ABSTRACT
Title of dissertation: ACTIVE CONTROL OF PERFORMANCE
AND VIBRATORY LOADS
USING TRAILING-EDGE FLAPS
AND LEADING-EDGE SLATS
Kumar Ravichandran
Doctor of Philosophy, 2019
Dissertation directed by: Professor Inderjit Chopra
Department of Aerospace Engineering
The objective of this research work is to develop a comprehensive analysis
version of UMARC (University of Maryland Advanced Rotor Code) to study the
capabilities of trailing-edge flaps (TEFs)and leading-edge slats (LESs) for helicopter
vibration reduction and performance improvement and recommend flap and slat
configurations for a typical helicopter rotor such as UH-60A rotor, which maximize
these benefits. This study uses propulsive free-flight trim except in hover. Using
TEFs , the rotor performance in hover was improved with a combination of torsion-
ally softer blades and positive TEF deflections. For the vibration reduction studies,
a multicyclic control algorithm was used to determine the actuation schedule . Suit-
able combinations of lower harmonic TEF inputs were shown capable of reducing the
rotor power requirement by about 4-5 % at an advance ratio of µ = 0.4. The TEF
was shown to be capable of suppressing the vibratory loads at a range of forward
speeds, using half peak-to-peak deflections of about 5◦ − 10◦. Softening the blades
in torsion resulted in larger flap actuation requirements for vibration reduction.
Parametric sweeps of TEF actuations were carried out to determine suitable combi-
nations of steady and various frequencies of actuation of flaps , which yield overall
power reductions and it is observed that a combination of 1, 2, 3, 4 and 5/rev TEF
inputs resulted in a power reduction of 1.5% , while also reducing certain vibratory
loads by more than 50% in high speed-forward flight.
To explore the advantages of leading-edge slats, the slatted airfoils with config-
urations S0, S1 and S6 (used by Sikorsky) were used.The slatted blade sections had
the SC2110 baseline/slatted airfoils in place of the baseline UH-60A airfoils. Dy-
namic actuations are chosen to retain the high-lift benefits of the slats while seeking
to minimize profile drag penalties over regions of the rotor disk operating at lower
angles of attack, i.e., the advancing side.The effects of leading-edge slats extending
over 20%, 30% and 40% of the blade span on rotor performance and vibratory hub
loads were examined. The study uses propulsive free flight trim. In moderate to
high-speed forward flight,leading-edge slats were shown to enhance the maximum
rotor thrust by 15-30% at advance ratios larger than 0.2 and reduce power require-
ments by 10-20% at high thrust levels. 20% span slats offered a good compromise
between power reductions and adverse effect on vibratory hub loads.The rotor with
leading-edge slats could be trimmed at a maximum forward speed that was about
20 knots greater than for the baseline rotor with no slats.
This study also shows that additional power reduction is achievable by suitable
TEF deployments superimposed on certain slat actuations in high-speed forward
flight.
ACTIVE CONTROL OF PERFORMANCE AND
VIBRATORY LOADS USING TRAILING-EDGE FLAPS
AND LEADING-EDGE SLATS
by
Kumar Ravichandran
Dissertation submitted to the Faculty of the Graduate School of the
University of Maryland, College Park in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy
2019
Advisory Committee:
Professor Inderjit Chopra, Chair/Advisor
Professor James Baeder
Professor Olivier A. Bauchau
Associate Professor Anubhav Datta
Associate Professor Nikhil Chopra (Dean’s representative)
Acknowledgments
I am pleased to put down all that went through my mind as part of this
experience. I would like to thank my advisor, Dr. Inderjit Chopra, my longtime
pillar of support, for his dedication and single-mindedness. He guided me first and
foremost, but for all my mistakes he put up with, I have to thank him over again.He
was instrumental in shaping a great deal of my research.
My special thanks to Dr. V. Nagaraj for his help.
In addition, former students of my advisor, most notably Dr. Jaye Falls and
Dr. Anubhav Datta (now Associate professor,Department of Aerospace Engineering,
UMD), for sharing their expertise with UMARC.
This research was partially funded by the Aviation Applied Technology Direc-
torate (AATD) and I wish to record my gratitude to Sikorsky Aircraft, Stratford,
CT, for their longtime support.
My colleagues at the Alfred Gessow Rotorcraft Center have been very helpful
in providing technical assistance. I would like to thank Benjamin Hein, Senior
Engineer of Sikorsky Aircraft and Brian E. Wake, Technical Fellow, UTRC(now at
Sikorsky), for many discussions.
I would like to mention my colleagues Anand Saxena, Ananth Sridharan, Gra-
ham Bowen-Davies, Chen Friedman, Sivaji Medida, for their contributions to my
work.
I would like to acknowledge Dr. Shreyas Ananthan, who helped me with so
much throughout this research he served as the additional advisor whenever I had
ii
doubts. He was the bedrock for an entire office of students.
A special and grateful bow to my parents who have displayed a firm conviction
which has truly astonished me considering how long this process has lasted. I would
like to thank my brother as well, who stood with me during my difficult phases.
iii
Table of Contents
Preface ii
Foreword ii
Dedication ii
Acknowledgements ii
Table of Contents iv
List of Tables vii
List of Figures viii
1 Introduction 1
1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Vibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Vibration reduction techniques . . . . . . . . . . . . . . . . . . . . . . 6
1.3.1 Higher harmonic control . . . . . . . . . . . . . . . . . . . . . 9
1.3.2 Individual Blade Control . . . . . . . . . . . . . . . . . . . . . 10
1.4 Performance enhancement techniques . . . . . . . . . . . . . . . . . . 11
1.5 Trailing-edge flaps . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.6 Trailing-edge flaps for primary control . . . . . . . . . . . . . . . . . 12
1.7 TEFs for Vibration Reduction and Performance Enhancement . . . . 13
1.8 Dynamic Stall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.9 LESs for vibration reduction and Performance Enhancement . . . . . 18
1.10 Goal of this research . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
1.10.1 Analysis with Trailing-edge flaps . . . . . . . . . . . . . . . . 24
1.10.2 Analysis with Leading-edge slats . . . . . . . . . . . . . . . . 24
1.10.3 Analysis of Superimposition of TEFs and LESs . . . . . . . . 25
1.11 Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
1.11.1 TEF studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
1.11.2 LES studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
1.11.3 Studies of superimposition of TEFs and LESs . . . . . . . . . 29
List of Abbreviations 1
iv
2 Methodology 31
2.1 Validation of UMARC and determination of Stall Boundaries . . . . . 32
2.2 Analytical Model:TEFs . . . . . . . . . . . . . . . . . . . . . . . . . . 44
2.3 TEF blade section aerodynamic characteristics . . . . . . . . . . . . . 45
2.4 Multicyclic Controller for TEFs . . . . . . . . . . . . . . . . . . . . . 45
2.5 Analytical Model: LES . . . . . . . . . . . . . . . . . . . . . . . . . . 58
2.5.1 Leading-edge slat structural model . . . . . . . . . . . . . . . 58
2.5.2 Description of slat motion . . . . . . . . . . . . . . . . . . . . 62
2.5.3 Hamilton’s principle . . . . . . . . . . . . . . . . . . . . . . . 64
2.5.4 Strain Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
2.5.5 Kinetic Energy . . . . . . . . . . . . . . . . . . . . . . . . . . 71
2.5.6 Non-conservative forces - virtual work . . . . . . . . . . . . . . 81
2.5.7 Assembly of final equations of motion . . . . . . . . . . . . . . 81
2.6 Slatted airfoil characteristics: . . . . . . . . . . . . . . . . . . . . . . 82
2.7 Validation of the leading-edge slat model . . . . . . . . . . . . . . . . 82
3 Trailing-Edge Flaps 91
3.1 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 91
3.2 Blade torsional stiffness and TEF effectiveness . . . . . . . . . . . . . 92
3.3 Hover performance with TEFs . . . . . . . . . . . . . . . . . . . . . . 93
3.4 Rotor performance in high speed forward flight with TEFs . . . . . . 96
3.4.1 Case I: Advance ratio µ = 0.3 . . . . . . . . . . . . . . . . . . 100
3.4.2 Case II: Advance ratio µ = 0.4 . . . . . . . . . . . . . . . . . 103
3.5 Rotor vibration reduction with TEFs : High speed flight condition
(C8534) - µ=0.368, CW/σ=0.0783 . . . . . . . . . . . . . . . . . . . . 108
3.5.1 Contours of vibratory loads: . . . . . . . . . . . . . . . . . . . 109
3.5.2 Multicyclic Controller - different targets: . . . . . . . . . . . . 112
3.5.3 Vibration reduction at various speeds: . . . . . . . . . . . . . 114
3.5.4 Effect of torsional stiffness on vibration reduction: . . . . . . . 116
3.5.5 Effect of not using 5/rev TEF inputs for vibration reduction: . 121
3.5.6 Stall alleviation with TEFs - ‘down-only’ 1/rev TEF inputs . 121
3.6 Simultaneous power, vibration and stall reduction with ’down-only’
1/rev TEF inputs: High thrust flight condition(C9017) . . . . . . . . 123
3.7 Power reduction with 1,2/rev TEF inputs:High speed flight condition
(C8534) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
3.8 Simultaneous power and vibration reduction with TEFs : High speed
flight condition (C8534) . . . . . . . . . . . . . . . . . . . . . . . . . 131
3.9 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
4 Leading-Edge Slats 137
4.1 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 137
4.2 Lift Boundary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
4.3 Visualising maximum lift flight condition . . . . . . . . . . . . . . . . 142
4.4 Power requirement with Leading-Edge Slats . . . . . . . . . . . . . . 147
4.5 Vibratory hub loads with Leading-Edge Slats . . . . . . . . . . . . . . 157
v
4.6 Varying span-size of Leading-Edge Slats . . . . . . . . . . . . . . . . 159
4.7 Forward flight speed limit with Leading-Edge Slats . . . . . . . . . . 160
4.8 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
6 Summary and conclusions 169
6.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
6.2 Conclusions-TEFs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
6.3 Conclusions-LESs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
6.4 My publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
6.4.1 Journal papers . . . . . . . . . . . . . . . . . . . . . . . . . . 176
6.4.2 Conference Papers . . . . . . . . . . . . . . . . . . . . . . . . 176
6.5 Future areas of research . . . . . . . . . . . . . . . . . . . . . . . . . 177
Bibliography 179
vi
List of Tables
2.1 Basic rotor,flap and slat data . . . . . . . . . . . . . . . . . . . . . . 47
2.2 3/rev and 4/rev TEF actuations for minimization of diferent loads . 49
2.3 5/rev TEF actuations for minimization of diferent loads . . . . . . . 50
2.4 Multicyclic control for minimization of 4/rev vibratory loads:C8534 . 55
2.5 Multicyclic control for minimization of J :C8534 . . . . . . . . . . . . 56
2.6 Multicyclic control for minimization of J : CW/σ = 0.08,at various
forward flight speeds . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
vii
List of Figures
1.1 Flow structure and some aerodynamic problem areas on a helicopter
in forward flight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Stages of dynamic stall on a helicopter blade . . . . . . . . . . . . . . 17
1.3 Flight envelope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.1 Comparison of the McHugh lift boundary with UMARC prediction . 35
2.2 Trim settings for points on the predicted UMARC lift boundary . . . 36
2.3 Trend of the trim angles for constant CT/σ=0.07-0.1 . . . . . . . . . 37
2.4 Angle of attack distribution for µ=0.237,CT/σ=0.09 . . . . . . . . . . 38
2.5 Pitching moment distribution for µ=0.237,CT/σ=0.09 . . . . . . . . . 38
2.6 Angle of attack for static Cm stall;µ=0.237,CT/σ=0.09 . . . . . . . . 38
2.7 Angle of attack distribution for µ=0.237,CT/σ=0.011 . . . . . . . . . 39
2.8 Pitching moment distribution for µ=0.237,CT/σ=0.011 . . . . . . . . 39
2.9 Angle of attack for static Cm stall;µ=0.237,CT/σ=0.011 . . . . . . . . 39
2.10 Angle of attack distribution for µ=0.237,CT/σ=0.1325 . . . . . . . . 40
2.11 Pitching moment distribution for µ=0.237,CT/σ=0.1325 . . . . . . . 40
2.12 Angle of attack for static Cm stall;µ=0.237,CT/σ=0.1325 . . . . . . . 40
2.13 Angle of attack distribution for µ=0,CT/σ=0.153 . . . . . . . . . . . 41
2.14 Pitching moment distribution for µ=0,CT/σ=0.153 . . . . . . . . . . 41
