The Pennsylvania State University

The Graduate School

College of Engineering

AN INVESTIGATION OF THE AERODYNAMICS OF MINIATURE

TRAILING-EDGE EFFECTORS APPLIED TO ROTORCRAFT

A Thesis in

Aerospace Engineering

by

Bernardo Augusto de Oliveira Vieira

 2010 Bernardo Augusto de Oliveira Vieira

Submitted in Partial Fulfillment of the Requirements for the Degree of

Master of Science

August 2010

The thesis of Bernardo Augusto de Oliveira Vieira was reviewed and approved* by the following:

Mark D. Maughmer Professor of Aerospace Engineering Thesis Advisor

Jacob W. Langelaan Assistant Professor of Aerospace 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

The aerodynamics of Miniature Trailing-Edge Effectors (MiTEs) is explored in many aspects with regards to their applicability to rotorcraft. MiTEs are active Gurney flaps that have the ability to modify the lift and moment characteristics of the blades around the rotor disk. MiTEs hold strong potential to be used as active devices to improve performance, reduce vibrations, and reduce noise of rotors. The present work explores the static and unsteady aerodynamic performance of MiTEs by the aid of experimental, numerical, and analytical methods.

A static experimental investigation of Gurney flaps is undertaken at The

Pennsylvania State University Low-Speed, Low-Turbulence Wind Tunnel. Aerodynamic results are obtained for three distinct rotorcraft airfoils equipped with Gurney flaps of various sizes and placed at different chordwise locations. The effects of Gurney flaps are found to be very dependent on the combination of their height and location, as well as on the airfoil shape. It is observed that when positioned upstream from the trailing edge, the

Gurney flap can become sometimes ineffective and provide a decrease in the cl,max of the airfoil, suggesting that great care must be taken into sizing these devices.

An experimental investigation of oscillating upstream-located MiTEs is conducted at the Mid-Sized Wind Tunnel at Penn State. Measured unsteady aerodynamic data prove the effectiveness of MiTEs in providing variations in the forces and moments of the airfoil. The amplitude and phase lag of the lift results are in good agreement with the trends predicted by unsteady linear theory. In some cases, however, the occurrence of non-linear effects is observed. These effects are believed to be caused by vortex shedding

iv in the lower surface of the airfoil, and seem to be aggravated as the frequency of deployment increases.

Analysis of available computational fluid-dynamic (CFD) predictions on upstream MiTEs indicates the formation and convection of an unsteady vortex in the lower surface of the airfoil, right after MiTE deployment. This disturbance can introduce non-harmonic components in the aerodynamic response, substantially affecting the loads and complicating the analysis.

In order to account for these effects during routine helicopter performance and design studies, available CFD results are used to develop a reduced-order, less computer- intensive model based on indicial concepts. The model extends a work previously done for trailing-edge MiTEs by incorporating a vortex model to predict the unsteady lift of upstream MiTEs. A physics-based approach is adopted to minimize the number of constants and improve overall generality. The results from the unsteady-lift model are compared with CFD for different airfoils, MiTE deployment schedules, MiTE chordwise positions, and Mach numbers. Very good agreement is shown for a wide range of conditions that are typical of rotorcraft. Different model constants and correlations may have to be considered in order to improve the predictions for different airfoil shapes.

v

TABLE OF CONTENTS

LIST OF FIGURES ...... vii

LIST OF TABLES ...... xiii

LIST OF SYMBOLS ...... xiv

ACKNOWLEDGEMENTS ...... xvi

Chapter 1 Introduction...... 1 1.1 Introduction and Motivation ...... 1 1.2 MiTE Applications to Rotorcraft ...... 3 1.3 Research Objectives ...... 8

Chapter 2 Background and Literature Review ...... 10 2.1 Gurney Flaps ...... 10 2.2 MiTEs ...... 21

Chapter 3 Static Wind Tunnel Investigation...... 33 3.1 Wind tunnel description and validation ...... 34 3.2 Model description ...... 38 3.3 Data acquisition system ...... 38 3.4 Results ...... 39 3.5 Conclusions ...... 55

Chapter 4 Unsteady Wind Tunnel Investigation ...... 57 4.1 Previous efforts ...... 58 4.2 Wind Tunnel Description ...... 60 4.3 Model and acquisition system ...... 61 4.4 Experimental Results ...... 64 4.4.1 Static Verification ...... 64 4.4.2 Dynamic MiTEs ...... 68 4.5 Comparison with unsteady aerodynamic model ...... 79 4.6 Conclusions ...... 84

Chapter 5 CFD Investigation ...... 86 5.1 Flow Physics ...... 88 5.2 Overview of Results ...... 96 5.3 Conclusions ...... 101

vi

Chapter 6 Unsteady Aerodynamic Modeling ...... 103 6.1 Indicial Methods ...... 104 6.1.1 Incompressible Flow ...... 105 6.1.2 Subsonic Compressible Flow ...... 108 6.2 Unsteady Aerodynamic Model for MiTEs ...... 110 6.2.1 Circulatory Lift ...... 114 6.2.2 Apparent Mass Lift ...... 116 6.2.3 Vortex Lift ...... 119 6.3 MiTE Model Results ...... 123 6.3.1 Effect of Deployment Time ...... 128 6.3.2 Effect of Mach number ...... 133 6.3.3 Retraction Cases ...... 135 6.3.4 Sinusoidal Deployments ...... 137 6.3.5 Effects of airfoil shape and MiTE position ...... 141 6.4 Summary ...... 145

Chapter 7 Conclusions ...... 147 7.1 Summary of Results ...... 147 7.1.1 Static Gurney Flap Experiments ...... 147 7.1.2 Unsteady MiTEs Experiments ...... 148 7.1.3 Unsteady Aerodynamic Modeling ...... 149 7.2 Conclusions ...... 150 7.3 Recommendations for Future Work ...... 151 7.3.1 Experimental and Numerical Efforts ...... 151 7.3.2 Unsteady MiTE Modeling ...... 152

References ...... 154

vii LIST OF FIGURES

Figure 1.1. Complex flowfield around a helicopter in forward flight [1]...... 1

Figure 1.2. Typical configurations of a Gurney flap and a MiTE [3]...... 2

Figure 1.3. Definition of the helicopter rotor stall boundary [17]...... 4

Figure 1.4. Interaction of tip vortices with the rotor disk for level and descending flights [19]...... 6

Figure 1.5. Representative power required breakdown for a helicopter versus airspeed [21]...... 7

Figure 2.1. Hypothesized flow physics of a Gurney flap [15]...... 10

Figure 2.2. Flow Structure downstream of a Gurney flap [27]...... 12

Figure 2.3. Pressure distributions for the S903 airfoil at cl,max with and without Gurney flaps [16]...... 14

Figure 2.4. Aerodynamic characteristics of a S903 airfoil equipped with Gurney flaps of various heights positioned at the trailing edge [16]...... 17

Figure 2.5. Lift to drag ratio versus lift coefficient for the S903 airfoil equipped with Gurney flaps of various heights...... 17

Figure 2.6. Aerodynamic characteristics of a S903 airfoil equipped with Gurney flaps positioned at various chordwise locations [16]...... 19

Figure 2.7. Trailing edge flow structure of a GU 25-5(11)8 airfoil with a 0.01c high Gurney flap located at 0.80c at R = 1 x 106 and α = 4°...... 20

Figure 2.8. Predicted increase in lift coefficient for sinusoidal deployments of a MiTE positioned at the trailing edge of a S903 airfoil [6]...... 23

Figure 2.9. Lift amplitude for a MiTE positioned at the trailing edge at various deployments frequencies, free-stream conditions and compared to incompressible theory [6]...... 24

Figure 2.10. Lift phase for a MiTE positioned at the trailing edge at various deployments frequencies, free-stream conditions and compared to incompressible theory [6]...... 25

Figure 2.11. Predicted increase in lift coefficient for sinusoidal deployments of a MiTE placed at the chordwise position of 0.90c on a S903 airfoil [6]...... 27

viii

Figure 2.12. Lift coefficient for sinusoidal deployments of a MiTE placed at chordwise position of 0.90c of a VR-12 airfoil at M=0.45 [3]...... 27

Figure 2.13. Lift coefficient for sinusoidal deployments of a MiTE placed at different chordwise position on a VR-12 airfoil at M=0.40 [6]...... 28

Figure 2.14. MiTE configurations studied in [14]...... 31

Figure 3.1. Test section of The Pennsylvania State University Low-Speed, Low- Turbulence Wind Tunnel. View is facing downstream of the tunnel...... 35

Figure 3.2. Comparison of aerodynamic characteristics of the S805 airfoil measured in the low-speed wind tunnels at Pennsylvania State University and Delft University of Technology [16]...... 37

Figure 3.3. Increase in cl,max due to Gurney flaps of different heights and positioned at different chordwise positions of various airfoils at R = 1.0 x 106. . 40

Figure 3.4. Aerodynamic characteristics of the working section of a XV-15 tilt- rotor equipped with Gurney flaps at two Reynolds numbers...... 43

Figure 3.5. Lift-to-drag ratio for the XV-15‟s airfoil with and without Gurney flaps...... 43

Figure 3.6. Aerodynamic characteristics of a S408 airfoil equipped with Gurney flaps of different sizes positioned at various chordwise locations...... 46

Figure 3.7. Lift-to-drag ratio for the S408 airfoil with and without Gurney flaps. .. 46

Figure 3.8. Pressure distributions of the S408 airfoil comparing baseline airfoil and with Gurney flaps positioned at 0.90c...... 47

Figure 3.9. Aerodynamic characteristics of a S415 airfoil equipped with Gurney flaps of 0.010c height positioned at various chordwise locations...... 49

Figure 3.10. Pressure distributions at cl,max of the S415 airfoil with and without 0.01c high Gurney flaps positioned at several chordwise positions...... 50

Figure 3.11. Aerodynamic characteristics of a S415 airfoil equipped with Gurney flaps of 0.024c height positioned at various chordwise locations ...... 53

Figure 3.12. Lift-to-drag ratio for the S415 airfoil with and without Gurney flaps. .. 54

Figure 4.1. Wind tunnel results for a NACA 0012 airfoil equipped with 0.025c high MiTEs placed at 0.90c [52] compared with Theodorsen‟s theory [1]...... 59

Figure 4.2. Schematic drawing of the PSU Mid-Sized Wind Tunnel [50]...... 60

ix

Figure 4.3. S903 airfoil equipped with segmented MiTEs at the Mid-Sized Wind Tunnel test section. View is facing downstream of the tunnel...... 63

Figure 4.4. Static aerodynamic results for the S903 airfoil with and without Gurney flaps taken at two different wind tunnels...... 66

Figure 4.5. Normalized lift due to the ramp deployment of 0.019c high MiTEs positioned at 0.90c of a S903 airfoil...... 68

Figure 4.6. Deployment frequency breakdown for the experimental ramp cases. ... 70

Figure 4.7. Normalized lift response due to ramp deployments at different flow velocities for 0.019c high MiTEs positioned at 0.90c of a S903 airfoil...... 71

Figure 4.8. Smoothed lift response due to ramp deployments at different flow velocities...... 72

Figure 4.9. Oscillatory deployments at several frequencies for R = 1 x 106...... 73

Figure 4.10. Lift response due to MiTEs oscillating at f = 5 Hz and R = 1 x 106...... 74

Figure 4.11. Lift response due to MiTEs oscillating at f = 8 Hz and R = 1 x 106...... 75

Figure 4.12. Lift response due to MiTEs oscillating at f = 10 Hz and R = 1 x 106. ... 75

Figure 4.13. Lift response due to MiTEs oscillating at f = 12 Hz and R = 1 x 106. ... 76

Figure 4.14. Lift response due to MiTEs oscillating at f = 15 Hz and R = 1 x 106. ... 76

Figure 4.15. Lift response due to MiTEs oscillating at several frequencies with free-stream conditions: V = 113 ft/s and R = 1 x 106...... 77

Figure 4.16. Instantaneous MiTE heights of the cases with different oscillation frequencies and flow velocities...... 78

Figure 4.18. Comparison between the model and experiments for a ramp deployment at V = 77 ft/s (R=0.7x106 and M=0.07)...... 81

Figure 4.19. Comparison between the model and experiments for a ramp deployment at V = 135 ft/s (R=1.2x106 and M=0.12)...... 81

Figure 4.20. Comparison between the model and experiments for an oscillatory deployment with f = 5 Hz and V = 77 ft/s (R=0.7x106 and M=0.07)...... 82

Figure 4.21. Comparison between the model and experiments for an oscillatory deployment with f = 10 Hz and V = 113 ft/s (R=1.0x106 and M=0.10)...... 83

x

Figure 4.22. Comparison between the model and experiments for an oscillatory deployment with f = 8 Hz and V = 135 ft/s (R=1.2x106 and M=0.12)...... 84

Figure 5.1. Shapes of the airfoils in consideration...... 88

Figure 5.2. Normalized ∆cl results for different airfoils equipped with a 0.02c high MiTE after a half-sine ramp deployment at k = 10 (adapted from [51])...... 90

Figure 5.3. Selected time stations shortly after a nearly-inidicial MiTE deployment on the VR-7 airfoil...... 92

Figure 5.4. Pressure contours results for a VR-7 airfoil equipped with a 0.02c high MiTE located at 0.90c after a half-sine ramp deployment at k=10. The operating conditions are M = 0.3, R = 4 x 106, and α = 5° (adapted from [51])...... 94

Figure 5.5. Entropy contours for a VR-7 airfoil equipped with a 0.02c high MiTE located at 0.90c after a half-sine ramp deployment at k=10. The operating conditions are M = 0.3, R = 4 x 106, and α = 5° (adapted from [51])...... 95

Figure 5.6. Increase in lift due to sinusoidal MiTE deployments at three reduced frequencies for a VR-7 airfoil equipped with a 0.02c high MiTE positioned at 0.90c [51]...... 96

Figure 5.7. Effect of different reduced frequencies of MiTE deployments in the lift response of a VR-7 airfoil equipped with a 0.02c high MiTE positioned at 0.90c, operating at M=0.3 [adapted from 51]...... 97

Figure 5.8. Effect of different Mach numbers in the lift response of a VR-7 airfoil equipped with a 0.02c high MiTE positioned at 0.90c after a ramp deployment [adapted from 51]...... 98

Figure 5.9. Lift results for retracting MiTEs at different Mach numbers and reduced frequencies for a VR-7 airfoil equipped with a 0.02c high MiTE positioned at 0.90c [adapted from 51]...... 99

Figure 5.10. Lift results for deploying and retracting MiTEs at k=0.10 for the VR-7 airfoil operating at M=0.3 [adapted from 51]...... 100

Figure 5.11. Lift results for nearly-indicial MiTE deployments at three different angles of attack for a VR-7 airfoil equipped with a 0.02c high MiTE positioned at 0.90c [adapted from 51]...... 101

Figure 6.1. Wagner‟s and Küssner‟s functions for a step change in angle of attack...... 106

xi

Figure 6.2. Vortex lift modeling of the L-B dynamic stall model [77]...... 111

Figure 6.3. Breakdown of the indicial model into its three components...... 114

Figure 6.4. Vortex speed dependency on reduced frequency...... 121

Figure 6.5. Local reduced frequency of MiTE deployment for f = 17.2 Hz and μ = 0.4...... 126

Figure 6.6. Non-dimensional time necessary for MiTE deployment at f = 17.2 Hz and μ = 0.4...... 127

Figure 6.7. Model comparison with CFD results obtained for a VR-7 airfoil equipped with a MiTE positioned at 0.90c deploying through a half-sine at k=0.05 and M=0.3...... 130

Figure 6.8. Model comparison with CFD results obtained for a VR-7 airfoil equipped with a MiTE positioned at 0.90c deploying through a half-sine at k=0.1 and M=0.3...... 130

Figure 6.9. Model comparison with CFD results obtained for a VR-7 airfoil equipped with a MiTE positioned at 0.90c deploying through a half-sine at k=0.25 and M=0.3...... 131

Figure 6.10. Model comparison with CFD results obtained for a VR-7 airfoil equipped with a MiTE positioned at 0.90c deploying through a half-sine at k=0.50 and M=0.3...... 131

Figure 6.11. Model comparison with CFD results obtained for a VR-7 airfoil equipped with a MiTE positioned at 0.90c deploying through a half-sine at k=1.0 and M=0.3...... 132

Figure 6.12. Model comparison with CFD results obtained for a VR-7 airfoil equipped with a MiTE positioned at 0.90c deploying through a half-sine at k=10 and M=0.3...... 132

Figure 6.13. Model comparison with CFD results obtained for a VR-7 airfoil equipped with a MiTE positioned at 0.90c deploying through a half-sine at k=0.05 and M=0.5...... 134

Figure 6.14. Model comparison with CFD results obtained for a VR-7 airfoil equipped with a MiTE positioned at 0.90c deploying through a half-sine at k=0.25 and M=0.5...... 134

Figure 6.15. Model comparison with CFD results obtained for a VR-7 airfoil equipped with a MiTE positioned at 0.90c retracting at different speeds at M=0.3...... 136

xii

Figure 6.17. Time domain comparison between model and CFD results for a VR- 7 airfoil equipped with a MiTE positioned at 0.90c during sinusoidal deployment at k=0.25...... 139

Figure 6.18. Model comparison with CFD results obtained for a VR-7 airfoil equipped with a MiTE positioned at 0.90c for sinusoidal deployments at k=0.1 and M=0.3...... 140

Figure 6.19. Model comparison with CFD results obtained for a VR-7 airfoil equipped with a MiTE positioned at 0.90c for sinusoidal deployments at k=0.25 and M=0.3...... 140

Figure 6.20. Model comparison with CFD results obtained for a VR-7 airfoil equipped with a MiTE positioned at 0.90c for sinusoidal deployments at k=1.0 and M=0.3...... 141

Figure 6.21. Model comparison with CFD results obtained for a S902 airfoil equipped with a MiTE positioned at 0.88c deploying at different speeds at M = 0.3...... 142

Figure 6.22. Model comparison with CFD results obtained for a VR-12 airfoil equipped with a MiTE positioned at 1.0c for sinusoidal deployments at k=0.2 and M=0.4...... 144

Figure 6.23. Model comparison with CFD results obtained for a VR-12 airfoil equipped with a MiTE positioned at 0.9c for sinusoidal deployments at k=0.2 and M=0.4...... 144

xiii LIST OF TABLES

Table 3-1. Summary of static experimental data on Gurney flaps taken at the Penn State Low Speed, Low Turbulence Wind Tunnel...... 34

Table 4-1. Test matrix for the wind tunnel investigation...... 58

Table 4-2. Comparison on the specifications of the two wind tunnels at Penn State [50]...... 61

Table 6-1. Indicial response constants of the MiTE model...... 125

Table 6-2. Other parameters of the MiTE model...... 125

xiv LIST OF SYMBOLS

c airfoil chord length cl sectional lift coefficient cl,am apparent mass component of the sectional lift coefficient cl,circ circulatory component of the sectional lift coefficient cl,max maximum lift coefficient cl,vtx vortex component of the sectional lift coefficient cP pressure coefficient cT thrust coefficient

Dvtx,decay exponential vortex decay f frequency of deployment hMiTE MiTE or Gurney flap total height k reduced frequency, ωc/(2V)

L/D lift-to-drag ratio

M Mach number nexp exponent of the vortex speed in the vortex decayment function

R Reynolds number based on chord and freestream conditions s Distance traveled in semi-chords (reduced time), 2Vt/c sDEP non-dimensional time (reduced time) for MiTE deployment sOSC non-dimensional time (reduced time) for complete MiTE

oscillation cycle

xv sVTX non-dimensional time necessary for the vortex to reach the trailing

edge of the airfoil t time

Tdecay vortex decayment time constant

Tvtx,decay vortex decayment function

V local velocity

Vvtx speed of the vortex x chordwise coordinate

α airfoil angle of attack

β Prandtl-Glauert compressibility correction, 1 − 푀2

δ MiTE instantaneous height

δvtx deployment height of the MiTE during vortex decayment

μ advance ratio

σ helicopter solidity

l, vtx vortex indicial function

ω angular frequency of deployment, 2πf

Subscripts circ, nc, vtx circulatory, non-circulatory, vortex dep, ret deployment, retraction

xvi ACKNOWLEDGEMENTS

I would like to dedicate this thesis to my parents, Levindo and Lúcia. This accomplishment would not have been possible without their love and guidance throughout all my life. They have always given me unconditional support to pursue my dreams, and I am eternally grateful.

