

a highly curved airfoil.

After validating the capability of CSR on reference airfoil measurements, finally the

AERTS experimental measurements and LEWICE predictions previously shown in Figure 5-5

were compared in terms of CSR values, as presented in Figure 5-14.

Figure 5-14. Example scaled heat transfer measurement comparison – CSR

In Figure 5-14, the AERTS experimental measurements were depicted as a black line with

local standard deviation denoted by the grey shaded area. This time, the two curves could be

compared at the same level due to the proposed scaling method. It can be clearly seen that the

LEWICE prediction curve was in agreement with AERTS experimental measurements at the

overall amplitude and at the onset of the flow transition. The LEWICE predicted transition was

abrupt compared to a gradual transition observed for all the AERTS experiments. This difference

140

was believed due to the limitation of current heat transfer modeling equations used in the ice

accretion prediction tool and will be further improved and explained in detail in following sections.

5.1.6 Recommendation for Use of Heat Transfer Scaling Parameters

To summarize, the proposed CSR scaling approach has been validated against a wide range

of test data on various surfaces and is of special interest for turbulent regimes, such is the case of

early-stage ice accretion. For instance, several turbulent trend lines in the CSR domain for reference

cylinder and turbine blade measurements were observed to contribute in a virtual “ceiling” effect

(upper envelope of measurements). The heat transfer curves first followed the laminar trend line

and then transition at various locations due to different surface roughness condition. The transition

curves happened at different locations and had the same curve slope. After transition, heat transfer

curves hit the “ceiling” prescribed by the turbulent trend line and then followed the line until

separation. This effect of CSR representation is especially useful to describe a group of heat transfer

data obtained under different Reynolds numbers.

Based on the above observations from both reference database and the AERTS

experimental measurements, it is then recommended to use CSR to scale the fully turbulent regime,

whereas Fr should be used for laminar regime. If comparing results at the same Reynolds number

level, the Fr and CSR representations will show the same distribution trend in comparing different

roughness configurations under the same test speed. Using Fr as a dimensionless heat transfer

coefficient is still recommended, such as those used in discussions made in Chapter 4. On the other

hand, CSR is very suitable for correlation and model development where the majority of the

monitoring area are in turbulent regime. In the next section, the CSR scaling approach was used for

the development of heat transfer correlation for ice-roughened airfoils.

141

5.2 AERTS Empirical Correlation for Heat Transfer on Ice Roughened Surface

The experimental measurements of ice roughness distribution and heat transfer distribution

have been discussed in Chapter 3 and Chapter 4 respectively. After the proper scaled turbulent heat

transfer curves were obtained, the relationship between the roughness distribution and heat transfer

could be studied. Following the same rationale used in the heat transfer parametric study in Chapter

4, the heat transfer (black, primary axis) and surface roughness distribution (red, secondary axis)

were plotted together in one chart, as shown in Figure 5-15.

Figure 5-15. Example heat transfer (CSR) and roughness distribution comparison

As can be seen in Figure 5-15, LEWICE was able to accurately predict the transition

chordwise location compared to the AERTS experimental measurements. The onset of flow

transition predicted by LEWICE corresponded to a sharp rise of roughness prediction. After the

transition, the curve started a constant decreasing trend similar to the heat transfer curve of a flat

plate, as shown in Figure 5-8. On the other hand, the AERTS measurements featured a gradual

growth of heat transfer over the entire rough zone region. The heat transfer curve continued

increasing until the end of the roughness distribution. Based on the fact that this kind of distribution

has been repeatedly observed for all the 10 cases in the AERTS measurements (Han & Palacios,

2014), an empirical correlation was proposed to capture the heat transfer trend and also to shed

0

0.5

1

1.5

2

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0 0.05 0.1 0.15 0.2

Ro

ugh

ne

ss H

eig

ht,

mm

CSR

= S

t s/R

es-0

.2

Dimensionless Surface Wrap Distance, s/c

AERTS Exp

LEWICE

142

light onto later analytical model development. An integral term based on the local roughness height

was formulated in Equation (5-4):

𝐶𝑆𝑅𝑐𝑜𝑟𝑟(𝑥) = 𝐶𝑆𝑅𝑡𝑢𝑟𝑏(𝑠𝑡𝑟𝑎𝑛𝑠) + 1500 ∙ 𝑉∞ 𝑢𝑒(𝑥)⁄ ∙ ∫ (𝑘𝑒𝑥𝑝(𝑥) 𝑐ℎ𝑜𝑟𝑑⁄ )𝑑𝑥𝑠

𝑠𝑡𝑟𝑎𝑛𝑠

(5-4)

where, the first term in Equation (5-4) was a reference level calculated from the laminar flow heat

transfer at the location of transition. For almost all AERTS cases tested, this number actually was

close to the constant in Equation (5-2) for a flat plate case with constant free-stream velocity and

constant surface temperature, which was found to be 𝐶𝑜𝑛𝑠𝑡 = 0.0287 𝑃𝑟𝑡0.4 ≈ 0.030⁄ . The kexp

term used in Equation (5-4) indicated that the experimental measured roughness distribution could

be used to correlate the experimental measured heat transfer. No additional prediction / assumption

was made so as to keep the correlation in its most simplified form. After flow passed the rough

zone, the heat transfer curve used the same modeling equations as LEWICE to predict the surface

roughness behind the roughness. The detailed model will be introduced in next section.

After calculating the heat transfer based on the proposed empirical equation, a good

correlation between all AERTS experimental measurements and the proposed prediction were

obtained. A sample comparison of the proposed correlation to the experimental result and LEWICE

prediction is shown in Figure 5-16.

Figure 5-16. Example heat transfer (CSR) and proposed correlation comparison

143

The blue curve captures the gradual transition behavior very favorably when compared to

the AERTS experiments. The empirical correlation for heat transfer for ice roughened airfoils have

been extensively validated against the AERTS experimental measurements. However, the

usefulness of such a correlation is limited by the requirement for experimental measurement of

roughness as input parameter. On the other hand, due to the inaccurate roughness height prediction

from current ice predicting tools as seen in Figure 5-15, the predicted heat transfer will be erroneous

based on this incorrect roughness input. To achieve a broader application based on above findings,

a complete analytical model that can incorporate an integrated roughness and heat transfer

prediction module was desired. In the next section, the proposed analytical heat transfer prediction

module based on the prediction of ice roughness is introduced.

5.3 AERTS Analytical Prediction for Heat Transfer on an Ice Roughened Surface

The success in the empirical correlation of ice roughness and heat transfer described in the

above sections provided insights on the development of an analytical model of heat transfer

applicable to varying icing conditions. As previously shown in Figure 5-16, the proposed empirical

heat transfer correlation was simple in form, and it could capture the correct gradual transition

trend. However, the correlation relied on an experimental roughness measurement, which

significantly limited its application. The goal of this section was to develop an analytical model

that can be integrated with an ice roughness distribution prediction and that will be able to predict

heat transfer under a broad range of icing conditions and Reynolds numbers, independent of

experimental measurements. The detailed model is explained in the following six subsections.

144

5.3.1 Model Overview

Overall, the proposed heat transfer model was developed in a similar manner as the heat

transfer calculation equations used of LEWICE. It was based on a simple 2D, steady,

incompressible assumption. A full 3D, grid-based model solving Navier-Stokes equations was not

pursued due to the complexity of the accreted ice shapes which inevitably raises computational

cost. Instead, Integral Boundary Layer (IBL) equations were solved to calculate a heat transfer rate.

Flow field predictions were obtained using a panel method based on the potential flow solution.

Current flow predictions were not coupled with the IBL Method to predict the exact boundary layer

extent. The flow field prediction was used only to provide the local boundary layer edge velocity

(ue) needed for heat transfer calculation. This study mainly focused on different treatments for

boundary layer heat transfer calculations in laminar, transitional, and turbulent regimes.

In the laminar regime, boundary layer velocity profiles at chordwise locations have been

experimentally observed to be geometrically similar, differing only by a multiplying factor.

Therefore, a prescribed velocity profile by Pohlhausen (Pohlhausen, 1921) is adequate for

calculating momentum boundary layer equations in laminar regime. In addition, the thermal

boundary layer and the momentum boundary layer could also be assumed to be geometrically

similar. Therefore, only one energy integral equation needed to be directly solved to get heat

transfer rate based on this similarity assumption, as recommended by Kays and Crawford (Kays &

Crawford, 1993).

The effect of roughness was not observed in laminar boundary layer heat transfers, both

from past research in literature, and experimental results obtained in this research. The roughness

only affects the laminar flow transition. Transition and laminar separation criteria for the Reynolds

number based on roughness height will be introduced later in this section. The length of transition

region before flow turning into fully turbulent can be as long as, or even longer than, the proceeding

145

laminar flow region. Unfortunately, there is no exact theory for transition region found in literature.

Most of the 2D non-grid-based heat transfer solutions exhibit a sudden over-prediction in transition

heat transfer calculation. Special attention is needed to model laminar-to-turbulent transition

behavior. This is also the goal of this research, which was to find an improved heat transfer

analytical model that can correlate with experimental measurements better in the transition region.

After transition, as mentioned in the scaling parameter development section, the heat and

mass transfer in the turbulent regime is much different from that seen in the laminar flow regime.

Viscous effects are no longer the driving force for the momentum and heat transfer. Viscous

sublayer only accounts for 5% of the total boundary layer thickness. The remaining 95% of the

boundary layer is not affected by viscous shear and molecular conduction effects. The boundary

layer velocity profile is highly dependent of time and eddy motion. Similarity flow assumption for

laminar flow is no longer valid in turbulent boundary layers due to flow complexity. The

momentum boundary layer thickness used in turbulent regimes is determined from the logarithmic

law of wall (Kays & Crawford, 1993) and assumed power law velocity profile (Prandtl 1/7 law

(Prandtl, 1935)). This is, again, a simplified yet effective assumption based on the condition of

constant free-stream velocity, no transpiration, and aerodynamically smooth surface. The Reynolds

analogy that assumes shear stress and heat flux transported by turbulent motion of the same mass

element is used for turbulent flow on smooth surfaces. For rough bodies, due to the presence of

surface roughness, the shear stress is attributed to be transmitted by pressure drag resulting from

the impact or dynamic pressure on the upstream side of each roughness element. Therefore,

different correlations for skin friction coefficients on aerodynamically smooth and rough surfaces

have to be determined. The turbulent heat transfer coefficients then can be obtained from empirical

functions of surface shear stress.

A good discussion of the equations for heat transfer prediction on an artificially roughened

cylinder surface has been published by Makkonen (Makkonen, 1985). Detailed definitions of most

146

terms in following equations can also be found in reference textbooks (Kays & Crawford, 1993)

(White, 2006). Makkonen’s work was derived from earlier editions of these two textbooks. In this

section, only the essential equations used in the proposed heat transfer model will be listed. The

predicted results will be labeled as AERTS prediction, since the prediction was developed at the

AERTS facility. This is to differentiate predictions from AERTS experimental measurements, often

abbreviated as AERTS Exp.

5.3.2 Laminar Flow Regime

The momentum thickness, δ2,lam, in a laminar regime can be obtained from:

𝛿2,𝑙𝑎𝑚(𝑥) =0.664𝜈0.5

𝑢𝑒2.84(𝑥)

(∫ 𝑢𝑒4.68(𝑥)𝑑𝑥

𝑠

0

)

0.5

(5-5)

Heat transfer in terms of Nusselt number based on the model dimension is defined as:

𝑁𝑢𝐷(𝑥) = 0.293𝑢𝑒

1.435(𝑥) 𝜐0.5⁄

(∫ 𝑢𝑒1.87(𝑥)𝑑𝑥

𝑠

0)

0.5 (5-6)

where, the subscript D is characteristic model dimension. For this case, it is airfoil chord.

Then, Nusselt number can be converted to the proposed scaling parameters, Fr and CSR as

shown in Equation (5-7) and (5-8) respectively:

𝐹𝑟(𝑥) =𝑁𝑢𝐷(𝑥)

√𝑅𝑒𝐷

(5-7)

𝐶𝑆𝑅(𝑥) =𝑁𝑢𝐷(𝑥)

𝑠(𝑥)𝐷

𝑃𝑟𝑙𝑅𝑒𝑠0.8(𝑥)

(5-8)

Notice that the conversion from model dimension (D) to surface wrap distance (s) is based

on the x coordinate for CSR. Also, the Prandtl number for laminar regime (Prl), which was defined

as a ratio between momentum diffusivity and thermal diffusivity, was set to be a constant of 0.72

for this equation; whereas this number for turbulent regime (Prt) was 0.9.

147

To validate the laminar flow model using above equations, the flow field and heat transfer

prediction in terms of Frossling number were shown in Figure 5-17, with comparison from

LEWICE.

Figure 5-17. Validation of the laminar flow field and heat transfer prediction

Source of NASA Exp. Data: (Newton, Van Fossen, Poinsatte, & DeWitt, 1988)

Both flow field and heat transfer for a laminar flow on an airfoil surface were successfully

determined from the simple 2D potential flow and IBL models above. The next task is to model the

turbulent flow regime with and without roughness effects.

5.3.3 Turbulent Flow Regime

In the turbulent regime, momentum thickness, δ2,turb, was defined differently from laminar

flow. The integral calculation of the turbulent momentum thickness started from the transition point

and began with the value of δ2,lam at the transition location for continuity consideration, which was

denoted as δ2,trans:

𝛿2,𝑡𝑢𝑟𝑏(𝑥) =0.036𝜐0.2

𝑢𝑒3.288(𝑥)

(∫ 𝑢𝑒3.86(𝑥)𝑑𝑥

𝑠

𝑠𝑡𝑟𝑎𝑛𝑠

)

0.8

+ 𝛿2,𝑡𝑟𝑎𝑛𝑠 (5-9)

For a smooth surface in the turbulent region not affected by roughness, the empirical

equation for the skin friction coefficient is defined as:

0

1

2

3

4

5

0 0.05 0.1 0.15 0.2

Fr =

Nu

D/(

Re

D)0

.5


AERTS PredictionLEWICE PredictionNASA Exp

0

0.5

1

1.5

0 0.05 0.1 0.15 0.2

No

rmal

ize

d V

el,

ue/V

∞


AERTS Prediction

LEWICE Prediction

148

𝑐𝑓/2(𝑥)𝑠𝑚𝑜𝑜𝑡ℎ = 0.0125𝑅𝑒𝛿2

−0.25(𝑥) (5-10)

For the cases in which surface roughness is present, the empirical equation used by Pimenta

et al. (Pimenta, Moffat, & Kays, 1975) was adopted

𝑐𝑓/2(𝑥)𝑟𝑜𝑢𝑔ℎ =0.168

(𝑙𝑛(864𝛿2(𝑥) 𝑘𝑠⁄ (𝑥)))2 (5-11)

where, ks was originally defined as the equivalent sand roughness height used in Pimenta’s

experiment. The measured arithmetic roughness height (k) usually has to be converted into ks due

to different definition of roughness spacing and roughness element type (sphere, hemisphere, or

pyramid etc.) by different researchers. For Pimenta’s (Pimenta, Moffat, & Kays, 1975) and

Healzer’s (Healzer, Moffat, & Kays, 1974) experiments, the uniform roughness spherical diameter

was 1.27 mm (0.05 inch). After multiplying by a conversion factor of 0.62 (because their roughness

was not as dense as the densely packed sand roughness in reference experiment), the equivalent

sand grain roughness height was determined to be 0.787 mm. The difference between the turbulent

skin friction coefficients on smooth and rough surfaces are compared in Figure 5-18. The

experimental measurements are taken from the previously mentioned Pimenta’s work (Pimenta,

Moffat, & Kays, 1975). The grey dashed line is based on Equation (5-10) for turbulent smooth

surfaces, whereas the grey solid line is from Equation (5-11) defined for turbulent rough surfaces.

Notice that there is an almost constant increase ranging from 85.2% to 87.4% in the skin friction

prediction for rough flat plate compared to smooth flat plate.