2.15 Angle of attack distribution for µ=0.15,CT/σ=0.14 . . . . . . . . . . 42
2.16 Pitching moment distribution for µ=0.15,CT/σ=0.14 . . . . . . . . . 42
2.17 Angle of attack for static Cm stall;µ=0.15,CT/σ=0.14 . . . . . . . . . 42
2.18 Angle of attack distribution for µ=0.3,CT/σ=0.12 . . . . . . . . . . . 43
2.19 Pitching moment distribution for µ=0.15,CT/σ=0.12 . . . . . . . . . 43
2.20 Angle of attack for static Cm stall for µ=0.3,CT/σ=0.12 . . . . . . . 43
2.21 2D CFD-generated airfoil characteristics (SC1094R8) with −5◦ and
5◦ TEF deflections at M = 0.5 . . . . . . . . . . . . . . . . . . . . . . 46
2.22 Multicyclic control of three hub forces for optimal TEF actuations
for various GJ: C8534 . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
2.23 2 degree-of-freedom slat model . . . . . . . . . . . . . . . . . . . . . . 58
2.24 3 degree-of-freedom slat model . . . . . . . . . . . . . . . . . . . . . . 60
2.25 2 and 3 degrees of freedom slat models . . . . . . . . . . . . . . . . . 60
2.26 Slat configurations with respect to baseline airfoil . . . . . . . . . . . 62
viii
2.27 Definition of ’effective’ chord . . . . . . . . . . . . . . . . . . . . . . . 63
2.28 Definition of slat degrees of freedom . . . . . . . . . . . . . . . . . . . 64
2.29 Correlation between experiments and slat motion . . . . . . . . . . . 85
2.30 2D CFD-generated airfoil characteristics . . . . . . . . . . . . . . . . 86
2.31 Hover performance with slatted airfoils . . . . . . . . . . . . . . . . . 87
2.32 UH-60A main rotor power in forward flight(flight 85) . . . . . . . . . 88
2.33 UH-60A main rotor power in forward flight(flight 84) . . . . . . . . . 89
2.34 Slat actuations.Actuation 1 passes through S1 at ψ = 90◦ and S6 at
ψ = 270◦, and Actuation 2 passes through S0 at ψ = 90◦ and S6 at
ψ = 270◦ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
3.1 Baseline UH-60A hover performance . . . . . . . . . . . . . . . . . . 92
3.2 Uh-60A rotor blade frequencies in vacuo;F:Flap, L:Lead-Lag,T:Torsion 93
3.3 Effect of TEF (10%R, 15%c, midspan location at 65%R) deflection
on baseline UH-60A rotor figure of merit; hover . . . . . . . . . . . . 95
3.4 Percent change in induced, profile and total power for UH-60A rotor
in comparison to baseline for different TEF deflections; hover . . . . . 96
3.5 Effect of GJ with no TEF on baseline UH-60A rotor figure of merit;
hover . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
3.6 Effect of a 25% reduction in GJ and 10◦ TEF deflection on UH-60A
rotor figure of merit; hover . . . . . . . . . . . . . . . . . . . . . . . . 98
3.7 Effect of a 25% reduction in blade GJ and 10◦ TEF deflection on the
spanwise variation of UH-60A rotor blade elastic twist and section
normal force; hover, CT/σ=0.12 . . . . . . . . . . . . . . . . . . . . . 98
3.8 Effect of 2/rev phasing of TEF (10%R, 15%c, midspan location at
65%R) inputs δ = δsteady + δ2pcos(2ψ+φ2p) on UH-60A rotor power
for different weights; µ = 0.3 . . . . . . . . . . . . . . . . . . . . . . . 99
3.9 Effect of 1/rev phasing of TEF (10%R, 15%c, midspan location at
65%R) inputs δ = δsteady + δ1pcos(ψ + φ1p) + δ2pcos(2ψ + φ2p) on
UH-60A rotor power for different weights; µ = 0.3 . . . . . . . . . . . 100
3.10 Effect of 2/rev phasing of TEF (10%R, 15%c, midspan location at
65%R) inputs δ = δsteady + δ2pcos(2ψ+φ2p) on UH-60A rotor power
for different weights; µ = 0.4 . . . . . . . . . . . . . . . . . . . . . . . 102
3.11 Change in UH-60A rotor disk loading from baseline rotor, due to
2/rev TEF (10%R, 15%c, midspan location at 65%R) input δ =
2.5◦ + 5◦cos(2ψ+ 30◦); µ = 0.4, CW/σ = 0.085; Blue-decrease, Red-
increase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
3.12 Effect of 1/rev phasing of TEF (10%R, 15%c, midspan location at
65%R) inputs δ = δsteady + δ1pcos(ψ + φ1p) + δ2pcos(2ψ + φ2p) on
UH-60A rotor power for different weights; µ = 0.4 . . . . . . . . . . . 103
3.13 Change in UH-60A rotor disk loading due to 1/rev TEF (10%R, 15%c,
midspan location at 65%R) input 5◦cos(ψ + 30◦) superimposed on
2/rev input δ = 2.5◦ + 5◦cos(2ψ + 30◦); µ = 0.4, CW/σ = 0.085;
Blue-decrease, Red-increase . . . . . . . . . . . . . . . . . . . . . . . 103
ix
3.14 Effect of 1/rev phasing of TEF (10%R, 15%c, midspan location at
65%R) inputs δ = δsteady + δ1pcos(ψ + φ1p) + δ2pcos(2ψ + φ2p) on
UH-60A rotor power for CW/σ = 0.08. . . . . . . . . . . . . . . . . . 107
3.15 Effect of 1/rev phasing of TEF (10%R, 15%c, midspan location at
65%R) inputs δ = δsteady + δ1pcos(ψ + φ1p) + δ2pcos(2ψ + φ2p) on
vibration index J1 for UH-60A rotor; CW/σ = 0.08. . . . . . . . . . . 107
3.16 Effect of 1/rev phasing of TEF (10%R, 15%c, midspan location at
65%R) inputs δ = δsteady + δ1pcos(ψ + φ1p) + δ2pcos(2ψ + φ2p) on
UH-60A rotor L/D for CW/σ = 0.08 . . . . . . . . . . . . . . . . . . 108
3.17 UH-60A 4/rev hub loads with 4/rev TEF inputs; high speed forward
flight (C8534: µ=0.368, CW/σ=0.0783). Values shown are % changes
in vibratory amplitude relative to the baseline (no flaps). The high-
lighted region corresponds to reduction of the respective vibratory
load. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
3.18 Vibration objective function J1 and Vibration Intrusion Index with
4/rev TEF inputs; UH-60A rotor in high speed forward flight (C8534).
Values shown are % changes relative to the baseline (no flaps). The
highlighted regions correspond to reduction of the respective vibra-
tory index. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
3.19 UH-60A rotor baseline (no flap) and reduced 4/rev vibratory loads for
different targets for reduction using the multicyclic control algorithm;
high speed forward flight (C8534). Fx: longitudinal shear, Fy: lateral
shear, Fz: vertical shear, Mx: rolling moment, My: pitching moment,
J : target Fx, Fy, Fz, Mx and My. The horizontal lines indicate the
baseline vibratory hub loads (uncontrolled). . . . . . . . . . . . . . . 112
3.20 UH-60A rotor baseline (no flap) vibratory loads and optimal TEF
actuation amplitudes for various speeds; moderate thrust forward
flight (Flight 85), CW/σ=0.0783 . . . . . . . . . . . . . . . . . . . . . 113
3.21 UH-60A rotor baseline (no flap) and reduced vibratory loads; high
thrust forward flight (C9017: µ=0.237, CW/σ=0.1325). Fx: longitu-
dinal shear, Fy: lateral shear, Fz: vertical shear, Mx: rolling moment,
My: pitching moment. The loads targeted for reduction were Fz, Mx
and My. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
3.22 UH-60A rotor baseline (no flap) and reduced vibratory loads for differ-
ent blade torsional stiffnesses (GJ); high speed forward flight (C8534).
Fx: longitudinal shear, Fy: lateral shear, Fz: vertical shear, Mx:
rolling moment, My: pitching moment. The loads targeted for reduc-
tion were Fx, Fy, Fz, Mx and My. . . . . . . . . . . . . . . . . . . . . 117
3.23 Components of UH-60A rotor baseline (no flap) HPP blade root loads
for different blade torsional stiffnesses (GJ); high speed forward flight
(C8534). fx: lateral shear, fy: longitudinal shear, fz: vertical shear,
mx: torsion bending moment, my: flapwise bending moment . . . . . 118
3.24 Flap deflection amplitudes for UH-60A vibration reduction for differ-
ent blade torsional stiffnesses (GJ); high speed forward flight (C8534).
HPP: half peak-to-peak amplitude of optimal actuation . . . . . . . . 119
x
3.25 Comparison of UH-60A vibration reduction obtained with 3–5/rev
TEF deflections and only 3 and 4/rev deflections; high speed forward
flight (C8534) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
3.26 Effect of phasing of down-only 1/rev TEF inputs δ = δ0 +δ0 cos(ψ−φ)
on UH-60A rotor power and stall metric CTors; high thrust forward
flight (C9017). φ is thus the azimuth for maximum positive (down-
ward) TEF deflection. . . . . . . . . . . . . . . . . . . . . . . . . . . 125
3.27 TEF actuation combining inputs for UH-60A power, vibration and
stall reduction; high thrust forward flight (C9017). The individual
components for vibration reduction and power/stall reduction are also
shown. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
3.28 Effect of phasing of down-only 1/rev TEF inputs δ = δ0 +δ0 cos(ψ−φ)
on UH-60A vibratory loads; high thrust forward flight (C9017). φ is
thus the azimuth for maximum positive (downward) TEF deflection. . 126
3.29 Change in UH-60A rotor disk loading from baseline, due to 2/rev
TEF input δ = 5◦cos(2ψ + 15◦); high speed forward flight (C8534);
Blue-decrease, Red-increase . . . . . . . . . . . . . . . . . . . . . . . 126
3.30 Effect of phasing of 1/rev TEF inputs δ = δ0 cos(ψ + φ) on UH-60A
vibratory loads; high speed forward flight (C8534) . . . . . . . . . . . 127
3.31 Effect of phasing of 2/rev TEF inputs δ = δ0 cos(2ψ+φ) on UH-60A
vibratory loads; high speed forward flight (C8534) . . . . . . . . . . . 128
3.32 Effect of phasing of 2/rev TEF inputs δ = δ0 cos(2ψ+φ) on UH-60A
rotor power (% change from baseline); moderate thrust forward flight
(Flight 85), CW/σ=0.0783 . . . . . . . . . . . . . . . . . . . . . . . . 129
3.33 Effect of phasing of 1 and 2/rev TEF inputs on UH-60A rotor power;
high thrust forward flight (C9017) . . . . . . . . . . . . . . . . . . . . 131
3.34 Effect of phasing of 1/rev TEF inputs δ = δ0 cos(ψ + φ) on UH-60A
vibratory loads; high thrust forward flight (C9017) . . . . . . . . . . . 131
3.35 Effect of phasing of 2/rev TEF inputs δ = δ0 cos(2ψ+φ) on UH-60A
vibratory loads; high thrust forward flight (C9017) . . . . . . . . . . . 132
3.36 Separate and combined effects of 1 plus 2/rev TEF input δ = 3◦cos(ψ+
φ1p)+3
◦cos(2ψ+30◦) on UH-60A rotor power, for three cases: (i) only
1, 2/rev, (ii) only vibration optimization and (iii) vibration optimiza-
tion including 1, 2/rev; high speed forward flight (C8534); vibration
objective function: J1. . . . . . . . . . . . . . . . . . . . . . . . . . . 133
3.37 Separate and combined effects of 1 plus 2/rev TEF input δ = 3◦cos(ψ+
φ ◦1p)+3 cos(2ψ+30
◦) on UH-60A vibratory hub shears and moments,
for three cases: (i) only 1, 2/rev, (ii) only vibration optimization and
(iii) vibration optimization including 1, 2/rev; high speed forward
flight (C8534); vibration objective function: J1. . . . . . . . . . . . . 134
4.1 UH-60A rotor lift boundary with and without fixed (S1,S6) slats from
50-90%R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
xi
4.2 UH-60A rotor lift boundary with and without active slats from 50-
90%R ; Actuations 1 & 2: dynamic actuations between low drag
positions on advancing side and high lift position on retreating side . 140
4.3 UH-60A rotor lift boundary with attached flow assumption and dy-
namic stall model: baseline rotor and with fixed S6 slats from 50-90%R141
4.4 Baseline UH-60A rotor: stalled blade sections for different operating
thrust levels, µ = 0.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
4.5 UH-60A rotor with fixed S6 slats from 50-90%R: stalled blade sections
for different operating thrust levels, µ = 0.3 . . . . . . . . . . . . . . 144
4.6 UH-60A rotor without and with fixed slats from 50-90%R: % of rotor
disk with stalled airfoil sections . . . . . . . . . . . . . . . . . . . . . 146
4.7 UH-60A rotor without and with fixed slats from 50-90%R: dynamic
indicator of rotor stall Cmx/σ . . . . . . . . . . . . . . . . . . . . . . 147
4.8 UH-60A components of rotor power vs thrust at µ = 0, without and
with slats from 50-90%R ; Actuations 1 & 2: dynamic actuations
between low drag positions on advancing side and high lift position
on retreating side . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
4.9 UH-60A rotor without and with fixed slats from 50-90%R: dynamic
indicator of rotor stall Cmx/σ . . . . . . . . . . . . . . . . . . . . . . 149
4.10 UH-60A components of rotor power vs thrust at µ = 0, without and
with slats from 50-90%R ; Actuations 1 & 2: dynamic actuations
between low drag positions on advancing side and high lift position
on retreating side . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
4.11 UH-60A components of rotor power vs thrust at µ = 0.1, without
and with slats from 50-90%R ; Actuations 1 & 2: dynamic actuations
between low drag positions on advancing side and high lift position
on retreating side . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
4.12 UH-60A components of rotor power vs thrust at µ = 0.2, without
and with slats from 50-90%R ; Actuations 1 & 2: dynamic actuations
between low drag positions on advancing side and high lift position
on retreating side . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
4.13 UH-60A components of rotor power vs thrust at µ = 0.3, without
and with slats from 50-90%R ; Actuations 1 & 2: dynamic actuations