I would also like to express my deepest gratitude to my advisor and mentor

Dr. Mark Maughmer. He deserves all the credit for everything I learned. Thanks for giving me the opportunity of being your student. Through your patience, extensive knowledge, and guidance, I have grown both academically and personally.

I would like to thank the Penn State Vertical Lift Research Center of Excellence for providing the funding for this project, as well as the Technical Monitor

Dr. Preston Martin from Army/LaRC.

I would like to acknowledge Dr. Jack Langelaan, for taking the time to read this manuscript and provide valuable comments.

Furthermore, I would like to thank James Coder, for all the CFD calculations performed and the many discussions on the physics of MiTEs. We have learned a lot together during this work.

I would also like to thank Mike Kinzel for his many inputs in the beginning of the research, Amandeep Premi for helping set up the experimental tests, and my colleagues,

Dave Maniaci, Julia Cole, and Penelope Campbell, who indirectly contributed for the completion of this study. Also, I would like to thank all my friends here in State College for their support.

xvii Finally, and most especially, I must thank Laura for all the love and care throughout all these years. For many times, she was the one that kept me motivated and with strength to pursue my goals. At this last month, her support and understanding were essential during the final writing of this thesis.

Chapter 1

Introduction

1.1 Introduction and Motivation

Helicopters operate in a much more complex environment than do fixed-wing

aircraft. The presence of unsteady flow, asymmetries of airloads in the retreating and

advancing sides of the rotor, and a complex three-dimensional wakes are just examples of

the many challenges with which the designer must deal (Figure 1.1). As in almost all

areas of technology, there has been an increasing need for more capable, efficient,

economical, and environmentally friendly vehicles. The next generation helicopters will

call for improvements that include higher payload capabilities, increased range and

Figure 1.1. Complex flowfield around a helicopter in forward flight [1].

2 endurance, better maneuverability, higher forward speeds, reduced vibration, and reduced

noise. The achievement of these goals is very dependent on enhancements in the

aerodynamic performance of rotors, and for this purpose great potential is seen on the

implementation of active devices.

Miniature trailing-edge effectors (MiTEs) have been considered by many

researchers as being a feasible and effective solution for active load control in various

applications [2-14]. MiTEs are essentially deployable Gurney flaps that have the ability

to modify the lift and moment characteristics of the blade around the rotor disk. Typical

configurations of both Gurney flaps and MiTEs are shown in Figure 1.2. A Gurney flap is

simply a flat plate, typically with the height of up to around 2 percent chord (0.02c),

mounted normal to the airfoil surface near the trailing edge [15]. It was first introduced

by Indy car race driver Dan Gurney, with the goal of increasing the force on the

download wings and consequently increase the car‟s cornering speeds. Gurney flaps with

a height of 0.02c have been shown to increase the maximum lift coefficient of an airfoil

by up to 30-percent [16]. As opposed to Gurney flaps, MiTEs can be deployed as needed

and, therefore, have the potential to increase rotor performance [2-5] and/or reduce rotor

vibration [13,14] and noise, for instance. Compared to other conventional control

Figure 1.2. Typical configurations of a Gurney flap and a MiTE [3].

3 devices, MiTEs have the advantage of having smaller size and less inertia and, therefore, have lower actuation power requirements [5].

The goal of the present research is to expand current understanding of the aerodynamics of Miniature Trailing-Edge Effectors (MiTEs) and describe the development of an unsteady aerodynamic model based on indicial methods. Both experimental and computational fluid dynamic results are used as a basis to create the model. Wind tunnel investigations are also performed to increase the database of static

Gurney flap aerodynamic performance. The focus of the research is on rotorcraft-related applications, although the results should also be pertinent to any other area in which such active devices can be beneficial.

1.2 MiTE Applications to Rotorcraft

MiTEs demonstrate great potential to help solve many of the challenges of the future helicopter at all conditions of its flight envelope.

The concept of a helicopter rotor stall boundary is presented in Figure 1.3, where the forward speed is limited by either the retreating or advancing blades, depending on the blade loading, CT/σ [17]. At low blade loading, the forward speed limit is governed by the advancing blade Mach number, which is temperature dependent. At low temperatures, the speed of sound is lower and, therefore, the critical Mach number is reached at lower advance ratios. This boundary is often called the soft boundary, as many rotors do not have enough power to overcome increased drag due to drag divergence and fuselage drag. With the use of new engines and advanced tip shapes, however, some

4 helicopters are now able to surpass this limit and the occurrence of shock-stall can result in severe torsional vibration on the rotor through an event so-called Mach tuck. At high blade loading, the occurrence of retreating blade dynamic stall limits the advance ratio.

This stall boundary typically represents the high-altitude, heavy-lift, hot-day operation [18]. It is accompanied by a large increase in pitching moment that result in high torsional loads and the possibility of flutter instabilities. These could rapidly consume the fatigue life of the rotor blades and the control system components such as pitch-links and swashplates [17]. These instabilities are associated with negative aerodynamic damping in pitch that is a direct consequence of dynamic stall. In some aircraft, the event of dynamic stall can be avoided by a system that monitors the high loads induced by stall. Other aircraft, however, are very sensitive to the onset of stall, experiencing abrupt changes in attitude that could potentially lead to a loss of control [18].

Figure 1.3. Definition of the helicopter rotor stall boundary [17].

5 It is concluded that, at the boundaries of the rotor flight envelope, the events of shock stall or dynamic stall can occur leading to high levels of vibration and increased rotor drag. Being able to prevent these events indicate one of the challenges of designing airfoils for rotorcraft applications. At the advancing side of the rotor disk, high Mach number conditions suggest the design of thin airfoils suitable to transonic conditions; at the retreating side, high operating lift coefficients at moderate Mach numbers require airfoils with high maximum lift coefficients (cl,max). In addition, there is an extremely limiting constraint placed on the value of the airfoil pitching-moment coefficient. These contradicting requirements dictate that only a very compromised design is possible, but also elucidates a room of opportunities for active design solutions.

MiTEs can be deployed at the retreating side of the disk, delivering the necessary increase in airfoil‟s cl,max, and somewhat relaxing the high-lift requirements over currently compromised rotorcraft airfoils. In other words, an hybrid active/passive approach would be applied in which MiTEs would assure the attainment of high cl,max at the retreating side of the rotor, and less compromised transonic airfoils would assure better performance at the advancing side of the rotor. Overall, both shock-stall and dynamic stall boundaries would be expanded until more extreme conditions occur, such as higher forwards speeds or CT/σ, for instance.

Even at the core of the operation envelope of helicopters, MiTEs can turn out to be very beneficial as they can help alleviate both rotor induced vibration and noise. One of the highest levels of vibration and noise found on helicopter rotors are caused by the so-called blade-vortex interactions (BVI) [1, 19]. Trailing vortices emanating from the preceding blades induce rapid variations in the downwash field of the following blades,

6

Figure 1.4. Interaction of tip vortices with the rotor disk for level and descending flights [19].

causing unsteady fluctuations on their lift. The BVI problem is more pronounced at low

forward speed conditions, especially during descending flight where the trailing rotor

wake is forced into the rotor disk plane (Figure 1.4). Being able to attenuate these high

levels of vibration and noise is essential for the desired “jet smooth ride” conditions [20].

There have been a number of investigations on the use of active rotor devices for

vibration control, including individual blade control (IBC), higher harmonic control

(HHC), active twist, active trailing-edge flaps and MiTEs. MiTEs again show great

promise as they are able to deliver the required changes in lift and moment at the high

bandwidths necessary for vibration control, and with low actuation power requirements

compared to other devices [4, 8, 14].

Another possible application for rotorcraft is the use of spanwise segmented

MiTEs, optimally deployed to minimize the induced power on the rotor. Great

performance gains could be achieved as the induced power represents a large component

of the total power required of the helicopter. A breakdown of the power curve can be

7

Figure 1.5. Representative power required breakdown for a helicopter versus airspeed [21].

seen in Figure 1.5. The induced power is the highest contribution at hover and then

initially decreases with airspeed just like in a fixed-wing aircraft. At higher airspeeds,

however, the increased asymmetry between the advancing and retreating side of the rotor

and the necessity of maintaining trim results in an increased non-optimum lift distribution

on the rotor disk. This phenomenon leads to less efficient spanwise loadings in the blades

and consequently increases the induced power at high speeds. This is added by the fact

that the rotor needs to produce more and more lift as it starts to tilt forward to meet its

propulsive requirements. Both these events contribute to an increase in the induced power

at high speeds as presented in Figure 1.5. As already mentioned, segmented MiTEs have

the potential to help mitigate these problems by tailoring the lift distribution along the

span of the blades, maintaining the optimum loading at all flight conditions.

8 The applications for MiTEs are not restricted to those mentioned above. Every condition in which it is beneficial to control changes in lift and moment on the rotor can be a potential utilization for MiTEs. For non-rotorcraft applications, MiTEs have been studied as means of control of tailless aircraft [7], to mitigate flutter [22], and to alleviate wake vortex [10].

1.3 Research Objectives

The goal of the present research is to use both experimental and computational methods to expand current understanding of MiTEs and their application to rotorcraft, and also to develop tools that can be incorporated into comprehensive codes to predict the aerodynamics of these devices.

Static wind-tunnel investigations are performed in order to expand current experimental database of Gurney flaps. Data for different airfoils, equipped with different

Gurney flap sizes, and placed at several chordwise positions are generated. The use of a common facility to provide the measurements is of great value in order to evaluate the dependency of the results on the airfoil shape. These data are extremely important for helping sizing these devices for many applications, as well as to be used as validation of

CFD predictions.

A wind tunnel investigation of oscillating MiTE is also conducted. Although mainly aimed at evaluating the performance of the actuating system, aerodynamic data is also measured by the use of a 6-component load balance. This test can provide good

9 information about the unsteady aerodynamics of MiTEs at various frequencies and could prove the effectiveness of these devices as to control the forces and moments in an airfoil.

CFD predictions are used to better understand the physics of MiTEs positioned upstream from the trailing edge, and quantify the effects of the non-harmonic disturbances on the aerodynamic loads. The CFD data are used to develop an unsteady lift model that is able to account for those effects. Following the work done in [3, 5], an indicial, physics-based methodology is applied, and a systematic set of numerical results from CFD used as a guide to develop a generalized MiTE unsteady aerodynamic model.

Chapter 2 Background and Literature Review

2.1 Gurney Flaps

The mechanisms in which Gurney flaps produce lift have been extensively

studied for the past 40 years. The flow physics of Gurney flaps were first hypothesized by

Liebeck [15] and are presented in Figure 2.1. A short separated region with increased

pressure is formed upstream from the Gurney flap, and two counter-rotating vortices are

formed downstream of it. Tuft flow visualizations on a Newman airfoil equipped with a

1.5% chord Gurney flap indicated significant turning of the flow over the back side of the

flap suggesting that the vortices acted as to increase the effective camber of the airfoil.

Later on, similar flow features were identified in a water-tunnel test on a NACA 0012

airfoil equipped with several different Gurney flap configurations at very low Reynolds

Figure 2.1. Hypothesized flow physics of a Gurney flap [15].

11 numbers (R = 8.6 ∙ 103) [23]. A numerical study presented in [24] attributed the Gurney flap‟s increase in lift to the shift in the location of the Kutta condition. It was also observed that the low pressure behind the Gurney flap makes the flow turn downward, and increases its capability to overcome the adverse pressure gradient in the upper surface of the airfoil, reducing its likelihood to separate. These numerical results were compared later on with wind-tunnel experiments and showed good agreement [25].

Another relevant study is presented in [26], and comprises an experimental investigation of the effects of Gurney flaps with different heights. It was found that the effectiveness of Gurney flaps is related to the boundary-layer thickness at the lower surface trailing edge of the airfoils. When their height did not exceed the boundary-layer thickness, Gurney flaps caused little increase in drag and, therefore, an increase in the lift-to-drag ratio (L/D) of the airfoil was possible. It was also observed that the two attached counter-rotating vortices behave as a fluid-extension of the airfoil, allowing for an off-the-surface pressure recovery and, therefore, a finite pressure difference between trailing-edge upper and lower surfaces.

A more complete experimental study of the flowfield near the trailing edge of a wing equipped with a Gurney flap is presented in [27]. Measurements include surface pressures, forces and velocities by use of laser Doppler anemometry (LDA). It was found that the instantaneous flow structure behind a Gurney flap consists of a wake of alternately shed vortices, similar to a von Kármán vortex street. When time-averaged, the flow is seen as two counter-rotating vortices, just as first hypothesized in [15]. Both time- averaged and the instantaneous flow structures are presented in Figure 2.2. The shedding frequency of the vortices was found to relate to the height of the Gurney flap and the

12 boundary-layer thickness near the trailing-edge of the airfoil. These vortices were found to be responsible for sustaining the low pressure downstream of the Gurney flap.

a) Time-averaged LDA results

b) Instantaneous smoke-flow visualization

Figure 2.2. Flow Structure downstream of a Gurney flap [27].

Based on the research described, the flow physics of Gurney flaps seem to be generally understood. With the recent increase interest in both Gurney flaps and MiTEs, however, more detailed information was necessary to help sizing these devices. Several studies have been made to try to quantify the aerodynamic loads and their dependency on

Gurney flap size, geometry and flow conditions.

13 In general, Gurney flaps have been shown to increase the lift and pitching moment of airfoils, but with some penalties in drag. This have been suggested by previous experimental studies utilizing a Newman airfoil [15], a NACA 4412 airfoil [25],

LA203A and Gottingen 797 airfoils [26], NACA 0011 and GA(W)-2 airfoils [29], an

E 423 airfoil [27], a modified LS(1)-0413 airfoil [28], a GU25-5(11)-8 [30], a NACA

0012 airfoil [27, 31], a S903 airfoil [3, 16], and a S809 airfoil [32]. The wind-tunnel investigation on the S903 airfoil deserves special attention due to its high quality, two- dimensional force and moment data, available along with pressure distributions and wake surveys.

The pressure distributions for the S903 airfoil equipped with a 0.02c high Gurney flap are compared with the baseline airfoil for the maximum lift condition in Figure 2.3

[3, 16]. The cl,max‟s are 1.15, 1.35 and 1.50 for the baseline airfoil, and for the Gurney flaps located at 0.90c and trailing-edge, respectively. The Gurney flaps considerably increase the pressures upstream from them, being one of the main reasons for the increase in maximum attainable lift. Downstream from the flap, the pressure drops significantly becoming very similar for all three cases at the trailing edge. At lower angles of attack, this downstream pressure due to the Gurney flap can drop even below the baseline pressures [16]. Other contributions for the increased lift are due to an overall delay in the pressure recovery, accompanied to lower pressures compared to the baseline case, and a postponement in the movement of trailing-edge separation point. The reasons for the difference in the maximum lift between the two Gurney flap cases can also be inferred from the pressure distributions. Up to about 0.85c, the upstream flap influences the pressures ahead of it as much as the trailing-edge Gurney flap, not being able to increase

14 the pressures even further. Therefore, this does not help compensate the earlier drop in the pressure that is inherent of an upstream positioned Gurney flap. The result is a loss of lift production from the flap location up to the trailing edge. Slightly higher pressures during the upper surface pressure recovery also contribute to a lower cl,max.

Figure 2.3. Pressure distributions for the S903 airfoil at cl,max with and without Gurney flaps [16].

The lift, drag, and pitching-moment coefficients of a S903 airfoil equipped with

Gurney flaps of various heights are presented in Figure 2.4 [3, 16]. Compared to the baseline configuration, the values of the maximum lift coefficients increase substantially for all cases, being about 9%, 16% and 29% higher for the 0.005c, 0.010c and 0.020c

15 high Gurney flaps, respectively. As first noticed in [26], the effectiveness of the Gurney flap is highly dependent on the boundary-layer thickness. As the angle of attack increases, the boundary layer becomes thinner and the Gurney flap gradually improves its effectiveness. On the contrary, when angles of attack become low enough, the Gurney flap does not affect the flowfield and the loads gradually converge into the baseline ones

[16]. Gurney flaps usually cause an increase in the nose-down pitching moment and in the drag coefficient, except at high lift coefficients, condition in which the drag can become lower than the baseline. The Gurney flaps postpone the movement of both transition and separation points on the upper surface of the airfoil until higher lift coefficients, allowing for lower drag at these conditions. The lift-to-drag ratio (L/D) versus the lift coefficient is presented in Figure 2.5. As the Gurney flaps increase in height, the maximum L/D generally decreases, but occur at a higher cl. At a value of cl of

1.2 or higher, the 0.02c high Gurney flap provides the best L/D.

16

a) Lift coefficient vs. angle of attack

b) Pitching-moment coefficient vs. angle of attack

17

c) Lift coefficient vs. drag coefficient

Figure 2.4. Aerodynamic characteristics of a S903 airfoil equipped with Gurney flaps of various heights positioned at the trailing edge [16].

Figure 2.5. Lift to drag ratio versus lift coefficient for the S903 airfoil equipped with Gurney flaps of various heights.

18 For MiTE applications, it is necessary to be able to fully store the device inside the airfoil during full retraction; therefore, a likely solution is to place it at an upstream position where the airfoil has enough thickness. The effect of the Gurney flap chordwise location on the aerodynamic loads is presented in Figure 2.6 [3, 16]. The cl,max decreases about 8% and the cd increases an average of about 12% as the Gurney flap is moved from the trailing edge to 0.90c. The absolute values of cm also decrease, indicating that the overall effectiveness of the Gurney flap was reduced. These general results were also observed for the NACA 0012 airfoil [31], and the GU25-5(11)-8 airfoil [30]. For the present case, the drag coefficient seems to be more dependent on the Gurney flap height than its chordwise location.

a) Lift coefficient vs. angle of attack

19

b) Pitching-moment coefficient vs. angle of attack

c) Lift coefficient vs. drag coefficient

Figure 2.6. Aerodynamic characteristics of a S903 airfoil equipped with Gurney flaps positioned at various chordwise locations [16].

20 Another wind-tunnel investigation emphasizes the importance of a careful selection of the Gurney flap height and location in the airfoil surface to assure its effectiveness [32]. Aerodynamic measurements with a 6-component balance and a wake probe have been performed for the S809 airfoil equipped with Gurney flaps of different sizes, placed at different chordwise locations. An interesting result is obtained for a

0.011c high Gurney flap positioned at 0.90c, in which the maximum lift is decreased compared to the baseline airfoil. This loss of lift is then explained to be caused by flow reattachment before the trailing edge. This was identified in an earlier computational study on a GU 25-5(11)8 airfoil, and is presented in Figure 2.7 [33]. According to [33], this reattachment eliminates the shift in the Kutta condition, usually caused by the

Gurney flap, and results in a loss of lift due to the flap-generated separation bubble.

Figure 2.7. Trailing edge flow structure of a GU 25-5(11)8 airfoil with a 0.01c high Gurney flap located at 0.80c at R = 1 x 106 and α = 4°.

21 Other studies have been made to quantify the effects of mounting Gurney flaps at different angles [30, 34], and Gurney flaps with different shapes [23, 35, 36]. For these, a good review is presented in [36]. In general, it has been found that reducing the mounting angle of the Gurney flap reduces its effectiveness. Therefore, compared with the 90⁰ case, the Gurney flap provides less increase in lift, drag and nose-down pitching moment coefficients. Evaluating Gurney flaps with different shapes, it has been found that the drag produced by a regular Gurney flap can be dramatically reduced with saw-toothed or

Gurney flaps with holes. The penalty is a decrease in the lift augmentation. For the present study, a basic Gurney flap configuration is considered as it is understood that these modifications do not promote drastic changes in the flow physics. Later on, when the research reaches a more mature level, these should be further investigated and maybe considered as refinements of the concept.