149

Figure 5-18. Comparison of empirical equations for skin friction coefficient

Conversion of the roughness element height into ks has been studied in a wide range of

applications, such as works on simulating ice roughness done by McClain’s group (Bhatt &

McClain, 2007) (McClain & Kreeger, 2013). Unfortunately, there is no well-established conversion

factor for natural ice roughness found in the literature. In this study, the term ks is defined as

effective ice roughness, which was based on a modified roughness prediction.

As inspired by observations of the integral effect of roughness distribution in Figure 5-16,

the effective roughness (ks) was obtained by modifying the ice roughness prediction described in

Chapter 3 and illustrated in Figure 5-19. The green line denotes the effective roughness distribution

ks, whereas predicted ice roughness are presented in red line.

Figure 5-19. Schematics of the definition of effective roughness, ks

0.0005

0.0010

0.0015

0.0020

0.0025

0.0030

1.E+02 1.E+03 1.E+04 1.E+05

Skin

Fri

ctio

n C

oef

f., C

f/2

Reδ2

Exp. SmoothEmp., SmoothExp. RoughEmp., Rough

w Ice limit

xkmin

k

ks

xkmax

150

As can be seen in Figure 5-19, ks starts at the minimum value of the k curve, and increase

linearly until the end of the roughness, i.e. the ice limit (l), where it reaches its maximum value of

xk, determined in Equation (3-8). This conversion of the peak roughness into an effective roughness

ensured the analytically predicted transition still behaved in a gradual way, rather than the flat plate

behavior as seen in Figure 5-16.

The turbulent heat transfer on a rough surface can then be defined in terms of Stanton

number (St) in Equation (5-12). This equation suggested that there is a balance between the heat

transfer resistances offered by the molecular-conduction process in the cavities between the

roughness elements (Kays & Crawford, 1993). As the roughness height grew bigger, the Prandtl

number term became less important. Large values of skin friction coefficient have the same effect.

𝑆𝑡𝑠(𝑥) =𝑐𝑓/2

(𝑃𝑟𝑡 + √𝑐𝑓/2 𝑆𝑡𝑘⁄ ) (5-12)

where roughness Stanton number (Stk) was proposed by Dipprey and Sabersky (Dipprey &

Sabersky, 1963) in Equation (5-13). This number has to be determined experimentally as a function

of different types of roughness. The constant in the equation was then determined from the AERTS

experimental dataset specifically for icing roughness.

𝑆𝑡𝑘(𝑥) = 𝐶𝑜𝑛𝑠𝑡 ∙ 𝑅𝑒𝑘𝑠−0.2(𝑥)𝑃𝑟𝑡

0.44 = 1.16𝑅𝑒𝑘𝑠−0.2(𝑥) (5-13)

where the Reynolds number based on the proposed effective ice roughness height (ks) played a

dominant role in the definition of Stk and was defined as:

𝑅𝑒𝑘𝑠(𝑥) =𝑢𝜏(𝑥) ∙ 𝑘𝑠(𝑥)

𝜈=

√𝜏0(𝑥) 𝜌⁄ ∙ 𝑘𝑠(𝑥)

𝜈 (5-14)

where, the shear velocity uτ was defined as a function of shear stress, which could be expressed in

terms of Equation (5-15):

𝜏0(𝑥) = 0.0125𝜌𝑢𝑒2(𝑥) (

𝑢𝑒(𝑥)𝛿2(𝑥)

𝜈)

−0.25

(5-15)

151

5.3.4 Transition / Separation Criteria

As mentioned in Chapter 1, the transition location on a rough surface is primarily due to

roughness protruding out of the boundary layer thickness. This location usually is much earlier in

the upstream than the natural transition location. Therefore, a criterion by White (White, 2006) for

flow transition onset on a rough surface was used and was defined as:

𝑅𝑒𝑘(𝑥) > 𝑅𝑒𝑡𝑟(𝑥) = 𝐶𝑜𝑛𝑠𝑡 ∙ 𝑒𝑥𝑝(−0.9𝜆(𝑥)) (5-16)

where, the constant in the equation was determined from the AERTS experimental datasets. This

constant was experimentally determined to be: Const = 220 for airfoils, 390 for cylinders. The term,

λ, is defined by laminar boundary layer integral terms as:

𝜆(𝑥) =𝛿1

2 (𝑥)

𝜈

𝑑𝑢𝑒(𝑥)

𝑑𝑥 (5-17)

where the δ1 is displacement thickness of the boundary layer.

If there is no transition due to roughness, eventually the laminar flow will separate and

possibly reattach to the surface, as shown in Chapter 4 during rough cylinder heat transfer

evaluation studies. The laminar flow separation criterion was defined as:

𝐾𝑇ℎ𝑤𝑎𝑖𝑡𝑒𝑠(𝑥) < 𝐾𝑐𝑟 = −0.09 (5-18)

where, the KThwaites is Thwaites’ parameter. When this parameter goes to -0.09, the shear stress is at

value of 0, as calculated using Thwaites’ laminar boundary layer analysis (Thwaites, 1949). The

Thwaites’ parameter is defined in Equation (5-19). The format is very similar to Equation (5-17).

The only difference is that the δ1 (displacement thickness) is replaced by δ2 (momentum thickness):

𝐾𝑇ℎ𝑤𝑎𝑖𝑡𝑒𝑠(𝑥) =𝛿2

2 (𝑥)

𝜈

𝑑𝑢𝑒(𝑥)

𝑑𝑥 (5-19)

152

5.3.5 Post-roughness Region Treatment

Based on experimental observation, flow past the roughness region tends to relax down to

a curve representative of laminar flow again (similar curve slope), but with a constant magnitude

shift from the clean airfoil / cylinder laminar heat transfer curve. This is believed to be resulted

from an upstream turbulence intensity increase due to the local energized flow past the rough zone.

This effect of uniform increase of laminar flow heat transfer level has been seen in another natural

ice roughened surface heat transfer testing on an artificially roughened airfoils (Newton, Van

Fossen, Poinsatte, & DeWitt, 1988), as shown in Figure 1-16 in Chapter 1. Notice that these

observations were based on results for leading edge roughness condition only, not for artificially

fully roughened surfaces. For those cases with a uniform roughness distribution on the entire

surface, such as Achenbach’s cylinder testing in Figure 1-12, Figure 5-3, and Figure 5-4, this

relaxation phenomenon was not observed.

The treatment process is then determined as: to run laminar flow prediction for the entire

surface (CSRlam), to predict the transition location (strans), and then to calculate the shifted magnitude

at transition

𝐶𝑆𝑅𝑠ℎ𝑖𝑓𝑡@𝑡𝑟𝑎𝑛𝑠 = 𝐶𝑆𝑅𝑡𝑢𝑟𝑏(𝑠𝑡𝑟𝑎𝑛𝑠) − 𝐶𝑆𝑅𝑙𝑎𝑚(𝑠𝑡𝑟𝑎𝑛𝑠) (5-20)

and finally:

𝐶𝑆𝑅𝑝𝑜𝑠𝑡−𝑟𝑜𝑢𝑔ℎ = 𝐶𝑆𝑅𝑙𝑎𝑚 + 𝐶𝑆𝑅𝑠ℎ𝑖𝑓𝑡@𝑡𝑟𝑎𝑛𝑠 (5-21)

An important note on this treatment is that the constant shift was only observed in the CSR

domain, not in Fr or NuD domain. The detailed thermal physics explanation needs further study.

153

5.3.6 Final Heat Transfer Model Comparison

After incorporating the above prediction equations into a complete heat transfer model, the

final comparisons of the proposed heat transfer modeling in terms of CSR are shown in Figure 5-20.

Figure 5-20. AERTS heat transfer correlation and model comparison

It can be seen that both the blue line (Empirical correlation using experimental roughness

as input) and red line (heat transfer prediction based on ice roughness correlation) agreed well with

experimental measurements. The discrepancy between the AERTS prediction and the

experimentally measured heat transfer in the rough zone region only varied in a maximum range

of ±15%, which was still within the measurement uncertainty range. The advantage of using the

AERTS prediction is that it only requires icing conditions as inputs, which are independent of any

other experimental measurements (no need for experimentally measured ice roughness). This

feature together with its validated capability of predicting the transition behavior on ice-roughened

airfoil enabled the model to be coupled with existent ice accretion prediction tools. Therefore, the

proposed heat transfer model was then integrated with LEWICE to study the effect of the improved

heat transfer prediction on the final ice shape prediction. In the next section, the fidelity of the

proposed new ice shape prediction tool is examined.

154

Chapter 6

Improved Ice Accretion Predicting Tool

The heat transfer model proposed in Chapter 5 has been coupled into LEWICE (a NASA

developed ice accretion prediction tool) to improve ice shape representation fidelity. During the

past 25 years, LEWICE has been evaluated against various sources of experimental ice shapes. It

has been proven that the code features fast-execution, robustness, and a capability to simulate ice

shapes within its validated icing envelope. Its authors have also identified, since the first version of

LEWICE, that the way heat transfer is being handled in the internal heat transfer module needs to

be improved given its empirical nature. Two ice prediction comparisons before and after applying

the improved heat transfer module are first shown in Figure 6-1 and Figure 6-2 to demonstrate the

necessity of this study to address the inaccurate and unrealistic predictions currently provided by

LEWICE under certain glaze ice regimes outside its validation envelope.

Figure 6-1. Example improvement of ice prediction (1)

Icing condition: V = 100 m/s, chord = 0.267 m, AOA = 4° NACA 0012

LWC = 1.5 g/m3, MVD = 40 μm, Tst = -15°C, Time = 500s

155

A typical icing condition for a helicopter is shown in Figure 6-1. The blue dashed line is

obtained from LEWICE predictions using the icing conditions listed under the figure. The multiple

gray-scaled lines are obtained from implementing the proposed heat transfer model over multiple

time steps. The blue ice shape is not realistic and would not be encountered under natural icing.

The protruded ice horn indicates a sharp rise in the heat transfer coefficient in this region, which

corresponds to the over-prediction in heat transfer provided by LEWICE as discussed in previous

chapters.

Figure 6-2. Example improvement of ice shapes and heat transfer predictions (2)

Icing condition: V = 67 m/s, chord = 0.267 m, AOA = 0° NACA 0012

LWC = 1 g/m3, MVD = 20 μm, Tst = -8°C, Time = 360s

In addition to the helicopter icing condition, a more general icing condition with zero (0)

angle of attack is shown in Figure 6-2. Similar ice predictions are observed between both heat

transfer models in this case, since this icing condition is closer to the icing envelope that LEWICE

was calibrated against. The left chart of Figure 6-2 illustrates the heat transfer coefficient

distribution on the upper surface of the airfoil. Notice that LEWICE significantly over-predicted

the heat transfer, as already shown in Figure 1-14. In return, this resulted in a different ice growth

direction, as shown in the right chart of Figure 6-2. The 200% over prediction of heat transfer

essentially moves the highest growth rate of ice to the edge of the predicted ice horns while there

156

were concave ice shape trends close to the stagnation region, which are not present in natural ice

growth obtained in ice accretion experiments. The improved ice shape prediction smoothens out

this uneven distribution of ice. If following the incorrect heat transfer prediction, as time increases,

the ice prediction gradually forms a more severe ice horn shape that still leads to an over-estimate

the performance penalties.

With this inaccurate prediction in ice shape, the predicted aerodynamic losses and heat

transfer over the surface of the airfoil are not representative, which may result in erroneous design

of ice protection systems. Taking the case in Figure 6-2 as an example, the expected aerodynamic

penalty under the given icing conditions will be much less that the ones calculated based on the

protruded horn shape provided by LEWICE. With an inaccurate prediction like the one seen in this

case or the reference example case shown in Figure 1-14, approximately 100% more thermal energy

is used to eliminate the unrealistic ice horn that would not exist in a natural icing environment.

To improve the current ice prediction tool, the following coupling scheme between

LEWICE 2D and the proposed ice roughness and heat transfer modeling developed in this study is

shown in Figure 6-3.

Figure 6-3. LEWICE coupling schematic

To get the simulation started, LEWICE is used to feed in the flow field information

(boundary layer edge velocity, ue) for the AERTS roughness prediction described in Chapter 3. The

LEWICE internal heat transfer module is then bypassed to use the heat transfer prediction tool

Icing

Condition

Flow Field

Simulation

Roughness Prediction

Heat Transfer Modeling

AERTS Testing & Modeling

Mass & Energy Balance

to Get Ice ShapeInternal

Heat Transfer

157

developed in this research. The improved heat transfer is then imported into LEWICE for surface

mass and energy balance calculations at each individual control volume on the airfoil surface, and

the ice shape of this time step is then obtained. The LEWICE module is called multiple times for a

selected time step sequence outside the main batch running code. After each time step calculation

is finished, the predicted ice shape of this cycle is used as the input airfoil shape for the next ice

accretion calculation cycle. The number of time steps is determined by an equation suggested by

LEWICE (Wright, 2008) as shown in Equation (6-1):

𝑛𝑠𝑡𝑒𝑝 = 𝑟𝑜𝑢𝑛𝑑 {𝑚𝑎𝑥 [𝑚𝑖𝑛 (𝐿𝑊𝐶 ∙ 𝑉∞ ∙ 𝑡𝑖𝑚𝑒

𝑐ℎ𝑜𝑟𝑑 ∙ 𝜌𝑖𝑐𝑒 ∙ 0.01, 30) , 𝑚𝑖𝑛 (

𝑡𝑖𝑚𝑒

60, 15)]} (6-1)

The coupled prediction tool has gone through an extensive validation process at the AERTS

facility, with comparisons against both shapes found in literature and from AERTS experiments.

A comprehensive literature survey on reference ice shapes has been conducted. The

improved prediction tool has been compared to reference ice shapes found in the literature (Gray

& Von Glahn, 1958) (Olsen, Shaw, & Newton, 1984) (Flemming & Lednicer, 1985) (Shin & Bond,

1992) (Addy, Potapczuk, & Sheldon, 1997) (Anderson & Ruff, 1999) (Federal Aviation

Administration, 2000) (Han, Palacios, & Smith, 2011) (Han, Palacios, & Schmitz, 2012) (Han &

Palacios, 2012) (Han & Palacios, 2013). The improved ice shape prediction tool has achieved better

(when comparing ice thickness and horn formation location) ice shape matching compared to

LEWICE in the glaze-to-rime icing regime. Ice shape comparison charts are categorized into three

groups and are shown in Figure 6-4, Figure 6-5, and Figure 6-6, respectively.

6.1 Ice Shape Prediction for Cold, Rime Ice Regime

The reference ice shapes on NACA 0012 airfoils from Shin and Bond’s work (Shin &

Bond, 1992) were used for comparison in cold ambient temperature cases. As mentioned before,

158

rime ice cases are mostly encountered in a cold ambient environment, typically colder than -13°C.

In this rime icing regime where cold temperatures cause instant freezing, heat transfer is not a

dominant parameter for macro ice shape growth. Therefore, the coupled prediction tool achieved

equivalent performance if not better than that of LEWICE, as shown in Figure 6-4.

(a) V=67.1 m/s, chord=0.53 m, Re=2.4e+06, AOA=4.0

LWC=1.0, MVD=20, Temp=-28.2°C, Time=360 s

(b) V=67.1 m/s, chord=0.53 m, Re=2.4e+06, AOA=4.0


Figure 6-4. Reference ice shapes from Shin & Bond’s Experiment

Source of experimental ice shapes: Ref. (Shin & Bond, 1992)

There was no ice horn found under this icing condition, thus, the ice thickness could be

used to evaluate the overall ice prediction accuracy for rime ice shape regimes. In Figure 6-4 (a),

159

the two predictions from LEWICE and the AERTS improved ice prediction tool were found to

coalesce into the same curve. The two predictions also matched the reference experimental ice

shape very well. The accuracy based on thickness difference between the experimental ice shape

and both of the predictions was within 1% of the experimental measured ice shape thickness. In

Figure 6-4 (b), the improved prediction tool had an error of 1.5%, whereas the error number for

LEWICE was 18.6%. Similar icing conditions were also tested by Olsen et al. (Olsen, Shaw, &

Newton, 1984). The differences between the LEWICE prediction and the AERTS improved

prediction tool were more noticeable for this set of data, as can be seen in Figure 6-5 and Figure

6-6.