between low drag positions on advancing side and high lift position
on retreating side . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
4.14 UH-60A hub vibratory loads vs thrust at µ = 0.1, without and with
slats from 50-90%R ; Actuations 1 & 2: dynamic actuations between
low drag positions on advancing side and high lift position on retreat-
ing side . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
4.15 UH-60A hub vibratory loads vs thrust at µ = 0.2, without and with
slats from 50-90%R ; Actuations 1 & 2: dynamic actuations between
low drag positions on advancing side and high lift position on retreat-
ing side . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
xii
4.16 UH-60A hub vibratory loads vs thrust at µ = 0.3, without and with
slats from 50-90%R ; Actuations 1 & 2: dynamic actuations between
low drag positions on advancing side and high lift position on retreat-
ing side . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
4.17 UH-60A components of rotor power vs thrust at CW/σ = 0.08, with-
out and with slats of varying spanwise lengths; Actuation 2: dynamic
actuation between low drag positions on advancing side and high lift
position on retreating side . . . . . . . . . . . . . . . . . . . . . . . . 161
4.18 UH-60A vibratory hub loads vs thrust at CW/σ = 0.08, without and
with slats of varying spanwise lengths; Actuation 2: dynamic ac-
tuation between low drag positions on advancing side and high lift
position on retreating side . . . . . . . . . . . . . . . . . . . . . . . . 162
4.19 UH-60A components of rotor power vs thrust at CW/σ = 0.1, without
and with slats of varying spanwise lengths; Actuation 2: dynamic
actuation between low drag positions on advancing side and high lift
position on retreating side . . . . . . . . . . . . . . . . . . . . . . . . 163
4.20 UH-60A vibratory hub loads vs thrust at CW/σ = 0.1, without and
with slats of varying spanwise lengths; Actuation 2: dynamic ac-
tuation between low drag positions on advancing side and high lift
position on retreating side . . . . . . . . . . . . . . . . . . . . . . . . 164
4.21 UH-60A components of rotor power vs thrust at CT/σ = 0.08, without
and with slats from 50-90%R ; Actuations 1 & 2: dynamic actuations
between low drag positions on advancing side and high lift position
on retreating side . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
4.22 Effect of slats on rotor performance and rotor envelope;slats increase
Vmax by 20 knots,indicated by the double-ended horizontal arrows . . 166
xiii
Chapter 1: Introduction
1.1 Background
In recent years, modern rotor technology has been evolving to target the re-
quirements for next generation rotorcraft by extending the operational flight en-
velopes in terms of achievable forward flight speeds, payload capability and maneu-
verability. Each of these objectives is a function primarily of the aerodynamic per-
formance of the main rotor, which operates in a complex aerodynamic environment,
varying from low dynamic pressures and high angles of attack on the retreating side
of the disk to high dynamic pressures and low angles of attack on the advancing
side. The overall aerodynamic environment of the helicopter in forward flight in
(Fig. 1.1) is discussed in Refs. 1-2.
The maximum speed that a helicopter can attain depends on the maximum
lift that the rotor disk can produce on the retreating side. Today, all helicopters
use cyclic pitch control for varying their lift as the blades rotate but the lift can
only be maintained by increasing the angle of attack upto the stalling point of the
airfoil. In the case of the blade, the stall is dynamic due to the unsteady nature of
1
Figure 1.1: Flow structure and some aerodynamic problem areas on a helicopter in
forward flight
2
the flow. Blade stall causes a significant increase of vibratory loads.Hence, the rotor
technology has tended toward methods of active control to minimize vibrations and
enhance performance over a wide range of operating conditions.
Passive designs involving blade geometry that seek to improve the aerodynamic
performance of the main rotor usually focus on airfoil sections as a first step and
are faced with the conflicting challenges of the advancing blade compressibility and
retreating blade stall. Designs for higher lift in low speed regimes lead to high drag
at higher speeds and designs that target low drag under high speed conditions do
not achieve the desired lift enhancement at lower speeds. While airfoil technology
has come a long way in overcoming specific aerodynamic limitations, any further
dramatic improvements in lift characteristics without associated moment or drag
penalties may not be feasible for conventional fixed-geometry rotors with single-
element airfoils. Targeting vibration reduction can improve the helicopter blade life
while stall alleviation can expand the lift envelope.
1.2 Vibration
Helicopters are prone to high vibration levels, which affect the lives of struc-
tural components adversely. The primary source of vibration in the helicopter is the
main rotor. Vibratory loads can be attributed to the highly unsteady edgewise flow-
field and complex wake structure surrounding the rotor, the aeroelastically coupled
blade motions, rotor-fuselage interactions and time-varying control inputs, which
3
affect the lives of structural components adversely.
Considerable emphasis is being laid on the reduction of helicopter noise to im-
prove community acceptance because many of the helicopters in civilian use operate
close to urban and populated areas. Further,the impact of vibrations on the comfort
of passengers and crew, as well as on the reliability of onboard equipment is also
important.
Vibration is the dynamic response of the helicopter airframe and other com-
ponents in the non-rotating frame due to the rotor hub forces and moments. The
aerodynamic loads on the main fuselage and tail produced by the rotor wake can
also contribute to airframe vibration. There are also other important sources of
helicopter vibration,notably the engine and transmission, but the primary source
of vibration in the helicopter is the main rotor. In steady-state forward flight, the
periodic forces at the root of the blade are transmitted to the helicopter, produc-
ing a periodic vibratory response. For a rotor with Nb identical blades, the main
rotor hub acts as a filter for the blade loads and only transmits harmonic loads
at multiples of Nb/rev to the fuselage. This is based on the assumption that all
the blades are identical and have the same periodic motion. Although this is not
practically true, the Nb/rev harmonics still dominate the vibrations.Thus, typically,
the Nb /rev components of the vibratory hub loads are the most dominant. The
vibration is generally low in hover, where the aerodynamic environment is nearly
axisymmetric and cyclic pitch nearly zero, and increases with forward speed to high
levels at the maximum speed of the helicopter. There is also a high level of vibra-
tion at transition (µ ∼ 0.15) because of the dominance of rotor wake influence on
4
the blade airloads. The vibration increases with descent at low speed and increases
with thrust at high speeds ( [2] and [3]). Because the helicopter drag is small at
low speeds, the tip path plane incidence remains small, and the tip vortices in the
wake remain close to the disk plane. The advance ratio is low enough so that the
blades sweep past the tip vortices from preceding blades. Such close blade-vortex
interactions produce significant higher harmonic airloading, that is transmitted to
the hub.This vibration is increased by operations that keep the wake near the disk
plane, such as decelerating or descending flight. As the speed increases, the heli-
copter rotor tip-path-plane tilts forward to provide the propulsive force,which means
that the wake is convected away from the disc plane and the wake-induced vibration
decreases.At still higher speeds, the vibration increases again,primarily as a result
of the higher harmonic loading produced by stall and compressibility effects. Large
vibratory loads can limit the maximum speed of the aicraft, as any aerodynamic or
inertial dissimilarity between the blades primarily generates 1/rev vibrations.
The specifications for rotorcraft vibration have been gradually evolving over
time. The specification is in terms of acceleration,velocity or displacement, which
can be converted to acceleration in g’s as a function of frequency. The U.S. Gov-
ernment documents MIL-8501(1952)(Ref [4]) and MIL-8501A(Ref [5]) provide the
limits for various locations in the rotorcraft (pilot,crew,passengers,litters) and for
steady flight upto cruise speed. The MIL-H-8501A(1961) refined the limit at high
frequency,but also increased the limit to 50 % relative to MIL-H-8501(1952), reflect-
ing an assessment of what the technology could provide.
The design standard ADS-27A-SP(2006)( [6]] defines an intrusion index, based
5
on the vibration spectra,for the longitudinal, lateral and vertical directions at a lo-
cation. The intrusion index is the square root of the sum of the squares of the 4
largest peaks(excluding 1/rev) for each of the 3 normalized spectra.An intrusion
index limit is defined for various operating conditions and positions in the aircraft.
The vibration requirement is that the intrusion index be lower than the intrusion
index limit. Keeping in view what is possible with the technology available,the
specifications have become more elaborate. The vibration level permitted has been
increased,especially at low speeds,but a distinction is made between the levels per-
missible in the cabin and cockpit. Specifications for particular rotorcraft have used
the Intrusion Index,but with increased limits. The requirements for the comfort
of the crew and passengers are only likely to get more demanding over time and
hence vibration prediction and control will continue to pose significant challenges in
rotorcraft design.
1.3 Vibration reduction techniques
Vibration reduction can be accomplished by minimizing the source vibratory
loads at the source,i.e.the rotor .The oscillatory hub forces and moments,including
the aerodynamic loads acting on the fuselage and tail must be reduced to minimize
the response of the structure. Vibration reduction methods can be passive or active.
Passive vibration reduction methods such as pendulum absorbers ( [7], [8]
and [9]) or rotor blade modal shaping ( [10] and [11]) or frequency attenuators gen-
erally have poor off-design performance as well as a significant weight penalty( [12]
6
and [13]). Further, proper operation of the pendulum absorbers requires minimum
friction in the pendulum hinges.A centrifugal pendulum absorber was developed by
Viswanathan [14] et.al, which employs mercury as the tuning weight and flight tests
performed on Bell Helicopter models 206LM and 412 showed that the mercury pen-
dulum absorbers were effective in reducing cabin vibration.This has not been put
to commercial use,probably because of environmental and corrosion considerations.
Blade-mounted pendulum absorbers also change orientation with changes in
blade collective and cyclic pitch,resulting in adverse coupling of the blade flatwise
and inplane motions ( [15]). Both bifilar and pendulum absorbers produce aerody-
namic drag penalties.Other passive methods such as aeroelastic optimization( [16])
and composite couplings ( [17]) may not have the weight penalty, but may not be
optimum for a range of flight conditions.
Active vibration control in the fixed frame enhances vibration reduction, pos-
sibly at reduced weight penalty ( [18]). However,these systems cannot address the
source of the vibration but have significant effect on drive system space around
the gearbox. Regarding the various categories of frequency attenuators, they are
broadly related to the topic of blade structural optimization ( [19], [20], [21], [22]).
However,it is not evident whether structural optimization alone without additional
vibration treatment can lead to acceptable vibration reduction. The various other
methods of rotor control include:
• Blade camber control-asymmetric actuation using smart materials around the
blade sections.Harmonic actuations at 2/rev could reduce the noise and vibra-
tory loads on the rotor,improving the rotor performance ( [23], [24]).
7
• Blade twist control-differential actuation using smart materials arranged along
the blade span. The idea behind active twist is to modify twist distribution
of the rotating blade, not only to improve the lift and overall helicopter per-
formance, but also to actively control vibrations.