2.2 MiTEs

As already mentioned, there are many advantages in actuating Gurney flaps. As active devices, they can be deployed when desired and therefore, have potential to increase the performance of rotors. Also, when deployed in a harmonic sense, they can provide variations in the lift and moment of the blades and, consequently, be used to reduce vibrations, noise, and possibly the induced power of rotors. For MiTEs (the given name for actuating Gurney flaps), however, the aerodynamic analysis becomes substantially more complicated, as unsteady aerodynamics associated with their deployment starts to be relevant.

22 Recently, several computational fluid dynamics (CFD) investigations have been performed in order to assess the effects of the unsteady aerodynamics on MiTE performance [3-6, 8, 9, 13, 14]. The work described in [8] evaluates the aerodynamics of

MiTEs placed at the trailing edge using an incompressible flow solver. Two airfoil configurations are used: a NACA 0012 airfoil and a blunt trailing-edge NACA 0012.

Time accurate calculations on impulsively started MiTEs are found to agree with the

Wagner‟s function [1], except for a slight delay. In the frequency domain, the result for oscillating MiTEs also reveals an increased lag with respect to Theodorsen‟s function [1], but overall, a close agreement is found. These results provide an indication of the unsteady behavior of MiTEs, but the flow conditions are not adequate for rotorcraft applications. A more rotorcraft-oriented and more complete study is found in [3-6]. In this investigation, the unsteady aerodynamics of MiTEs are explored with regards to their dependency on airfoil shape, airfoil‟s angle of attack, Mach number, reduced frequency (k), and chordwise position of the MiTE. Some results of this study are described here.

Two airfoils have been used for the dynamic calculations, the S903 and the VR-

12 airfoils. The first is a wind turbine airfoil, and it has been used because of the availability of reliable static Gurney flap data; the second is a rotorcraft airfoil, generally used at inboard sections of rotor blades. The CFD results obtained for a S903 airfoil equipped with a MiTE at the trailing edge are shown in Figure 2.8 [6]. These results are for sinusoidal deployments at two reduced frequencies, 0.14 and 0.56. The y-axis represents the increase in the lift coefficient due to the MiTE, normalized by the increase due to a static Gurney flap. A counter-clockwise loop is formed suggesting a phase lag in

23 the response. For k=0.14, the amplitude of the response is already substantially smaller

than a quasi-steady result, and decreases even further at a higher reduced frequency.

These results, just like the ones from [8], follow the same trend as the

Theodorsen‟s circulatory function (C(k)) on both amplitude and phase lag response, as

seen in Figures 2.9 and 2.10. Cases for the VR-12 equipped with a 0.01c MiTE

positioned at the trailing edge, at various flow conditions and airfoil‟s angle of attacks are

also plotted for comparison [6], along with the NACA 0012 results from [8].

Compressibility effects, different airfoils and angle of attacks seem to shift the curves up

and down, but general trends are similar and the response can be described simply

changes in amplitude and phase lag. Apparent mass effects seem to be very small as well.

Typical unsteady linear theory would suggest an increasing domination of the apparent

Figure 2.8. Predicted increase in lift coefficient for sinusoidal deployments of a MiTE positioned at the trailing edge of a S903 airfoil [6].

24 mass terms over the circulatory ones at high reduced frequencies resulting on increases in the lift amplitude and the phase lead. These trends are not seen on the response even at k=1.0 implying that circulatory terms are the dominant terms in the range of reduced frequencies relevant to rotorcraft applications.

Figure 2.9. Lift amplitude for a MiTE positioned at the trailing edge at various deployments frequencies, free-stream conditions and compared to incompressible theory [6].

25

Figure 2.10. Lift phase for a MiTE positioned at the trailing edge at various deployments frequencies, free-stream conditions and compared to incompressible theory [6].

As previously described in this text, one solution for storing a MiTE when fully retracted is to place it at an upstream position where the airfoil has enough thickness. It is, then, necessary to investigate the effects of the chordwise position in the unsteady aerodynamics. CFD results obtained in [6] for the MiTE at an upstream position of 0.90c on a S903 airfoil are shown in Figure 2.11 . The aspect of the response is dramatically different from the results obtained for a MiTE at the trailing edge (Figure 2.8). Most noticeable is the distinction between the response during the deployment and retracting phases, and the minimum lift occurring at very different moments on the cycle, depending on the reduced frequency. At high reduced frequencies, the increase in lift is abrupt and occurs only at the end of the deployment cycle. The drop in lift is mainly due

26 to the formation of a strong vortex downstream of the MiTE that advects along the lower surface of the airfoil as the MiTE deploys [6]. While in the surface, the vortex causes a decrease in pressure that counteracts the production of lift. During the retraction, a weaker vortex remains and is shed away only after the MiTE fully retracts [6].

The effect of this vortex is also evaluated at a Mach number of 0.45 for a 0.02c

MiTE positioned at 0.90c on a VR-12 airfoil (Figure 2.12). This represents more realistic conditions of the retreating side of a helicopter rotor in forward flight. These CFD results, although plotted differently here, have been done as part of the investigation in [3]. As it can be seen, even at higher Mach numbers, the vortex on the lower surface of the airfoil seems to have a relevant effect on the lift. The magnitude of the minimum lift and its position in the cycle appears to be very dependent on Mach number and/or airfoil shape, but the minimum point still seems to shift towards the end of the deployment as the reduced frequency increases. This shift in the minimum point is a indication of the vortex effect.

27

Figure 2.11. Predicted increase in lift coefficient for sinusoidal deployments of a MiTE placed at the chordwise position of 0.90c on a S903 airfoil [6].

Figure 2.12. Lift coefficient for sinusoidal deployments of a MiTE placed at chordwise position of 0.90c of a VR-12 airfoil at M=0.45 [3].

28 The effects of the MiTE chordwise position have been also studied and are presented in Figure 2.13 for a 0.02c MiTE on a VR-12 airfoil at M=0.40 [6]. As the

MiTE is moved from the trailing edge to 0.85c, the gradual shift in the minimum lift towards the end of the deployment indicate that the vortex stays higher and higher percentage of the deployment time in the surface of the airfoil, degrading overall lift enhancement.

Figure 2.13. Lift coefficient for sinusoidal deployments of a MiTE placed at different chordwise position on a VR-12 airfoil at M=0.40 [6].

Another relevant study uses a NACA 0012 airfoil equipped with a MiTE at the chordwise location of 0.95c at M=0.25 [9]. In this investigation, ramp deployment and retraction cases are performed to assess the unsteady aerodynamics of MiTEs in the time domain sense. Computations are performed to explore the aerodynamic effects of different MiTE heights, airfoil‟s angle of attacks, and ramp deployments at different

29 speeds. The effects of the vortex on the lower surface are also recognized in the time domain, and appear to depend on all the variables previously listed. The study, however, did not address the effects of compressibility, which are very important for rotorcraft applications. Also, it was limited to MiTEs with heights up to 0.012c, and placed at only one chordwise position (0.95c). MiTEs with heights of 0.02c have been proved to be a good compromise when used for stall-alleviation on rotors [3,5].

Overall, all the CFD analyses described in this text provide good physical insight about the aerodynamics of MiTEs, but their computational requirements become prohibitively expensive for design studies, which may require several iterations. It is, therefore, desired to develop more computationally efficient, design-level models that can accurately predict the unsteady aerodynamics of MiTEs. Such models can be readily implemented into current comprehensive rotorcraft codes, used for parametric studies, and for simulating the use of MiTEs on aircraft.

There have been only a few studies that are aimed at developing reduced-order models for predicting the unsteady aerodynamics of MiTEs. A work presented in [22] evaluates MiTEs at the trailing edge and assumes that they behave aerodynamically as trailing-edge flaps. Theodorsen theory including trailing-edge flap terms is then used to model the unsteady aerodynamics. Thin airfoil theory is adopted to calculate an equivalent flap size and deflection angle that would produce the same static lift and pitching moment increments. The aerodynamic model is then combined to an aeroelastic model to evaluate flutter suppression capabilities of MiTEs. Another work follows on this one, but it does include the flap rate terms from Theodorsen‟s theory [37]. The model is coupled with a linear unsteady vortex panel method and a finite element structural model

30 and then used to stabilize a wing operating beyond its flutter speed. This model does not attempt to modify the amplitude and phase response based on the CFD results obtained, so discrepancies such as previously shown in Figures 2.9 and 2.10 are expected. It is also not adequate for rotorcraft applications as it does not consider any compressibility corrections.

The work presented in [3, 5] addresses these problems by adapting the Hariharan-

Leishman (H-L) model [38] to predict the unsteady aerodynamics of MiTEs fitted at the trailing edge. The H-L model is a time-domain, unsteady aerodynamic model that is able to account for compressibility effects, different free-stream conditions, and variable deployment schedules and, therefore, is well-suited for rotorcraft applications. It was developed for plain flaps, but subsequently modified based on CFD results to be able to model MiTEs [3, 5]. The resulting model is very versatile, and can be easily coupled with other models such as the Leishman-Beddoes dynamic stall model. It also tries to be as physically-based as possible reducing its number of constants compared to other models.

For these reasons, this model was selected as the basis for the one that is developed in this text. Detailed information is given in Chapter 6.

Another model, described in [14], uses a state-space, time-domain approach based on the Rational Function Approximation (RFA) to predict the unsteady aerodynamics of

MiTEs. The RFA coefficients are set based on CFD results and are made to vary with respect to Mach number, angle of attack, and deployment height. It is not clear from the published material how many constants are necessary for accurate predictions of the unsteady aerodynamics of MiTEs. CFD results are generated for three configurations of active devices: a MiTE at a blunt trailing edge, a MiTE at the chordwise position of

31 0.94c, and a microflap. The MiTE configurations can be seen in Figure 2.14. For the case of upstream MiTEs, it is recognized the presence of vortical disturbances, and that they introduce non-harmonic behavior in the response. Even so, the model, which is harmonic in nature, is used to predict the loads of upstream MiTEs.

Figure 2.14. MiTE configurations studied in [14].

The last two models described in this text [5, 14], although very different in nature, are able to capture the harmonic components of the aerodynamic loads, which are usually characterized simply by changes in amplitude and phase lag, and is often accurate enough for the cases of MiTEs placed at the trailing edge. Unless using airfoils with blunt trailing edges [8, 14], it is likely necessary to move the MiTEs upstream from the trailing edge in order store them inside the airfoil [3, 39]. As already mentioned, upstream MiTEs introduce strong vortex shedding in the lower surface of the airfoil that result in significant non-harmonic components on the aerodynamic loads. This was first observed in the frequency domain for the VR-12 and S903 airfoils using CFD [3, 5], and

32 confirmed both in the time and frequency domains for the NACA 0012 airfoil [9, 14].

These effects must be further investigated and then taken into account, especially considering the retreating side of rotor blades where the combination of high reduced frequencies, high angles of attack, and relatively low Mach numbers are present.

Chapter 3

Static Wind Tunnel Investigation

A static wind tunnel investigation of Gurney flaps is described in this chapter. A number of airfoils designed to VTOL/Rotorcraft applications are used to study the effects of Gurney flaps of different heights and positioned at different chordwise positions.

These tests are conducted at the Penn State University Low Speed, Low Turbulence

Wind Tunnel. The main goal of these tests is to provide a consistent set of experimental data, taken in a common facility, to facilitate the analysis of the effects of airfoil shape on the aerodynamics of Gurney flaps. Lift and moment data are obtained using surface- pressure measurements and the drag by measuring the momentum loss using a wake- traverse probe. Previous tests in the same facility have been done to study Gurney flaps on the S903 airfoil, designed for wind-turbine applications [16]. In this text, the emphasis is in analyzing Gurney flaps on airfoils designed for rotorcraft. A summary of all the static experimental data on Gurney flaps taken at the Penn State Low Speed, Low

Turbulence Wind Tunnel is shown in Table 3-1. For all cases the Mach number is less than 0.2.

34 Table 3-1. Summary of static experimental data on Gurney flaps taken at the Penn State Low Speed, Low Turbulence Wind Tunnel.

Airfoil shape R GF height GF position S903 1.0 x 106 0.5%c 1.00c S903 1.0 x 106 1.0%c 1.00c, 0.95c S903 1.0 x 106 2.1%c 1.00c, 0.95c, 0.90c XV-15 1.0 x 106 1.0%c 1.00c XV-15 1.5 x 106 1.0%c 1.00c S408 1.0 x 106 1.0%c 0.90c S408 1.0 x 106 2.4%c 0.90c, 0.85c S408 1.5 x 106 2.4%c 0.90c S415 1.0 x 106 1.0%c 0.95c, 0.90c, 0.85c S415 1.0 x 106 2.4%c 0.95c, 0.90c, 0.85c

3.1 Wind tunnel description and validation

The Pennsylvania State University Low-Speed, Low-Turbulence Wind Tunnel is a closed-throat, single-return atmospheric facility. The test section is rectangular, 101.3 cm (39.9 in) high and 147.6 cm (58.1 in) wide, with filleted corners, and is shown in

Figure 3.1. The maximum test-section speed is 67 m/s (220 ft/s). Airfoil models are mounted vertically in the test section and attached to computer-controlled turntables that allow the angle of attack to be set. The turntables are flush with the floor and ceiling and rotate with the model. The axis of rotation is between the quarter- and half- chord locations of the model. The gaps between the model and the turntables are sealed to prevent leaks [16].

35

Figure 3.1. Test section of The Pennsylvania State University Low-Speed, Low- Turbulence Wind Tunnel. View is facing downstream of the tunnel.

36 The flow quality of the Penn State wind tunnel has been measured and documented [40]. At a velocity of 46 m/s (150 ft/s), the flow angularity is everywhere below 0.25 in the test section. At this velocity, the mean velocity variation in the test section is below 0.2%, and the turbulence intensity is less than 0.045%.

As described in [16], the Penn State wind tunnel has been validated by comparison with two highly regarded two-dimensional, low-speed wind tunnels: the

Low-Turbulence Pressure Tunnel (LTPT) at the NASA Langley Research Center [41] and the Low-Speed Wind Tunnel at Delft University of Technology in The Netherlands

[42]. The comparison with the Delft wind tunnel is presented in Figure 3.2 for Reynolds numbers ranging from R = 0.7 x 106 to 1.5 x 106. The measurements have been done on a

S805 wind-turbine airfoil using the same wind-tunnel model [43, 44]. The agreement is really good except for post-stall where the flow becomes 3-D in nature and 2-D measurements are not very meaningful. Pressure distributions and transition locations were also found to agree as presented in [44]. Low Reynolds number aerodynamic comparison has been made with results from LTPT for the Eppler 387 airfoil and excellent agreement was also found [45].

37

Figure 3.2. Comparison of aerodynamic characteristics of the S805 airfoil measured in the low-speed wind tunnels at Pennsylvania State University and Delft University of Technology [16].

38 3.2 Model description

The models used in the Gurney flap experiments were mounted vertically in the wind tunnel and completely spanned the height of the test section. Details of the S903 model can be found in [16, 46]. The remaining models were produced from solid aluminum using a numerically-controlled milling machine. Each model has approximately 33 pressure orifices on the upper surface and roughly the same number on the lower surface. Each orifice has a diameter of 0.51 mm (0.020 in) and is drilled perpendicular to the surface. The orifice locations are staggered in the spanwise direction to minimize the influence of an orifice on those downstream.

3.3 Data acquisition system

To obtain drag measurements, a wake-traversing, Pitot-static pressure probe is mounted from the ceiling of the tunnel. A traversing mechanism incrementally positions the probe across the wake, which automatically aligns with the local wake-centerline streamline as the angle of attack changes.

The basic wind-tunnel pressures are measured using pressure-sensing diaphragm transducers. Measurements of the pressures on the model are made by an automatic pressure-scanning system. Data are obtained and recorded with an electronic data- acquisition system. The surface pressures measured on the model are reduced to standard pressure coefficients and numerically integrated to obtain section normal- and chordal- force coefficients, as well as the section pitching-moment coefficient about the quarter- chord point. Section profile-drag coefficients are computed from the wake total and static

39 pressures using standard procedures [47]. Wake surveys are not performed, however, at most post-stall angles of attack, in which case the profile drag coefficients are computed from normal- and chordal-force coefficients as obtained from pressure integration. Low- speed wind-tunnel boundary corrections are applied to the data [48]. A total-pressure- tube displacement correction, although quite small, is also applied to the wake-survey probe [47].

As is clear from the applying the procedures prescribed in [49], the uncertainty of a measured force or moment coefficient depends on the operating conditions and generally increases with increasing angles of attack. In the higher lift regions, for which the uncertainty is the greatest, the measured lift coefficients have an uncertainty of

cl = ±0.005. The uncertainty of drag coefficients measured in low-drag range is

cd = ±0.00005 while, as the angle of attack approaches stall, this increases to

cd = ±0.00015. The pitching-moment coefficients have an uncertainty of cm = 0.002.

3.4 Results

A summary of the Gurney flap lift data taken at Penn State is shown in Figure 3.3.

The y-axis represents the increase in cl,max due to Gurney flaps normalized by the baseline airfoil cl,max and the x-axis the Gurney flap chordwise location. Only results for R = 1 x

106 are plotted. Data for two different sizes of Gurney flaps, 0.01c and 0.02c, are fitted through linear trend lines. For the 0.02c case, the curve fit describes the data remarkably well, indicating little influence of the airfoil shape on the result. For the 0.01c case, however, a larger amount of scatter is seen over the range of chordwise locations.

40

Interestingly, a decrease in cl,max is observed for three of the conditions tested. This is discussed with more detail later in the text. Overall, the two linear fits are close to parallel to each other evidencing some trend in the Gurney flap results taken.

Figure 3.3. Increase in cl,max due to Gurney flaps of different heights and positioned at different chordwise positions of various airfoils at R = 1.0 x 106.

Next, the results for lift, pitching-moment, and drag coefficients are presented for the cases that were tested in the current study. The aerodynamic loads for the working section of the XV-15 tilt-rotor are shown in Figure 3.4. Baseline airfoil results and those of the airfoil with a 0.01c high Gurney flap located at the trailing edge are shown for the

Reynolds numbers: R = 1 x 106 and R = 2 x 106. The maximum lift is increased 22% and

15%, respectively. Interestingly, the stall angle of attack is not affected by the Gurney flap for R = 1 x 106, contradicting general results obtained in the literature. The pitching-

41 moment increases about the same amount for both Reynolds numbers. As expected, the drag is increased at low lift coefficients and decreased near cl,max. As discussed earlier, the Gurney flap induces a “camber effect” that delays the movement of the separation point until higher cl‟s, and results in an upward shift in the drag polar. The shift is only recognized at higher angles of attack when the boundary layer becomes thin compared to the height of Gurney flap, making it effective. At low angles of attack, the drag is higher than the baseline due to the increased skin-friction drag and pressure drag across the

Gurney flap. A lift-to-drag ratio plot can be seen in Figure 3.5. At cl values higher than

1.20 and 1.30, for R = 1 x 106 and R = 2 x 106 respectively, the airfoil equipped with a

Gurney flap becomes more efficient than the baseline, reaching its maximum efficiency at a higher cl value. Interestingly, the magnitude of the maximum lift-to-drag ratio is also higher for the Gurney flap cases, contradicting previous results for the S903 airfoil, in which, for the same Gurney flap configuration, the maximum L/D was shown to decrease. This elucidates a great potential in using Gurney flaps on the XV-15 airfoil, especially if better performance at high lifts is desired. For MiTE applications, however, the Gurney flap would likely have to be placed at an upstream position, so a degradation in the maximum L/D compared to the trailing edge case is expected.

42

a) Lift coefficient vs. angle of attack

b) Pitching-moment coefficient vs. angle of attack

43

c) Lift coefficient vs. drag coefficient

Figure 3.4. Aerodynamic characteristics of the working section of a XV-15 tilt-rotor equipped with Gurney flaps at two Reynolds numbers.

Figure 3.5. Lift-to-drag ratio for the XV-15‟s airfoil with and without Gurney flaps.