6.2 Ice Shape Prediction for Rime-to-Glaze Transition Regime

For the cases in Figure 6-5, the ambient temperatures used for ice accretion were still low.

However, the accreted ice shapes started to deviate from the aerodynamic smooth ice shapes

commonly seen in the rime ice regime, such as the ones shown in Figure 6-4.



Figure 6-5. Reference ice shapes from Olsen’s Experiment (cold regime)

160



(c) V=93.9 m/s, chord=0.53 m, Re=3.3e+06, AOA=4.0


Figure 6-5 (continued). Reference ice shapes from Olsen’s Experiment (cold regime)

Source of experimental ice shapes: Ref. (Olsen, Shaw, & Newton, 1984)

There was a consistent inaccuracy trend in the LEWICE prediction. Due to a 4° angle of

attack, the LEWICE tended to predict a protruding horn at the upper surface edge, which resulted

from a local high peak of heat transfer prediction. In contrast, the areas close to leading edge

stagnation line were not predicted to have enough ice thickness. This phenomenon has been seen

in the three example ice shape comparisons. Icing conditions used in the first two cases, (a) and (b)

in Figure 6-5, had a similar range to those in Figure 6-4. The overall ice shapes were not too far off

161

the reference ice shapes. However, when moving on to a higher test velocity, the kinetic heating

effect increased the total temperature for the ice accretion region. For reference, the definition of

total temperature is shown in Equation (6-2):

T𝑡𝑜𝑡

𝑇𝑠𝑡= 1 +

𝛾 − 1

2∙ 𝑒 ∙ 𝑀𝑎2 (6-2)

where e is an empirical recovery factor, γ = 1.4, R = 287. For most common situation of aircraft

icing, e could be treated as a constant of 0.98. Therefore, for this case, although the static

temperature was -16°C, the reported total temperature was actually -11.7°C. In return, the accreted

ice shape already exhibited a fishtail-like ice shape, indicating that it is possible to obtain glaze ice

at a low ambient temperature of -16°C with high impact speed.

In this rime-to-glaze transition regime, the heat transfer on the surface dominates the ice

shape growth. As denoted by the comparison in Figure 6-5, the proposed improved ice prediction

tool achieved better performance, which resulted from the new physics-based heat transfer model.

6.3 Ice Shape Prediction for Warm, Glaze Ice Regime

In Figure 6-6, test cases in warm glaze icing regimes were selected for comparison. Similar

to the parametric study shown in Chapter 4, Olsen et al. conducted this series of tests with only one

controlled variable, which was the icing temperature. The warm temperature testing range listed in

this figure included four cases (-9.4°C, -6.6°C, -3.9°C, and -2.8°C).

In this regime, the run back water effect was due to the warm temperature and relatively

high LWC-MVD combination. The warm and glaze ice growth environment resulted in a large

amount of ice behind the predicted ice horns. Both ice predictions from LEWICE and the improved

prediction tool suffered from an inaccurate surface water dynamics model, thus an incorrect ice

162

shape prediction. The improved prediction tool performed slightly better than LEWICE as can be

seen in the matching of the blue line and the experimental shape on the lower surface of ice shape.





Figure 6-6. Reference ice shapes from Olsen’s Experiment (warm regime)

163



(d) V=58.1 m/s, chord=0.53 m, Re=2.1e+06, AOA=4.0


Figure 6-6 (continued). Reference ice shapes from Olsen’s Experiment (warm regime)

Source of experimental ice shapes: Ref. (Olsen, Shaw, & Newton, 1984)

This set of data demonstrated the primary limitation of LEWICE (and consequently, the

proposed improved prediction tool) was the surface water dynamics model in the warm temperature

regime, rather than the heat transfer model. With or without an improved heat transfer prediction,

both of the predictions for the warm temperature range failed to match the experimental ice shape

measurements. A significant amount of water mass was missing from the predicted ice shapes. At

warm temperatures close to the freezing point, the surface water dynamics dominates the ice

164

accretion behavior and both the coupled and uncoupled tools had problems predicting the ice shape

with run-back effect. Further study on the surface water dynamics under warm temperature is

desirable.

6.4 Ice Shape Prediction Compared to Experimental Ice Shapes

Aside from the ice shapes obtained from the literature survey, ice accretion experiments

have also been conducted at the AERTS lab for ice prediction tool validation in the rime-to-glaze

transition ice regime where ice shapes are dominated by heat transfer. Samples of the experimental

ice shapes are showing below in Figure 6-7. Corresponding icing conditions and ice shape

prediction comparisons are also listed below the figures. The black dashed lines are LEWICE

predictions, whereas the solid blue lines are from the improved modeling tool. The outlines of the

experimental ice shapes are also shown for reference in red lines in both pictures and comparison

charts.



Figure 6-7. Example ice shape matching comparisons

165





(d) V=63.0 m/s, chord=0.61 m, Re=2.6e+06, AOA=0.0


Figure 6-7 (continued). Example ice shape matching comparisons

The four (4) example ice shapes shown above in Figure 6-7 are typical helicopter ice

shapes, often called “fishtail” ice shapes. The first three ice shapes (a)(b)(c) were accreted on

NACA 0016 profile, whereas the last case (d) was based on a NACA 0012 airfoil. Compared to the

rime ice shapes from the previously mentioned ice shape categorization shown in Figure 2-4, these

166

fishtail ice shapes account for major aerodynamic performance penalties. A performance

degradation study on artificially roughened rime ice shapes such as the example (Bragg, 1982)

shown in Chapter 1, is not representative of this kind of ice accretion. Motivated by these

observations, ice shapes previously shown in Figure 2-8 with icing conditions in Table 2-4 were

accreted at the AERTS facility. The example ice shapes are shown here again in comparison to the

proposed improved prediction tool, as illustrated in Figure 6-8.

Figure 6-8. Improved ice prediction compared to AERTS ICE1-4 ice shapes

The quality of the experimental ice shape matching has already been shown in Figure 2-8.

In this new figure, the proposed improved ice shape prediction (solid blue lines) was compared to

the three different sources of ice shapes. It can be seen that the blue lines successfully matched both

of the experimental ice shapes with higher accuracy than when using the LEWICE heat transfer

prediction model, shown with a dashed black line.

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6.5 Summary of Ice Shape Prediction Comparison

In this chapter, the proposed improved ice prediction tool has been validated against

reference experimental ice shapes in three different icing regimes. For a very cold ambient

temperature environment, the impact water droplet tends to freeze upon impingement. This process,

then, is less dependent on heat transfer than warmer cases. As a result of the instant freezing

phenomenon, the accreted rime ice shape is usually in an aerodynamic smooth shape, and could be

accurately determined by both LEWICE and the proposed tool. However, as one of the example

cases in Figure 6-5 suggested, other icing parameters, such as impact speed, can also affect the rime

ice shape accretion. The examples shown in Figure 6-5 exhibited a mixed rime-to-glaze transition

trend. In this regime, heat transfer dominates the ice accretion in terms of ice thickness, ice horn

growth, etc. The proposed ice prediction tool performed better than LEWICE as a result of the

physics-based ice roughness and heat transfer prediction models. At very warm temperatures, both

the LEWICE and the proposed tool failed to determine the accreted ice shape. The discrepancy

could result from either the excessive water content in the tunnel during reference experiments or

a misinterpretation of surface water dynamics. These two concerns are out of the scope of this

study. Overall, the proposed ice prediction tool achieved more precise ice shape prediction,

especially in the rime-to-glaze regime.

The ice prediction tool has also been validated using the AERTS experimental ice shape

database. Four (4) ice shapes were also chosen for the following aerodynamics evaluation. The test

matrix and wind tunnel setup for aerodynamics testing have already been shown in Chapter 2. With

the accreted ice shapes and casting models, the detailed aerodynamics study of these four glaze ice

shapes are shown in next chapter.

168

Chapter 7

Aerodynamics Testing and Modeling with Accreted Ice Structures

As mentioned in Chapter 1 from the reference work by Bragg (Bragg, 1982), at an angle

of attack of 4°, a smooth airfoil with additional leading edge roughness resulted in a 20% reduction

in lift and 50% increase in drag, which was a similar result achieved for a 2.5%-chord-length

smooth rime ice shape. If the tested rime ice shape is combined with surface roughness effects, the

drag penalty increased to 100%. The drag penalty was found most sensitive to icing conditions,

whereas the lift reduction was found to be constant for different conditions, and pitching moment

was unaffected by the ice accretion. In addition, specifically for helicopters, the failure to maintain

altitude caused by increased torque requirement is one of the biggest concerns for the vehicle safety.

Therefore, the drag penalty due to accreted ice structures was the focus of this chapter.

To comprehensively understand the aerodynamics performance degradation due to ice

accretion, both experimental and analytical studies have been conducted at the AERTS facility. The

four (4) ice shapes shown in Figure 6-8 in the previous chapter were obtained based on a test matrix

tabulated in Table 2-4. Ice shapes were captured using the molding and casting method and were

tested at the Penn State Hammond Building low-speed wind tunnel introduced in Chapter 2.

Measurements in terms of lift coefficient (Cl), drag coefficient (Cd), pitching moment coefficient

(Cm) were recorded with angles of attack from 0° to 18°. In this chapter, a literature survey of the

past research on aerodynamics measurements on iced airfoils is presented first. An empirical

correlation based on both the reference database and AERTS experimental measurements is then

be developed and compared to various sources of data. Finally, the proposed correlation between

icing condition and aerodynamics performance degradation is coupled with a rotor aerodynamics

169

code to predict rotor torque increase. Comparison between torque prediction and experimental

measurements at the AERTS are then presented. A discussion follows at the end of the chapter.

7.1 Analytical Correlation between Drag Increase and Icing Conditions

7.1.1 Existing Database for Correlation Development

Due to the limited icing test facilities, limited data sets were available in terms of tabulated

icing condition matrices together with aerodynamics performance data in the literature. Gray et al.

conducted a series of tests on several airfoils under icing conditions in the late 1950’s (Gray, 1958),

(Gray & Von Glahn, 1958). Flemming and Lednicer investigated high-speed ice accretion on

various rotorcraft airfoils (Flemming & Lednicer, 1985). Wind tunnel airfoil drag measurements

with ice shapes obtained under different icing conditions have been carried out by Shaw et al.

(Shaw, Sotos, & Solano, 1982), Olsen et al. (Olsen, Shaw, & Newton, 1984), Shin & Bond (Shin

& Bond, 1992), and Addy et al. (Addy, Potapczuk, & Sheldon, 1997). Simulated ice shapes have

also been used for dry air wind tunnel aerodynamics testing (Bragg, 1982) (Papadakis, Alansatan,

& Seltmann, 1999) (Broeren, et al., 2010). Experiments on simulated ice shapes can shed light on

the icing severity study, but are not representative of natural icing condition, therefore were not

used in this study.

During the literature survey, a comprehensive icing aerodynamics database comprising a

total of 490 sets of experiments was identified from published data. The reference experimental

data were primarily obtained at the NASA IRT (Gray & Von Glahn, 1958), (Olsen, Shaw, &

Newton, 1984), and (Shin & Bond, 1992); except Flemming’s data (Flemming & Lednicer, 1985)

which were taken from the Canadian National Research Council (NRC) High Speed Icing Wind

Tunnel. A summary of this icing aerodynamics database is shown in Table 7-1.

170

Table 7-1. Summary of Experimental Icing Aerodynamic Degradation Database

Ref. Airfoil #

Ch

ord

(cm

)

Test Condition Range

Temperature

(°C)

Velocity

(m/s)

MVD

(µm)

LWC

(g/m3)

Time

(min)

AOA

(deg)

min / max min / max min/max min / max min/max min/max

Gray

(1958)

NACA

63A009 4 210 -12.2 -3.9 116 116 14 17 0.39 0.83 14 15 2 4

NACA

0011 16 222 -12.2 -3.9 78.2 123 14 18 0.3 1 8 27 0 8

NACA

651212 6 244 -17.8 -3.9 80.5 116 15 20 0.52 1.4 4 20 2 5

NACA

632015 2 33 -17.8 -3.9 80.5 112 15 16 0.52 0.7 4 10 2 4

Olsen

et al.

(1984)

NACA

0012 53 53.3 -30.5 -2.7 41.4 93.9 12 36 1 2.1 3 8 0 8

Flemming

&

Lednicer

(1985)

NACA

0012 73 15.2 -32.4 -5.4 86.9 212 20 20 0.24 3.8 0.3 5 0 9

SC1095 73 15.2 -36.4 -4.3 85.5 212 20 20 0.16 1.75 0.3 2 -6 9

SSC-

A09 43 15.2 -31.5 -9.5 87.2 209 20 20 0.3 1.75 0.3 1 0 11

VR7 52 16.2 -32.6 -4.4 90.3 211 20 20 0.3 1.4 0.3 2 0 9

SC1094

R8 39 15.9 -28.8 -6.3 61.0 197 11 30 0.3 1.5 0.3 1 0 12

SC1012 59 15.4 -32.6 -4.3 91.2 223 11 50 0.3 1.75 0.3 5 0 12

OH58 (0012)

28 13.3 -32.4 -13.4 93.5 215 20 20 0.29 1 0.3 1.5 0 9

H34

(0011) 17 6.8 -26.8 -15.1 86.9 186 20 20 0.3 3.8 0.8 1.5 0 9

CCW* 8 15.2 -26.8 -14.3 93.5 186 20 20 0.66 0.66 0.8 1 0 6

Shin &

Bond

(1992)

NACA

0012 17 53.3 -31.0 -4.5 67.1 103 20 30 0.55 1.8 6 12 4 4

Summary 490 -36.4 -2.7 41.4 223 11 50 0.16 3.8 0.3 27 -6 12

7.1.2 Performance Degradation Correlation Development

As mentioned in the introduction section in Chapter 1, empirical correlations between test

conditions and the resultant aerodynamic coefficients are most widely used as engineering tools

during the design of airfoils and ice protection systems. During the literature survey, three existing

* CCW: Circulation Control Wing

171

aerodynamics performance correlations for iced airfoils were identified. These correlations were

established by Gray (Gray, 1964), Bragg (Bragg, 1982), and Flemming (Flemming & Lednicer,

1985) respectively. A brief introduction of the three existing correlations are shown here for later

comparison convenience. Detailed definitions of every parameter used in each individual reference

equation are not presented since they are irrelevant to the results in this study. The readers are

encouraged to consult the referenced papers for detailed explanation.

Gray published his correlation for the ΔCd between a clean and an iced airfoil based on his

experiments and previous data (Gray, 1964). The equation was complicated in formulation, as can

be seen in Equation (7-1). The advantage of this equation was that it also incorporated the effects

of angle of attack in ice accretion and wind tunnel evaluation, as denoted by αIcing and αAero, which

were not used in other correlations. This feature was also adopted by the AERTS correlation

development.

11sin17.0

35.1

1

35.1

13.65

8132

543

sin

12sin52.21

61

32107.8

4

31

02

41.0

3.0

0max

5

r

T

Ew

r

Twc

uC

AeroIcing

d

(7-1)

In 1982, Bragg provided a simplified correlation using icing condition scaling parameters

that were introduced in Chapter 2 of this dissertation. The expression of ΔCd is shown in Equation

(7-2).

172

Cleandcd CIEAc

kC

28000ln8.1501.0 (7-2)

where, for NACA 0012 airfoil cases, k/c = 0.001, and the constant I is 184.

