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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
ii
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
iii
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
iv
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.
v
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
vi
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
vii
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
viii
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
ix
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
x
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 4-4. Clean cylinder heat transfer - ReD = 2×105 ........................................................... 102
Figure 4-5. Clean cylinder heat transfer - ReD = 3×105 ........................................................... 103
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 4-8. Comparison of heat transfer on ice roughened cylinder surface - ReD = 2×105 .... 107
Figure 4-9. Comparison of heat transfer on ice roughened cylinder surface - ReD = 3×105 .... 108
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
xi
Figure 4-15. Effect of LWC (2) ................................................................................................ 117
Figure 4-16. Effect of time (1) ................................................................................................. 118
Figure 4-17. Effect of time (2) ................................................................................................. 118
Figure 4-18. Effect of time (3) ................................................................................................. 119
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
xii
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-2. AERTS ICE2 Iced Airfoil Polar Data .................................................................... 226
Table B-3. AERTS ICE3 Iced Airfoil Polar Data .................................................................... 226
Table B-4. AERTS ICE3-FR Iced Airfoil Polar Data ............................................................. 227
Table B-5. AERTS ICE4 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.
1
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
Data source: Ref. (Healzer, Moffat, & Kays, 1974)
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
Data source: Ref. (Healzer, Moffat, & Kays, 1974)
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
Data source: Ref. (Achenbach, 1977)
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
Data source: Ref. (Achenbach, 1977)
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⁄
𝑥𝑘 𝑐⁄ 𝑏𝑎𝑠𝑒
]𝐿𝑊𝐶
[𝑥𝑘 𝑐⁄
𝑥𝑘 𝑐⁄ 𝑏𝑎𝑠𝑒
]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⁄
𝑥𝑘 𝑐⁄ 𝑏𝑎𝑠𝑒
]𝑉∞
= 0.4286 + 0.0044139 ∙ 𝑉∞ (3-3)
[𝑥𝑘 𝑐⁄
𝑥𝑘 𝑐⁄ 𝑏𝑎𝑠𝑒
]𝐿𝑊𝐶
= 0.5714 + 0.2457 ∙ 𝐿𝑊𝐶 + 1.2571 ∙ 𝐿𝑊𝐶2 (3-4)
[𝑥𝑘 𝑐⁄
𝑥𝑘 𝑐⁄ 𝑏𝑎𝑠𝑒
]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
Figure 4-4. Clean cylinder heat transfer - ReD = 2×105
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.
Figure 4-5. Clean cylinder heat transfer - ReD = 3×105
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
2
2.5
3
0 30 60 90 120 150
Fr =
Nu
/sq
rt(R
e)
Azimuth Angle, deg
Ref CleanC7 - 120 sC8 - 90 sC9 - 60 sC10 - 30 s
0
0.5
1
1.5
2
2.5
3
0 30 60 90 120 150
Fr =
Nu
/sq
rt(R
e)
Angle, deg
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.
Figure 4-8. Comparison of heat transfer on ice roughened cylinder surface - ReD = 2×105
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
0.5
1
1.5
2
2.5
3
0 30 60 90 120 150
Fr =
Nu
/sq
rt(R
e)
Angle, deg
Ref CleanC3 - 120sC4 - 90sC5 - 60sC6 - 30s
0
0.5
1
1.5
2
2.5
3
0 30 60 90 120 150
Fr =
Nu
/sq
rt(R
e)
Azimuth Angle, deg
Ref CleanC7 - 120 sC8 - 90 sC9 - 60 sC10 - 30 s
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.