44 The aerodynamic results for the S408 airfoil, also designed for tilt-rotor applications, are presented in Figure 3.6 for R = 1 x 106. As the main focus of this test is to provide information about potential application of MiTEs, the Gurney flaps are placed only at positions upstream from the trailing edge. Three configurations with Gurney flaps are investigated: a 0.010c high Gurney flap placed at 0.90c, and 0.024c high Gurney flaps placed at 0.85c and 0.90c. The two configurations with 0.024c high Gurney flaps cause increases in cl,max compared to baseline of about 5.3% and 17%, respectively, and increases in the nose-down pitching moment. The drag behaves again as expected, increasing at low lift and decreasing near cl,max. The lift-to-drag behavior can be seen in

Figure 3.7. Both cases allow the airfoil to reach higher cl‟s, but maximum lift-to-drag ratio is reduced. The case of the Gurney flap positioned at 0.85c shows little benefit over the baseline, indicating that it is probably the most upstream location that the 0.024c high

Gurney flap should be placed.

The results for the 0.010c high Gurney flap placed at 0.90c exemplify a case that the Gurney flap does not work as a lift enhancer. The cl,max decreases about 12% compared to the baseline airfoil, the drag is higher at all angles of attack, and the nose- down pitching moment decreases. The lift-to-drag ratio is everywhere lower than the baseline as seen in Figure 3.7. One comment needs to be made about this particular test.

As seen in Figure 3.6 for the case of 0.010c high Gurney flap, the test was stopped before occurrence of stall. Therefore, it is not certain that the last data point really represents the cl,max condition. However, analyzing the character of the lift curve in comparison with the results for the other Gurney flap configurations, it is believed that stall is probably close to imminent. Further discussions in this text makes this assumption.

45

a) Lift coefficient vs. angle of attack

b) Pitching-moment coefficient vs. angle of attack

46

c) Lift coefficient vs. drag coefficient

Figure 3.6. Aerodynamic characteristics of a S408 airfoil equipped with Gurney flaps of different sizes positioned at various chordwise locations.

Figure 3.7. Lift-to-drag ratio for the S408 airfoil with and without Gurney flaps.

47

A comparison of the pressure distributions at cl,max for the baseline and two

Gurney flaps with different heights positioned at 0.90c is presented in Figure 3.8. As mentioned before, one large contributor to the increase in lift due to Gurney flaps is the increase in pressure upstream from the device. As seen, the 0.01c high Gurney flap barely increases the pressure upstream of it, and it is still able to lower the downstream pressure below the baseline values. These low pressures near the trailing edge also cause a decrease in the peak pressure near the leading edge at the upper surface. All these effects contribute to a total decrease in lift for this configuration. The 0.024c high Gurney flap, on the other hand, is large enough to provoke an increase in the pressures upstream of the flap, as well as a delay in the pressure recovery in the upper surface, being effective in increasing the maximum lift of the airfoil.

Figure 3.8. Pressure distributions of the S408 airfoil comparing baseline airfoil and with Gurney flaps positioned at 0.90c.

48 The last airfoil tested in this static wind tunnel investigation is the S415, designed to maximize the hover performance of a helicopter rotor. For this airfoil, the effects of the

Gurney flap chordwise position are studied for two Gurney flap heights, 0.01c and

0.024c, at the Reynolds number of R = 1 x 106. The aerodynamic forces and moments for the height of 0.01c are presented in Figure 3.9. The Gurney flap positioned at 0.95c increases the cl,max of the airfoil about 9%, increases the nose-down pitching moment, and has lower drag than the baseline airfoil above a cl of 1.31. The Gurney flaps positioned at

0.90c and 0.85c are another example of Gurney flaps that are not high enough and, therefore, fail to enhance the lift of the airfoil. Compared to the baseline airfoil, cl,max is decreased about 6% in both cases. The nose-down pitching moment is also decreased, and the drag coefficient increased everywhere for both cases, with the largest changes being caused by the most upstream Gurney flap.

a) Lift coefficient vs. angle of attack

49

b) Pitching-moment coefficient vs. angle of attack

c) Lift coefficient vs. drag coefficient

Figure 3.9. Aerodynamic characteristics of a S415 airfoil equipped with Gurney flaps of 0.010c height positioned at various chordwise locations.

50 Once again it is worthwhile analyzing the pressure distributions as they can

provide valuable information about the aerodynamics of Gurney flaps. The pressure

distributions for the baseline airfoil and the 0.01c high Gurney flaps positioned at three

different chordwise locations are presented in Figure 3.10. Similarly to previous results

for other airfoils, the increase in lift for the flap positioned at 0.95c is mainly due to the

increased pressure upstream of the Gurney flap in the lower surface, as well as the

delayed pressure recovery in the upper surface that exhibits lower pressure compared to

the baseline airfoil. For the two ineffective Gurney flap cases, the loss of lift is also

mainly due to the region between the flap and the trailing edge. Again, the early drop in

the pressure not only impedes the production of lift in that region, but creates negative lift

Figure 3.10. Pressure distributions at cl,max of the S415 airfoil with and without 0.01c high Gurney flaps positioned at several chordwise positions.

51 as the pressures are lower than the upper surface pressures. The upper surface pressure recovery is also not affected by the Gurney flaps placed at these two chordwise locations.

Based on the results obtained, it becomes evident that depending on the Gurney flap height and how forward it is located on the lower surface of the airfoil, a decrement in lift can be achieved. It seems that the physical mechanism responsible for the lower lift is directly related to the length of the low pressure, separated region behind the flap, which is dependent on the size of the Gurney flap. If the flap is small and positioned enough forward, reattachment can occur upstream from the trailing edge. This was previously observed in a CFD study on the GU25-5(11)-8 airfoil and is presented in

Figure 2.7 [33]. Evidences of this reattachment can be clearly inferred from the experimental pressure distributions for the S415 airfoil with a 0.01c Gurney flap at 0.85c, presented in Figure 3.10. Downstream of the flap, the pressure drops in the recirculating region, and then increases, merging with the baseline pressures and indicating reattachment for the last three data points before the trailing edge. With the flow reattached near the trailing, there is no physical mechanism to shift the Kutta condition away from the trailing edge, and to increase airfoil circulation. Therefore, no increased lift is possible, and in fact, the low pressure in the lower surface behind the flap acts as to decrease the lift instead. Another way of interpreting this decrease in lift would be by suggesting that the separation region “de-cambers” the airfoil towards the trailing edge.

In other words, the separation bubble effectively increases the displacement thickness behind the Gurney flap, acting as a reflex in the airfoil, causing an overall decrease in cl,max.

52 The last set of aerodynamic data is for the S415 equipped with 0.024c high

Gurney flaps positioned at three chordwise locations. The lift, pitching-moment, and drag coefficients can be visualized in Figure 3.11. The results for the lift coefficient suggest a moderate loss in cl,max as the flap is moved from 0.95c to 0.85c. All three configurations are effective as lift-enhancers, and show gains over the baseline cl,max of about 24.5%,

15%, and 8.5%, respectively. The effect on the nose-down pitching moment is as expected, with increasing magnitudes as the Gurney flap is placed more upstream from the traling edge. The drag coefficients of the three Gurney flap cases are relatively similar, indicating little effect caused by changes in the chordwise position. Interestingly, the Gurney flap placed at 0.95c has the highest drag at moderate cl‟s, contradicting the notion that placing a Gurney flap more upstream tends to always increase drag.

a) Lift coefficient vs. angle of attack

53

b) Pitching-moment coefficient vs. angle of attack

c) Lift coefficient vs. drag coefficient

Figure 3.11. Aerodynamic characteristics of a S415 airfoil equipped with Gurney flaps of 0.024c height positioned at various chordwise locations

54 Having investigated the S415 airfoil with several Gurney flaps configurations, it

would be interesting to see which configuration would be more promising for being used

as an active device. To have enough thickness to store the MiTEs when in the retracted

position, a 0.01c high MiTE would have to be placed at 0.95c, and a 0.024c high MiTE at

0.90c. Of course, this would depend on the design of the actuator system, and therefore, it

might be necessary to place both flaps at even more upstream positions. The results for

the lift-to-drag ratio of these Gurney flap configurations, compared with the baseline

airfoil are presented in Figure 3.12. The results for the same Gurney flaps placed 0.05c

upstream from the original locations are also plotted for reference, in case a more forward

location is needed. As seen in the plot, there is a clear trade-off between maximum lift

Figure 3.12. Lift-to-drag ratio for the S415 airfoil with and without Gurney flaps.

55 and maximum L/D. The baseline airfoil is designed to have high efficiency near its maximum lift. If more lift is needed, the 0.01c Gurney flap could provide about 8% increase in cl with a 27% penalty in L/D, and the 0.024c Gurney could provide about

16% increase in cl with a 36% penalty in L/D. The decision about which one is more advantageous would certainly depend on the specifics of each design, but most importantly on the relevance of the airfoil profile drag with respect to total drag and the benefits that higher lift could bring to the overall design. Also, depending on the actuator design, it is possible that these Gurney flaps would have to be placed more upstream. In that case, it is seen from Figure 3.12 that the 0.01c high Gurney flap is a lot more sensitive to a change in the chordwise position. Moving its position 0.05c forward, the

0.01c Gurney flap becomes ineffective and ceases to provide any benefit to the airfoil.

The 0.024c high Gurney flap, on the other hand, is much less affected by the change in location, and it is still able to deliver an increase in the maximum lift of the airfoil.

3.5 Conclusions

A static experimental investigation of Gurney flaps undertaken at The

Pennsylvania State University Low-Speed, Low-Turbulence Wind Tunnel has been presented. Aerodynamic results are obtained for three distinct rotorcraft airfoils equipped with Gurney flaps of various sizes and placed at different chordwise locations. The effects of Gurney flaps are found to be very dependent on the combination of Gurney flap height and location, as well as the airfoil shape. It is observed that in some cases, the

Gurney flap can become ineffective and provide a decrease in the cl,max of the airfoil. This

56 is noticed for cases in which a 0.01c high Gurney flap is placed at or upstream from

0.90c. Pressure distributions suggest that the flow downstream of the flap reattaches before reaching the trailing edge. This could be the mechanism that impedes the increase in lift, by eliminating the shift in the Kutta condition, and preventing any major changes in the pressures at the upper surface of the airfoil. The trends suggest that Gurney flaps with different heights may also decrease cl,max if placed far enough forward from the trailing edge. For the cases where the Gurney flaps are effective, a general agreement is observed with respect to results obtained from other researchers.

Considering the variability of the results obtained in this study, it is concluded that great care is necessary when sizing Gurney flaps. Whenever possible, wind tunnel measurements should be used to explore the effects of these devices, as they are still the most reliable source of aerodynamic data. The experimental data presented herein, including high-quality drag measurements and pressure distributions, provide a valuable database for computational code validations, and should be used whenever experiments are not feasible.

Chapter 4

Unsteady Wind Tunnel Investigation

This chapter describes recent experimental efforts undertaken at Penn State as part of the research on Miniature Trailing Edge Effectors (MiTEs). A wind tunnel investigation of oscillating MiTEs is conducted at the Mid-Sized Wind Tunnel located at the Hammond building at Penn State University. Even though the test‟s primary goal is to evaluate the performance of a newly designed actuating system, aerodynamic data is also measured using a 6-component load balance.

Very few experimental data are available on oscillating MiTEs. The goal of this test is to provide some understanding of the unsteady aerodynamics of these devices, and gain some confidence on their effectiveness when under dynamic motion. Also, it is expected that the experience acquired would facilitate the design of a more comprehensive experimental investigation at a larger and higher flow quality wind tunnel.

For the test, an S903 airfoil is equipped with spanwise segmented MiTEs of heights of about 0.019c and placed at 0.90c. These MiTEs are oscillated at frequencies ranging from 2 Hz to 15 Hz, and at three different Reynolds numbers: R = 0.7 x 106,

1.0 x 106, and 1.2 x 106. Some selected ramp deployments are also performed. The test matrix for the experiments is presented in Table 4-1.

58 Table 4-1. Test matrix for the wind tunnel investigation.

Reynolds Numbers Frequencies [Hz]

0.7 x 106 2, 5, 8, 10, 12, 15

1.0 x 106 5, 8, 10, 12, 15

1.2 x 106 2, 5, 8, 10, 12, 15

4.1 Previous efforts

As MiTEs are a relatively new concept, experimental investigations of their unsteady aerodynamics are very rare in the literature. One relevant work is presented in

[52], and comprises a wind tunnel investigation of oscillating MiTEs using unsteady pressure transducers. The wind-tunnel airfoil model, however, had very few pressure orifices near the trailing edge, which limits the applicability of the results as validation for CFD calculations. Near the MiTE, the presence of near-surface vortex shedding induces large pressure variations that can affect the aerodynamic loads substantially.

Therefore, being able to measure the pressure fluctuations in this region is essential for the accuracy of the results [6, 9].

One of the results obtained in [52] is depicted in Figure 4.1, and compared to the unsteady linear Theordorsen‟s theory [1]. The lift coefficient results are for a NACA

0012 airfoil equipped with 0.025c high MiTEs that are positioned at 0.90c. The Reynolds number is R = 0.348 x 106, and the airfoil‟s angle of attack is 5°.

59

Figure 4.1. Wind tunnel results for a NACA 0012 airfoil equipped with 0.025c high MiTEs placed at 0.90c [52] compared with Theodorsen‟s theory [1].

The wind tunnel results show no decrease in the amplitude at a reduced frequency of 0.204, contradicting the results obtained by the linear theory. Even not considering non-linear effects such as vortex shedding, a decrease in amplitude would be expected at this case, as observed in previous CFD investigations [6, 37]. Further experiments are necessary before conclusions can be drawn about these results.

60 4.2 Wind Tunnel Description

The Pennsylvania State University Mid-Sized Wind Tunnel (MS-WT) is a vertical

closed-circuit wind tunnel located in room 8 of the Hammond Building at the Penn State

University Park Campus [50]. A schematic view of the wind tunnel is presented in

Figure 4.2. The closed-jet test section, originally designed for boundary layer research, is

approximately 240 in (6.1 m) long and has the constant cross sectional dimensions of 24

in (0.61 m) wide by 36 in (0.92 m) high. The 48 in diameter fan has blade settings that

are adjustable in pitch such that the maximum wind speed inside the test section can

reach nearly 150 ft/s. The contraction ratio of this facility is approximately 10:1 and the

turbulence management consists of 5 screens, 1 perforated plate and a 6 in long

honeycomb section. The turbulence intensity in the center of the test section ranges from

5% at 20 ft/s, to 0.3% at 140 ft/s [50]. The fan is belt-driven by a 25 hp motor suspended

below the fan casing. A comparison between this wind tunnel and the Penn State Low-

Speed, Low-Turbulence Wind Tunnel is shown in Table 4-2.

Figure 4.2. Schematic drawing of the PSU Mid-Sized Wind Tunnel [50].

61 Table 4-2. Comparison on the specifications of the two wind tunnels at Penn State [50].

Low-Speed, Low-Turbulence Mid-Sized Wind Tunnel Wind Tunnel 117 Academic Projects Bldg Rm 8 Hammond Bldg

Test Section Size & 39”(high) x 57”(wide) 36”(high) x 24”(wide) Shape: Rectangular with fillets Rectangular with fillets

Test Section Area: 14.9 sq. ft. 5.9 sq. ft. Max. Test Section 220 ft/sec, 67 m/s 145 ft/sec, 44 m/s Velocity: Contraction Ratio: 9.6 : 1 9.9 : 1

5 Screens, 1 Hexagonal Turbulence 4 Screens, 1 Perforated Plate Perf. Plate & Management: & Honeycomb Honeycomb

Streamwise Turbulence u'/U = 0.045% u'/U = 0.6 % Intensity: @ 150 ft/sec @ 30 ft/sec

Fan Diameter: 78” 48”

Electric Motor: 300 hp 25 hp

Horizontal Closed Circuit, Vertical Closed Circuit, Configuration in Room: Closed Jet Closed Jet

4.3 Model and acquisition system

The model used for the dynamic MiTEs measurements is the same used in the experiments performed in [16]. It is a 12%-thick S903 airfoil, designed for wind-turbine applications. The airfoil shape is shown in Figure 2.3. The model is constructed with fiberglass skins formed in molds that were produced using a numerically controlled milling machine. For this particular test, the span of the model is cut to fit the smaller test

62 section of the Mid-Sized Wind Tunnel at Penn State. The 1.5 ft-chord model is mounted horizontally in the wind tunnel and completely spans the 2 ft width of the test section, except for small gaps near the walls. These gaps are necessary because of the way the balance is mounted, but are properly sealed to prevent any 3-D effects. A 6-component balance is connected to the airfoil and used to measure aerodynamic forces (lift, drag, and side-force) and moments (roll, pitch, and yaw). The balance is able to measure unsteady loads at frequencies that exceed the ones required for this test. The instantaneous height of the MiTE is obtained with the aid of a Hall sensor, placed inside the airfoil model. All data are obtained and recorded the same sampling rate with an electronic data-acquisition system. Nine MiTEs with heights of about 0.019c are placed along the span of the airfoil at the chordwise point of 0.90c. A view of the airfoil equipped with MiTEs inside the wind tunnel test section can be seen in Figure 4.3. The MiTEs are actuated by a pneumatic actuator system designed for the purpose by Dr. Joe Szefi (INVERCON,

LLC).

63

Figure 4.3. S903 airfoil equipped with segmented MiTEs at the Mid-Sized Wind Tunnel test section. View is facing downstream of the tunnel.

64 4.4 Experimental Results

4.4.1 Static Verification

Static aerodynamic measurements of the S903 airfoil with the MiTEs both fully retracted and fully deployed are taken and compared to the high-quality data previously taken at the Low-Speed, Low-Turbulence Wind Tunnel (LSLT-WT) at Penn State [16,

46]. When fully retracted, the slots that store the MiTEs are properly sealed. The results for lift, drag, and pitching-moment coefficients are presented in Figure 4.4 for R =

1 x 106. As the turbulence levels at the Mid-Sized Wind Tunnel (MS-WT) located at

Hammond building are considerably higher than the ones from LSLT-WT, results for fixed transition and NACA standard roughness are also plotted for comparison. Details on the grit sizes and their chordwise placement in the airfoil are given in [46].

The lift coefficients agree reasonably well between the wind tunnels. The lift- curve slope is similar in the linear range, but a shift of about 1° is apparent in the zero-lift angle of attack. For the MiTE fully retracted case, the value of the cl,max is about 8% higher than the no flap result obtained in LSLT-WT. The measured increase in cl,max due to the deployed MiTEs and Gurney flaps have a better agreement, being 14% and 18%, as measured at MS-WT and LSLT-WT, respectively. The lower effectiveness of the

MiTE configuration may be due to the gaps between the segmented MiTEs, as well as the small difference in height. The fair agreement in lift gives some confidence in the lift measuring capability of the set-up.

65

(a) Lift coefficient vs. angle of attack

(b) Pitching-moment coefficient vs. angle of attack

66

(c) Lift coefficient vs. drag coefficient

Figure 4.4. Static aerodynamic results for the S903 airfoil with and without Gurney flaps taken at two different wind tunnels.

The same cannot be said about the pitching moment and the drag measurements.

The pitching-moment coefficients measured at MS-WT are very different from the ones obtained at LSLT-WT; in fact, not even the trends agree with one another. The drag measurements also do not agree, being everywhere higher than the ones obtained at

LSLT-WT. For the case of retracted MiTEs, the value of the drag coefficient at low lifts is only slightly higher than the standard roughness case, but then increases much more rapidly as the lift increases. The drag coefficient of fully deployed MiTEs is about twice as high as the values measured for the Gurney flap at LSLT-WT. There are many possible reasons for these discrepancies. One contributor is the fact that a balance is being used instead of pressure taps and wake measurements for drag, which are preferred

67 for 2-D experiments. The way the balance is set-up requires gaps near the walls that, even being properly sealed, could be contributing to increased three-dimensionality of the flow. Also, the balance measures the total drag produced by the “wing”, therefore, the interference drag between the airfoil and the walls are also contributing to the increased drag. This fact is even aggravated by the smaller test section and subsequent low-aspect ratio airfoil model. Another important reason may be the much higher turbulence levels of the MS-WT that could be limiting the amount of laminar flow in the airfoil. All these conditions contribute to the higher drag obtained in the measurements.