Flemming and Lednicer, in 1985, also proposed a set of correlations for both lift and drag

penalties based on their comprehensive experimental database on rotorcraft airfoils (Flemming &

Lednicer, 1985). Again, the equation was either complicated in equation form or required numerical

methods since some parameters did not have closed-form expressions. The correlations for

increased drag coefficient (ΔCd) for different regimes are shown in Equation (7-3).

2.12.0

4.2

2

5.1

0

1

1524.01524.0

006.00313.0

600686.0

:Glaze

10

6

17017500ln8.15 01.0:Rime

ccw

MKDc

r

c

tK

KDC

Cd

EAc

kC

c

d

Clean

cd

(7-3)

Due to the limited database available, the three existing drag correlations are validated only

to their own experimental datasets which were obtained when the empirical prediction tools were

developed. The three correlations have limitations when applied to a more comprehensive icing

condition range (Miller, Korkan, & Shaw, 1987). Bragg, in a later paper, also stated that: “Several

researchers have attempted to fit airfoil drag and lift as a function of icing conditions. For various

reasons, the accuracy of even these relatively simple models is low” (Bragg, Hutchison, Merret,

Oltman, & Pokhariyal, 2000).

173

Motivated by this status of current performance degradation correlation development, a

new correlation based on a much more comprehensive database was developed at the AERTS

facility. Given that even under the same icing condition, the ice shape and its corresponding

aerodynamic coefficients will vary for different airfoil shapes, this study focused on one type of

airfoil to reduce the possible variation on the resultant correlation. For this research, the well

documented NACA 0012 airfoil performance under icing conditions is studied. A total of 171 sets

of NACA 0012 icing aerodynamics data was used to derive an empirical correlation between the

icing conditions and corresponding drag coefficient (Cd). The rest of experimental data were used

to confirm the validity of the proposed correlation between predictions and experimental results.

The icing parameters considered in this study are: Leading edge radius (r), Chord (c), Static

temperature (T), Velocity (V), Median Volume Diameter (abbr.: MVD, δ), Liquid Water Content

(LWC), Icing time (τ), Angle of Attack (AOA), Reynolds number (Re) and Mach number (Ma). Of

these conditions, the five most important parameters identified during the study were T, V, MVD,

LWC, and Icing time. The extent of data coverage used for correlation development in this study is

shown in Figure 7-1 together with comparison to three other performance correlations.

In Figure 7-1, each axis of icing parameters are normalized to the maximum value that

exists in the database. There are two rings for each correlation to denote the upper and lower limit

of their database. A larger area means a more comprehensive database. The database coverage for

the current study is represented by the blue shaded area to illustrate the extensive data used for this

correlation development.

174

Figure 7-1. Comparison of performance database used for different correlations

As suggested by Miller (Miller, 1986), to identify the use of certain variables before the

development of the correlation tool, the icing parameters were transformed using Buckingham’s Pi

Theorem (Buckingham, 1914) into several new dimensionless scaling parameters. The use of icing

condition scaling parameters can aid in avoiding scaling effects, since each ice testing database was

based on different airfoil dimensions. The dimensionless parameters chosen to generate the

correlation are: Stagnation Line Collection Efficiency (β0), Reynolds number based on MVD (Reδ),

Accumulation Parameter (Ac) and normalized temperature (T/T0). The first three icing scaling

parameter have already been introduced in Chapter 2. The last dimensionless parameter (T/T0) was

used to take temperature effect into account, where the T is the static temperature in Kelvin and T0

is the reference temperature. In this study, the reference temperature (T0) is chosen to be the freezing

point of water, 273.15K.

175

Similar to Gray’s correlation, one last parameter based on angle of attack was used to

account for the effect of angle of attack in evaluating iced airfoil performance. Icing Angle of

Attack of the airfoil, αIcing was used, in addition to αAero. The icing angle (αIcing) is the angle of attack

at which the ice shape was accreted; whereas, the aerodynamic angle (αAero) is the angle of attack

at which the drag was evaluated in a wind tunnel with the accreted ice shape.

In the Pi theorem, there are no other dimensional variables that can be combined with αIcing

to produce a dimensionless parameter. Given that there is a potential second order polynomial

correlation between the target response CdIcing and αIcing, an approach similar to that used in drag

estimation on wings (Spedding & McArthur, 2010) was used. The αIcing was added into a statistics

analysis with a transformation into its second order term, as shown in Equation (7-4). The reference

value of α0 was determined by the statistical results obtained from the experimental data.

𝐶𝑑 ∝ (𝛼𝐼𝑐𝑖𝑛𝑔 − 𝛼0)2 (7-4)

With all the parameters defined, the β0, Reδ, Ac, T/T0 and αIcing were analyzed for the

experimentally measured CdIcing using transformed linear regression methods (Kutner, Nachtsheim,

Neter, & Li, 2004). The derived regression model is shown in Equation (7-5).

𝐶𝑑𝐼𝑐𝑖𝑛𝑔 = [2.69 ∙ 𝛽0 ∙ 𝐴𝑐 ∙ 𝑅𝑒𝛿 + 3800𝑇

273.15+ 9.65(𝛼𝐼𝑐𝑖𝑛𝑔 − 3.352)

2− 3663]

× 10−4 (7-5)

Out of 171 samples evaluated, 71 sets of data were used to develop the regression model,

the remaining 100 sets of data were also used for validation. The R-square value for this model is

0.884 for the 71 sets of data. The effectiveness of this proposed correlation will be discussed in

detail in following subsections.

176

7.1.3 Correlation Compared to Experimental Database

For simplicity, the proposed model will be referred to as the Han-Palacios Correlation and

abbreviated as HPC in the text. The HPC model was applied to the complete 171 case database

(Flemming & Lednicer, 1985), (Olsen, Shaw, & Newton, 1984), (Shin & Bond, 1992) for model

validation in this subsection. The comparison between the calculated value and the experimentally

measured results is shown in Figure 7-2. The diagonal line in the figure is the perfect agreement

line, which means a zero-error between the measured Cd and calculated Cd is obtained on this line.

Figure 7-2. Comparison of Cd from HPC and measured Cd from three ref. experiments

The mean absolute deviation in percentage (|CdCalc.-CdMeasured| / CdMeasured ×100%) for this

validation dataset is 33.40%. In Figure 7-2, the two other lines at the side of the agreement line

indicate the 33.40% Cd error line denoting the upper and lower errors obtained with the proposed

tool. The accuracy of the HPC model can also be expressed in terms of mean error with a standard

deviation. For this case, the quantified error is 7.65% ±46.00%. The term, mean error, is simply the

mean value (not the mean absolute value) of the all the errors. A low mean error for a large sample

177

of estimation indicates that the prediction is not biased toward either over-prediction or under-

prediction.

The second parameter, standard deviation, is a measure of how spread the errors are. A low

standard deviation indicates that the error data tend to be close to the mean error, whereas high

standard deviation indicates that the data points are spread out over a large range of errors. For an

error distribution following a normal distribution trend with moderate skewness, the standard

deviation can be used to evaluate the range of the error that can be described using a certain model

(for example, HPC in this study). The physical meaning of the standard deviation in a normal

distribution is that, 68.3% of the data points can be found within the range of one (1) standard

deviation of the mean error; 95.4% of the data are within two (2) standard deviations from the mean

error value; and 99.7% are within three (3) standard deviations. This means that within the

experimental database used during this study, any calculated error by HPC is likely (68.4%

possibility) to fall within the range of 7.65% ±46.00%, and highly possible (95.4% possibility) to

fall within the range of 7.65% ±92.00%. These numbers may sound large, however, as will be

shown in next subsection, this is already a significant improvement. A 200% deviation predicted

by the three existing correlations is not uncommon.

Overall, the Cd values calculated by the proposed HPC model correlated well with all the

datasets conducted by the three referenced researchers. The accuracy of the model predicting

experimental Cd for Shin’s and Flemming’s data were very satisfactory, showing a mean absolute

deviation of 22.46% and 31.50%, respectively. The HPC generally over-estimated Olsen’s

experimental data (the mean absolute deviation was 52.65%), compared to a 33.40% mean absolute

deviation for the entire 171 sets of data used in this comparison

178

7.1.4 Correlation Compared to Existing Models

The improvement of the proposed correlation is examined by comparing with other

existing correlations in this section. A set of calculated ∆Cd from HPC and two (2) other existing

models (Gray’s and Bragg’s) were compared to measured ∆Cd for a NACA 0012 airfoil (Olsen,

Shaw, & Newton, 1984).

Several critical factors used in Gray’s and Bragg’s correlations were unavailable; hence

numerically reproduction of their predictions was not feasible. The two reference correlation results

were obtained by digitizing available graphs from published literature. The 37 sets of Bragg’s

correlation data were taken from one of the later publications of the same author who developed

this correlation. (Figure 4 in the reference literature (Bragg, Hutchison, Merret, Oltman, &

Pokhariyal, 2000)). The 45 sets of Gray’s correlation data were obtained from Figure 20 of the

same paper where the experimental data were reported (Olsen, Shaw, & Newton, 1984).

The predictions by Gray and Bragg provided drag coefficient increments (∆Cd), whereas

the experiments conducted by Olsen et al. (Olsen, Shaw, & Newton, 1984) at the NASA IRT only

provided direct drag measurements (Cd). In addition, the HPC model only offers direct drag

coefficient calculation based on icing conditions (no need of clean Cd values as an input parameter).

The drag coefficient increment, ∆Cd, was therefore obtained by subtracting the measured drag

coefficient of the clean airfoil, CdClean, published in the literature. For the comparison in this case,

the HPC ∆Cd was calculated using the CdClean recorded by Olsen et al. (αIcing = 0, CdClean = 0.00615;

αIcing = 4, CdClean = 0.00814; αIcing = 8, CdClean = 0.01039). During practical icing aerodynamics

experiments, the surface roughness and tunnel turbulence conditions might vary for different airfoil

models and facilities. It is very likely to introduce uncertainties during the transformation from

HPC Cd calculation to ∆Cd calculation by assuming an equal clean Cd for every icing

aerodynamics test. Despite this uncertainty, the HPC results still achieved similar acceptable

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correlation as compared to Bragg’s correlation and much better results as compared to Gray’s

correlation.

The comparison chart is shown in Figure 7-3. Similar to Figure 7-2, the diagonal line in

the figure is the agreement line and the 30% error lines on each side serve as guidelines for

comparison.

Figure 7-3. Comparison of ∆Cd predictions against Olsen's experiments

In this case, the mean absolute deviation in percentage was defined as |∆CdCalc. -

∆CdMeasured| / ∆CdMeasured ×100%. For HPC, the mean absolute deviation was 68.00%. This number

for Bragg’s and Gray’s correlations were 75.40% and 243.45%, respectively, which means

improvements of 7.4% and 175% were achieved by using HPC. All the three correlations generally

tended to over-estimate the drag coefficient increment based on the icing experiments conducted

by Olsen et al.

Another comparison between HPC and a third available correlation, Flemming’s

correlation (Flemming & Lednicer, 1985), is shown in Figure 7-4. The experimental NACA 0012

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datasets used for reference data were taken from the same report where Flemming’s correlation

was presented. Again, several critical factors to apply Flemming’s correlation were unavailable;

hence, the Flemming’s correlation dataset were obtained by digitization of Figure 59 in the

reference literature (Flemming & Lednicer, 1985). To compare the two correlations on the same

basis, the figure was plotted in the original fashion shown in Flemming’s report. The horizontal

axis of this figure is still the measured drag coefficient increment, whereas, unlike Figure 7-3, the

vertical axis is the error between measured Cd increment and Calculated Cd increment. The

agreement line (horizontal) and other guidelines were also shifted according to the change of the

axes.

Figure 7-4. Comparison of ∆CdError predictions against Flemming's experiments

The ∆CdError correlations from the two models were fairly scattered, as can be seen in

Figure 7-4. The mean absolute deviation in percentage (|∆CdError/∆CdMeasured| ×100%) is 48.42%.

This deviation is still a 20% improvement compared to Flemming’s correlation (60.31%).

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7.1.5 Correlation Applied to Cambered Airfoils

As mentioned above, the HPC model was developed solely based on the symmetric, NACA

0012 airfoil databases. Other airfoil icing aerodynamics datasets were used to explore the potential

applicability of the HPC model for cambered airfoils. Icing aerodynamics data obtained from

experiments conducted by Flemming & Lednicer (Flemming & Lednicer, 1985) on 5 different

helicopter airfoils (SC1095, SC1094 R8, SC1012 R8, SSC-A09 and VR-7) were used to test the

capability of the HPC model to predict drag degradation on cambered airfoils. The Cd calculations

from HPC for 2 cambered airfoils were found to be satisfactory. Fifty-two (52) sets of data for VR-

7 and 39 sets of data for SC1094 R8 were available. The comparison between the calculated Cd

and measured Cd for these two airfoils are shown in Figure 7-5.

Figure 7-5. HPC model applied to cambered airfoil cases

The resultant mean absolute deviation for the VR-7 correlation is 22.06%. This number for

SC1094 R8 is higher but still deemed acceptable (35.04%). The guidelines in Figure 7-5 were

determined by the larger absolute error, i.e. the 35.04% error line. The mean of the errors for the

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VR-7 Cd calculation, with corresponding standard deviation is -7.78% ±28.01%; whereas this error

range for SC1094 R8 correlation is -18.96% ±38.18%.

The success of applying the proposed HPC to cambered airfoils is thought to be related to

the fact that the cambered airfoils had similarities to NACA 0012 airfoils used to develop the model.

The cambers of the two airfoils are both relatively small (3.1% for VR-7 and 0.8% for SC1094 R8).

Also, the leading edge radiuses of the two airfoils are very close to that of NACA 0012 airfoils.

The leading edge radius, r, is defined as a characteristic dimension of the airfoil nose area. It is the

largest possible radius that fits to the nose arc. The value of r is usually expressed as a percentage

of the total airfoil chord. The value of r for the VR-7 airfoil is 1.938% and that for SC1094 R8

airfoil is 1.911% (only a 1.40% difference). Another characteristic dimension of the airfoil that may

affect the airfoil icing aerodynamics is the maximum thickness. This term is also expressed as a

percentage of the airfoil chord. This number for VR-7 airfoil is the same as the NACA 0012 airfoil,

which is 12%, whereas the SC1094 R8 airfoil has a lower thickness of 9.3%. The exact reason for

the satisfactory matching between HPC model and the two cambered airfoils are still unknown at

the time of this dissertation, but this positive correlation showed the promise for the HPC model to

predict drag degradation due to icing for both cambered and symmetric airfoils with similar

thickness and leading edge radiuses.

7.1.6 Correlation for Varying Angles of Attack

The HPC model (Equation (7-5)) only provides one Cd corresponding to one set of icing

conditions (CdIcing). In some applications, it is also desirable to have one ice shape tested in a wind

tunnel under different aerodynamic AOAs to find a full range of Cd polar data for this specific ice

shape. For instance, during forward flight, this situation represents when a helicopter escapes from

an icing cloud with a certain amount of ice already accreted on the airfoil. The performance of the

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airfoil remains altered as the angle of attack of the blades changes azimuthally outside of the icing

cloud. Another example can be found during a wind tunnel testing using an artificial casting ice

shape model that was accreted previously under a certain icing condition with constant AOA.

To enable the proposed HPC model to generate a full range of Cd polar data, one additional

correlation is needed to convert the calculated CdIcing measured under one icing spray angle (Icing

AOA, αIcing) to CdAero calculations under different aerodynamics testing AOAs (Aero AOA, αAero).