Chen et.al.( [25]) pioneered torsion actuation by designing and testing a Froude-
scale model embedded with specially-shaped piezoelectric elements. Blade
twist of the order of ±0.4◦ at the tip showed the potential of the system for
vibration suppression.
Wilbur et.al.( [26]) carried out experimental studies in the NASA Langley
Transonic Dynamics Tunnel on a 4-bladed, active twist rotor, and reported
significant reductions in fixed-system loads of 60−95% with active blade twist
upto 1.4◦.
Studies by Thakkar et.al.( [27]) show that about 69 % reduction can be
achieved using a distributed actuation system, to modify the blade twist with
the actuation of two sections.
The disadvantage in this approach is it requires significantly increased actua-
tion for twisting the entire blade compared to that required for small flaps.
• Blade pitch control: individual blade pitch actuation in the rotating frame.It
results in the complexity of power slipring.
• Tilting shaft: In order to orient the rotor thrust suitably.It requires a large
actuation force.
8
• Servo flaps: on-blade airfoil sections located aft of the trailing edges of the
rotor blades.These result in large drag penalty.
Direct blade control as in the first three methods, requires large actuation
forces and complex actuation systems, as does the tilting shaft concept. Servo flaps
incur extra weight and drag penalties due to the extra supports, and gaps between
the flaps and the hinges.
Other active control methods that use multicyclic pitch excitation of the swash-
plate, can be far more effective because they eliminate vibration at its source.These
systems actuate the rotor blades at higher harmonics to generate unsteady forces,
which counteract existing vibratory airloads. These techniques include higher har-
monic control and individual blade control.
1.3.1 Higher harmonic control
Higher harmonic control(HHC),where the blades are activated in the non-
rotating frame by the swashplate by introducing pitch commands at Nb/rev result-
ing in blade pitch oscillations at frequencies of Nb-1/rev, Nb/rev, Nb+1/rev in the
rotating frame. If applied with the correct phasing, HHC can result in significant vi-
bration reduction. If these blade pitch actuations are applied appropriately,they can
generate a combination of aerodynamic and inertial loads to counteract the existing
blade loads,which cause airframe vibration. HHC has been studied using numerical
simulations ( [28], [29], [30], [31], [32]), model-scale ( [33], [34], [35], [36])as well
9
as full scale rotor tests( [37], [38], [39]) in wind tunnels.HHC produces substantial
reductions in vibration. A comprehensive analytical formulation was developed to
examine the problems associated with the implementation of HHC to reduce vibra-
tion for hingeless rotors ( [40]).The study showed that flap,lag and torsion charac-
teristics,offset of blade centre of mass from elastic axis, offset of elastic axis from
blade quarter-chord axis,and blade thrust greatly affect the HHC actuator power re-
quirement. However, HHC can not address other control objectives like performance
improvement,stall alleviation and power reduction as these may require excitation
of the blades at harmonics other than Nb/rev. The search for a solution to these
issues resulted in the development of Individual Blade Control(IBC).
1.3.2 Individual Blade Control
In IBC, each blade can be controlled independently in the rotating frame. Sev-
eral implementations of IBC are available. In HHC for a N -bladed rotor, excitation
of the swashplate allows only Nb/rev, Nb -1/rev and Nb +1/rev excitation of the
rotor blades.IBC can be used to generate 2/rev and other harmonics in the rotat-
ing frame.IBC also allows feedback loops for each blade in the rotating frame.Kretz
( [41]) used a rotor-control system characterized by the fact that each blade is
governed independently by a fixed feedback system comprising an electrohydraulic
actuator as the main power element to alleviate instabilities at high advance ra-
tios and high lift coefficients. Significant work on IBC was conducted by Ham
( [42], [43], [44]). In the conventional IBC approach,the pitch of each rotor blade
is individually controlled in the rotating frame using servo-actuators. This higher
10
harmonic pitch input is superimposed on the pilot pitch input. The IBC shows
considerable potential to achieve not only vibration reduction,but also noise reduc-
tion and performance enhancement. However,both HHC and IBC require complex
mechanisms for actuation and associated weight penalties and considerable actua-
tion forces.
1.4 Performance enhancement techniques
Gurney flap is a small flap deployed vertically at the trailing edge of the rotor
blade. It modifies the flow at the trailing-edge and brings the separation point closer
to the trailing-edge and this results in an increase in the lift over a large range of
angles of attack with a small drag penalty ( [45], [46]). Studies have shown an
increase in drag and pitching moments with increasing lengths ( [45], [46], [47]).
Hence, Gurney flaps have advantages depending on the application.
Concepts that enhance performance over a wide range of operating condi-
tions are: fixed and dynamic slats, variable droop leading-edge (VDLE) airfoils,
circulation control blowing, trailing-edge flaps(TEFs) and leading-edge slats(LESs).
These have been considered for active aerodynamic flow control. VDLE airfoils have
shown dynamic stall mitigation capability, as discussed in subsequent sections.TEFs
and LESs appear attractive for their conceptual simplicity and wide-ranging appli-
cability to minimizing vibratory loads and noise signatures and improving rotor
performance.
11
1.5 Trailing-edge flaps
The advent of complex and lightweight smart-material actuators, which have
large stroke and energy density, makes vibration control with TEFs an attractive
alternative,especially as the blade-integrated flaps are capable of other functions, in
addition to vibration control, while being aeromechanically stable( [49]). Flaps on
helicopters are not designed for primary control as in aeroplanes. They are designed
to act as a secondary control to improve the efficiency of the rotor blade by modifying
the lift of the profile and by reducing the vibration of the rotor. However, there has
been some interest in using TEFs for primary control in a swashplateless rotor also
and hence it would be pertinent to include some observations in this regard.
1.6 Trailing-edge flaps for primary control
Eliminating the swashplate and the associated control system can lead to sig-
nificant reductions in weight, drag and cost and an improvement of rotor perfor-
mance.
Kaman used servo flaps since 1947 on K-125,which inspired the work by Ormis-
ton( [48]) of the ways to replace the helicopter rotor swashplate and blade pitch con-
trol system with on-blade elevon control surfaces for primary flight control . Results
indicated that with aeroelastic design for pitch frequencies in the neighbourhood of
2/rev,reasonable elevon control effectiveness may be achieved.
12
Shen et.al ( [49], [50], [51], [52] and [53]) conducted a comprehensive aeroelastic
analysis of the effectiveness of trailing-edge flaps for primary control using University
of Maryland Advanced Rotorcraft Code(UMARC). The swashplateless rotor was
shown to achieve better rotor performance and was overall more stable than the
conventional helicopter. Simulations of TEFs performing both primary control and
active vibration control were carried out,and it was shown that TEFs are capable
of simultaneously trimming the rotor and reducing vibratory hub loads.
Falls et.al continued Shen’s pioneering work on TEFs for swashplateless control
( [54], [55]). Design was investigated through parametric studies of the TEFs for a
conceptual rotor , such as a UH-60A swashplateless variant. Performance analysis of
TEFs in helicopter primary control was carried out ( [55]) using UMARC. The TEF
design features,such as index angle, aerodynamic overhang, chord and length were
identified to be important, especially at high speed flight conditions.The swashplate-
less rotor required less main rotor power than the conventional UH-60A helicopter
from hover to µ=0.25.The swashplateless UH-60A was found less efficient than the
baseline UH-60A at higher advance ratios( [55]).
1.7 TEFs for Vibration Reduction and Performance Enhancement
The trailing-edge flap actuators, hinges and supports are placed within the
rotor blade. Deflecting the flaps causes pitching moment changes, which in turn force
the blade to pitch about the root bearing, thus controlling the blade pitch.The blade
must have a pre-collective (pitch index)larger than the expected trim value, since the
13
flaps produce an augmentation in lift and hence nose-down pitching moment when
deflected downwards. It must also be hinged behind its leading edge(overhang) to
reduce hinge moments and hence actuation requirements.
The geometry of the flap includes key design parameters: the outboard span-
wise locations experience higher dynamic pressures and hence smaller deflections
are required. Also, larger flap length results in smaller deflections; these combine
to suggest a location close to 75% R ( [56]). Flap chord determines whether it acts
primarily as a lift flap or a moment flap. Deflections are smaller for larger flap chord
but actuation requirements increase, so a compromise is required here.
A blade-mounted trailing edge flap driven by a piezoelectric actuator, such as
in a MD900 light utility helicopter was studied for reduction of vibration and noise
and aerodynamic performance improvements ( [57]). The active flap system was
whirl tower tested to demonstrate its excellent authority.
A review of the state of the art in vibration reduction in rotorcraft using
active control is given by Friedmann and Millott ( [58]), showing that the actively
controlled flap has remarkable potential for vibration reduction.
Koratkar et.al. ( [59]) developed a Mach-scaled rotor blade with piezoelec-
tric bender-actuated trailing-edge flaps for vibration control. UMARC was used to
determine the optimal flap span,chord and spanwise location of the TEF for this
study,which showed upto 90% hub load vibrations were reduced with flap deflections
of about ±4◦.
TEFs have also been analyzed with great success for active vibration con-
trol, notably through numerical simulations performed by Milgram and Chopra
14
( [56], [60])), using an analytical model for helicopter main rotor with plain trailing-
edge flaps in compressible flows. The analysis incorporated a nonlinear aeroelastic
rotor model and a multicyclic flap controller, and it was validated using experi-
mental wind tunnel data. The trailing-edge flap system was found to be effective
in reducing vibration at all advance ratios,but the reduction was not great at low
speeds (µ=0.10) and high speeds(µ ≥ 0.35). The parametric study for Sikorsky S-76
main rotor suggested that a flap with the smallest possible chord and the largest
possible deflection is preferred.
Wind tunnel testing of Mach-scaled rotors with active TEFs with each blade
controlled independently was performed by Roget and Chopra and the results show
that multiple fixed-frame loads can be minimized simultaneously ( [61] on a demo
aircraft with reduced payload.
Full-scale tests by Eurocopter on the BK-117 ( [62]) show that active rotor
control can provide considerable reduction of rotor-induced vibration.
Jain et. al,using coupled CFD-CSD simulations, showed that TEFs can im-
prove rotor performance in high-speed forward flight ( [63]). The study was on a
UH-60A Blackhawk rotor for two key flight conditions in forward flight: high speed
and high thrust. It showed that active controls could reduce rotor loads,improve
rotor performance and reduce vibrations,by careful selection of operating conditions.
Cheng et al. ( [64]) carried out a study using 2/rev inputs on the UH-60A
rotor specifically for performance improvement, demonstrating the benefits of lower
harmonic inputs to performance.
Yeo ( [65]) explored different active control concepts for rotor performance
15
improvement including TEFs.The study was conducted to assess the capability of
active controls to cause rotor performance improvements,using the comprehensive
analysis CAMRAD II.The baseline rotor considered was a 4-bladed articulated rotor
with a VR-12 airfoil. The study showed that with 2/rev harmonic excitation, TEFs
are capable of improving rotor performance.
To exploit the benefits of TEFs and minimize the drag penalties, they need