Due to the lack of accuracy on the measurements obtained for pitching moment and drag, these are not considered from the results obtained for oscillating MiTEs. The measurements of lift, as discussed, have shown good agreement and are presented in this text. Overall, it is recognized the limitation of the current experimental set-up in providing definitive and detailed information on the aerodynamics of MiTEs. In any case, the data collected for lift is accurate enough to provide some understanding of the unsteady aerodynamics involved, as well as a “proof of concept” of the device.

68 4.4.2 Dynamic MiTEs

All data presented in this section are for 0.019c high MiTEs positioned along the

0.90c of a S903 airfoil at angle of attack of 5°. The results for a ramp deployment are

presented in Figure 4.5 for R = 1 x 106. The y-axis on the left represents the normalized

lift, which is calculated based on steady-state lifts of both deployed and retracted MiTEs.

On the right, the instantaneous normalized height of the MiTEs is presented, with the

unity value representing fully deployed MiTEs. The x-axes on the bottom and on top

represent the reduced time and the dimensional time in seconds, respectively. The

reduced time is calculated as s = 2Vt/c.

Figure 4.5. Normalized lift due to the ramp deployment of 0.019c high MiTEs positioned at 0.90c of a S903 airfoil.

69 As seen in the plot, the lift response lags the deployment of the MiTEs. In the initial stages of the deployment, a slight decrease in lift occurs and stays constant for a couple of half-chords of travel. Next, a sudden increase in lift happens followed by another small decrease. The lift then increases more or less exponentially until it converges to the steady-state fully deployed MiTE values. The small plateaus, usually followed by sudden increases in lift, are an indication of vortex shedding downstream of the MiTEs. The effects shown here somewhat resemble the ones obtained in the CFD investigation in [9], where the unsteady aerodynamics of MiTEs are investigated in the time domain. Agreement in the trends is also found by comparing with recent CFD investigations conducted at Penn State [51]. More details on the latter investigation are presented in Chapter 5 and in [51]. The direct comparison between the CFD and the experiments are not available at this point, as this would require the use of exactly the same deployment function as the forcing function in the CFD predictions. In the studies performed in [9, 51], half-sine waves are used as the ramp deployment functions, therefore, an equivalent reduced frequency of deployment could be derived, with

NORM  0.5 1  cosks   . Due to the nature of the pneumatic actuator, the shape of the deployment is fixed, but has variable reduced frequencies. For the ramp case at

R = 1 x 106, the deployment starts slowly with an equivalent reduced frequency of 0.17 and then speeds up reaching a reduced frequency of 0.80, as presented in Figure 4.6.

70

Figure 4.6. Deployment frequency breakdown for the experimental ramp cases.

At the other two Reynolds numbers tested, R = 0.7 x 106 and R = 1.2 x 106, the different flow velocities result in reduced frequencies of deployment that are slightly higher and smaller, respectively. Therefore, even with the deployments occurring at about the same rate, the unsteady aerodynamics affect the loads differently, resulting in distinct build-ups of lift. A comparison between the results obtained at the three different

Reynolds numbers is presented in Figure 4.7. The data are also processed using a smoothing function and are shown in Figure 4.8. As expected, the lift at the lower flow velocity condition is more influenced by the unsteady aerodynamics and, therefore, takes more time to achieve the steady state condition. Also, the lift oscillates more at this condition suggesting higher vortex shedding activity. Comparing the lift responses at the early stages of the deployments, it becomes apparent that the initial drop in lift is more severe for the lowest flow velocity, agreeing with the CFD results obtained in [9, 51] that suggest stronger vortex shedding with increasing reduced frequency. It should be

71 emphasized that the different effects seen here are mainly due to differences in flow velocity rather than a Reynolds number effect. The Reynolds number can have a big influence in the static values of lift, as it directly affects the boundary layer and consequently the effectiveness of Gurney flaps. But it is expected to play only a minor role in the unsteady aerodynamic behavior of MiTEs.

Figure 4.7. Normalized lift response due to ramp deployments at different flow velocities for 0.019c high MiTEs positioned at 0.90c of a S903 airfoil.

72

Figure 4.8. Smoothed lift response due to ramp deployments at different flow velocities.

Also as part of this investigation, MiTEs are oscillated at different frequencies and different flow velocities to evaluate their effectiveness in providing harmonic variations in the loads. As mentioned before, the actuation system used in this study does not have the authority to change the rate of deployment with respect to time. The different frequencies, therefore, only change the periodicity in which the deployments and retractions occur. This can be better visualized in Figure 4.9, where the deployments are presented for each of the frequencies studied at R = 1 x 106. The lower the frequency of deployment, the more time the MiTE stays at either fully deployed or retracted positions. Also, if the frequency is high enough, the actuator is not able to fully deploy the MiTEs before it is time to start retracting. The consequences are lower deployment amplitudes for these cases.

73

Figure 4.9. Oscillatory deployments at several frequencies for R = 1 x 106.

The results of the lift response for MiTEs oscillating at the frequencies of 5, 8, 10,

12, and 15 Hz are presented in Figures 4.10 to 4.14 for a flow velocity of 113ft/s

(R = 1 x 106). The results shown here are taken after a number of oscillations and, therefore, represent the converged harmonic response. Again, the lift is normalized by the static lift values obtained for the MiTEs fully retracted and fully deployed. As it would be expected, the amplitude of the lift response decreases as the frequency of deployment increases, following the same trend as Theodorsen‟s linear theory. Again, a direct comparison is not possible, as the deployments presented here are not sinusoidal in nature. The trends can be even better visualized when the lift response is smoothed as presented in Figure 4.15. The x-axis is scaled with respect to the period of oscillation

(sOSC) to synchronize all the deployments. At the lower frequencies, the MiTE stays deployed for longer periods, allowing the lift to approach the steady state values more

74 closely. The magnitudes of the minimum lifts seem to be about constant for all cases, but occur for slightly longer periods as the frequency increases. For the 12 Hz case, the actuator already starts to saturate, but the MiTEs are still deployed enough to cause a considerable amplitude in the lift. At 15 Hz, the MiTEs only reach about 70% of the total deployment, and so the lift amplitude also decreases considerably.

Figure 4.10. Lift response due to MiTEs oscillating at f = 5 Hz and R = 1 x 106.

75

Figure 4.11. Lift response due to MiTEs oscillating at f = 8 Hz and R = 1 x 106.

Figure 4.12. Lift response due to MiTEs oscillating at f = 10 Hz and R = 1 x 106.

76

Figure 4.13. Lift response due to MiTEs oscillating at f = 12 Hz and R = 1 x 106.

Figure 4.14. Lift response due to MiTEs oscillating at f = 15 Hz and R = 1 x 106.

77

Figure 4.15. Lift response due to MiTEs oscillating at several frequencies with free- stream conditions: V = 113 ft/s and R = 1 x 106.

The MiTEs are also oscillated at two other flow velocities, at 77 ft/s (R=0.7x106) and 135 ft/s (R=1.2x106). To facilitate comparison, the instantaneous MiTE heights for the different oscillation frequencies at the three flow velocities are plotted altogether in

Figure 4.16. The x-axes are again scaled with respect to the period of oscillation (sOSC) to synchronize the deployments. As it can be seen in the plots, the actuator behaves differently for the 133 ft/s (R=1x106) case. At this condition, the actuator starts saturating at about 12 Hz, while for the other two cases it already shows a decrease in effectiveness at about 8 Hz. The reasons for this are not fully understood at this point, but a probable explanation is either a change in the settings or a defect in the actuator system that could

78 have happened in between tests. This would be possible as the first test was done at 113 ft/s (R=1x106), and then at 77 ft/s (R=0.7x106), and 135 ft/s (R=1.2x106).

Figure 4.16. Instantaneous MiTE heights of the cases with different oscillation frequencies and flow velocities.

The differences in the deployment do not invalidate the results, but only limits the comparison of the results altogether. Therefore, only the results obtained for V = 77 ft/s

(R=0.7x106) and 135 ft/s (R=1.2x106) are compared in Figure 4.17. Results for deployment frequencies higher than 8 Hz are not presented as the actuators were only able to provide a maximum of 40% of the total deployment amplitude for these conditions. With the high frequencies being filtered in the smoothed-lift plot, an indication of the levels of vortex shedding is not available, but the differences in the amplitudes are more easily recognizable. Once again, the results shown for each of the flow velocities follow the trends of Theordorsen‟s theory: decreased lift amplitudes as the oscillation frequency increases. Comparing the results for the two flow velocities, it is

79 seen that the case with the higher flow velocity has higher lift amplitudes for the same deployment frequency, as well as an increased phase lag. This is expected because the higher the flow velocity, the lower the effective reduced frequency of deployment and, consequently, the unsteady aerodynamic effects. Again the behavior is qualitatively the same as predicted by the unsteady linear theory.

Figure 4.17. Lift response due to MiTEs oscillating at different oscillation frequencies and flow velocities.

4.5 Comparison with unsteady aerodynamic model

In this section, the experimental results obtained for ramp and oscillating MiTE cases are confronted with an unsteady aerodynamic model developed for MiTEs positioned at the trailing edge [3, 5]. More details about this model are presented in

Chapter 6. Although not particularly suitable for the present case with MiTEs placed at

80 0.90c, a comparison would still be valuable to identify some of the limitations of the

CFD-based model with respect to the experiments.

For all the model results presented in this section the forcing function is taken as the measured instantaneous height of the MiTEs. Also, the circulatory constants are set to be the same as the ones used in Chapter 6. First, experimental results for ramp deployments are compared to the unsteady model. The lift response obtained for the

MiTEs being deployed through a ramp at V = 77 ft/s (R=0.7x106) and

V = 135 ft/s (R=1.2x106) are compared to the model in Figures 4.18 and 4.19, respectively.

The model predicts the response at the lower flow velocity quite well. The high frequency components of the response are not captured, as the model does not have any mechanism to do so. These components are believed to be caused by vortex shedding, but it is not clear how much of it is actually noise from the balance measurements. At the higher flow velocity, the model seems to have a higher lag than the experiments, taking more time to reach the steady state solution. The negative normalized lift (decrease in lift from the baseline condition) is also not captured, as expected. As already mentioned, this model does not include any terms to predict the effects of the vortex advection in the lower surface of the airfoil (see Chapter 5), which are characteristic of MiTEs positioned upstream from the trailing edge.

81

Figure 4.18. Comparison between the model and experiments for a ramp deployment at V = 77 ft/s (R=0.7x106 and M=0.07).

Figure 4.19. Comparison between the model and experiments for a ramp deployment at V = 135 ft/s (R=1.2x106 and M=0.12).

82 Next, the lift results obtained for oscillating MiTEs are contrasted with the unsteady aerodynamic model. The first case is for the MiTE oscillating with a frequency of 5 Hz at a flow velocity of 77 ft/s, and is presented in Figure 4.20. Again, the agreement of the lift predicted by the model at R=0.7x106 is remarkably good, showing only a slightly smaller lift amplitude than the wind tunnel result. The upper peak value is predicted very well until the retraction starts. At this point the model predicts a sharp decrease in the lift, while the experiment seems to take a little longer to start the decline in lift. Good agreement is found for a significant part of the retraction, but the lower peak predicted by the model is slightly higher than the result obtained from the wind tunnel.

Figure 4.20. Comparison between the model and experiments for an oscillatory deployment with f = 5 Hz and V = 77 ft/s (R=0.7x106 and M=0.07).

The lift predicted by the model for the MiTEs oscillating at a frequency of 10 Hz and V = 113 ft/s is presented in 4.21 along with the wind tunnel results. The lift

83 amplitude predicted is about 20% lower than experiments. This difference is largely due to the decrease in lift experienced during the initial phases of the deployment. It is interesting to notice that some of the rapid variations in lift, shown in the wind tunnel results, are also predicted by the model. This indicates that some of the noise in the results is in fact an aerodynamic effect due to sharp changes in the MiTE height. For the present case, the variation near the high peak of the lift is due mainly to apparent mass effects.

Figure 4.21. Comparison between the model and experiments for an oscillatory deployment with f = 10 Hz and V = 113 ft/s (R=1.0x106 and M=0.10).

84

Figure 4.22. Comparison between the model and experiments for an oscillatory deployment with f = 8 Hz and V = 135 ft/s (R=1.2x106 and M=0.12).

4.6 Conclusions

An experimental investigation of the unsteady aerodynamics of MiTEs undertaken at the Mid-Sized Wind Tunnel at Penn State has been presented. A S903 airfoil has been equipped with spanwise segmented MiTEs with heights of 0.019c and positioned at the 0.90c of the airfoil. Static measurements have been taken and compared to results obtained at the Low-Speed, Low-Turbulence Wind Tunnel using the same airfoil model. Only the lift results have shown fair agreement and, therefore, are the only ones considered from the unsteady measurements. Both ramp and oscillatory MiTE deployments have been investigated at frequencies ranging from 2 to 15 Hz and at flow velocities of 77, 113, and 135 ft/s. The amplitude and phase lag of the results generally

85 agree with the trends predicted by the unsteady linear Theordorsen‟s theory. It is noticed for some cases, however, the occurrence of non-linear effects that are believed to be caused by vortex shedding in the lower surface of the airfoil. These effects seem to be aggravated as the frequency of deployment increases, but the variability of the results made it difficult to draw any formal conclusions.

The wind tunnel results have been contrasted with predictions of an unsteady aerodynamic model that was previously adapted from an unsteady trailing-edge flap model. The results show good agreement at the lowest flow velocity cases, but not so much at higher velocities. As expected, the model is not able to capture any of the non- linear effects caused by the fact that the MiTEs are placed upstream from the trailing edge.

The effectiveness of the MiTE in providing variations in lift under dynamic oscillations has been proved. Due to limitations of the wind tunnel and the experimental set-up used, it is not believed that the results obtained here are ultimate and definitive.

Better quality data needs to be taken before experimental results can be used with confidence for the validation of CFD computations and the development of aerodynamic models. This test, however, has provided valuable information about the unsteady aerodynamic of MiTEs that will certainly help planning and guiding future experimental efforts.

Chapter 5

CFD Investigation

In this chapter, a computational fluid dynamic (CFD) investigation of MiTEs is briefly described. These predictions have been performed as part of the work presented in

[51]. Here, the results are used to better understand the physics involved and to provide a database for the development of an unsteady aerodynamic model for MiTEs. Further details of the computations, as well as validation of the procedures are presented in [51].

Details on the model are found in Chapter 6.

Prior to developing an unsteady aerodynamic model for MiTEs positioned upstream of the trailing edge, it is essential to have a good understanding of the physics involved. As experimental investigations of MiTEs are both complex and expensive,

CFD simulations seem to be a promising tool to provide preliminary aerodynamic loads.

CFD demonstrate additional advantages for developing physics-based models, as it gives valuable insight into the detailed physics of the phenomena that would be more costly to extract experimentally [6].

In the study described in [51], the CFD calculations are performed using

OVERFLOW 2.1, a Reynolds-averaged Navier-Stokes flow solver. The Spalart-Allmaras one-equation turbulence model is adopted. Several airfoils are used in the calculations, including the VR-7, the VR-12, the S902, and the NACA 0012 airfoils. The shape of

87 these airfoils can be seen in Figure 5.1. The first two are Boeing-Vertol rotorcraft airfoils, the third is designed for wind turbine applications [46], and the last is a NACA 4-series airfoil, which is considered a first generation rotorcraft airfoil. The VR-7 airfoil geometry was initially selected, first because it is a rotorcraft airfoil, but most importantly because of the vast number of experimental results available for validation. There is an extensive set of unsteady aerodynamic data for the VR-7 airfoil under pitching oscillations in [53].

Although not perfectly adequate for the current application, comparison with these experiments can provide some confidence about the capability of the code to predict complex unsteady flows with the presence of vortical disturbances. After gaining some experience with the CFD calculations, other airfoils are evaluated at selected operating conditions [51].

a) VR-7 airfoil

b) VR-12 airfoil

c) S902 airfoil

88

d) NACA 0012 airfoil

Figure 5.1. Shapes of the airfoils in consideration.

For developing an unsteady aerodynamic model, a set of numerical cases becomes necessary, encompassing different flow conditions that are relevant for rotorcraft applications. The work presented in [51] provides a systematic approach in which the variables of interest are independently varied to facilitate the understanding of cause- effects on the unsteady aerodynamics of MiTEs.

A baseline case is selected as a VR-7 airfoil equipped with a MiTE of height

6 hMiTE = 0.02c, positioned at x/c = 0.90, at R = 4∙10 , M = 0.30, and α = 5⁰. Ramp and sinusoidal deployment cases are run for reduced frequencies ranging from 0.05 to 1.0, with additional indicial and nearly-indicial (k=10) cases. Having these results as baselines, cases with a different Mach number are performed (M=0.5), as well as other angles of attack (0°, 10°), different airfoils, and different MiTE positions (0.88c, 1.00c).

These results are then used as a reference for the development of an aerodynamic model based on indicial methods.

5.1 Flow Physics

As already been mentioned, the physics of the flow change considerably when

MiTEs are placed upstream from the trailing edge of the airfoil. CFD results for nearly indicial MiTE deployment cases, taken from [51], are presented in Figure 5.2 in the time-

89 domain. The results are for the VR-12 airfoil equipped with a 0.02c MiTE positioned at the trailing edge and at 0.90c, for the VR-7 airfoil equipped with a 0.02c MiTE positioned at 0.90c, and for the S902 airfoil equipped with a 0.02c MiTE positioned at

0.88c. The MiTEs are deployed through a half-sine wave that follows the expression:

NORM  0.5 1  cosks   (5.1) where k = 10, s represents the distance traveled in half-chords (reduced time), and the time to deploy (sDEP) is 0.31 half-chords of travel. The y-axis represents the increase in lift coefficient and the instantaneous MiTE height, both with the same scale. These are normalized by the values obtained for the airfoil with the MiTEs retracted and deployed.

There is a clear difference in the build-up of lift for MiTEs positioned at the trailing edge and at upstream positions. For the trailing-edge MiTE case, just after the deployment starts, the lift rapidly increases up to about 60% of the final value and then gradually approaches the steady state solution. All three cases of upstream MiTEs, on the other hand, have the initial half-chords of travel characterized by large variations in lift including regions with decreased lift compared to the baseline airfoil. After these transients are over, the lift rapidly increases and then asymptotes the steady state value with an overall increased lag with respect to the trailing-edge MiTE case. These results in the time domain qualitatively agree with other CFD investigations [9]. The high frequency oscillations are evidence of vortex shedding, just like the ones observed in

Gurney flaps [27], and have been also shown to appear in other CFD predictions of

MiTEs [8]. Interestingly, the S902 airfoil does not shown any evidence of vortex shedding. It seems that the decrease in lift in the initial stages of the deployment is very

90 dependent on the airfoil shape, with the drop being the highest for the S902 airfoil, and then followed by the VR-7 airfoil, and the VR-12 airfoil. The fact that the MiTE on the

S902 airfoil is positioned 0.02c more upstream than the other two cases could also be contributing for the increased adverse lift. However, no formal conclusion can be drawn at this point.

Figure 5.2. Normalized ∆cl results for different airfoils equipped with a 0.02c high MiTE after a half-sine ramp deployment at k = 10 (adapted from [51]).

CFD tools can provide details of the flowfield that can be useful to identify the physics. In order to better understand the initial transients in the upstream MiTE cases, time stations of interest are selected and labeled (I) to (IV) in Figure 5.3, for the nearly- indicial MiTE deployment case on the VR-7 airfoil. The corresponding pressure contours are presented in Figure 5.4, where dark blue color denotes low pressures and red color

91 denotes high pressures. Entropy contours are also plotted for two time stations in Figure

5.5, as they more clearly represent the losses in the vortex cores.

During the deployment, the MiTE blocks the flow upstream from it, dramatically decreasing its velocity and increasing its pressure. The increase in the upstream pressure seems to be more pronounced than the decrease in the downstream one such as a small increase in lift is noticed, reaching its maximum peak when the MiTE finishes deploying.