To develop such a correlation between CdIcing and CdAero, 81 sets of aerodynamic testing data (9

from Olsen’s work (Olsen, Shaw, & Newton, 1984) and 72 from Flemming’s work (Flemming &

Lednicer, 1985)) have been identified during the literature survey of this study. These aerodynamic

datasets were obtained in icing wind tunnels during ice accretion testing, i.e., after the ice accretion

tests and corresponding Cd measurement for this ice shape, the ice was retained on the airfoil for

several more aerodynamics tests at varying AOA. With the same ice shape, icing aerodynamic

coefficients under different αAero were tested and recorded. In this way, the reference icing condition

(including αIcing) and reference CdIcing measurement, with several CdAero data under various αAero

could be obtained. These experimental measurements are needed for the development of the

proposed tool. This additional correlation was developed based on CdIcing, αIcing and αAero. The goal

was to correlate these three parameters to obtain the CdAero. As mentioned previously, the drag

coefficient is positively correlated with the square power of AOA. A second order polynomial

function was pre-assumed and tested using a transformed linear regression method. The resultant

correlation model matched the measured CdAero well at various αAero. The empirical equation for

this correlation is shown in Equation (7-6):

𝐶𝑑𝐴𝑒𝑟𝑜 = 1.21𝐶𝑑𝐼𝑐𝑖𝑛𝑔 + [0.872(𝛼𝐴𝑒𝑟𝑜 − 2.425)2 − 1.02(𝛼𝐼𝑐𝑖𝑛𝑔 − 1.2)2

− 5.99]

× 10−3 (7-6)

The R-square value of this regression model is 0.865. The mean absolute deviation is

27.44% compared to the database. The errors between the calculated CdAero and measured CdAero

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have a mean with a standard deviation of 1.31% ±37.48%. The maximum AOA used in correlation

development was 9°. The comparison between the calculated Cd and the measured Cd is shown in

Figure 7-6.

Figure 7-6. Comparison between Exp. Cd at various AOA and HPC prediction

Equations (7-5) and (7-6) together are the proposed analytical correlation (HPC model) for

airfoil drag coefficient degradation. This HPC model was developed based on a wide range of

experimental icing aerodynamics database, and has shown promise in correlation over the full range

of Cd polar data under various icing conditions and varying angles of attack. This proposed

correlation will be compared to experimental rotor icing results in the following sections.

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7.2 Experimental Validation

7.2.1 Experimental Polar Data

Wind tunnel test result data for the four ice shape models are plotted in terms of Cd vs. α

and Cl & Cm vs. α in Figure 7-7. The Cd plots comprise 2D Cd measured by the wake probe (blue

circle) and 3D Cd measured by the external force balance (red square). In Figure 7-7, the reference

clean airfoil drag, lift and pitching moments for NACA 0012 airfoil (Ladson, 1988) are presented

in green triangle symbols. The results are also compared to Olsen’s experimental drag results as

denoted by the open diamond symbols. Raw result data are tabulated in the Appendix B.

(a) ICE1

(b) ICE2

Figure 7-7. Summary of aerodynamics polar results (ice shapes ICE 1 - 4)

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(c) ICE3

(d) ICE4

Figure 7-7 (continued). Summary of aerodynamics polar results (ice shapes ICE 1 - 4)

As it can be seen from the Cd plots in Figure 7-7, the 2D wake survey and 3D force balance

Cd behave very similarly for the low AOAs. It is assumed that at the low AOA, no separation or

very little separation prevented 3D vortex shedding along the span. Therefore, the averaged 3D Cd

has the same magnitude as that measured by the wake survey at the tunnel center-line (2D drag).

After the stall angle was reached, flow separation and the associated unsteady features of the flow

became dominant in determining the drag coefficient. The 3D Cd measured by the whole span was

more prone to be affected by this 3D unsteady flow. The 3D Cd value increase rapidly when the

AOA is beyond the stall angle.

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The Cl polar graphs of the four ice shape casting models followed similar trends as that of

the clean airfoil at low AOA region. The performance degradation of Cl is not as severe as the Cd

increase with respect to the clean airfoil. ICE1 and ICE4 models are ice shapes with similar

stagnation line ice thickness (2% of the chord). The ice shapes can be thought of as leading-edge

flap structures that introduce an equivalent camber angle to the airfoil. The measured Cl for these

two models had a higher value compared to the clean airfoil Cl at the same AOA, and before the

stall angle. This temporary increase in measured lift due to leading edge flap effect was also

observed in similar wind turbine icing studies (Jasinski, Noe, Selig, & Bragg, 1998). After the AOA

reached a value of 8 degrees, the measured Cl decreased below the clean airfoil Cl value.

In this study, the change on pitching moment coefficient (Cm) from positive to negative

was used as an identifier of stall angle. For NACA 0012 airfoils, the pitching moment starts at the

zero point due to its symmetric body. A positive value of the pitching moment indicates the airfoil

is front-loaded, which means the generated lift is acting in front of the quarter-chord pitching axis.

The positive value of Cm increases with lift and generates a nose-up moment on the airfoil. It can

be seen from the Cm vs. α plot that stall angle of the iced airfoil happens much earlier than for a

clean airfoil. The stall angles, determined based on Cm measurements, for the four ice shape casting

models are 11° (ICE1), 11.5° (ICE2), 9.5° (ICE3) and 11° (ICE4) respectively.

The stall behavior of the four ice casting models is, as expected, different from the clean

NACA 0012 airfoil. The clean NACA 0012 airfoil exhibits leading edge stall as categorized by

McCullough & Gault (McCullough & Gault, 1951), whereas the iced airfoils exhibited a

combination of leading edge stall and trailing edge stall features, i.e.: a sudden break in pitching

moment but a gentle rounding of lift. It can also be observed that the break in the lift and moment

curves no longer occur at the same AOA, which is similar as to what was reported by researchers

during dynamic stall experiments on NACA 0012 airfoil (McAlister, Carr, & McCroskey, 1978).

The stall of the airfoil is then divided into two kinds of stalls: moment stall and lift stall. It was

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determined by McAlister et al. that the moment stall is due to the onset of vortex shedding and the

lift stall is generated by vortices passing into the wake. When the vortex passes into the wake, the

pressure distribution no longer yields an increase in lift with further increases of incidence.

Although wind tunnel testing results in this dissertation were static measurements (time-averaged)

in nature, the stall concept observed during dynamic stall testing (McAlister, Carr, & McCroskey,

1978) was used to explain the unusual stall behavior of the iced NACA 0012 airfoil. Under this

specific situation, it was believed that the initial shedding of the vortex was generated by the upper

ice shape horn and feathers. The pressure distribution, however, was not greatly altered by this

vortex shedding. The lift curve still exhibits a leveled lift curve even when the AOA is already

beyond the point where a sharp break in pitching moment occurred. In the absence of supporting

evidence, such as dynamic pressure measurements and flow/wake visualization techniques, the lag

between the lift and moment stall cannot be explained by the available static stall theories.

7.2.2 Experimental Performance Degradation Comparison

A Cl vs. Cd comparison of the tested ice shape casting models is shown in Figure 7-8. Two

reference datasets for the clean NACA 0012 airfoil are also plotted in the figure for reference. The

experimental reference results are data taken at a Ma = 0.15 & Re = 2×106, and were obtained by

Ladson at NASA Langley Research Center LTPT wind tunnel (Ladson, 1988). A XFLR5

simulation (a code based on XFOIL panel solver, (Deperrois, 2012)) with Ma = 0.13 & Re =

1.6×106 that matched the experimental tunnel condition is also shown for comparison.

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Figure 7-8. Cl vs Cd comparison among the testing airfoils

It can be observed from Figure 7-8 that the performance of the iced airfoils is significantly

different from the reference clean NACA 0012 airfoil. For the four ice shape casting models, the

Cl vs. Cd graphs share the same common characteristics. Before the stall angle is reached, Cl vs.

Cd slope is slightly lower than the clean airfoil. The curve starts at a higher Cd value (4-8 times of

the clean value for this study) at the zero-lift condition. The stall angle was reached much earlier

for the iced airfoils than for the clean airfoil (in the range of 9° to 11° compared to 16° for clean

airfoil). After the stall angle is passed, as discussed before, the Cl still gradually increases for some

degrees while the Cd rises drastically. This gradual increase of lift at post-stall angles is a unique

feature of iced airfoil that needs further evaluation. The term Clmax is not very meaningful for the

four iced airfoil tested in this study, since at the point of Clmax, the airfoil had already stalled.

From Figure 7-8, the overall performance degradation can be evaluated by comparing the

Cd value of different airfoils at a constant Cl value. This is the situation when a helicopter escapes

from an icing cloud but already has ice accretion on the blade. To maintain the same altitude in

hover, the pilot changes blade pitch to keep the same thrust. The required power output from the

engine largely depends on the Cd changes due to different icing conditions. It can be observed in

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Figure 7-8 that, among the four (4) ice shape casting models tested, the AERTS ICE3 model has

the most severe performance degradation. This is because the ice was accreted under AOA = 0°

condition, whereas the other three were accreted at AOA = 4°. The ice shapes accreted with a non-

zero angle of attack generally form an aerodynamic shape which follows the leading edge shape of

the airfoil, whereas the ice shape accreted under zero angle of attack was non-aerodynamic (fishtail-

like) and had additional protruding ice feathers. This explains why the Cd measurement for ICE3

was larger than other cases at zero-lift AOA. When the iced airfoil was tested with an non-zero Aero

AOA, the resultant Cd increase of ICE3 was higher than the others due to the more vigorous flow

transition and separation provoked by its non-aerodynamic shape. ICE2 model displayed the least

degraded performance of the four models, despite having the longest stagnation line ice thickness

and longest icing exposure time. The stall angle for ICE2 was the highest among the four models.

It is apparent that the ice thickness should be considered as a secondary factor when determining

the performance degradation of an airfoil. More importantly, the additional ice roughness (ice

feathers) and the Icing AOA need to be considered when trying to correlate the icing conditions to

the final performance degradation.

7.2.3 Effect of Additional Ice Roughness Element

As mentioned in the previous section, the protruding ice feathers are suspected to aggravate

the performance degradation. For most of the icing wind tunnel aerodynamics tests, the surface of

accreted ice structure was supposed to be aerodynamically smooth, whereas the aerodynamics

performance is only affected by the macro shape of the accreted ice structure. Limited observations

of the additional effect of ice roughness are available in literature, such as the testing observed by

Bragg (Bragg, 1982) that is already mentioned in Chapter 1. The effect of ice feathers (additional

ice roughness behind of the main ice shape) have also been observed both in the NASA IRT and

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in-flight natural icing tests reported by Olsen et al. (Olsen, Shaw, & Newton, 1984). As stated by

the authors, the effect of ice feathers was believed to be small, compared to the effect of the ice

shape and the frost. In that paper, ice feathers were removed for all the tests (as shown in Figure

7-7 as reference data points) before performing Cd measurements. The effect of ice feathers was

only compared for 3 Cd data points.

To confirm the importance of the mentioned feather effect, ice shape casting model number

3 (ICE3) was used. The same wind tunnel testing was repeated on the same model with trimmed

feather (i.e. the main ice shape on the model remained, but the feathers were removed). The new

model was denoted by ICE3-FR (Feather Removed). A photograph of the close-up view of the

removed feathers is shown in Figure 7-9.

Figure 7-9. Ice feathers Removed from ICE3

Lift, drag and pitching moment were measured for both the two configurations of ICE3

model and the aerodynamic coefficient comparisons are shown in Figure 7-10 and Figure 7-11. For

the lift coefficient, as can be seen in Figure 7-10-(a), change is not discernible between the two

configurations. The ice feathers had virtually no effect on the pressure difference between upper

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and lower surfaces of the airfoil. In contrast, the effect of ice feathers on the Cd measurements by

wake survey are more profound, as depicted in Figure 7-10-(b).

At the zero AOA, which was the same icing spray AOA when the ice shape was accreted,

the measured Cd for ICE3 with the feathers was 0.03730 and the one for ICE3-FR was 0.02872,

thus a 29.9% difference. The two Cd measurements were also compared to the reference Cd

measured at the NASA IRT (Olsen, Shaw, & Newton, 1984), which has a value of 0.02294. The

Cd for ICE3-FR measured was closer to the reference value with an error of 25.2%, while the error

for ICE3 was 62.6%. It is important to note that this 25.2% error is at the same order of the errors

measured for ice shape reproduction and consequent Cd measurements conducted at the NASA

IRT. For instance, in the same reference by Olsen et al., the case O-10 and case O-4 were conducted

with the same icing conditions, whereas the Cd measurements were 0.02767 and 0.03382,

respectively. The error between these two repeat tests was 22.2%. This unavoidable error is

observed from the differences in ice shapes at identical icing conditions at the same test facility.

Taking this error into account, the Cd measurement of ICE3-FR was considered satisfactory in

terms of accuracy when compared to the target Cd from case O-8 in the reference literature.

(a) Cl comparison (b) Cd comparison

Figure 7-10. Cl and Cd comparisons between ICE3 and ICE3-FR (Feather Removed)

At non-zero Aero AOAs, the trends of the two Cd measurements are different. As the AOA

increasing from 0° to 6°, the effect of the ice feathers decreases. The main ice shape dominates the

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Cd value. At the point of 6°, the ice feathers have no effect on the Cd. As the AOA continues to

approach the stall angle (around 10° for these two cases), since the flow transition on the upper

surface becomes more significant, the effect of ice feathers on the turbulent boundary layer

development also becomes more apparent. This feather effect on the Cd values was observed by a

nearly constant 15% increase in drag for the ice model with feathers. As the AOA increases to 18°,

the Cd difference and the corresponding ice feather effect become again less significant. This is

because the flow separation at these high AOAs moved towards the leading edge of the airfoil. At

the AOA = 18°, the flow on the upper surface is separated at the horn of the main ice shape. The ice

feathers have no interaction with the flow and thus resulting in no effect on the final measured Cd.

The effect of ice feathers can be seen more clearly in the Cm measurements, as shown in

Figure 7-11. The Cm trends of the two configurations behave in a similar manner at low AOA

ranges (from 0° to 4°) and at high AOA ranges (from 11° to 18°). At the AOA region approaching

the stall angle (from 4° to 11°), the Cm of ICE3-FR increases to be larger than Cm of ICE3. The

stall angle is delayed by 1°, i.e., the stall angle for ICE3 is 9.5° and is 10.5° for ICE3-FR. Contrary

to the finding in a reference work by Olsen et al. (Olsen, Shaw, & Newton, 1984), the ice feather

effect on the pitching moment cannot be neglected.

Figure 7-11. Cm comparison between ICE3 and ICE3-FR (Feather Removed)

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7.3 Comparison between Correlation and AERTS Experimental Results

The HPC prediction was correlated to the experimental drag measurements of the ice

models obtained at the AERTS facility. Equations (7-5) and (7-6) were used to generate the

analytical calculated Cd (Calc. Cd) for a full range of AOAs. The Cd values calculated from HPC

were compared to both the experimental Cd obtained at the AERTS and the reference experimental

measurement obtained at the NASA IRT by Olsen et al., as shown in Figure 7-12.

Figure 7-12. Comparison between AERTS experiments and HPC calculation

As illustrated in Figure 7-12, at the high AOA region, the HPC results always

underestimated Cd, compared to the experimental data. At these high AOAs, it is believed that the

3D vortex shedding and energy dissipation induced by flow separation across the airfoil span may

increase the Cd. At the low AOA region, on the other hand, the HPC calculations and the AERTS

experimental data correlated with Olsen’s reference data very well. The absolute errors between

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the two experimental results for the four models were: 6.19% (ICE1), 23.60% (ICE2), 25.21%

(ICE3-FR) and 80.65% (ICE4). The relatively large deviation of ICE4 experimental Cd compared

to Reference Cd was due to the larger discrepancies between ice shapes. As can be seen in the ice

shape comparison in Figure 2-8, the additional ice horn at the upper leading edge of ICE4

contributed to the higher Cd measurement at the AERTS facility. For the same case, the HPC

calculation using the ICE4 reference icing condition resulted in a much better correlation, the error

of which was 14.05%, compared to the reference experimental Cd. The ICE2 case was the best

matching case where the experimental data and analytical data matched each other. Even with the

largest ice thickness (4% of the chord) and longest icing exposure time (8 min.), ICE2 model still

resulted in the least degraded airfoil performance, as already discussed in Figure 7-8. ICE2 had the

coldest icing temperature (-16.6°C) among the four models. This model belongs to a rime ice

growth case, which had an ice shape that followed the airfoil shape. Compared with more severe

cases under glaze icing conditions, which had protruding ice horns like ICE3, rime ice shapes are

more suitable for ice shape prediction and icing aerodynamics predictions. To summarize, the HPC

Cd calculations of the four ice shape casting models generally matched the same trend as the

experimental data from both the AERTS facility and the NASA IRT.