to be actively controlled to address phenomena occurring at multiples of rotor fre-
quency. Different objectives, such as vibration and power reduction, needed different
actuation requirements. Fixed-frame vibration is targeted by exciting the flaps at ro-
tor harmonics, so as to generate forces to counteract the ones causing vibrations.For
the reduction of Nb/rev fixed frame vibration, the TEF input frequencies used were
Nb,Nb ±1/rev. Power reduction is achieved by the redistribution of the disk loading
to make it more uniform and modify blade angle of attack to minimize associated
drag penalties.The TEF input frequencies used for this purpose are 1 and 2/rev.
Hence, it is inevitable that a compromise must be arrived at between the various
benefits of using TEFs.
1.8 Dynamic Stall
Dynamic stall is a critical phenomenon occurring in high-thrust forward flight
conditions. The rotor blade sections operate at low dynamic pressures and high
angles of attack on the retreating side of the disk. The unsteady flow conditions
and proximity to the airfoil stall limit leads to a phenomenon called dynamic stall,
16
characterized by the production of a leading edge vortex which convects over the
upper surface of the airfoil. There is a large increase in the nose-down pitching mo-
ment as the vortex convects over the airfoil.The large pitching moment oscillations
lead to severe vibratory hub loads and performance penalties. The details of the
dynamic stall are available in Ref. ( [1]). The schematic is shown in (Fig. 1.2).
Figure 1.2: Stages of dynamic stall on a helicopter blade
It has been shown ( [66]) that under high-speed forward-flight conditions,the
surface pressures and the force coefficients indicate that the slat is beneficial in
reducing retreating blade dynamic stall. It was found that the slat reduces the
torque and pitching moments on the retreating side compared to the baseline. An
17
approach to combating dynamic stall is to design airfoil sections with improved
dynamic characteristics.
Martin et.al.( [67]) showed with numerical computations and experimental
tests that a Variable Droop Leading Edge (VDLE) airfoil is a feasible concept for
application to a rotor high-lift condition. The ability of the VDLE airfoil to control
the dynamic stall process was demonstrated. However, the ultimate integration of
a VDLE airfoil into a full-scale rotor is likely to pose several challenges. Carr et.al.(
[71]) conducted wind-tunnel tests on a RC(6)-08 airfoil with 2 different leading-edge
slat configurations and showed that slats are capable of suppressing dynamic stall.
Wong ( [68]) compared predicted dynamic stall characteristics with experi-
mental data on a VR-7 airfoil with a modified upper surface to obtain better static
characteristics. The results showed the minor upper-surface modification led to
alleviation of dynamic stall effects.These airfoils are limited to a narrow range of
operating conditions.
Another approach involves active control using TEFs or LE Slats, with suitably
prescribed inputs to target the retreating blade.
1.9 LESs for vibration reduction and Performance Enhancement
Leading edge slats are high-lift devices, which delay the onset of stall on an
airfoil by energizing the airfoil and delaying separation. The use of slats for primary
control is expected to be possible, but is likely to be very different from trailing-
18
edge flaps,because a slat naturally causes nose-up pitch. However, the control of
unsteady loads(vibrations) resulting from retreating blade stall in forward flight can
be readily addressed by the use of slats.
To explore the benefits of leading-edge slats,we have to keep in mind the
fact that the maximum thrust generated by the rotor is limited by blade stall. In
high speed forward flight,the reduced dynamic pressures on the retreating blade
and phenomenon of dynamic stall lead to loss of thrust.On the other hand, shock-
induced flow separation on the advancing blade, which sees transonic flow,imposes
a limit on maximum achievable forward speed. Leading edge slats help increase the
maximum static lift coefficient of the base airfoil,thus may mitigate the problem of
retreating blade stall.
Experimental studies were conducted by McAlister ( [69]), on a VR-7 airfoil
at fixed angles of attack upto 30◦ in a water tunnel. The addition of slat was found
to delay the static drag and static moment stall. The study showed the slat caused
a more gradual advance of trailing-edge separation to occur over the main airfoil
section. This translates into a significant improvement in the maximum rotor thrust
capability. However, using fixed slats is accompanied by an increased drag penalty
especially at low thrust conditions.
Wind tunnel tests conducted by Noonan ( [70]), in the Langley Transonic
Dynamics Tunnel to evaluate rotor performance using slotted airfoils in the rotor
blade tip region. This study tested four rotor configurations and reported benefits
at high thrust levels and speeds for the forward-slotted airfoils with −6◦ slat.
A study was also conducted by Narramore, et al ( [73]) using high-lift airfoils
19
generated by inverse design techniques. Rotor performance using the slotted airfoils
was better than the baseline rotor.
Carr et al.( [71]) designed a Multi-Element Airfoil(MEA) RC(6)-08 with 2
slat configurations and tested it in the NASA Compressible Dynamic Stall Facility.
The results showed the improvements that can be attained through suitable slat
design,achieved after comparing the slatted variant with the basic single-element
airfoil.The slot is the space between the slat and the blade. Interferograms obtained
in the studies indicate that the slat/slot combination continues to energize the flow
on the main airfoil through the jet in the slot.
Studies were conducted by Chandrashekhara( [72]) through experiments con-
trolling dynamic stall using the Dynamically Deforming Leading-Edge (DDLE) air-
foil,the slatted airfoil, the airfoil with zero-mass flux synthetic jet and the Variable
Droop Leading Edge (VDLE) airfoils. The conclusion was that the DDLE airfoil,
the slatted airoil and the VDLE airfoil demonstrated significant capability to control
and delay the onset of compressible dynamic stall. The slatted airfoil was found to
use natural blowing through the slat passage to mitigate dynamic stall effects.
Yeo et. al. ( [74]) studied analytically the benefits of multi-element forward
slotted airfoils for a UH-60A helicopter. Baseline SC1095 and SC1094R8 airfoil
characteristics were modified based on CFD calculations of an A3C slotted airfoil to
incorporate aerodynamic characteristics of a high-lifting airfoil. The slotted airfoil
increased maximum thrust of the UH-60A helicopter by up to 25%, but a significant
penalty is observed at CT/σ < 0.11. Performance of the slotted airfoil with the wide
chord blade showed that the slotted airfoil has limited advantages over the regular
20
wide chord blade.
Lorber et al.( [75]) have made computational and experimental fixed- geometry
slat-blade configurations to determine slat positions for maximum lift and minimum
drag performance. These Multi-Element Airfoil studies used the optimized A3C slat
airfoil shape. Tests conducted on a model rotor fitted with four interchangeable slots
showed that the most effective slats significantly improved the rotor stall boundary,
but the performance was subdued at low thrusts.An active slat actuation was pro-
posed for improving the slat performance.
Asitav et.al.( [76]).carried out a CFD-CSD simulation of the effects of leading-
edge slats on rotor performance.For this study of the various slat positions investi-
gated by Lorber et.al. ( [75]), two slat positions -S1 and S6- were identified for their
low drag and high lift characteristics respectively. A harmonic actuation of the slat
that completely retracts it on the advancing side(S1)and completely deploys it in
downward position (S6)on the retreating side, minimizes the drag penalty while en-
hancing the lift capability of the blade( [76]). The results indicated that the slatted
airfoils are able to perform significantly better than the unslatted baseline. The re-
sults indicated that the slatted airfoil is able to achieve higher static lift coefficients
compared to the baseline by delaying the onset of boundary layer separation on the
main airfoil section. The drop in the pitching moment coefficient is less severe in
the presence of a slat. It allows better performance in unsteady conditions. The
4-bladed UH-60A rotor geometry was studied operating in the high-altitude,high
thrust flight condition,identified as C9017.It was found from this study that both
static and dynamic slat actuations effectively mitigated dynamic stall.
21
Yeo( [77]) compared different active control concepts for rotor performance
improvement using the comprehensive analysis CAMRAD-II, including LESs and
TEFs, and concluded that leading-edge slats were effective in increasing the blade
maximum loading capability.Carefully chosen actuations are capable of reducing
rotor hub vibration levels( [78]).
1.10 Goal of this research
The overall goal of the present research is flight envelope expansion through
the use of active control of the rotor using trailing-edge flaps and leading-edge slats
(Fig. 1.3).
It is obvious that one single rotor design cannot achieve all the desired char-
acteristics:
1. Reduction in vibration and noise levels.
2. Increase in blade loading (pushing out the rotor stall boundary).
3. Increase in the maximum flight speed.
Comprehensive rotor analyses are well suited for evaluation of active control
concepts through parametric studies to determine configurations that yield maxi-
mum benefits as well as understand the mechanisms of their operation. Performance
gains with active control surfaces are expected to be largest at high speeds and high
thrust levels, where a small redistribution of loading can result in significant reduc-
tions.
22
Figure 1.3: Flight envelope
23
Using trailing-edge flaps and leading-edge slats can allow the designers to
tune the rotor for increased performance and/or vibration and noise reduction over
a broad range of flight conditions.
1.10.1 Analysis with Trailing-edge flaps
To systematically study the effects of active control with TEFs on performance
in terms of power consumption and vibration, first, hover performance is considered.
Next, high-speed flight conditions are explored for power reduction using a combi-
nation of TEF inputs at different frequencies. Then, the standard high speed, high
vibration, moderate thrust flight condition (such as C8534) from the UH-60A air-
loads program( [79]) is explored for vibration reduction.Then, the posssibility of
simultaneous power and vibration reduction with TEFs is addressed.
1.10.2 Analysis with Leading-edge slats
Because of the complexities and challenges of slat actuations in a rotating
environment, the merits of using active slatted rotor blades need to be examined
systematically before the concept can be implemented in blade design. Accordingly,
in this study, a comprehenensive analysis has been made to assess and quantify the
impact of leading-edge slats on rotor performance, vibratory loads, blade bending
and thrust capability for a range of flight conditions.
24
1.10.3 Analysis of Superimposition of TEFs and LESs
Having developed prediction capability for slatted rotor which shows signifi-
cant gains in maximum rotor thrust and dynamic stall alleviation with slats, another
subject of research that excited interest was to study the superimposition of TEFs
and leading-edge slats in an effort to improve the power benefits by alleviating the
negative loading on the advancing side.
1.11 Approach
The primary research objective was to analyze,validate and optimize TEFs/LESs
for active vibration control and performance enhancement.The tasks identified,to
achieve these goals,were:
The University of Maryland Advanced Rotor Code(UMARC) was utilized;
the primary focus of the present research was the determination of the operating
conditions and the rotor geometry for which the flight envelope could be expanded.
The UH-60A rotor geometry and structural properties, as specified by the UH-60A
Airloads Program was used as the base geometry for the initial performance analysis.
The baseline rotor was the UH-60A,with SC1095 and SC1094R8 airfoils.For the
LES studies,the slatted blade sections had the SC2110 baseline/slatted airfoils in
place of the baseline UH-60A airfoils:SC1095 and SC1094R8. The structural,inertial