Figure 4-9. Comparison of heat transfer on ice roughened cylinder surface - ReD = 3×105
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
0.5
1
1.5
2
2.5
3
0 30 60 90 120 150
Fr =
Nu
/sq
rt(R
e)
Angle, deg
Ref CleanC3 - 120sC4 - 90sC5 - 60sC6 - 30s
0
0.5
1
1.5
2
2.5
3
0 30 60 90 120 150
Fr =
Nu
/sq
rt(R
e)
Azimuth Angle, deg
Ref CleanC7 - 120 sC8 - 90 sC9 - 60 sC10 - 30 s
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
2
4
6
8
10
12
0% 2% 4% 6% 8% 10% 12% 14% 16% 18% 20%
Fro
ssli
ng
Nu
mb
er,
Fr=
Nu
/Re
1/2
Dimensionless Surface Distance, s/c
NASA Clean
LEWICE R1
LEWICE R2
AERTS R1
AERTS R2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0% 2% 4% 6% 8% 10% 12% 14% 16% 18% 20%
Ro
ug
hn
ess H
eig
ht,
mm
Dimensionless Surface Distance, s/c
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
2
4
6
8
10
12
0% 2% 4% 6% 8% 10% 12% 14% 16% 18% 20%
Fro
ssli
ng
Nu
mb
er,
Fr=
Nu
/Re
1/2
Dimensionless Surface Distance, s/c
NASA Clean
LEWICE R10
LEWICE R5
AERTS R10
AERTS R5
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0% 2% 4% 6% 8% 10% 12% 14% 16% 18% 20%
Ro
ug
hn
ess H
eig
ht,
mm
Dimensionless Surface Distance, s/c
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
2
4
6
8
10
12
0% 2% 4% 6% 8% 10% 12% 14% 16% 18% 20%
Fro
ssli
ng
Nu
mb
er,
Fr=
Nu
/Re
1/2
Dimensionless Surface Distance, s/c
NASA Clean
LEWICE R9
LEWICE R3
AERTS R9
AERTS R3
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0% 2% 4% 6% 8% 10% 12% 14% 16% 18% 20%
Ro
ug
hn
es
s H
eig
ht,
mm
Dimensionless Surface Distance, s/c
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
2
4
6
8
10
12
0% 2% 4% 6% 8% 10% 12% 14% 16% 18% 20%
Fro
ssli
ng
Nu
mb
er,
Fr=
Nu
/Re
1/2
Dimensionless Surface Distance, s/c
NASA Clean
LEWICE R6
LEWICE R9
AERTS R6
AERTS R9
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0% 2% 4% 6% 8% 10% 12% 14% 16% 18% 20%
Ro
ug
hn
es
s H
eig
ht,
mm
Dimensionless Surface Distance, s/c
LEWICE R6
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
2
4
6
8
10
12
0% 2% 4% 6% 8% 10% 12% 14% 16% 18% 20%
Fro
ssli
ng
Nu
mb
er,
Fr=
Nu
/Re
1/2
Dimensionless Surface Distance, s/c
NASA Clean
LEWICE R3
LEWICE R2
AERTS R3
AERTS R2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0% 2% 4% 6% 8% 10% 12% 14% 16% 18% 20%
Ro
ug
hn
es
s H
eig
ht,
mm
Dimensionless Surface Distance, s/c
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.
Figure 4-17. Effect of time (2)
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.
0
2
4
6
8
10
12
0% 2% 4% 6% 8% 10% 12% 14% 16% 18% 20%
Fro
ssli
ng
Nu
mb
er,
Fr=
Nu
/Re
1/2
Dimensionless Surface Distance, s/c
NASA Clean
LEWICE R0
LEWICE R10
AERTS R0
AERTS R10
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0% 2% 4% 6% 8% 10% 12% 14% 16% 18% 20%
Ro
ug
hn
es
s H
eig
ht,
mm
Dimensionless Surface Distance, s/c
LEWICE R0
LEWICE R10
AERTS R10
0
2
4
6
8
10
12
0% 2% 4% 6% 8% 10% 12% 14% 16% 18% 20%
Fro
ssli
ng
Nu
mb
er,
Fr=
Nu
/Re
1/2
Dimensionless Surface Distance, s/c
NASA Clean
LEWICE R9
LEWICE R7
AERTS R9
AERTS R7
0
0.2
0.4
0.6
0.8
1
1.2
0% 2% 4% 6% 8% 10% 12% 14% 16% 18% 20%
Ro
ug
hn
ess H
eig
ht,
mm
Dimensionless Surface Distance, s/c
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.