After validating the applicability of the proposed correlation on airfoil drag penalty

prediction, the correlation was incorporated into a Blade Element Momentum Theory (BEMT) code

to calculate the rotor performance due to ice accretion. The BEMT theory is a combination of Blade

Element Theory and Blade Momentum Theory. It assumes a rotor can be segmented into multiple

blade elements. At each element location, a uniform, steady inflow (no spanwise interference) is

assumed. Then, the lift and drag forces can be calculated using a Blade Momentum Theory. Thus

a rotating device, such as helicopter rotor (in hover) or wind turbine blade, can be regarded as

comprised of multiple annulus. The blade performance then can be estimated by integrating the

local lift and drag forces along different annulus. The detailed theoretical analysis can be found in

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a textbook by Leishman (Leishman, 2006). One of the unique features of the helicopter

aerodynamics is that there are always two velocity components in aerodynamics analysis for a rotor

blade, i.e., a tangential velocity from rotation, and a normal velocity from inflow. The two

components vary along rotor radial locations, and therefore, result in a variation of local angle of

attack. An example of angular variation on a rotor span calculated by the BEMT code is shown in

Figure 7-13. The sum of pitch angle plus local twist angle is a sum of local effective angle of attack

and inflow angle.

Figure 7-13. Angle of Attack variation along a rotor blade

This variation in AOA also results in a varying performance degradation on local blade

element. This is also the motivation for the effort of correlating calculated Cd to various AOA, as

already mentioned in the Section 7.1.6. By coupling the performance degradation correlation

(HPC) and the BEMT code, the total torque requirement to maintain a certain RPM due to local

drag on each blade element can be calculated.

To validate the BEMT code, a sample calculation of required torque on a clean NACA 0012

rotor for rotation setting of 100, 200, 300, 400, and 470 RPM are presented in Figure 7-14 together

with experimental measurements at the AERTS facility. During the test, the rotor was started from

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0 RPM and then ramped up with increments of 100 RPM. After arriving at a certain target RPM,

the rotor was maintained at that RPM for data recording (the flat curve segments in figure). In

Figure 7-14, the leveled curve at different time indicates the steady torque requirement for a specific

RPM, whereas the sharp spikes and fluctuating curves with slopes are resulted from rotor increasing

speed towards the next target RPM.

Figure 7-14. Sample torque calculation – clean NACA 0012 rotor, pitch angle 8°

The largest error in prediction occurred at a very low speed (RPM = 100), where a -33.4%

error in prediction was found. This is believed to be due to friction at rotor hub under low rotating

speed. For the higher RPM cases, the prediction errors are -14.3%, -5.5%, 1.5%, and 4.3% for 200

RPM to 470 RPM respectively. As can be seen from this clean rotor torque calculation, the BEMT

code could provide an accurate prediction of torque with ±5% error for 300-500 RPM regime. Next,

the BEMT code was coupled with the performance degradation correlation to predict the increased

torque due to ice accretion. An example of the calculated torque requirement for iced rotor

compared to experimental measurements is shown in Figure 7-15. For clean rotor condition, again,

the BEMT achieved very good accuracy, i.e., a 5.4% in predicted torque. The torque increase due

to icing could also captured by the proposed coupling prediction tool. As clearly indicated by the

0

20

40

60

0 200 400 600 800

Torq

ue

(N

m)

Time (second)

100 RPMExp. 3.2BEMT 2.1





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measurement, the torque requirement varied linearly with time, indicated a uniform ice formation

as a function of icing time. After 300 seconds of icing, there was a 37.3% increase in experimentally

measured required torque to maintain the same RPM. The prediction was within a reasonable

discrepancy range, 10.8% lower than the experimental measured torque.

Figure 7-15. Sample torque calculation – iced rotor, pitch angle 10°

For validation, a total of 17 ice accretion tests was conducted at the AERTS facility. Torque

measurements both with and without ice accretion for each cases have been recorded. A summary

of the torque calculation for clean rotors is shown in Figure 7-16.

Figure 7-16. Summary of torque calculation – clean rotor

0

20

40

60

80

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Torq

ue

(N

m)

Test case number

BEMT

Exp

470 RPMpitch (θ)= 8°

408 RPMθ= 8 θ= 10 θ= 9

472 θ= 9

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The mean absolute deviation between the predicted value and experimental measurement

has been calculated for each case. The averaged mean absolute deviation for clean cases is 9.8%.

The prediction of torque for clean rotors achieved good accuracy.

Figure 7-17. Summary of torque calculation – iced rotor

When comparing the results for iced rotors in Figure 7-17, again, a good match was

observed for the iced cases. In spite of an outlier of 61.6% over-prediction, the averaged mean

absolute deviation for iced cases was 15.6%. The clear correspondence between both the clean and

iced rotor torque proved that the proposed performance degradation can be applied to the helicopter

rotor icing problem. The main error source during testing is related to inaccurate estimations of the

icing cloud properties, especially LWC.

0

20

40

60

80

100

120

140

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Torq

ue

(N

m)

Test case number

BEMT

Exp

470 RPMpitch (θ)= 8°

408 RPMθ= 8 θ= 10 θ= 9

472 θ= 9

200

Chapter 8

Conclusions

Experimental and analytical studies have been conducted to gain physical understanding

of ice accretion surface roughness effects on heat transfer and ultimately ice accretion shape

prediction. Testing was conducted at the Adverse Environment Rotor Test Stand (AERTS) facility

at The Pennsylvania State University. The studies focused on changes in heat transfer and

aerodynamics performance due to accreted ice structures.

For the experimental efforts presented in this dissertation, novel experimental

measurement techniques have been developed to quantify heat transfer. Molding and casting

techniques were developed to capture ice shapes into solid models. Infrared thermal imaging was

used to monitor unsteady temperature variations used for transient heat transfer calculations.

Profilometer and digital dial indicator were introduced to measure ice roughness. A 3D scan

technique was applied to the casting models to acquire digitized surface roughness values and to

compare these values to the direct profilometer roughness measurements. Multiple thermal

measurement sensors, such as thin-film heat flux sensors, were used for monitoring thermal

variations during the experiments and to validate the new non-intrusive transient infra-red

approach.

To experimentally evaluate the effect of accreted ice roughness and ice shapes, two

separate groups of experiments have been conducted. The effect of ice roughness on heat transfer

was studied using experimentally accreted roughness on both 0.1143 m (4.5 inch) diameter

cylinders and 0.5334 m (21 inch) chord NACA 0012 airfoils. A total of eight (8) ice roughness tests

has been carried out on a cylinder rotor and another ten (10) tests were conducted on airfoil shapes.

201

Roughness measurements confirmed that a typical roughness distribution is comprised of a smooth

zone, a rough zone, and sometimes also a runback zone due to the surface water movement at warm

conditions. A novel measurement technique to quantify the transient heat transfer of the accreted

ice roughness structures was validated against reference data for smooth flat plates, cylinders, and

airfoils. Once the heat transfer measurement approach was validated, the heat transfer of ice-

roughened surfaces was measured. Based on heat transfer measurements, different

transition/separation regimes were successfully reproduced on ice-roughened cylinders over a

range of Reynolds numbers. The full coverage of Reynolds number over the flow transition

regimes, obtained during heat transfer measurements of cylinders, would have been impossible

using airfoil shapes given the capabilities of the available facilities. As Reynolds number increases,

laminar separation, flow reattachment, natural transition, and early transition due to surface

roughness were observed. Based on the knowledge gained from cylinder tests at various Reynolds

numbers, a parametric study of ice roughness effects on airfoil heat transfer was conducted. The

parametric study provided insight of the effect of each individual icing parameter on the measured

roughness and corresponding heat transfer distribution. Flow transition and separation analyses for

the icing parametric study were also conducted, and shed light on the requirements needed to

develop a modeling tool to predict ice roughness and associated heat transfer on ice-roughened

surfaces.

The effects of accreted ice shapes and additional roughness elements on the aerodynamic

performance of an airfoil were also investigated experimentally. Rotor ice accretion and wind

tunnel testing on a 0.5334 m (21 inch) chord airfoil were conducted. Wind tunnel aerodynamic

measurements were compared to reference database values in terms of lift, drag, and pitching

moment coefficients. The effect of additional roughness on drag measurements of accreted ice

shapes was demonstrated by comparing the penalties incurred with and without ice feathers.

202

Analytical research efforts based on experimental heat transfer measurements have been

conducted on cylinders. A new scaling factor, labeled as the Coefficient of Stanton and Reynolds

Number (𝐶𝑆𝑅 = 𝑆𝑡𝑥 𝑅𝑒𝑥−0.2⁄ ), was developed to eliminate the effect of Reynolds number when

comparing different-sized models tested under different speed in a turbulent regime. The CSR

scaling was validated against extensive databases found in the literature for generic shapes with

roughened surfaces, such as flat plates, cylinders, and airfoils. Both reference heat transfer datasets

obtained at different Reynolds numbers and experimental measurements conducted in this research

could be represented by distinctive trend lines provided by the CSR turbulent scaling relationship

proposed. More importantly, based on the understanding gained during the scaling factor

development, icing-physics-based predictions for ice roughness and heat transfer on both cylinders

and airfoils were developed. These two modeling tools (surface roughness and heat transfer

prediction) have also been incorporated into an existing ice prediction tool (LEWICE) to improve

the ice prediction capability in the glaze ice regimes. The roughness predictions were validated to

both reference databases and also experimental measurements conducted in this work. The

predicted ice shapes with the new heat transfer prediction tools have been compared for icing

condition ranges outside the validated icing envelope of LEWICE, showing clear improvements

over current LEWICE prediction capabilities.

Predictions for drag penalty due to the accreted ice structures were also developed

alongside with the aerodynamic testing conducted. A comprehensive literature survey including

490 sets of performance degradation data on various iced airfoils and under varying angles of

attack, was presented. Drag increases due to ice accretion has been modeled using icing-physics

based parameters using a transformed linear regression method. The proposed drag penalty

prediction was also coupled with a Blade Element Momentum Theory to assess the performance

of a rotor system in terms of required torque to maintain RPM under icing conditions.

203

The main findings of this research have been summarized into three groups, namely:

surface roughness observations and prediction, heat transfer enhancement due to roughness, and

aerodynamics performance degradation due to accreted ice structures. The detailed findings are

presented as follows:

Surface roughness observations and prediction

1. For early stages of ice roughness accretion, based on 10 airfoil tests and 8 cylinder tests

conducted at varying icing conditions and accretion times, experimentally measured ice

roughness height ranged from 0.006 mm to 1.10 mm. Artificially simulated roughness typically

used by other authors with large roughness element heights (e.g. 2 mm spherical roughness)

are not representative of natural ice roughness, since the maximum roughness measured within

2 minutes was in the order of 1 mm as seen both in the AERTS laboratory and other facilities.

2. Ice roughness predictions were developed for cylinders and airfoils separately. The airfoil

database from both experimental measurements conducted in this research and 82 tests from

the literature were also compared to existing ice roughness predictions models. Given their

empirical nature, the referenced prediction models were found heavily biased towards the

datasets that they were developed from. The two reference predictions found in the literature

had a 76% and 54% maximum error with respect to measurements respectively, whereas the

new ice roughness prediction model developed during this study achieved a 31% accuracy in

prediction and showed no bias over the total dataset. It must be noted that the uncertainty

reached with the proposed ice roughness prediction tool is within the ice shape reproduction

capabilities of the used icing facilities.

204

Heat transfer enhancement due to roughness

3. When comparing experimental heat transfer measurements from different testing facilities and

at different testing speeds, a scaling factor is necessary for the comparison of results. For a

laminar regime, the Frossling number (𝐹𝑟 = 𝑁𝑢 √𝑅𝑒⁄ ) has been demonstrated capable of

scaling the effect of Reynolds number.

4. For scaling heat transfer measurements in the turbulent regime, a separate scaling factor, called

Coefficient of Stanton and Reynolds number (𝐶𝑆𝑅 = 𝑆𝑡𝑥 𝑅𝑒𝑥−0.2⁄ ), was proposed and validated

against a comprehensive database on flat plates, cylinders, and airfoils. When implementing

CSR, both experimental measurements from other facilities and from the AERTS laboratory

could be successfully scaled into a single scaled curve that represents the unique turbulent heat

transfer behavior. The proposed scaling factor provided physical insights for correlation

development between heat transfer, surface roughness, and icing conditions.

5. Predictions for ice roughness and heat transfer were developed for cylinders and airfoils. The

proposed tools were coupled with LEWICE. For rime ice shape predictions the improved

prediction tool achieved an average of 2% accuracy with respect to experimental

measurements, compared to LEWICE prediction providing an average of 18% discrepancy in

ice thickness. In the glaze regime, the LEWICE internal heat transfer module was shown to

exhibit an over 100% over-prediction at the ice horn region for both cylinder and airfoil ice

accretion, whereas the heat transfer module developed in this study could capture the correct

heat transfer transition behavior and also the correct magnitude. The discrepancy between the

proposed heat transfer prediction tool and the experimental measured heat transfer in the rough

zone region only varied by maximum ±15%, which was still within the measurement

uncertainty range of the facilities.

205

Aerodynamics performance degradation due to accreted ice structure

6. The experimental aerodynamic data for ice castings made from rotor blade ice accretion

correlated well with reference data obtained at the NASA IRT (maximum 25% discrepancy

from outlier data). A novel, physics-based performance degradation correlation due to icing

conditions (HPC, Han and Palacios Correlation) was developed. The HPC drag calculation and

drag measurements from the AERTS rotor icing experimental results correlated well. The HPC

correlation made favorable drag coefficient calculations with discrepancies of less than 6% for

rime icing conditions and at low AOA regions.

7. The drag penalty prediction tool was developed based on 490 sets of experimental database. A

mean absolute deviation of 33.40% was found when implementing the proposed prediction tool

(HPC model) to experimental datasets available in the literature. The mean of the errors and

standard deviation were 8% ±46%, whereas, for the same set of experimental reference data,

60% to 243% discrepancies were observed using legacy drag penalty prediction tools. The

proposed tool showed better correlations on a broader icing condition envelope when compared

to other available empirical correlations created by Gray (Gray, 1964), Bragg (Bragg, 1982),

and Flemming & Lednicer (Flemming & Lednicer, 1985).

8. The HPC model was also applied to cambered airfoil icing aerodynamics database. The

calculated drag coefficients by HPC for two cambered airfoils (VR-7 and SC1094 R8)

correlated very well with available experimental measurements (with a mean absolute

deviation of 22% and 35%, respectively).

9. Additional roughness elements, such as ice feathers, can affect the measured drag coefficients

by up to 25%, as demonstrated during experimental testing conducted in this study. The effect

of ice feathers over the measured drag is different for varying aerodynamic testing angles of

attack (AOA). At the AOA region around the stall condition, the turbulence boundary layer

growth was largely dependent on the existence of the ice feathers. An average of 15% increased

206

drag was measured between the model without and with feathers in this region. The effect of

ice feathers on the airfoil pitching moment measurement is also profound. The abrupt change

of the pitching moment curve for the two configurations (ice feathers vs. no ice feathers)

occurred at different AOAs. Correspondingly, the stall angle of the model without feathers was

delayed by 1°, which limited the usable AOAs down to a range from 0° to 9° for the tested

NACA 0012 airfoil. Maintaining feather formations during aerodynamic performance

degradation testing is critical to develop an accurate ice accretion degradation model based on

experimental testing. It must be mentioned, that many of the results presented in the literature

eliminated the effects of feather ice accretion.