and aerodynamic contributions of trailing edge flaps and leading-edge slats were
25
integrated into the baseline blade analysis in UMARC.
For the TEF/LES studies, the flap is modeled as a single additional degree of
freedom while the slat motion is modeled with 3 additional degrees of freedom to
improve conformity of the slat airfoil with the blade airfoil and the motion of the
flap and slat is prescribed in the analysis. The baseline rotor analysis is a coupled
trim procedure that solves the blade equations of motion in time and space(using the
finite element method)to obtain the blade response. The response is used to calculate
blade and hub loads, which define the necessary control settings for vehicle trim.
This process is iterated till the convergence of response and trim(in steady flight).
Adding the modeling of flaps and slats to the baseline rotor analysis UMARC was
the single most important step of the study: the addition of active rotor surfaces
results in incremental inertial and aerodynamic loads which are added to the blade
equations of motion with additional degrees of freedom for the flap/slat.
1.11.1 TEF studies
For the TEF studies, UMARC was used to quantify the capabilities of the
flaps for helicopter vibration reduction and performance enhancement. UH-60A
performance data are computed using UMARC, which has been validated against
data from the UH-60 Airloads Project. The TEF used in this model was a ’moment
flap’, meaning it operates by modifying the section pitching moments and inducing
a blade elastic twist in response to the moments. A parameter that directly affects
the blade twist,and therefore effectiveness of the TEF, is the torsional stiffness(GJ)
26
of the blade.
Vibration was studied at various flight speeds,particularly for the C8534 and
C9017 flights.
TEFs(span 10% R, 10-15% c, midspan at 65% R) were evaluated for perfor-
mance improvement in hover, reduction of 4/rev hub vibratory loads and power
at the high speed flight condition C8534 and reduction of dynamic stall loads,hub
vibratory loads and power at the high thrust forward flight condition C9017. The
TEF was shown to be capable of multiple functions,namely vibration reduction, stall
alleviation and power reduction,using HPP actuation amplitudes of 5-10◦.
The rotor performance in hover was improved with a combination of torsionally
softer blades and positive TEF deflections,which contribute to a positive elastic twist
response and reduced induced losses. The effect of torsional stiffness is primarily on
the blade first torsional mode: the first torsion frequency reduces from 4.3/rev for
the baseline blade to 3.3/rev for the 50% stiff blade.
The rotor performance in high speed forward flight was improved by suitable
conbination of steady,1/rev and 2/rev TEF inputs to reduce the negative loading
on the advancing blade and thus off-load the front and rear parts of the disk. Power
reductions of the order of 2% at µ = 0.3 and 4− 5% at µ = 0.4 were observed using
HPP actuation amplitudes of 5-10◦.
Power reductions of the order of 10 − 20% at various speeds were achieved
using dynamic slat actuations combining high-lift and low-drag orientations in a
1/rev fashion across azimuth.The maximum slat rotation angle between different
orientations was about 10◦.
27
1/rev TEF inputs were prescribed to the slatted rotor to further target the
areas of negative loading on the rotor disk. Additional power reductions of about
2% were achieved by this method at the maximum baseline rotor thrust level at
µ=0.4.
1.11.2 LES studies
Airfoils with leading-edge slats, by virtue of their higher maximum lift capabil-
ity, are capable of pushing the rotor maximum lift boundary above its conventional
level. Additionally, the dynamic behavior of slatted airfoils,in terms of delaying
boundary layer separation from the airfoil surface, is superior to airfoils without
slats. Properly modeling this requires refinement and validation of the parameters
in the Leishman-Beddoes dynamic stall model(used in UMARC), for slatted airfoils.
The current results are obtained without unsteady corrections to the airloads due
to airfoil dynamic properties,with the understanding that the improved dynamic
properties of slatted airfoils will further enhance the lift obtained here with the
assumption of fully attached flow.
The modified UMARC code is used to study the capabilities of leading-edge
slats for helicopter performance improvement in moderate to high-speed forward
flight.The 3 different slat configurations that were studied include: low drag (S0),high
lift (S6), and a compromise between the two extreme cases (S1). Dynamic actua-
tions were chosen to retain the high-lift benefits of the slat while seeking to reduce
the profile drag penalties over regions of the disk operating at lower angles of attack
28
i.e. the advancing side.
The UH-60A rotor lift boundary as predicted by UMARC was compared to
the McHugh lift boundary for the nominal rotor speed. The agreement was good
at intermediate advance ratios. CFD runs were performed to generate 2D airfoil
tables for the baseline SC2110 and two MEA (Multi-Element Airfoil) cases with
leading-edge slats at S6 and S1 positions. The slat actuation case studied includes
S1 on the advancing side and S6 on the retreating side. The airfoil aerodynamic
coefficient predictions were validated for the three positions using the experimental
data available from ( [75]). The maximum achievable rotor thrust was increased by
about 25−30% at advance ratios greater than 0.2 using leading-edge slats.The effects
of leading-edge slats extending over 20%,30% and 40% of the blade span on rotor
performance and vibratory hub loads were examined.These devices can extend the
maximum thrust achievable and reduce power requirements,at the cost of increased
vibration. The rotor with leading-edge slats could be trimmed at a maximum for-
ward speed that was about 20 knots greater than the baseline without slats.The
maximum achievable thrust is increased by 15− 30% at advance ratios greater than
0.2. Power requirements at high blade loading conditions may be reduced by as
much as 10 − 20%. Of the configurations investigated,the 20% span slats offered a
good compromise between power reduction and vibration minimization.
1.11.3 Studies of superimposition of TEFs and LESs
1/rev TEF actuations of the form δ = δ1pcos(ψ + φ1p) were imposed on the
29
slatted rotor operating at µ = 0.4, CW/σ = 0.095 in an effort to improve the power
benefits by alleviating the negative loading on the advancing blade. The increments
in section aerodynamic properties due to TEFs were assumed to be generic CFD-
generated values obtained for the SC1094R8 airfoil.
30
Chapter 2: Methodology
The University of Maryland Advanced Rotor Code (UMARC)( [80]) was utilised
to study the effects of TEFs and leading-edge slats. The blades are modeled
as second-order, nonlinear, Euler-Bernoulli beams, capable of undergoing coupled
flap,lag,torsion, and axial motion.Each blade was discretized into 20 spanwise beam
elements and each element consisted of 15 degrees of freedom. The equations of mo-
tion are solved using modal reduction (with 10 coupled rotating modes) and finite
element in time with 12 equally-spaced time elements (six nodes per element) to
calculate the steady periodic response solution. The structural, inertial and aerody-
namic contributions of trailing edge flaps and aerodynamic contributions of leading-
edge slats were integrated into the baseline blade analysis in UMARC. The flap is
modeled as a single, additional degree of freedom while the slat motion is modeled
with 3 additional degrees of freedom to improve conformity of the slat airfoil with
the blade airfoil and the motions of the flap and slat are prescribed in the analysis.
The lifting-line aerodynamic model incorporates sectional lift, drag, and moment co-
efficients obtained from C-81 lookup tables for both the main blade and the flapped
and slatted sections, a Weissinger-L near wake model, a refined Bagai-Leishman
pseudo-implicit free wake model ( [81])) with the capability of modeling multiple
31
free trailers, and Leishman-Beddoes unsteady models for attached flow/dynamic
stall( [82]).The near-wake model was modified to account for the effect of TEFs
and LESs on the blade bound circulation distribution.The coupled blade response
and vehicle trim equations are solved simultaneously to obtain the blade deflections
and trim control settings.The study uses propulsive free flight trim, except at hover.
Vehicle weight and speed are prescribed and the rotor control angles, tail rotor
collective and fuselage attitude angles are obtained to maintain force and moment
equilibrium about three axes. For hover cases, shaft orientation was fixed and the
rotor control angles were obtained to trim the rotor to the specified thrust and zero
hub rolling and pitching moments.
2.1 Validation of UMARC and determination of Stall Boundaries
The UH-60A performance data computed using UMARC has been validated
( [83])against flight data from the UH-60A Airloads Project. The determination of
stall boundary is essential for evaluation of the benefits of TEFs and LESs. UMARC
has been further modified to accommodate the effects of TEFs( [54]) and leading-
edge slats.
The choice of a suitable indicator that can be used to identify the onset of
blade stall is unclear. The main objective of this research effort was to analyze
the rotor airloads in highly stalled flow conditions to determine a suitable metric
that can be used as an indicator for blade stall. As a jump-off point, the McHugh
32
experimental lift boundary, which gives the thrust limits of the rotor for a range of
advance ratios, was used to identify this metric.
UMARC was used to obtain trim solutions for flight conditions near the
McHugh’s experimental lift boundary for the UH-60A rotor( [84]). At these high
values of blade loading, the rotor is operating in a highly stalled condition and so,
obtaining reliable trim solutions requires good initial guess values. To resolve this
issue, the rotor thrust setting was set to a low enough value (CT/σ = 0.08 has been
explored for a range of advance ratios) at a given advance ratio and progressively
increased till it reached the value of the desired lift boundary. At each step, the
converged trim control angles from the previously trimmed thrust condition were
prescribed as the initial guess for trim. In some conditions like hover where the
trim shaft angles are known (to be small), an alternative procedure to determine
the lifting limit consists of trimming the rotor to these settings.
Fig. (2.1) shows the comparison of the McHugh lift boundary with the pre-
dicted lift boundary using UMARC, as a function of advance ratio. The boundaries
agree very well for mid-range advance ratios but the limits predicted by UMARC
are slightly lower at low and high advance ratios. Figure (2.2) shows the predicted
trim settings for the points on the UMARC lift boundary. The general trends of
the trim angles are similar to those due to increase in advance ratio at a constant
thrust level. Fig. (2.3) shows the trend of the trim angles for cases of constant blade
loading (CT/σ=0.07-0.1).
The next step is to arrive at a suitable criterion for rotor stall. One possible
criterion is to examine the regions over the rotor disk where the blade airfoil is
33
stalled as per its static stall limits. To this end, the local angle of attack and section
pitching moment are plotted across the rotor disk (once trim is achieved), and the
regions where static stall is occurring are highlighted. The objective is to determine
whether the static stall condition is appropriate to identify rotor stall and, if possible,
to seek a parameter which clearly signals the onset of stall and hence places a bound
on the thrust level.
The flight condition at µ=0.237 has been explored at a range of thrust levels
(CT/σ=0.09-0.1325, the lifting limit, flight condition C9017). Figures (2.4)-(2.12)
show the contour plots of angle of attack, pitching moment coefficient and static stall
boundaries for CT/σ = 0.09,0.11 and 0.1325. It can be seen that static stall regions
exist for thrust levels far below the thrust limit, though they become more significant
at higher levels. Some quantities which have identified dynamic stall in the past,
under different flight conditions, are the higher harmonic blade root vibratory loads.
Figs. (2.13)-(2.20) show these contours for the points on the UMARC-predicted lift
boundary at advance ratios of 0, 0.15 and 0.3 .
34
Lift boundary for UH−60A rotor − UMARC vs experimental McHugh boundary
 