Figure 4-18. Effect of time (3)
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
2
4
6
8
10
12
0% 2% 4% 6% 8% 10% 12% 14% 16% 18% 20%
Fro
ssli
ng
Nu
mb
er,
Fr=
Nu
/Re
1/2
Dimensionless Surface Distance, s/c
NASA Clean
LEWICE R8
LEWICE R4
LEWICE R3
AERTS R8
AERTS R4
AERTS R3
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0% 2% 4% 6% 8% 10% 12% 14% 16% 18% 20%
Ro
ug
hn
es
s H
eig
ht,
mm
Dimensionless Surface Distance, s/c
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
Data source: Ref. (Achenbach, 1977)
Figure 5-4. Reference rough cylinder heat transfer in Fr – 0.9 mm roughness
Data source: Ref. (Achenbach, 1977)
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
Data source: Ref. (Healzer, Moffat, & Kays, 1974)
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
Dimensionless Surface Distance, s/c
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
∞
Dimensionless Surface Distance, s/c
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
LWC=1.0, MVD=20, Temp=-13.3°C, Time=360 s
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.
(a) V=58.1 m/s, chord=0.53 m, Re=2.1e+06, AOA=4.0
LWC=1.3, MVD=20, Temp=-16.6°C, Time=480 s
Figure 6-5. Reference ice shapes from Olsen’s Experiment (cold regime)
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(b) V=58.1 m/s, chord=0.53 m, Re=2.1e+06, AOA=4.0
LWC=1.3, MVD=20, Temp=-13.9°C, Time=480 s
(c) V=93.9 m/s, chord=0.53 m, Re=3.3e+06, AOA=4.0
LWC=1.1, MVD=20, Temp=-16.0°C, Time=372 s
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
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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.
(a) V=58.1 m/s, chord=0.53 m, Re=2.1e+06, AOA=4.0
LWC=1.3, MVD=20, Temp=-9.4°C, Time=480 s
(b) V=58.1 m/s, chord=0.53 m, Re=2.1e+06, AOA=4.0
LWC=1.3, MVD=20, Temp=-6.6°C, Time=480 s
Figure 6-6. Reference ice shapes from Olsen’s Experiment (warm regime)
163
(c) V=58.1 m/s, chord=0.53 m, Re=2.1e+06, AOA=4.0
LWC=1.3, MVD=20, Temp=-3.9°C, Time=480 s
(d) V=58.1 m/s, chord=0.53 m, Re=2.1e+06, AOA=4.0
LWC=1.3, MVD=20, Temp=-2.8°C, Time=480 s
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.
(a) V=85.1 m/s, chord=0.25 m, Re=1.4e+06, AOA=0.0
LWC=1.0, MVD=20, Temp=-11.8°C, Time=360 s
Figure 6-7. Example ice shape matching comparisons
165
(b) V=85.1 m/s, chord=0.25 m, Re=1.4e+06, AOA=0.0
LWC=1.4, MVD=20, Temp=-12.5°C, Time=360 s
(c) V=85.1 m/s, chord=0.25 m, Re=1.4e+06, AOA=1.0
LWC=1.8, MVD=20, Temp=-8.2°C, Time=225 s
(d) V=63.0 m/s, chord=0.61 m, Re=2.6e+06, AOA=0.0
LWC=2.0, MVD=20, Temp=-10.0°C, Time=600 s
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
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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.
167
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.
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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.
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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
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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
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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
196
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
197
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
200 RPMExp. 9.8BEMT 8.4
300 RPMExp. 20.0BEMT 18.9
400 RPMExp. 33.1BEMT 33.6
470 RPMExp. 44.5BEMT 46.4
198
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
199
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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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
Table B-2. AERTS ICE2 Iced Airfoil Polar Data
AERTS ICE2, Ref. Olsen S-69
AOA Cd_wake Cd_3d Cl Cm L/D Cd_HPC Cd_Ref
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
Table B-3. AERTS ICE3 Iced Airfoil Polar Data
AERTS ICE3, Ref. Olsen O-8
AOA Cd_wake Cd_3d Cl Cm L/D Cd_HPC Cd_Ref
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
AOA Cd_wake Cd_3d Cl Cm L/D Cd_HPC Cd_Ref
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
Table B-5. AERTS ICE4 Iced Airfoil Polar Data
AERTS ICE4, Ref. Olsen S-33
AOA Cd_wake Cd_3d Cl Cm L/D Cd_HPC Cd_Ref
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