10. The HPC model was coupled with a Blade Element Momentum Theory to calculate the

required torque to maintain the RPM of a rotor under icing conditions. For a total of 17

validation cases, the coupled prediction tool achieved a 10% predicting error for clean rotor

conditions (no ice accretion), and a 15% error for iced rotor conditions. The proposed

correlation for performance degradation could be used for assessing aircraft performance under

icing condition and also ice protection system design.

Recommendations for Future Work

This research focused on the aerodynamics and heat transfer physics of helicopter ice

accretion. Other physical components of the ice accretion process, such as flow field simulation,

surface energy exchange, surface water film dynamics, and comprehensive evaluation of iced

airfoil performance, still need further evaluation. In this section, specific recommendations for

future research based on the current research status are provided.

Further tests are still desirable. New datasets produced in this study are still scattered: 10

cases on airfoils and 8 cases on cylinders were conducted for ice roughness and heat transfer

research, 4 cases on iced airfoil shapes were tested in wind tunnel for aerodynamics modeling, and

207

17 cases were tested on rotor test stand for torque modeling. A more comprehensive database will

extend the current modeling efforts to a broader region of application.

Although the ice roughness prediction in this study yielded better prediction results than

legacy prediction tools, still, the approach continued to rely on previously developed empirical

methods. In addition, detailed roughness structures were averaged and represented by a 2D

roughness height distribution. Other parameters, such as the roughness element shapes and the

spacing between elements, are ignored in the presented modeling effort. The micro-physics of ice

accretion has to be studied in more detail. Furthermore, the ice roughness prediction and associated

heat transfer were evaluated at the early stage of ice accretion. The current method (both used by

AERTS model and LEWICE) assumes that the local heat transfer is a function of both macro ice

shape and the micro ice roughness structures. During the modeling effort, the effect of macro ice

shape has been taken into account during the flow field modeling. Therefore, the heat transfer can

be still evaluated using the same rough surface equations inside boundary layer; although for an

extended ice accretion event, the local heat transfer is dominated by the macro ice shapes rather

than early-stage ice roughness. The effect of ice roughness on heat transfer for longer ice accretion

time has to be further evaluated to validate current assumption.

In addition, for simplicity and coupling compatibility, both the AERTS model and

LEWICE utilized a potential flow method that ignores the viscous effects for the flow field

prediction. Only the heat transfer analysis utilized the integral boundary layer equations that

incorporated the viscous effects. Both the new heat transfer scaling parameter (CSR) and the heat

transfer modeling tool were originated from integral boundary layer equations. Significant

simplifications (2D, steady, incompressible) and many additional assumptions (Reynolds analogy,

empirical expressions for skin frictions, boundary layer velocity profiles, and thickness

approximations etc.) had to be made during the development of CSR and heat transfer modeling,

and therefore models are still empirical-based; although, through the integration process, the

208

physical meanings of the momentum equations can be properly conserved (which was favorable

for empirical correlation development). The physical meanings of proposed parameters and models

may be better revealed and improved by numerically solving N-S equations using 3D grid-based

method.

For the ice shape prediction model development, current coupling scheme between AERTS

heat transfer modeling and LEWICE prediction tool is one-way weak coupling. The heat transfer

model needs the boundary layer edge velocity and local velocity gradient as input for heat transfer

equation calculation. The robustness of the model needs further improvements.

For ice shape comparisons, a better quantification method has to be developed. Currently,

there is no universal rule for comparing glaze ice shapes, partly due to the irregular ice shapes under

complicated icing conditions. Ice thickness is not a representative parameter for comparison for

glaze ice shapes in terms of the degraded airfoil performance, as already demonstrated in Chapter

7. There is no comprehensive study to numerically describe ice horn and ice feathers for ice shape

comparison. Quantitative comparison can provide more convincible evidence when comparing

different ice shape prediction tools.

For the testing and modeling of the aerodynamic performance, this research focused on

drag penalty due to the additional ice accretion and ice roughness. Other aspects resulted from ice

accretion, such as effects on lift and stability, are still desirable for further investigation. Although

the modeling efforts in this study has been validated against 2D wind tunnel drag coefficients and

3D rotor test stand torque measurements, further comparisons would be desired. The empirical

model was still 2D-based. In more realistic configurations, such as swept wing ice accretion on

fixed-wing aircraft (“scallop” ice shapes), 3D ice shapes are hard to predict and evaluate. Extending

the findings from 2D measurements to 3D applications is possible, and needs further efforts. The

successful rotor torque estimation based on drag penalty model and blade element momentum

theory (BEMT) in this study provided evidence to support this argument.

209

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222

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223

Appendix A Experimental Measurements - Ice Roughness on Airfoil

The ice roughness measurements obtained during airfoil ice roughness experiments are

presented in this appendix. Transition locations for AERTS cases R1 to R10 are shown in Table

A-1. Raw data of measured roughness heights together with standard deviation and statistical

median of the measurement samples are reported in Table A-2 and Table A-3.

Table A-1. Roughness Zone Transition Location and Ice Limit on Airfoil

AERTS Casting # R1 R2 R3 R4 R5 R6 R7 R8 R9 R10

Smooth to Rough

Zone Transition, % s/c 0 1.5 1.6 1.5 1.4 1.8 1.5 1.8 1.0 1.4

Ice Limit, % s/c 15.2 7.6 7.8 7.8 8.0 4.4 7.6 5.4 7.2 6.6

Table A-2. Measured Roughness Heights (R1-R5)

AERTS

Casting # R1 R2 R3 R4 R5

Location

s/c

Ra,

mm

SD,

mm

Median

mm Ra,

mm

SD,

mm

Median

mm Ra,

mm

SD,

mm

Median

mm Ra,

mm

SD,

mm

Median

mm Ra,

mm

SD,

mm

Median

mm

0% 0.28 0.11 0.25 LE* LE LE LE

1% 0.34 0.15 0.32 0.06 0.04 0.06 0.08 0.03 0.09 0.03 0.02 0.03 0.05 0.02 0.05

2% 0.40 0.20 0.35 0.57 0.15 0.52 0.29 0.14 0.26 0.21 0.08 0.22 0.25 0.11 0.23

3% 0.57 0.24 0.55 1.01 0.26 1.03 0.46 0.14 0.42 0.39 0.11 0.41 0.35 0.10 0.34

4% 0.69 0.17 0.64 1.10 0.13 1.10 0.71 0.20 0.64 0.50 0.14 0.52 0.42 0.10 0.41

6% 0.77 0.18 0.76 0.82 0.18 0.88 0.29 0.09 0.30 0.45 0.17 0.43 0.32 0.10 0.34

8% 0.42 0.26 0.39 SS** SS SS SS

10% 0.26 0.26 0.19 SS SS SS SS

* LE: surface roughness measured for the leading edge smooth zone at the nose area, 0.00635 mm, exceeded

the lower limit of the digital dial indicator, measured by profilometer;

** SS: surface roughness measured at the smooth surface of the test specimen, 0.000305 mm, exceeded the

lower limit of the digital dial indicator, measured by profilometer;

224

Table A-3. Measured Roughness Heights (R6-R10)

AERTS

Casting # R6 R7 R8 R9 R10

Location

s/c

Ra,

mm

SD,

mm

Median

mm Ra,

mm

SD,

mm

Median

mm Ra,

mm

SD,

mm

Median

mm Ra,

mm

SD,

mm

Median

mm Ra,

mm

SD,

mm

Median

mm

0% LE LE LE LE LE

1% 0.01 0.01 0.01 0.03 0.02 0.03 0.04 0.02 0.04 0.08 0.03 0.08 0.06 0.03 0.04

2% 0.11 0.03 0.11 0.74 0.26 0.68 0.06 0.02 0.06 0.39 0.11 0.37 0.24 0.07 0.22

3% 0.10 0.04 0.10 0.86 0.20 0.81 0.09 0.02 0.09 0.41 0.11 0.38 0.28 0.08 0.31

4% 0.08 0.03 0.08 0.92 0.27 0.91 0.09 0.03 0.09 0.07 0.03 0.06 0.30 0.09 0.25

6% SS 0.63 0.29 0.49 SS SS 0.11 0.04 0.11

8% SS SS SS SS SS

10% SS SS SS SS SS

* LE: surface roughness measured for the leading edge smooth zone at the nose area, 0.00635 mm, exceeded

the lower limit of the digital dial indicator, measured by profilometer;

** SS: surface roughness measured at the smooth surface of the test specimen, 0.000305 mm, exceeded the

lower limit of the digital dial indicator, measured by profilometer;

225

Appendix B Experimental Measurements – Aerodynamics Testing

The wind tunnel aerodynamics testing results for the four ice shape casting models are

tabulated in tables below. The term Cd_wake denotes the drag coefficient measured by wake survey

method. The term Cd_3d denotes the drag coefficient measured by external force balance. Cl and

Cm were also experimentally measured by force balance. L/D denotes the lift-to-drag ratio, which

is calculated from Cd_wake and Cl in the same table. The term Cd_HPC is the Cd value calculated

using HPC in this study. Cd_Ref is the reference value from the reference literature (Olsen, Shaw,

& Newton, 1984). The reference case numbers are listed in the first row of every table.

Table B-1. AERTS ICE1 Iced Airfoil Polar Data

AERTS ICE1, Ref. Olsen O-10

AOA Cd_wake Cd_3d Cl Cm L/D Cd_HPC Cd_Ref

0 0.02026 0.02059 0.11369 -0.00479 5.61 0.04039 0.02199

2 0.02420 0.02283 0.34145 -0.00134 14.11 0.03542 0.02421

4 0.02961 0.03353 0.54819 0.00440 18.51 0.03743 0.02767

6 0.04158 0.05966 0.71473 0.00715 17.19 0.04641

8 0.06895 0.07490 0.90231 0.02058 13.09 0.06236 0.07647

9 0.08958 0.09894 0.92189 0.00982 10.29 0.07296

9.5 0.10905 0.11199 0.95933 0.01948 8.80 0.07891

10 0.12833 0.12605 0.98398 0.01200 7.67 0.08529

12 0.17099 0.17766 1.04841 -0.00876 6.13 0.11520

14 0.20404 0.24330 1.11936 -0.02583 5.49 0.15209

15 0.21588 0.25663 1.15709 -0.02518 5.36 0.17314

16 0.22121 0.27703 1.15978 -0.04486 5.24 0.19595

18 0.25441 0.32288 1.12197 -0.08028 4.41 0.24678

226


AERTS ICE2, Ref. Olsen S-69


0 0.02242 0.02172 0.01862 0.00051 0.83 0.03056

2 0.02279 0.02595 0.20377 0.01390 8.94 0.02559

4 0.02602 0.03452 0.41057 0.01441 15.78 0.02760 0.02105

6 0.03290 0.04148 0.61028 0.02179 18.55 0.03658

8 0.04405 0.05930 0.79972 0.02763 18.16 0.05253

9 0.05365 0.06713 0.86642 0.03803 16.15 0.06313

10 0.07061 0.08681 0.94888 0.04993 13.44 0.07546

11 0.09086 0.11921 0.99381 0.00637 10.94 0.08955

11.5 0.10603 0.14007 1.00821 0.01450 9.51 0.09724

12 0.12291 0.15926 1.04826 -0.01143 8.53 0.10537

13 0.16014 0.19306 1.05640 -0.03447 6.60 0.12294

14 0.18315 0.24821 1.12295 -0.08322 6.13 0.14226

15 0.19805 0.30413 1.13252 -0.08703 5.72 0.16331

16 0.22009 0.35170 1.18315 -0.15052 5.38 0.18612

18 0.26432 0.41775 1.17668 -0.16133 4.45 0.23695


AERTS ICE3, Ref. Olsen O-8


0 0.03730 0.03063 -0.01262 0.00094 -0.34 0.05955 0.02294

2 0.04014 0.03503 0.16151 0.01989 4.02 0.05457

4 0.04292 0.04086 0.35965 0.02954 8.38 0.05658

6 0.05382 0.05355 0.54568 0.02849 10.14 0.06556

8 0.08156 0.08762 0.69409 0.02369 8.51 0.08151

9 0.10173 0.11644 0.76218 -0.00354 7.49 0.09211

9.5 0.11522 0.12791 0.79245 0.00002 6.88 0.09806

10 0.12646 0.14130 0.82448 -0.00791 6.52 0.10445

12 0.17161 0.20750 0.91099 -0.06543 5.31 0.13435

13 0.19803 0.24314 0.91200 -0.07105 4.61 0.15192

14 0.21160 0.28671 0.93659 -0.10882 4.43 0.17124

15 0.22838 0.31723 0.91179 -0.15363 3.99 0.19230

16 0.22939 0.33738 0.90063 -0.12882 3.93 0.21510

18 0.23926 0.38188 0.90882 -0.14291 3.80 0.26593

227

Table B-4. AERTS ICE3-FR Iced Airfoil Polar Data

AERTS ICE3-FR, Ref. Olsen O-8


0 0.02872 0.02840 -0.02288 0.00263 -0.80 0.05955 0.02294

2 0.03134 0.02975 0.14639 0.02049 4.67 0.05457

4 0.03963 0.03416 0.33313 0.03550 8.41 0.05658

6 0.05185 0.04823 0.52280 0.04523 10.08 0.06556

8 0.07574 0.07452 0.69308 0.05072 9.15 0.08151

9 0.08958 0.09621 0.76639 0.03442 8.56 0.09211

9.5 0.09952 0.10929 0.79060 0.02827 7.94 0.09806

10 0.11069 0.12519 0.82137 0.01993 7.42 0.10445

10.5 0.12288 0.14437 0.84309 -0.00220 6.86 0.11127

11 0.13631 0.17173 0.85146 -0.04039 6.25 0.11853

12 0.16016 0.19640 0.91068 -0.04830 5.69 0.13435

13 0.18670 0.24281 0.91697 -0.07666 4.91 0.15192

14 0.20563 0.27363 0.92129 -0.11744 4.48 0.17124

15 0.22188 0.30068 0.92406 -0.14466 4.16 0.19230

16 0.22740 0.34434 0.91506 -0.15304 4.02 0.21510

18 0.23941 0.37532 0.87279 -0.18879 3.65 0.26593


AERTS ICE4, Ref. Olsen S-33


0 0.02162 0.01853 0.16437 0.00661 7.60 0.01691

2 0.02366 0.02426 0.29148 0.01110 12.32 0.01194

4 0.02930 0.02708 0.53797 0.02424 18.36 0.01394 0.01622

6 0.03914 0.03601 0.69620 0.04169 17.79 0.02292

8 0.05886 0.06975 0.83366 0.04896 14.16 0.03888

9 0.08320 0.09153 0.90089 0.03799 10.83 0.04947

10 0.11737 0.12182 0.94715 0.03913 8.07 0.06181

11 0.14147 0.17222 0.98491 -0.00319 6.96 0.07589

12 0.17263 0.20442 1.02973 -0.03500 5.96 0.09172

12.5 0.18235 0.22609 1.05084 -0.04790 5.76 0.10028

13 0.20549 0.25180 1.06319 -0.07638 5.17 0.10929

14 0.22454 0.28294 1.08225 -0.12906 4.82 0.12860

16 0.24653 0.36999 1.12303 -0.16390 4.56 0.17246

18 0.23948 0.43536 1.12333 -0.13517 4.69 0.22330

228

Appendix C Scaling Methods for Ice Accretion Testing

The icing scaling method is considered in the context that a given icing facility may only

be able to achieve a certain range of test conditions, in terms of velocity, temperature, geometry,

or icing cloud (LWC and MVD). An icing scaling method has to be implemented to obtain scaled

icing conditions due to dimension changes between reference model and scale model. To date,

several different scaling methods are available. The most widely used one is known as Modified

Ruff (AEDC) method (Ruff, 1986). The scaling method is used for geometry size-scaling and icing

test condition scaling. This method has been thoroughly tested and validated by NASA Glenn IRT

using fixed wing airplane test conditions. In 2009, Tsao and Kreeger (Tsao & Kreeger, 2009)

conducted several scaling tests using rotorcraft icing conditions. The test scaling method was a

modified Ruff method with scaled velocity determined by maintaining constant Weber number,

which will be introduced in the following sections. The test airfoils used were fixed-wing airfoils

with a NACA 0012 profile and with 0.9144 m (36 inch) and 0.3556 m (14 inch) chord. The fixed-

wing airfoils are tested at the IRT with 39 m/s and 52 m/s airspeed and with AOA of 0º and 5º. The

icing conditions were in the SLD regime (MVD = 150µm and 195 µm) and relatively high LWC

values, ranging from 0.6 g/m3 to 1.8 g/m3, which resulted in that the ice shapes were all in glaze

ice regime. It was suggested that the current scaling method can be directly applied to rotorcraft

icing with generic rotor blades and within a finite AOA range. The authors claimed that these

conclusions may not be valid for higher velocities and larger static angle of attack.