0.16 McHugh boundary
UMARC
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0  
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
µ
Figure 2.1: Comparison of the McHugh lift boundary with UMARC prediction
35
C /σ
T
Trim settings (degrees) for points on predicted UMARC lift boundary 
Main rotor collective Lateral cyclic
20 6
4
15
2
10 0
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
°
Longitudinal cyclic Fuselage longitudinal tilt ; pre−tilt = 3
0 10
−5 5
−10 0
−15 −5
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
µ
Fuselage lateral tilt Tail rotor collective
0 15
−1
−2 10
−3
−4 5
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
µ
Figure 2.2: Trim settings for points on the predicted UMARC lift boundary
36
θ
φ 1s θ
s 0
θ
0 α
t s θ
1c
37
Figure 2.3: Trend of the trim angles for constant CT/σ=0.07-0.1
Predicted trim settings (degrees) for constant C /σ 
C /σ=0.07 T
T Main rotor collective Lateral cyclic
20 C /σ=0.08  4  
T
C /σ=0.09
T
15 3
C /σ=0.1
T
10 2
5 1 
0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45
°
Longitudinal cyclic Fuselage longitudinal tilt ; pre−tilt = 3
0  10  
−5 5
−10 0
−15 −5 
0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45
Fuselage lateral tilt Tail rotor collective
0  15  
−2 10
−4 5
−6 0 
0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45
µ µ
θ
1 s
φ
θ
s
0
θ
α
0
s
t
θ
1 c
Angle of attack distribution : µ=0.237, C /σ=0.09
T
 