Also, shortly after the MiTE starts the deployment, a strong vortex is formed just downstream of the MiTE and starts convecting towards the trailing edge. The vortex behavior resembles that of a dynamic stall vortex, except that it has opposite circulation and is formed in the lower surface of the airfoil [6]. While it translates along the lower surface of the airfoil, the low-pressure region associated with the vortex increases its size, decreasing the lift of the airfoil and increasing its pitching moment. The effect of the vortex only starts to diminish when it approaches the trailing edge. After reaching the trailing edge, the low pressure disturbance then entrains air from the upper surface of the airfoil forcing the circulation of the airfoil to rapidly increase. This process, especially at high reduced frequencies, can occur through a formation of a secondary vortex, which has positive circulation and therefore can cause over peaks in the development of the lift

(Figure 5.5). After these two vortices convect away from the airfoil, a new Kutta condition is established, and the lift continues to increase mainly governed by shed wake effects until it asymptotically reaches a new equilibrium.

92

Figure 5.3. Selected time stations shortly after a nearly-inidicial MiTE deployment on the VR-7 airfoil.

a) Vortex forms downstream of the MiTE; Pressure upstream of the MiTE reaches its

maximum value during the cycle (I).

93

b) Vortex convects on the lower surface of the airfoil (II).

c) Vortex reaches trailing edge of the airfoil (III).

94

d) Secondary vortex forms (IV).

Figure 5.4. Pressure contours results for a VR-7 airfoil equipped with a 0.02c high MiTE located at 0.90c after a half-sine ramp deployment at k=10. The operating conditions are M = 0.3, R = 4 x 106, and α = 5° (adapted from [51]).

95

(a) Vortex convects on the lower surface of the airfoil (II).

(b) Secondary vortex forms (IV).

Figure 5.5. Entropy contours for a VR-7 airfoil equipped with a 0.02c high MiTE located at 0.90c after a half-sine ramp deployment at k=10. The operating conditions are M = 0.3, R = 4 x 106, and α = 5° (adapted from [51]).

When MiTEs are actuated in a harmonic sense, the effects of the vortex disturbances can remain during considerable fractions of the oscillation and, therefore, increased lags are observed in the response. This behavior has been shown for upstream

MiTEs on a S903 airfoil (Figure 2.11), and on a VR-12 airfoil (Figure 2.12). The same behavior is observed for the VR-7 airfoil in Figure 5.6, where results for lift due to sinusoidal deployments of a 0.02c high MiTE positioned at 0.90c are presented.

96

Figure 5.6. Increase in lift due to sinusoidal MiTE deployments at three reduced frequencies for a VR-7 airfoil equipped with a 0.02c high MiTE positioned at 0.90c [51].

5.2 Overview of Results

In this section, selected CFD results obtained in [51] are presented to illustrate some of the dependencies of the unsteady aerodynamics of MiTEs on the reduced frequency, the Mach number, and whether the MiTE is deploying or retracting. Special attention is given in quantifying the effects of vortex shedding in the lower surface of the airfoil, which are important for the development of the aerodynamic MiTE model described in Chapter 6. For all the cases presented here, a VR-7 airfoil equipped with a

0.02c high MiTE positioned at 0.90c is used, at a Reynolds number of R = 4 x 106.

The effect of the different reduced frequencies of deployment are presented in

Figure 5.7 at a Mach number of M = 0.3. The y-axis represents the increase in lift

97 coefficient normalized by the static values of fully retracted and deployed MiTEs. In the x-axis the reduced frequency is normalized by the non-dimensional time to fully deploy a

MiTE (sDEP) to facilitate the comparison between the results. As expected, the effect of an increase in the reduced frequency of deployment (decrease in sDEP) is to aggravate the initial decrease in lift, indicating the presence of a stronger vortex with higher circulation.

This trend agrees with the results presented in Figures 2.11 and 2.12 [3, 6], and other

CFD investigations [9]. Also, increases in the reduced frequency induce higher lags in the lift response, which takes longer (more deployment cycles) to achieve the steady state solution.

Figure 5.7. Effect of different reduced frequencies of MiTE deployments in the lift response of a VR-7 airfoil equipped with a 0.02c high MiTE positioned at 0.90c, operating at M=0.3 [adapted from 51].

The effect of increasing Mach number is presented in Figure 5.8. The lift results are shown for M=0.3 and 0.5, and for two different reduced frequencies of deployment,

98 k = 0.05 and 0.25. For all cases the Reynolds numbers are the same, R = 4 x 106. As seen in the plot for both reduced frequencies, an increase in the Mach number decreases the magnitude of the adverse lift in the initial stages after the deployment, suggesting a weaker vortex in the lower surface of the airfoil. After the vortex convects away from the airfoil, the higher Mach number cases demonstrate higher lags in the development of the lift, taking more deployment periods to achieve the steady state value.

Figure 5.8. Effect of different Mach numbers in the lift response of a VR-7 airfoil equipped with a 0.02c high MiTE positioned at 0.90c after a ramp deployment [adapted from 51].

The lift behavior during a MiTE retraction is presented in Figure 5.9. The results are shown for two Mach numbers, M = 0.3 and 0.5, and two reduced frequencies, k = 0.10 and 0.25. As seen in the plot, the lift decreases as soon as the retraction starts, with no relevant vortex effects in the response, except for high frequency oscillations

99 characteristic of vortex streets. The effects of Mach number and reduced frequency are qualitatively the same as for MiTE deployments. Increases in the reduced frequency of retraction and in the Mach number result in increased lags and more time (deployment periods) to achieve the steady state values. However, the responses between deployment and retraction seem to be fundamentally different. This can be seen in Figure 5.10, where the lift results for the VR-7 airfoil under MiTE deployment and MiTE retraction at k=0.10 are contrasted. The ∆cl values for the retraction case are inverted to facilitate comparison. The retraction lift response occurs more rapidly achieving 75% of the total lift change about four half-chords of travel earlier than the deployment case. These different flow physics were recognized in [3, 5] for MiTEs at the trailing edge. Here, the differences are aggravated by the presence of strong vortex shedding during the initial stages of the deployment.

Figure 5.9. Lift results for retracting MiTEs at different Mach numbers and reduced frequencies for a VR-7 airfoil equipped with a 0.02c high MiTE positioned at 0.90c [adapted from 51].

100

Figure 5.10. Lift results for deploying and retracting MiTEs at k=0.10 for the VR-7 airfoil operating at M=0.3 [adapted from 51].

The effects of having the airfoil at different angles of attack during a nearly- indicial MiTE deployment are presented in Figure 5.11. For this case, the x-axis represents the reduced time of deployment. At higher angles of attack, the initial increase in lift is slightly lower, indicating less increase in the pressure upstream of the MiTE during deployment. Soon after, the adverse lift seems to increase with increasing angle of attack. One reason could be that the vortex takes more time to reach the trailing edge of the airfoil and, therefore, would accumulate more circulation. This could be caused by slightly lower local velocities at the lower surface chordwise position of 0.90c, expected for higher angles of attack. Following, the abrupt increase in lift seems to decrease with increasing angles of attack, but soon after, the curves almost collapse to each other approaching the steady state solution at about the same rate.

101

Figure 5.11. Lift results for nearly-indicial MiTE deployments at three different angles of attack for a VR-7 airfoil equipped with a 0.02c high MiTE positioned at 0.90c [adapted from 51].

5.3 Conclusions

Some results from the CFD investigation conducted in [51] have been presented.

Integrated loads and flow visualizations have helped improve current understanding of the unsteady aerodynamics of MiTEs. The results suggest that for upstream MiTEs a vortex is formed and convects along the lower surface of the airfoil introducing adverse effects in the lift. For some conditions, these disturbances can affect a considerable percentage of the oscillation, introducing non-harmonic components in the lift. The results obtained agree but add upon previous CFD results obtained by other researchers.

More importantly, the calculations are done in a systematic way such as to facilitate the

102 development of an unsteady aerodynamic model for MiTEs that is able to account for these non-harmonic effects.

Chapter 6

Unsteady Aerodynamic Modeling

As previously shown, the unsteady aerodynamics of MiTEs seems to be influenced by several factors, including the deployment frequency, Mach number, free- stream velocity, chordwise position and height of the MiTE, airfoil‟s angle of attack, and airfoil shape. These effects have been identified from both wind tunnel experiments and

CFD predictions. However, these methods are impractical for use during routine performance and design studies, which may require predictions of multiple configurations at several flow conditions. For this purpose, reduced-order, approximate methods are better candidates to potentially provide faster estimations of the physics involved in deploying MiTEs. It is also expected that they can be easily implemented into current comprehensive helicopter codes.

In this chapter, the development of an unsteady aerodynamic model for MiTEs applied to rotorcraft is presented. The model is a physics-based, time domain model that is based on indicial concepts. It is formulated in a one-step recursive form that can be readily implemented into discrete-time rotor analyses. It expands the capabilities of the model presented in [3, 5], to be able to predict the unsteady lift of MiTEs positioned upstream from the trailing edge. As mentioned earlier in this text, moving the MiTEs away from the trailing edge introduces non-harmonic components in the aerodynamic

104 response, affecting the loads substantially and complicating the analysis. These changes are mainly due to the presence of shedding vortices downstream of the MiTE that convect along the lower surface of the airfoil affecting the local pressures. The model described herein incorporates these effects on lift by modeling the lower-surface vortex using indicial methods. As necessary in any rotorcraft-related application, the model also attempts to address the compressibility effects.

Due to the limitations of the current available unsteady experimental data on

MiTEs (Chapter 4), CFD results from [51] are used to set the constants and correlations present in the model. Comparisons of the model with the CFD calculations are presented for different flow conditions, deployment conditions, MiTE locations, and airfoil shapes.

6.1 Indicial Methods

Most of current methods and concepts used for predicting the unsteady aerodynamics in helicopters are somewhat based in the early works on thin airfoils by

Theodorsen [54], Küssner [55], and Wagner [56]. A detailed description of these works is presented in [1, 57]. Here, only an overview of the literature is given, focusing on the concepts that are important for understanding the indicial methods for subsonic compressible flow applications. The great advantage of using indicial methods is that if the indicial response due to a particular forcing mode is known, the cumulative response to an arbitrary forcing in that mode can be obtained using superposition principles [1, 57,

58]. The indicial theory has been used to solve many problems in unsteady aerodynamics

105 [38, 58-66]. These methods are the basis for the unsteady aerodynamic MiTE model presented in this chapter.

6.1.1 Incompressible Flow

Theodorsen‟s theory presents a solution for the 2-D unsteady airloads on an oscillating airfoil in potential flow and assuming small perturbations. The results are presented in the frequency domain, with the airloads divided in circulatory and non- circulatory components. The first component is due to the creation of the circulation about the airfoil as well as shed wake effects, and the second is due to apparent mass effects. Part of the circulatory term, the so-called Theodorsen‟s function, C(k), is responsible for introducing an amplitude reduction and a phase-lag effect on what would be the circulatory quasi-steady lift [1]. This function depends only on the reduced frequency of deployment and is given exactly in terms of Bessel functions. Although very applicable for flutter analysis in some fixed-wing aircraft, the Theodorsen‟s theory has some limitations for use in rotorcraft applications. The incompressibility assumption, for example, can be easily violated in a typical rotor, where moderate to high local Mach numbers can occur depending on radial and azimuthal positions, or whenever the reduced frequencies are high enough to cause the unsteady local airfoil pressures to exceed the critical values. Also, the fact that the theory is formulated in the frequency domain limits its usage in a rotor in forward flight, as the parameter k (reduced frequency) would not be constant around the azimuth.

106 Although still incompressible in nature, the work by Wagner [56] is more

applicable to rotorcraft as it is formulated in the time domain. Wagner derived the exact

solution of the lift response due to a step change in angle of attack [64], here referenced

as the indicial angle-of-attack response. An indicial response is defined as the

aerodynamic response to an instantaneous perturbation in the control input, a step input.

For incompressible flow, the response is expressed in terms of what became known as the

Wagner‟s function, presented in Figure 6.1. The Wagner‟s and Theodorsen‟s functions

are mathematically equivalent as they are solutions of the same linearized differential

equation [58]. It has been demonstrated that the results from the frequency domain can be

transformed to the time domain and vice-versa [58].

Figure 6.1. Wagner‟s and Küssner‟s functions for a step change in angle of attack.

107 Jones [67] seems to be the first to recognize the potential of using indicial responses to solve unsteady aerodynamics problems [66]. As mentioned, the indicial methods permit that if the indicial response is known a priori, the response to any arbitrary forcing function can be obtained using superposition through the Duhamel‟s integral [1, 57-59]. This is of great significance for rotorcraft applications, where arbitrary aerodynamic excitation and aperiodic flow conditions are possible. To facilitate the solution of the Duhamel‟s integral, it is desired to express the indicial response in an adequate exponential form. The Wagner‟s function has been approximated as a two-term exponential series with four coefficients [67]:

(s ) 1.0  0.165 e0.0455ss  0.335 e 0.3 (6.1)

The results are also plotted in Figure 6.1 for comparison. With this approximation, the

Wagner‟s function can be generalized using Duhamel‟s integral with the aid of several numerical methods [1, 57, 59]. The solutions to the integral can be given in a state-space form [61] and in a one-step recursive formulation [1, 57, 59].

Another relevant work in the field of incompressible-flow unsteady aerodynamics is the derivation of the transient lift response of a thin-airfoil entering a sharp-edged vertical gust [1]. The problem was initially addressed in [55], but properly solved in [68].

Analogous to the Wagner‟s function, the response is written in terms of what became known as the Küssner‟s function. This function is also plotted in Figure 6.1, along with an appropriate exponential approximation of the form [1]:

 (s ) 1.0  0.5 e0.13ss  0.5 e 1.0 (6.2)

108 Differently than the Wagner‟s problem, the quasi-steady angle of attack changes progressively as the gust penetrates into the airfoil, therefore, the Küssner‟s function has an initial value of zero rather than one-half [1].

Even though both Wagner‟s and Küssner‟s functions are developed in the time domain, their applicability for rotorcraft applications is limited due to incompressibility assumptions. Therefore, methods suited for subsonic compressible flows need to be adopted, and are presented in the next section.

6.1.2 Subsonic Compressible Flow

While the indicial response is known exactly for incompressible flows, there is no equivalent exact solution for subsonic compressible flows, except for very short periods of time. Therefore, the main challenge in the application of the indicial method in subsonic flow is to obtain the indicial responses themselves [66]. Since the work from

Wagner, there have been innumerous attempts to extend the results to compressible flows. As a complete analytical solution to the problem is not possible, three approaches are generally used: approximate analytical solutions, numerical calculations, or experimental measurements. An overview of the early efforts is presented in [57]. These works use different methods to convert available theoretical frequency domain data to obtain the indicial responses [69-71]. Although practical forms of exponential functions were obtained, these procedures require a large amount of data to accurately derive the initial behavior of the indicial responses [60]. In [72], exact subsonic indicial responses due to step changes in angle of attack, pitch-rate, and penetration of a sharp edge gust are

109 derived based on supersonic flow analogies. The analytical results, however, are limited to very short times after the motion. Later on, a series of studies, conducted initially by

Beddoes [59] and then extended by Leishman [58, 60, 61], present extensive derivation and validation of indicial functions based on numerical and experimental data. These works also comprise the development of numerical algorithms to extend the results to arbitrary forcing. These studies form the basis of the method adopted for modeling

MiTEs in this chapter.

As described in [58-60], the indicial response is assumed to be decomposed into independent circulatory and noncirculatory components. At the early values of time after the indicial motion, the response is dominated by the impulsive noncirculatory terms that, for compressible flow, are initially finite and can be calculated from piston theory [72].

These loads decay rapidly and almost exponentially with time, while the circulatory terms start from zero and gradually increase to reach the steady-state values. The build-up of the circulatory component has been shown to be similar to a Küssner‟s function, and is represented by a two-pole exponential function appropriately scaled with Mach number.

The time constant that govern the decay of the noncirculatory loads are set to match the exact solutions obtained in [72] for the initial instants of the response.

This method has been later adapted to model the unsteady aerodynamic of trailing-edge flaps [38, 64]. The exact indicial responses, analogous to the ones obtained in [72] but due to flap motion and flap rate perturbations, are derived based on reverse flow theorems. These are then used to set new time constants and, consequently, the initial noncirculatory behavior of the response. The indicial responses, on the other hand, are set to be the same as the ones obtained for pitching oscillations in [60]. This is based

110 on the notion that, analogous to the incompressible case, the circulatory lag in linearized subsonic flow also does not depend on the airfoil boundary conditions [38, 64]. This was examined with some detail in [72, 73]. The state-steady solutions for s=0 and s=∞ are obtained from piston theory and thin airfoil theory, respectively.

More recently, CFD calculations have been more widely used to derive indicial responses [66, 75, 76]. CFD predictions have the advantage of being able to simulate input conditions that are difficult to obtain experimentally. In the work presented in [66], the indicial method has been extended to model non-linear effects, such as the ones associated with supercritical flows and shock wave movement [66].

6.2 Unsteady Aerodynamic Model for MiTEs

In the previous section, an overview of the indicial method has been presented.

This method has proven to be very effective in solving many of the problems in unsteady aerodynamics.

In the work presented in [3, 5], this philosophy is applied to predict the aerodynamics of MiTEs positioned at the trailing edge by adapting the Hariharan-

Leishman unsteady flap model [38, 64]. It is recognized that the indicial lift responses for

MiTEs somewhat resemble the ones due to trailing-edge flap deflections and pitch motions. These observations have given confidence that the method is appropriate to model MiTEs. Indeed, good results are obtained for unsteady lift and pitching-moment of

MiTEs positioned at the trailing edge for several flow conditions [3, 5].

111 In the present work, the indicial concepts are used again to expand the work in

[3, 5] and develop a generalized unsteady lift model that is able to predict the different

flow physics of upstream MiTEs. For this purpose, it is essential to have a model to

predict the effects of the lower-surface vortex. This vortex induces non-harmonic

components in the loads that cannot be fully accounted as simply amplitude and phase-

lag changes; therefore, cannot be predicted by the trailing-edge MiTE model [3, 5].

As previously noticed in Chapter 5, the lower-surface vortex behavior resembles

that of a dynamic stall vortex. The dynamic-stall vortex has been successfully modeled

and coupled with an indicial model, as part of the Leishman-Beddoes (L-B) dynamic stall

model [77, 78], which has been extensively validated. Therefore, it would be expected

that similar methodologies could be used to solve the present problem on MiTEs.

However, the main difficulty lies on the calculation of the vortex strength. In the L-B

model, the vortex lift contribution is seen as the difference between the linear unsteady

Figure 6.2. Vortex lift modeling of the L-B dynamic stall model [77].

112 circulatory lift, and the non-linear unsteady circulatory lift determined by a separated- flow model (Kirchhoff approximation). A representation of the static components can be seen in Figure 6.2, adapted from [77]. Generally speaking, as long as the vortex is in the upper surface of the airfoil, the vortex lift is such that the total lift response follows the linear unsteady lift result. For the case of MiTEs, however, the conditions are fundamentally different. The vortex acts as to decrease the lift in the airfoil, and there is no analogous linearized solution that could be potentially used to help setting the vortex strength; therefore, a new formulation is necessary.

Recalling the flow visualizations in Chapter 5, it was shown that after the vortex is formed, the associated low-pressure region increases as the vortex convects along the lower surface of the airfoil. This increasing low pressure contributes to a decrease in the airfoil circulation, mainly caused by the vortex. With that in mind, it seems plausible to idealize the vortex effect as a build-up of negative circulation, and use a formulation that is similar to that of the circulatory lift component. The indicial response would then be derived based on CFD results from [51]. The position of the vortex during convection would be tracked by appropriate time constants until it reaches the trailing edge. The vortex lift would then be allowed to decay with time, forcing the total lift to gradually blend into the airfoil circulatory lift component.

The unsteady lift model has been developed so that the total lift at each instant of time is the sum of the circulatory, apparent mass (non-circulatory) and vortex effects, respectively:

cl,,,, total()()()() s c l circ s  c l nc s  c l vtx s (6.3)

113 The contribution of each of the three components can be seen in Figure 6.3 for a representative nearly-indicial MiTE deployment case (the model constants used in this plot do not reflect the ones used in Section 6.3, but are selected to maximize clarity; this will become clear in the results discussion). The model to calculate the circulatory and apparent mass effects was previously developed in [3, 5], and is outlined here with small modifications. These effects are sufficient to model MiTEs positioned at the trailing- edge. The vortex model, developed and also detailed in the present work, allows for predictions of the unsteady lift of upstream MiTEs.