Based on this assumption, this study used the conventional scaling method for rotating

icing testing. To get the scaled icing conditions, 6 similitude analyses have to be implemented,

namely: geometry, flow field, drop trajectory, water catch, energy balance, and surface water

229

dynamics similarities. The flow chart of a typical icing scaling similarity analysis is shown in

Figure C-1.

Figure C-1. Flow Chart of Icing Condition Scaling Method

The first three analyses characterize the ice accretion procedure as shown in Figure C-1.

The stagnation line ice thickness can be expressed as an analytical function of icing parameters.

With respect to the droplet trajectory similarity, collection efficiency, β, is defined in Reference

(Langmuir & Blodgett, 1946) to illustrate the fraction of the incoming water content that actually

impacted the monitoring control volume. By using analytical methods, the expression of β can be

expressed as a characteristic parameter of the flow trajectory. The collection efficiency calculated

at the stagnation line in Equation (C-1) was initially published for cylinders but was then validated

for airfoil cases and may be written as:

𝛽0 =1.40(𝐾0 − 1 8⁄ )0.84

1 + 1.40(𝐾0 − 1 8⁄ )0.84 (C-1)

230

At the stagnation line, it is assumed that there is no incoming interfering water into the control

volume for simplicity. K0 is the modified inertia parameter. It was initially defined for cylinders

but was then validated for airfoils (Langmuir & Blodgett, 1946). It is a function of MVD, impacting

velocity, air viscosity, air density and water density, as shown in the equation below:

𝐾0 =1

8+

𝜆

𝜆𝑆𝑡𝑜𝑘𝑒𝑠(𝐾 −

1

8) , for 𝐾 >

1

8 (C-2)

where, the inertia parameter, K, in can be expressed as:

𝐾 =𝜌𝑤 ∙ 𝛿2 ∙ 𝑉

18 ∙ 𝑑 ∙ 𝜇𝑎 (C-3)

The term 𝜆 𝜆𝑆𝑡𝑜𝑘𝑒𝑠⁄ is the dimensionless droplet range parameter defined as:

𝜆

𝜆𝑆𝑡𝑜𝑘𝑒𝑠=

1

0.8388 + 0.001483𝑅𝑒𝛿 + 0.1847√𝑅𝑒𝛿

(C-4)

where δ is the water droplet characteristic length (MVD) and the Reynolds number based on this

length is defined as follows:

𝑅𝑒𝛿 =𝑉 ∙ 𝛿 ∙ 𝜌𝑎

𝜇𝑎 (C-5)

where the V is the impacting velocity, ρa is the air density and µa is the air viscosity.

Although Angle of Attack (AOA) term was not incorporated into Equation (C-1), and the

flow trajectory apparently changes with the AOA variation, it was demonstrated that within a finite

range of angles (examples given in reference were 0° and 10°), the calculated collection efficiencies

still fell onto the same line and matched with LEWICE numerical predictions (Anderson, 2004).

This AOA study shows the potential applicability of the classical fixed-wing scaling method to the

helicopter scaling tests.

The second similarity analysis is for water catch similarity. An accumulation parameter,

Ac, is defined in Equation (C-6) to show normalized maximum local ice thickness to represent the

non-dimensionalized incoming water mass flux caught in the local surface control volume:

231

𝐴𝑐 =𝑉 ∙ 𝐿𝑊𝐶 ∙ 𝜏

𝜌𝑖 ∙ 𝑑 (C-6)

where, τ is the icing time, and d is the characteristic model dimension, which is usually the diameter

of the test cylinder and twice the leading edge radius for symmetric airfoils. The leading edge radius

is defined as the radius of airfoil nose circle centered on a line tangent to the leading-edge camber

(chord line of a symmetrical airfoil) and connecting the tangency points of the upper and lower

surfaces of the leading edge. Typical leading-edge radii are zero to 2 percent of the chord (e.g.

1.58% for NACA 0012 airfoil).

Moving onto the third similarity analysis, the energy balance similarity mainly considers

the water droplet status within the control volume after it impacts the model surface. The freezing

fraction, n, is then introduced to denote the ratio of impinging water that freezes within a control

volume. This term was first introduced by Messinger (Messinger, 1953) and later developed by

Ruff (Ruff, 1986) as shown in Equation (C-7):

𝑛0 = (𝑐𝑝,𝑤𝑠

Λ𝑓) (𝜙 +

𝜃

𝑏) (C-7)

where, the subscript, 0, denotes this freezing fraction is calculated at the stagnation line; the right-

hand-side of the equation comprises several characteristic energy coefficients: Cp,ws is the specific

heat of water on the model surface; Λf is the latent heat of freezing; ϕ is drop energy transfer

parameter; θ is air energy transfer parameter and finally b is relative heat factor. The definitions for

ϕ, θ, and b can be found in following equations:

𝜙 = 𝑡𝑓 − 𝑡𝑠𝑡 −𝑉2

2𝑐𝑝,𝑤𝑠 (C-8)

𝜃 = (𝑡𝑠 − 𝑡𝑠𝑡 −𝑉2

2𝑐𝑝,𝑤𝑠) +

ℎ𝐺

ℎ𝑐(

𝑝𝑤𝑤 − 𝑝𝑤

𝑝𝑠𝑡) Λ𝑣 (C-9)

The relative heat factor, b, is introduced by Tribus (Tribus, Young, & Boelter, 1948):

232

𝑏 =�̇� ∙ 𝑐𝑝,𝑤𝑠

ℎ𝑐=

𝐿𝑊𝐶 ∙ 𝑉 ∙ 𝛽0 ∙ 𝑐𝑝,𝑤𝑠

ℎ𝑐 (C-10)

The convective heat-transfer coefficient, hc, can be calculated from Nusselt number. For simplicity,

two numerical expressions of Nu are chosen, according to different Re:

𝑁𝑢 =ℎ𝑐𝑑

𝑘𝑎 (C-11)

for Re > 105, as per a reference paper by Anderson (Anderson, 2004):

𝑁𝑢 = 1.10𝑅𝑒𝑑0.472 (C-12)

and for Re < 105:

𝑁𝑢 = 1.14𝑃𝑟0.4𝑅𝑒𝑑0.5 (C-13)

The three previously mentioned similarity analyses in scaling method dealing with droplet

trajectory, water catch, and energy balance, are accomplished by matching the three ice scaling

parameters: β0, Ac, and n0. The rest of the similarity parameters deal with the similarity between the

test model dimension, flow field, and surface water dynamics under the reference and scaled icing

condition.

For geometric similarity analysis, the two airfoil profiles are required to have identical

cross-section. Flow field similarity requires that Mach and Reynolds number to match to ensure

the same flow field features (turbulence intensity, boundary layer behavior and compressibility

etc.). Since the chord of the blade is different, the Mach number and Reynolds number based on

model characteristic length cannot be matched at the same time. For simplicity, neither of them is

considered for matching during most of the current scaling methods. The Weber number based on

model size and water density is often used instead of these two numbers, as will be shown in the

surface water dynamics similarity equation.

In surface water dynamics similarity analysis, it is assumed that for the water droplet

impacting the model surface, the droplet motion can be characterized by the Weber number, which

233

denotes the ratio of a fluid’s inertia to surface tension. By matching the Weber number between the

reference case and the scaled case, the scaled testing velocity can be determined. The Weber

number based on characteristic length L of the model (usually, d, twice the leading edge radius, is

used here) can be shown as:

𝑊𝑒𝐿 =𝑉2𝜌𝑤𝐿

𝜎 (C-14)

The validity of this scaling method has been demonstrated (Han, Palacios, & Smith, 2011)

(Han, 2011). The icing condition scaling method has been used to conduct experimental ice shape

correlation between the AERTS shapes and those presented in the literature for airfoils with varying

chord dimensions. The icing scaling parameters such as freezing fraction (n0) and accumulation

parameter (Ac) have also been used in roughness and heat transfer prediction models in this

research, as already shown in previous chapters.

234

Appendix D Angular Variation of Thermal Infrared Emissivity

While taking infrared photographic data, each individual pixel on the IR camera out of the

total 640×480 pixels acts as a thermocouple that senses the radiant power emitted by the test

specimen. The radiant heat transfer is a strong function of the emissivity. Different body curvature

needs different emissivity settings. For the test setups with highly curved surfaces and skewed

viewing angles, a proper angular dependency analysis needs to be conducted before the tests. The

test cylinder has a high curvature and therefore is subject to angular variation of the emissivity

(Karev, Farzaneh, & Kollar, 2007) (Hori, et al., 2013). The airfoil was also considered, but regarded

as less dependent on angular variation. In this appendix, analysis of the cylinder IR test setup is

shown to serve as an example of IR measurement practice at the AERTS lab. The proposed

corrections for emissivity were applied to both cylinders and airfoils.

A comparison of the emissivity of water, ice, and the test cylinder material (urethane

plastic) is shown in Figure D-1.

Figure D-1. Angular emissivity of different materials

Experimental data (discrete points) taken from Ref. (Sobrino & Cuenca, 1999)

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

0 10 20 30 40 50 60 70 80 90

Emis

sivi

ty

Angle of Incidence, deg

Water, Ref expWater, IOR=1.4Ice, IOR=1.6Urethane Plastic, IOR=1.58

235

The experimental data for water was taken from experimental measurements by Sobrino

and Cuenca (Sobrino & Cuenca, 1999). The prediction of the angular dependency was calculated

from the Fresnel equation (Rees & James, 1992) and is defined in Equation (D-1)

휀 = 1 −1

2|(𝐼𝑂𝑅2 − 𝑠𝑖𝑛2𝜃)1 2⁄ − 𝑐𝑜𝑠𝜃

(𝐼𝑂𝑅2 − 𝑠𝑖𝑛2𝜃)1 2⁄ + 𝑐𝑜𝑠𝜃|

2

−1

2|𝐼𝑂𝑅2𝑐𝑜𝑠𝜃 − (𝐼𝑂𝑅2 − 𝑠𝑖𝑛2𝜃)1 2⁄

𝐼𝑂𝑅2𝑐𝑜𝑠𝜃 + (𝐼𝑂𝑅2 − 𝑠𝑖𝑛2𝜃)1 2⁄|

2

(D-1)

where IOR is Index of Refraction, as indicated in the legend of Figure D-1. The water emissivity

curve matched the experimental measurements very well. Both the experimental observations and

the predictions showed that the emissivity greatly depended on the incidence angle after the angle

passed 70°. The angle θ was angle of incidence, i.e., the angle between the incoming light direction

and the local normal vector that was perpendicular to the local panel surface. A similar definition

can also be found in a reference paper by Karev et al. (Karev, Farzaneh, & Kollar, 2007). The wind

tunnel setup and the resultant correlation between angle of incidence and azimuth angle are

illustrated in Figure D-2 for the cylinder test setup and in Figure D-3 for the airfoil test setup.

Figure D-2. Wind tunnel camera setup schematics – cylinder test

17’’

10’’

Flow

OD 4.5’’

θ

α

236

Figure D-3. Wind tunnel camera setup schematics – airfoil test

The Fresnel model was based on the assumption that the material was homogeneous and planar.

The effectiveness was also limited by the angle of incidence up to around 70-80°, as indicated by

the red lines in Figure D-4. For the cylinder roughness study, the camera view was limited to an

azimuth angle of 0° to 130° based on the resultant angle of incidence in Figure D-4 (a).

Figure D-4. (a) Angle of incidence, and (b) Emissivity vs. Azimuth angle on cylinder

The IR camera used for this study was only able to accept one unique emissivity for the

entire surface. Therefore, a uniform emissivity of 0.95 was used to capture the transient temperature

change, which corresponds to the flat curve region in Figure D-4 (b). During post-processing, the

temperature readings were then corrected with respective local emissivity. The relative humidity

was left at a default value of 50%, which was recommended by the FLIR user manual for short

distances and normal humidity environment. The camera settings were zeroed with reference to

-5

0

5

10

15

20

-25 -15 -5 5 15 25Ver

tica

l Lo

cati

on

(in

ch)

Horizontal Location (inch)

Schematic of Camera View Setup

θ

0

30

60

90

0 20 40 60 80 100 120 140

An

gle

of

Inci

de

nce

, θ

Azimuth Angle, α (deg)0 20 40 60 80 100 120 140

0.5

0.6

0.7

0.8

0.9

1

Azimuth Angle, α (deg)

Emis

sivi

ty, ε

237

water/ice mixture. The temperature readings were also calibrated against thin-film surface-mount

thermocouples on various angular positions. The temperature comparisons between the thermal

sensors and the IR camera readings are presented in the technique validation section in Chapter 4.

VITA

Yiqiang Han

Education

Ph.D. Aerospace Engineering, 08/2011 – 05/2016

The Pennsylvania State University, University Park, PA

M.S. Aerospace Engineering, 08/2009 – 08/2011

The Pennsylvania State University, University Park, PA

B.S. Architectural Engineering, 08/2005 – 05/2009

Nanjing University of Aeronautics and Astronautics, Nanjing, China

Work Experience

Research Assistant Penn State, University Park, PA 08/2009-05/2016

R&D Intern Innovative Dynamics Inc., Ithaca, NY 06/2015-08/2015

R&D Intern GE Global Research, Niskayuna, NY 05/2014-08/2014

Selected Publications

Han, Y. and Palacios, J. (2013), “Airfoil Performance Degradation Prediction based on

Non-dimensional Icing Parameters,” AIAA Journal, 51(11), 2570-2581

Han, Y., Palacios, J., and Schmitz, S. (2012), “Scaled Ice Accretion Experiments on a

Rotating Wind Turbine Blade,” Journal of Wind Engineering and Industrial

Aerodynamics, (109), 55-67

Palacios, J., Han, Y., Brouwers, E., and Smith, E. (2012), “Icing Environment Rotor Test

Stand Liquid Water Content measurement Procedures and Ice Shape Correlation,”

Journal of American Helicopter Society, 57(2), 022006 - 1-12

Han, Y. and Palacios, J. (2016), “Aircraft Ice Accretion Modeling Based on Improvements

in Surface Roughness and Heat Transfer Predictions,” Aviation 2016, Washington

DC

Han, Y. and Palacios, J. (2016), “Heat Transfer Evaluation on Ice-Roughened Cylinders,”

Aviation 2016, Washington DC

Han, Y., Soltis, J., and Palacios, J. (2015), “Inlet Guide Vane Ice Impact Fragmentation

Testing,” SAE 2015 International Conference on Icing of Aircraft, Engines, and

Structures, Prague, Czech Republic

Han, Y. and Palacios, J. (2014), “Transient Heat Transfer Measurements with Surface

Roughness on Ice Roughened Airfoil,” AIAA Aviation 2014, AIAA 2014-2464,

Atlanta, GA

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AERODYNAMICS AND THERMAL PHYSICS OF HELICOPTER ICE …