Note that the model presented here only addresses the effects of the vortex on the lift of the airfoil. It is believed that the effects on the pitching moment can be obtained by modeling the shift in the airfoil‟s center of pressure (CP) that is caused by the convection of the vortex in the lower surface. This has been done with success to model the pitching- moment change due to the dynamic-stall vortex [77, 78]. With the value of the vortex lift being calculated by the current model, the change in the pitching-moment could be derived simply by multiplying the shift in CP by the vortex lift. Only a correlation between the position of the vortex and the CP would have to be derived.

114

Figure 6.3. Breakdown of the indicial model into its three components.

6.2.1 Circulatory Lift

As for a step change in angle of attack [58, 60] or flap deflection [38], the increase in circulatory lift coefficient due to a indicial MiTE deployment is formulated as:

cl,,,, circ s,,, M   c l GF static h MiTE M  l circ  s M  (6.4) where ∆cl,GF,static represents the static lift coefficient increase due to a Gurney flap of height hMITE, and the indicial response function ϕl,circ represents the intermediate lift behavior between s=0 and s=∞. By comparing with CFD results, it was recognized that

115 the indicial response could be approximated by a two-term exponential function of the form:

circ circ l,circ sM,1 A1,circexp b 1, circ s A 2, circ exp( b 2,circ s ) (6.5) where A1,circ, A2,circ, b1,circ, b2,circ, are the indicial constants for the circulatory response, and γcirc is the exponent of the Prandtl-Glauert compressibility factor, β. In [3, 5], the indicial circulatory constants are varied for each Mach number; here the compressibility scaling is handled by βγ,circ. All these constants are derived based on the CFD results obtained in [51], and are presented in Tables 6-1 and 6-2.

As mentioned earlier, the indicial response can be generalized to any arbitrary forcing function by a finite difference approximation of the Duhamel‟s integral. Adopting a one-step recurrence solution to the integral, and using the mid-point rule algorithm [1], an effective MiTE height for the circulatory lift is obtained:

n n n n circ, effs  s  X 1, circ s  Y 1, circ  s (6.6)

n n n where  is the instantaneous height of the MiTE at the time step n; X1,circ and Y1,circ are circulatory deficiency functions that account for the time history between the forcing and the response, and are given by,

bs  circ Xnn X1 exp  b circ  s  A   exp 1,circ (6.7) 1,circ 1, circ 1, circ 1, circ  2

bs  circ Ynn Y1 exp  b circ  s  A   exp 2,circ (6.8) 1,circ 1, circ 2, circ 2, circ  2 where   nn   1 . The circulatory lift coefficient due to any arbitrary MiTE deployment motion can be obtained by the following:

116

cl,,,,,, circ s   c l GF static  circ eff s  c l base static (6.9) where cl,base,static is the static baseline lift coefficient that depends on the angle of attack of the airfoil, as well as the Mach number and Reynolds number.

It should be mentioned that, just like in [3, 5], different indicial responses are recognized for when the MiTEs are deploying or retracting (see Figure 5.10). Therefore, different indicial constants are used for deployment and retraction, and they assigned by subscripts, dep and ret, respectively. The values are obtained by comparing with CFD results of [51], and are presented on Table 6-1.

Similar to the work in [3, 5], the circulatory lift terms due to MiTE deployment rate are not included because of the nature of the deployment. Differently than for calculations of pitching airfoils and oscillating trailing-edge flaps, MiTEs do not oscillate about an axis, and therefore do not induce any camber-effect perturbations.

6.2.2 Apparent Mass Lift

As in [3, 5], the apparent mass terms are modeled based on piston theory applied for trailing-edge flaps [38, 64] by adjusting an equivalent flap-size to match the CFD results for MiTEs. It is recognized here that the dynamics of the deployments are fundamentally different between MiTEs and flaps, so as the apparent mass mechanisms.

Nevertheless, it is believed that this model can still provide an accurate representation of the physics involved.

Apparent mass effects are resultant of a pressure wave system that is characterized by compression and expansion waves [1, 72]. For pitching airfoils and

117 deploying trailing-edge flaps, these waves are created each at a different surface of the airfoil (upper or lower surfaces). Therefore, the total pressure difference across the surfaces, ∆p, acts together as to increase or decrease lift (depending on the direction of deployment). For MiTEs, the mechanisms are distinct than for flaps and are also believed to vary depending on the MiTE chordwise location. During MiTE deployment, the upstream high pressure waves contribute to an increase in lift, while the downstream low- pressure ones can in fact contribute to decreases in lift, as in the case of upstream MiTEs.

With that in mind, it is expected that the apparent mass terms would be substantially smaller than for either trailing edge flaps or pitching airfoils. This was previously recognized in [3, 5] by analyzing results for lift in the frequency domain for MiTEs

(Figures 2.9 and 2.10). In any case, it is believed that adjustments in the model developed for trailing-edge flaps can be made to account for smaller apparent mass effects, characteristic of MiTEs. Following the procedure in [3, 5], an effective flap size was used based on the indicial CFD results obtained in [51].

Differently than the approach taken in [3, 5], the apparent mass contributions due to deployment rates are not considered. As it can be inferred from [72], the contributions due to pitch rate (or rate of deployment) are solely due to linear variations of the perturbation velocity, which are only present in devices that rotate about an axis. Again because of the nature of the MiTE motion, these effects are not present. Other than that, the equations presented here are in agreement with the ones presented in [3, 5].

The initial loading at s = 0 due a indicial MiTE deployment can be derived from piston theory, and is found to be:

118

21  eeff  cs 0   (6.10) l, nc M where eeff is the effective hinge position that correspond to the effective flap size. It is measured by the distance in semi-chords from the mid-chord point. Again, due to different physics between MiTE deployment and retraction, each condition has a distinct value for eeff. The values are chosen based on CFD results and are presented in

Table 6-2. From the initial loading, the non-circulatory indicial lift due to a step MiTE deployment can be formulated as,

 21  eeff  c s,, M    s M  (6.11) l,, ncM l nc  where the indicial response function ϕl,nc represents the intermediate non-circulatory lift behavior between s=0 and s=∞. The non-circulatory indicial response in subsonic flow has been shown to decay approximately as an exponential function, so,

s  sM, exp (6.12) l, nc   ' Tl,

' where Tl, represents the decay rate of the non-circulatory loading. This time constant is defined by equating the sum of the time derivatives of the assumed forms of the non- circulatory and circulatory lift response at time zero (s=0) to the time derivative of the exact solutions obtained in [38]. Thus, the time constant can be expressed as:

1 TMeMe'2, 2 1  1  MF  2  circ 1 MAb  Ab (6.13) l,    eff  10 1,1,2,2, circ circ circ circ  where:

21 F10 1  eeff  cos  e eff  (6.14)

119 Again, the indicial response can be generalized to any arbitrary forcing function by a recurrence solution to the Duhamel‟s integral. Adopting the same algorithm as before, the non-circulatory lift coefficient due to any arbitrary MiTE deployment motion can be obtained by the following:

21 e  eff  nn' cl,,,, nc s  T l K l  K l   (6.15) M

where:

nn 1 K n  (6.16) l, s

ss     KKKK'n ' n 1exp  n  n 1 exp (6.17) l,,,, l ''  l  l     TTll,,  2 

'n Note that Kl, is also a deficiency function that accounts for time history effects due to the wave-like pressure disturbances.

6.2.3 Vortex Lift

A method to capture the vortex effects is presented in this section. As has been described, the vortex effects are idealized as a build-up of negative circulation. The indicial response is treated similarly to the circulatory component of the lift, except by the fact that a three-term exponential representation is used instead:

vtx vtx vtxs, M  1  A1, vtx exp  b 1, vtx  s  A 2, vtx exp(  b 2, vtx  s ) (6.18)  vtx A3,vtxexp( b 3, vtx s )

120

The indicial coefficients A1,vtx, A2,vtx, A3,vtx, b1,vtx, b2,vtx, b3,vtx are determined based on CFD results from [51], and are presented on Table 6-1. The compressibility scaling exponent for the vortex lift, γvtx, is also set from CFD results and is presented in

Table 6-2. The generalized response to any arbitrary MiTE deployment can be obtained through the superposition of indicial responses using the Duhamel integral [1, 57, 59].

Again, the recurrence solution is used, and the vortex lift is given by:

cl,,,,,, vtx s   c l GF static  vtx eff s  c l base static (6.19) and,

n n n n n vtx, effs  vtx s  X 1, vtx s  Y 1, vtx s  Z 1, vtx  s (6.20)

bs  vtx Xnn X1 exp  b vtx  s  A   exp 1,vtx (6.21) 1,vtx 1, vtx 1, vtx 1, vtx  2

bs  vtx Ynn Y1 exp  b vtx  s  A   exp 2,vtx (6.22) 1,vtx 1, vtx 2, vtx 2, vtx  2

bs  vtx Znn Z1 exp  b vtx  s  A   exp 3,vtx (6.23) 1,vtx 1, vtx 3, vtx 3, vtx  2

n where, vtx is the forcing function of the vortex lift. As presented next, this variable is manipulated to achieve proper behavior of the vortex lift.

The negative circulation of the vortex is only allowed to increase until the vortex reaches the trailing edge of the airfoil (when s = sVTX). Therefore, it is necessary to track the vortex along the lower surface of the airfoil. Based on the CFD results available for the different reduced frequencies, it is possible to define a correlation between the speed of the vortex (VVTX) and the reduced frequency of the deployment. This correlation was

121 found to scale with the Prandtl-Glauert compressibility factor, and can be seen in

Figure 6.4.

Figure 6.4. Vortex speed dependency on reduced frequency.

The vortex speed can then be found by:

2 exp 0.0728 lnkk  0.5788ln   3.1043 V  (6.24) VTX 

The known, time dependent speed of the vortex can then be integrated to provide its instantaneous chordal position. After it reaches the trailing edge, the vortex effect is forced to decay gradually to zero. This is accomplished by making the forcing function,

n vtx , approach zero through an exponential decay,

nn when s < s vtx VTX (6.25) nn vtx D vtx, decaywhen s  s VTX

122

s D exp (6.26) vtx, decay  Tvtx, decay where Tvtx,decay is a function that was found to correlate with the vortex convection speed.

Physically, the rate of decay of the vortex depends on how fast it convects away from the airfoil. The correlation was found to be:

T T  decay (6.27) vtx, decay nVTX Vvtx  where Tdecay is a time constant of the vortex decay, and nVTX is a scaling factor for the vortex speed (VVTX).

One more correlation was necessary to improve the agreement between the model and the CFD results, especially at low reduced frequencies. After setting the indicial constants of the vortex lift, it was noticed that a better agreement could be obtained by multiplying the vortex lift by an exponential growth of the form:

 ssinit, dep  c'  s  c s 1 exp (6.28) l,, vtx l vtx T vtx, growth

where sinit, dep represents the non-dimensional time in which the MiTE starts deploying;

and Tvtx, growth is function that correlates with the reduced frequency of deployment (k) as,

T T  growth (6.29) vtx, growth k

where Tgrowth is a time constant that governs the growth of the vortex lift. This constant was set based with comparison with CFD results at a spectrum of reduced frequencies, and is presented on Table 6-2. The effect of this modification is to increase the lags in the

123 initial phase of the vortex lift build-up. It became necessary after noticing that the vortex lift increases very slowly in the initial stages after deployment. Physically, it seems that the vortex does not influence the loads until it has reached a certain size and strength.

Similar behavior has been observed for the dynamic-stall vortex [78].

6.3 MiTE Model Results

In this section, the capability of the new unsteady MiTE model is evaluated by comparing selected results with the CFD data from [51]. Although the model was indeed created based on these results, a comparison between the two can prove the effectiveness and generality of the model and its constants in predicting the unsteady lift in the various conditions studied. It is worth mentioning that great effort was put into using a minimum number of constants and correlations possible, as well as attributing physical interpretations for every one of them. This certainly contributes to an overall increase in the generality of the model in application of practical problems.

The MiTE model is assessed for different MiTE deployment schedules, MiTE chordwise locations, Mach numbers, and airfoil shapes. Both ramp and sinusoidal deployment cases are presented. The MiTE motion is given by the following expression:

h  MiTE 1  cosks   (6.30) 2

Only half-cycle is performed for the ramp deployments. The ramp deployments are relevant if MiTEs are to be used for applications like stall alleviation in the retreating side of a rotor blade [2-5], for example. The sinusoidal deployments are important for

124 cases where oscillatory loads are needed, such as for vibration control [13,14], noise control, or tailoring the lift distribution in the blade for minimizing induced power, for instance.

The model constants used to generate the results presented in this section are given in Tables 6-1 and 6-2. The constants were set to give an overall agreement at the conditions that are relevant to rotorcraft. To have an idea of how unsteady is the environment around a helicopter rotor, the local reduced frequencies of MiTE deployment are plotted in Figure 6.5, at the radial locations of r = 0.50, 0.75, 1.00. The rotor specifications are for a representative Black Hawk helicopter rotor, and the advance ratio considered is μ = 0.40, which is slightly in excess of the maximum speed of this helicopter at sea level, and represent the condition in which variations in k are greatest.

The MiTE is deployed at a frequency f = 17.2 Hz, which corresponds to 4/rev for this configuration. As seen, the reduced frequency varies around the disk because of the different local flow velocities, which are dependent on radial location and azimuth position (for forward flight). The reduced frequency only exceeds k = 1.0 towards the mid-chord sections at retreating side of the disk, where the rotor is almost in reverse flow for this advance ratio. At most probable practical cases, the reduced frequency is expected to be in the range 0.1 ≤ k ≤ 1.0, unless the deployment is done at frequencies that are higher or lower than 4/rev.

125 Table 6-1. Indicial response constants of the MiTE model.

A1 A2 A3 b1 b2 b3

ϕl,circ,dep 0.350 0.650 - 0.100 1.400 -

ϕl,circ,ret 0.350 0.650 - 0.140 5.000 -

ϕl,vtx 0.350 1.100 -0.400 3.000 5.000 2.000

Table 6-2. Other parameters of the MiTE model.

γcirc 4.0

γvtx 13.0

eeff,dep 0.25

eeff,ret 0.50

Tdecay 0.050

nVTX 1.470

Tgrowth 0.500

126

Figure 6.5. Local reduced frequency of MiTE deployment for f = 17.2 Hz and μ = 0.4.

As the reduced frequency is varying around the rotor, a plot more representative and adequate of the rotor environment is presented in the time domain in Figure 6.6. The y-axis represents the non-dimensional time (half-chords of travel) necessary to fully deploy the MiTE (sDEP), while the x-axis represents the azimuth at which the MiTE starts its deployment. As the unsteady aerodynamics is varying, the value of the non- dimensional time had to be integrated around the azimuth. As shown in the plot, the effects of the unsteady aerodynamics are smallest when r = 1.00 and if the MiTE is deployed at around an azimuth of ψ = 67.5°. At this condition the deployment takes about

34 half-chords of travel to occur (sDEP = 10.8π). The most unsteady case is seen at r = 0.50 and when the MiTE starts its deployment at about ψ = 244.5°. At this condition

127 the deployment takes about 2.7 half-chords of travel to occur (sDEP = 0.85π) and, therefore, increased lags in the lift response are expected.

Figure 6.6. Non-dimensional time necessary for MiTE deployment at f = 17.2 Hz and μ = 0.4.

The plots presented in Figures 6.5 and 6.6 are particularly important to understand the range of deployment conditions that are of interest for rotorcraft applications. As it will be seen, CFD results are compared to the model in the range of deployment times from sDEP = 0.10π (k=10) to sDEP = 20π (k=0.05). However, during the development of the model, particular interest was given into maximizing the accuracy of the predictions in the range 0.1 ≤ k ≤ 1.0 (π ≤ sDEP ≤ 20π), due to its relevance for rotorcraft applications.

128 6.3.1 Effect of Deployment Time

In this section, the MiTE model is compared with CFD results from [51] to assess its capability to predict the MiTE aerodynamics at the full spectrum of MiTE deployment times. For all cases, the configuration used is of a VR-7 airfoil equipped with a 0.02c high MiTE positioned at 0.90c operating at M = 0.30, R = 4x106 and α = 5°.

The results for the unsteady lift are presented in Figures 6.7 to 6.12 due to MiTE ramp deployments at sDEP = 20π, 10π, 4π, 2π, π, and 0.1π (k = 0.05, 0.10, 0.25, 0.50, 1.0,

10). The y-axis represents the increase in cl normalized by the static values of the baseline airfoil and the airfoil equipped with a 0.02c high Gurney flap:

ccl l,, base static cl, norm (6.31) cl,, GF static

The model predicts the increase in lift coefficient very well, especially for when sDEP ≥ 2π. The progressive increase in vortex effect with increasing k is well captured by the vortex model, with minimum lift values being in close agreement with CFD for all but the two highest-k cases. The vortex decay also seems to be well captured, indicating good generality of decay time constant, Tdecay. The apparent mass terms are set to agree with the initial increase in lift, which is more characteristic at the nearly-indicial case, in

Figure 6.12. It is hard to assess the accuracy of the apparent mass model for the other deployment k‟s, other than noticing the good agreement during and right after MiTE deployment. In the circulatory-dominated part of the response, the accuracy of indicial circulatory constants can be evaluated. Again, good agreement is obtained with the CFD results for sDEP ≥ 2π, with both model and CFD results approaching the steady state solution at the same rate. At lower deployment times, on the other hand, the model

129 predictions seem to overpredict the lift increase right after the vortex effect decays

(Figures 6.11 and 6.12). At higher values of s, however, the difference reduces, and both model and CFD lift results approach the steady state solutions at about the same rate. It should be mentioned that no attempt was made to model the high frequency vortex shedding. In all cases evaluated, they happen at high enough frequencies and low amplitudes not to be very relevant in application.

In light of the results obtained, some considerations need to be made. As already mentioned, the indicial theory postulates that if the response to a step input can be approximated by a function, here an exponential function, then the result to any arbitrary forcing condition can be obtained by superposition using the Duhamel‟s integral. This theory assumes a linear relationship between the response and the forcing function, which might not be completely valid for MiTEs. Initially, the indicial circulatory constants were set to agree with results for the nearly-indicial MiTE deployment (Figure 6.3). In this case, however, not so satisfactory results were obtained in the full spectrum of reduced frequencies of deployment. In this regard, the constants had to be reset to prioritize the accuracy of the results at the range of frequencies that are practical in rotorcraft. Based on the results presented here so far, it seems fair to consider the linearity assumption to be valid for sDEP ≥ π.

130

Figure 6.7. Model comparison with CFD results obtained for a VR-7 airfoil equipped with a MiTE positioned at 0.90c deploying through a half-sine at k=0.05 and M=0.3.

Figure 6.8. Model comparison with CFD results obtained for a VR-7 airfoil equipped with a MiTE positioned at 0.90c deploying through a half-sine at k=0.1 and M=0.3.

131

Figure 6.9. Model comparison with CFD results obtained for a VR-7 airfoil equipped with a MiTE positioned at 0.90c deploying through a half-sine at k=0.25 and M=0.3.

Figure 6.10. Model comparison with CFD results obtained for a VR-7 airfoil equipped with a MiTE positioned at 0.90c deploying through a half-sine at k=0.50 and M=0.3.

132

Figure 6.11. Model comparison with CFD results obtained for a VR-7 airfoil equipped with a MiTE positioned at 0.90c deploying through a half-sine at k=1.0 and M=0.3.

Figure 6.12. Model comparison with CFD results obtained for a VR-7 airfoil equipped with a MiTE positioned at 0.90c deploying through a half-sine at k=10 and M=0.3.

133 6.3.2 Effect of Mach number

In this section, the capability of the MiTE model in capturing the unsteady lift at a different Mach number is assessed, again by comparing with CFD results from [51].

Here, the assumed compressibility scaling factors are evaluated. For all cases, the configuration used is of a VR-7 airfoil equipped with a 0.02c high MiTE positioned at

0.90c operating at R = 4x106 and α = 5°.

The results for the unsteady lift are presented in Figures 6.13 and 6.14 due to

MiTE ramp deployments at sDEP = 20π and sDEP = 4π (k = 0.05, 0.25). As seen in the plots, the MiTE model is able to handle the compressibility effects very well. The vortex model captures the behavior of the vortex with great accuracy, both during vortex growth as well as during vortex decay. The good agreement indicates that the compressibility scaling for both the vortex lift and the vortex speed are working as desired. At high values of s, the circulatory components also seem to be capturing the effects of a different

Mach number adequately.

Overall good agreement is observed for the two cases presented. The results presented only scope the lower range of reduced frequencies. Nevertheless, the higher the

Mach number, the more outboard it occurs in the blade and, the lower is the expected reduced frequency of operation.

134

Figure 6.13. Model comparison with CFD results obtained for a VR-7 airfoil equipped with a MiTE positioned at 0.90c deploying through a half-sine at k=0.05 and M=0.5.

Figure 6.14. Model comparison with CFD results obtained for a VR-7 airfoil equipped with a MiTE positioned at 0.90c deploying through a half-sine at k=0.25 and M=0.5.

135 6.3.3 Retraction Cases

In this section, the results for retracting MiTEs are contrasted between the unsteady MiTE model and the CFD results from [51]. As seen in Chapter 5, the physics involved during the retraction are different than the ones during deployment and so distinct indicial constants are necessary. Also, because there is no vortex effects involved, only the circulatory and apparent mass models are used. For all cases, the configuration used is of a VR-7 airfoil equipped with a 0.02c high MiTE positioned at 0.90c operating at R = 4x106 and α = 5°. Results for different Mach number and retraction times are presented.

First, the modeling capability at different reduced frequencies is assessed. The unsteady lift results due to MiTE ramp retractions at sDEP = 10π and sDEP = 4π (k = 0.10,

0.25) are compared with CFD in Figure 6.15 for M = 0.3. As seen, the agreement in the initial phases of the response is good, but then degrades as the reduced time increases.

The model seems to scale well between the two reduced frequencies, but the lift approaches the state-state results slightly earlier than predicted by CFD. Surprisingly, as it will be shown later, these retraction constants provided good agreement with the sinusoidal deployment cases.

Next, the Mach-number scaling capability of the model is evaluated. The unsteady lift results due to MiTE ramp retractions at M = 0.3 and M = 0.5 for sDEP = 10π

(k = 0.10) are compared with CFD in Figure 6.16. As it can be seen, the agreement of the unsteady lift result with respect to CFD for M = 0.5 is quite similar than for M = 0.3.

Both model and CFD responses match well for about half of the retraction cycle, but then

136 degrade with the model achieving the state-state lift earlier than predicted by CFD. It should be noted that part of the differences in the results are due to a change in behavior in the CFD lift response at about s = 20 for both Mach number cases. Nevertheless, the results show that the model is able to scale well from one Mach number to the other, proving the adequacy of the compressibility scaling adopted.

Figure 6.15. Model comparison with CFD results obtained for a VR-7 airfoil equipped with a MiTE positioned at 0.90c retracting at different speeds at M=0.3.

137

Figure 6.16. Model comparison with CFD results obtained for a VR-7 airfoil equipped with a MiTE positioned at 0.90c retracting at sDEP = 10π for different Mach numbers.

6.3.4 Sinusoidal Deployments

Having proved the effectiveness of the model in predicting both MiTE deployment and retraction cases, it is time to assess its capabilities to predict the unsteady lift of oscillating MiTEs. These conditions are of great interest in case MiTEs are used to decrease vibrations, noise, or the induced power of rotors, not to mention other applications. For all cases presented here, the configuration used is of a VR-7 airfoil equipped with a 0.02c high MiTE positioned at 0.90c operating at M = 0.3, R = 4x106, and α = 5°.

138 First, a plot in the time domain is presented, in which the lift responses from the model and CFD are compared in the first few deployment cycles before reaching the convergence. The unsteady lift results with respect to reduced time are shown in

Figure 6.17 for sinusoidal MiTE oscillations at k = 0.25. Starting from the static baseline solution, the evolution of the lift results from model and CFD follow close to each other until a converged oscillatory solution is obtained. The agreement is exceptionally good for all phases of the response. It is recognized here the importance of accurately capturing all three effects, circulatory, apparent mass, and vortex effects, to be able to achieve a reasonable converged solution.

Model results for the converged unsteady lift solutions for three MiTE oscillation reduced frequencies, k=0.1, k=0.25, and k=1.0, are contrasted with CFD predictions in

Figures 6.18 to 6.20. For these plots, the x-axes represent the normalized instantaneous

MiTE heights. Again, the agreement for all three cases is very good, considering the challenge of predicting all components of lift with accuracy.

In the lowest k case, the important features are captured well, including the maximum and minimum magnitudes of lift, as well as the phase lags. Towards the end of the retraction, discrepancies are observed that are due to sharp variations in the CFD lift results, observed previously in Figure 6.16. But these do not hurt the overall good agreement observed.

For the k = 0.25 case, the model again predicts the unsteady lift with great accuracy compared to the CFD results. The results are excellent during all the phases of the response, just as expected from the initial response presented in Figure 6.17.

Interestingly, the differences obtained in the ramp retraction response (Figure 6.15) are

139 not translated into the sinusoidal deployment. The reason is that good agreement was achieved up to about the point where the retraction ended (see Figure 6.15).

For the highest reduced frequency case, k = 1, the model predictions are in fair agreement with CFD results. The maximum and minimum lifts, as well as their position in the cycle, are very similar to the CFD predictions; however, details on the lift response shape are somewhat missed. It should be noted that this reduced frequency probably represents the edge of the envelope of operation for rotorcraft. Therefore, the overall agreement can be considered satisfactory.

Figure 6.17. Time domain comparison between model and CFD results for a VR-7 airfoil equipped with a MiTE positioned at 0.90c during sinusoidal deployment at k=0.25.

140

Figure 6.18. Model comparison with CFD results obtained for a VR-7 airfoil equipped with a MiTE positioned at 0.90c for sinusoidal deployments at k=0.1 and M=0.3.

Figure 6.19. Model comparison with CFD results obtained for a VR-7 airfoil equipped with a MiTE positioned at 0.90c for sinusoidal deployments at k=0.25 and M=0.3.

141

Figure 6.20. Model comparison with CFD results obtained for a VR-7 airfoil equipped with a MiTE positioned at 0.90c for sinusoidal deployments at k=1.0 and M=0.3.

6.3.5 Effects of airfoil shape and MiTE position

In this section, results of the model are contrasted with CFD results obtained for different airfoils and for different MiTE locations. The model constants were set based on results for the VR-7 airfoil with MiTEs positioned at 0.90c, therefore, the goal here is to assess the capability of the model in extrapolating the results to other airfoils and different MiTE locations.

The first set of results is for a S902 airfoil equipped with a 0.02c high MiTE positioned at 0.88c operating at M = 0.3, R = 4x106, and α = 5°. The unsteady lift response due to ramp deployments times of sDEP = 2π and sDEP = π ((k = 0.50, 1.0) for both CFD and the model are presented in Figure 6.21. Note that the position in which the

142 MiTE is located, 0.88c, is different than most results presented previously. Surprisingly, the model is able to predict most of the relevant features of the response. The vortex strength, speed, and decay, although set to agree with results of the VR-7 airfoil, are predicted quite well. The extra 0.02c travel for the vortex to reach the trailing edge acted as to let the vortex lift increase more than a MiTE at 0.90c would. On the other hand, it seems that the time constant that limits the growth of the vortex lift in the initial half- chords of travel (Tgrowth) is not very adequate and would need to be adjusted. Also, right after the vortex lift decays, the circulatory component seems to overpredict the increase in total lift. At about s = 15, however, the results converge and continue to approach the steady-state solution at about the same rate.

Figure 6.21. Model comparison with CFD results obtained for a S902 airfoil equipped with a MiTE positioned at 0.88c deploying at different speeds at M = 0.3.

143 Next, the model capabilities to predict the lift on the VR-12 airfoil with MiTEs positioned at both trailing edge and 0.90c are assessed with respect to CFD results. These cases are for a VR-12 airfoil equipped with a 0.02c high MiTE operating at M = 0.4,

R = 1.6x106, and α = 5°. The results are obtained for sinusoidal MiTE oscillations at a reduced frequency of k = 0.20. For the trailing-edge MiTE cases, the goal of the comparison is to evaluate the indicial circulatory constants that were set based on results for 0.90c.

Model results for the converged unsteady lift solution of oscillating MiTEs positioned at the trailing edge are contrasted with CFD predictions in Figure 6.22. With the MiTE at 1.0c, the vortex effects are zero and the model used is essentially the one presented in [3, 5] with slight modifications (Section 6.2) and different model constants

(Tables 6-1 and 6-2). As seen, the model seems to agree fairly well with the CFD on the magnitude of the amplitude and the phase lag, but the curve seems shifted down about

∆cl,norm = 0.07. This shift could be due to Reynolds number effects, as the model was set to agree with results at about R = 4x106. However, no formal conclusion can be made at this point. Model lift results for oscillating MiTEs positioned at 0.90c for the same reduced frequency as before are compared with CFD in Figure 6.23. As seen in the plot, the model overpredicts the effects of the vortex by a fair amount. This was somewhat expected, as the effect of the vortex in the VR-12 airfoil had been previously shown to be significantly smaller than for the S902 airfoil and the VR-7 airfoil (see Figure 5.2). Other than that, the amplitude of lift between the fully deployed and fully retracted positions are about the same for both CFD and model predictions. Again, about the same ∆cl,norm shift is seen in the lift response.

144

Figure 6.22. Model comparison with CFD results obtained for a VR-12 airfoil equipped with a MiTE positioned at 1.0c for sinusoidal deployments at k=0.2 and M=0.4.

Figure 6.23. Model comparison with CFD results obtained for a VR-12 airfoil equipped with a MiTE positioned at 0.9c for sinusoidal deployments at k=0.2 and M=0.4.

145 6.4 Summary

An aerodynamic model to predict the unsteady lift of MiTEs has been developed based on indicial concepts. The unsteady-lift model is a reduced-order, computationally- efficient, time domain model that is formulated in a one-step recursive form suitable to discrete-time rotor analyses. The model is an extension of a work previously done for

MiTEs at the trailing edge. Here, a vortex lift model has been developed and then incorporated into the previous MiTE model to be able to predict the aerodynamics of

MiTEs positioned upstream from the trailing edge.

A physics-based approach has been adopted to minimize the number of constants and correlations, but also to improve generality of the model. The vortex lift has been idealized as a build-up of negative circulation and then modeled using a formulation that is similar to that of a circulatory lift. The position of the vortex in the lower surface of the airfoil is tracked by a time constant to define the onset of vortex decay, and adequate functions are used to assure proper behavior of vortex growth and decay. Slight modifications in the circulatory and apparent mass terms of the original model have also been performed in order to improve consistency and decrease total number of constants.

Although only a model for lift has been described, it is believed that a pitching-moment model can be easily developed by modeling the shift in the airfoil‟s center of pressure due to the convection of the vortex.

The unsteady lift model has been compared with available CFD results on several configurations and flow conditions. Model results for MiTEs being deployed through ramps at several deployment times have shown very good agreement with CFD, proving

146 the validity of the superposition principle for sDEP ≥ π. Ramp deployment cases have been evaluated at a higher Mach number and have demonstrated the effectiveness of the adopted compressibility scaling. Assessment of the results at other Mach numbers may be necessary to check the adequacy of the scaling at other relevant rotorcraft conditions.

Results for retracting MiTEs have shown good agreement with CFD, especially in the initial phases of the response.

The model has also been evaluated to predict oscillating MiTE cases. Again, the lift results have been shown to follow closely the ones predicted by CFD, especially at the lower reduced frequency range. At high frequencies, the agreement deteriorates, but most features of the lift response are well captured.

At last, results of the model have been compared with CFD for different airfoils and MiTE chordwise locations. For the S902 airfoil with a MiTE positioned at 0.88c, the model has been successful in predicting the unsteady lift even though the model constants had been set based on results for the VR-7 airfoil. In this case, the vortex model was able to account for the higher vortex effects that are expected for more upstream MiTE locations. For the VR-12 airfoil with a MiTE positioned at 0.90c, however, the model failed to provide a good estimation of the unsteady lift. This was somewhat expected, as the vortex effect behavior on the VR-12 airfoil had been shown to be dramatically different than the other two airfoils. Therefore, new model constants are necessary to predict these differences.

Chapter 7

Conclusions

7.1 Summary of Results

In the present research, the steady and unsteady aerodynamics of MiTEs have been studied with the use of experimental, numerical, and analytical methods. In this section, a summary of the results obtained for each one of these is outlined.

7.1.1 Static Gurney Flap Experiments

A static experimental investigation of Gurney flaps is undertaken at a highly- regarded wind tunnel at Penn State. Aerodynamic forces and moments are obtained for distinct rotorcraft airfoils equipped with Gurney flaps of various sizes and placed at different chordwise locations. The effects of Gurney flaps are found to be very dependent on the combination of Gurney flap height and location, as well as the airfoil shape. It is observed that in some cases, the Gurney flap can become ineffective and provide a decrease in the cl,max of the airfoil. Pressure distributions suggest that the flow downstream of the flap reattaches before reaching the trailing edge. This could be the mechanism that impedes the increase in lift, by eliminating the shift in the Kutta condition, and preventing any major changes in the pressures at the upper surface of the

148 airfoil. The trends suggest that Gurney flaps with different heights may also decrease cl,max if placed far enough forward from the trailing edge. For the cases where the Gurney flaps are effective, a general agreement is observed with respect to results obtained from other researchers.

7.1.2 Unsteady MiTEs Experiments

An experimental investigation of the unsteady aerodynamics of MiTEs undertaken at the Mid-Sized Wind Tunnel at Penn State has been presented. A S903 airfoil has been equipped with spanwise segmented MiTEs with heights of 0.019c and positioned at the 0.90c of the airfoil. Static measurements have been taken and compared to results obtained at the Low-Speed, Low-Turbulence Wind Tunnel using the same airfoil model. Only the lift results have shown fair agreement and, therefore, are the only ones considered from the unsteady measurements. Both ramp and oscillatory MiTE deployments have been investigated at frequencies ranging from 2 to 15 Hz and at flow velocities of 77, 113, and 135 ft/s. The amplitude and phase lag of the results generally agree with the trends predicted by the unsteady linear Theordorsen‟s theory. It is noticed for some cases, however, the occurrence of non-linear effects that are believed to be caused by vortex shedding in the lower surface of the airfoil. These effects seem to be aggravated as the frequency of deployment increases, but the variability of the results made it difficult to draw any formal conclusions.

The wind tunnel results have been contrasted with predictions of an unsteady aerodynamic model that was previously adapted from an unsteady trailing-edge flap

149 model. The results show good agreement at the lowest flow velocity cases, but not so much at higher velocities. As expected, the model is not able to capture any of the non- linear effects caused by the fact that the MiTEs are placed upstream from the trailing edge.

7.1.3 Unsteady Aerodynamic Modeling

An aerodynamic model to predict the unsteady lift of MiTEs has been developed based on indicial concepts. The unsteady-lift model is an extension of a work previously done for trailing edge MiTEs, but includes a vortex model that allows it to predict the aerodynamics of upstream MiTEs. A physics-based approach has been adopted to minimize the number of constants and correlations, but also to improve generality of the model. Slight modifications in the circulatory and apparent mass terms of the original model have also been performed in order to improve consistency and decrease total number of constants. The lift model has been compared with available CFD results on different airfoils, MiTE deployment schedules, MiTE chordwise positions, and Mach numbers. Very good agreement has been shown for the wide range of conditions that are typical of rotorcraft. Different model constants and correlations may have to be considered in order to improve the results for different airfoil shapes.

150 7.2 Conclusions

The goals of the present study were presented in Chapter 1, and to some extent, these objectives were all well accomplished. Although there is still a lot to advance, great improvement in the understanding of MiTE aerodynamics has been achieved. Also, the development of a MiTE model that is able to predict the unsteady aerodynamics of upstream-located MiTEs will certainly help define the applicability and potential benefits of this active device to rotorcraft.

High quality static data on Gurney flaps was obtained on different airfoils.

Considering the variability of the results for different configurations or airfoil shapes, it is concluded that great care is necessary when sizing Gurney flaps or MiTEs. Whenever possible, wind tunnel measurements should be used as they are one of the most reliable sources of aerodynamic data. The experimental data presented herein, including high- quality drag measurements and pressure distributions, provide a valuable database for computational code validations, and should be used whenever specific experiments are not feasible.

The effectiveness of MiTEs in providing variations in lift under dynamic oscillations was proved. Due to limitations of the wind tunnel and the experimental set-up used, it is not believed that the results obtained here are ultimate and definitive. Better quality data needs to be taken before these results can be used with confidence for the validation of CFD computations and the development of aerodynamic models.

Nevertheless, this test provided valuable information about the unsteady aerodynamic of

MiTEs that will certainly help planning and guiding future experimental efforts.

151 An aerodynamic model to predict the unsteady lift of MiTEs was developed.

Comparison with CFD results at various flow conditions and MiTE configurations gave confidence in the capability of the model. Whenever applying it to different airfoils or conditions that go beyond the ones presented here, care must be taken. When possible, experimental or numerical validation of the constants and correlations obtained here should be performed, as they may change for one airfoil to another. The model is computationally efficient and can be easily incorporated into discrete-time rotor analysis codes.

7.3 Recommendations for Future Work

7.3.1 Experimental and Numerical Efforts

The wind tunnel investigation described in Chapter 4 provided some valuable information on the unsteady aerodynamic of MiTEs; however, limitations of the wind tunnel and the experiment set-up itself restricted the result from being used for validation purposes. Future efforts on the research of MiTEs should prioritize the development of a higher quality wind tunnel test on oscillating MiTEs. These would help validate current

CFD methodologies and give confidence into the accuracy of the approximate unsteady methods developed in the present work. Careful planning needs to be made to maximize the information obtained in these tests. If possible, unsteady pressure transducers should be used instead of load balances. The transducers should be properly placed at the

152 vicinity of the MiTE to assure no relevant details in the pressure distributions are being missed.

Also very important for the ultimate application of MiTEs to rotorcraft, an evaluation of the 3-D aerodynamic effects on MiTEs need to be performed. In a rotor,

MiTEs are expected to be deployed only at certain radius locations and, therefore, with finite span; also, it is not known if centrifugal effects may affect the results. Initially, results from CFD can help provide some understanding of the physics, but ultimately rotor-stand test may have to be performed.

Another relevant issue to consider for future work is the use of different MiTE shapes. Slight modifications on the shape of Gurney flaps have been shown to reduce the drag of Gurney flaps, with the penalty of small decrease in lift augmentation. These should be properly quantified computationally and experimentally to assess their real benefits in application.

7.3.2 Unsteady MiTE Modeling

Several suggestions can be made to improve the aerodynamic model developed for upstream MiTEs.

Models to predict the pitching-moment and drag coefficients need to be developed for a proper evaluation of all the effects of upstream MiTEs. It is believed that a pitching-moment model can be easily created by modeling the shift in the airfoil‟s center of pressure due to the convection of the vortex, following the work done for the dynamic stall vortex in [77, 78].

153 The model compressibility scaling has been validated with results for only two

Mach numbers, M = 0.3 and M = 0.5. CFD results at other Mach numbers need to be performed to assure accuracy of the model scaling at other conditions that may be relevant to rotorcraft.

CFD results have provided evidence that the unsteady response due to MiTE deployment depends on the airfoil‟s angle of attack (Figure 5.11). Effects on the apparent mass terms, as well as in the vortex effect are apparent and need to be addressed by the model. This can be achieved by modifying the expression for the vortex speed (VVTX) and the effective flap size (eeff, to be dependent on airfoil‟s angle of attack.

Non-linear indicial methods [66] could also be potentially incorporated into the unsteady-lift MiTE model to predict the aerodynamics at conditions that are inherently non-linear, such as high angles of attack near or post-stall, as well as supercritical flows with shock wave movement [66].

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