90
  1
120 60
20
150   0.5 30
15
10
180 0
5
210 330
0
240 300
−5
270
 
Figure 2.4: Angle of attack distribution for µ=0.237,CT/σ=0.09
Pitching moment coefficient : µ=0.237, C /σ=0.09
T −4x 10
 
90 0.5
  1
120 60
0
150   0.5 30
−0.5
−1
180 0
−1.5
210 330
−2
240 300 −2.5
270
 
Figure 2.5: Pitching moment distribution for µ=0.237,CT/σ=0.09
Angle of attack for static stalled(C ) region: µ=0.237, C /σ=0.09
m T
 
90
  1
120 60
20
150   0.5 30
15
180 0
10
210 330
5
240 300
270
 0
Figure 2.6: Angle of attack for static Cm stall;µ=0.237,CT/σ=0.09
38
Angle of attack distribution : µ=0.237, C /σ=0.11
T
 
90
  1
120 60
25
150   0.5 30
20
15
180 0
10
210 330
5
240 300
0
270
 
Figure 2.7: Angle of attack distribution for µ=0.237,CT/σ=0.011
Pitching moment coefficient : µ=0.237, C /σ=0.11
T −4x 10
 
90
  1
120 60 1
150   0.5 30
0
180 0 −1
−2
210 330
240 300
−3
270
 
Figure 2.8: Pitching moment distribution for µ=0.237,CT/σ=0.011
Angle of attack for static stalled(C ) region: µ=0.237, C /σ=0.11
m T
 
90
  1
120 60
25
150   0.5 30
20
180 0 15
10
210 330
5
240 300
270
 0
Figure 2.9: Angle of attack for static Cm stall;µ=0.237,CT/σ=0.011
39
Angle of attack distribution : µ=0.237, C /σ=0.1325
T
 
90
  1
35
120 60
30
150   0.5 30
25
20
180 0
15
10
210 330
5
240 300
270 0
 
Figure 2.10: Angle of attack distribution for µ=0.237,CT/σ=0.1325
Pitching moment coefficient : µ=0.237, C /σ=0.1325
T −4x 10
 
90
  1 1
120 60
0
−1
150   0.5 30
−2
−3
180 0
−4
−5
210 330
−6
−7
240 300
−8
270
 
Figure 2.11: Pitching moment distribution for µ=0.237,CT/σ=0.1325
Angle of attack for static stalled(C ) region: µ=0.237, C /σ=0.1325
m T
 
90
  1
120 60 35
30
150   0.5 30
25
20
180 0
15
210 330 10
5
240 300
270
 0
Figure 2.12: Angle of attack for static Cm stall;µ=0.237,CT/σ=0.1325
40
Angle of attack distribution : µ=0, C /σ=0.153
T
 
90 10
  1
120 60
9
  0.5 8150 30
7
6
180 0
5
4
210 330
3
240 300 2
270
 
Figure 2.13: Angle of attack distribution for µ=0,CT/σ=0.153
Pitching moment coefficient : µ=0, C /σ=0.153
T −5x 10
 
90
  1
2
120 60
1
0
150   0.5 30
−1
−2
180 0
−3
−4
−5
210 330
−6
−7
240 300
270
 −8
Figure 2.14: Pitching moment distribution for µ=0,CT/σ=0.153
41
Angle of attack distribution : µ=0.15, C /σ=0.14
T
 
90
  1
120 60
14
150   0.5 30 12
10
180 0 8
6
210 330
4
2
240 300
270
 
Figure 2.15: Angle of attack distribution for µ=0.15,CT/σ=0.14
Pitching moment coefficient : µ=0.15, C /σ=0.14
T −4x 10
 
90
  1 1
120 60
0.5
150   0.5 30
0
180 0
−0.5
210 330
−1
240 300
−1.5
270
 
Figure 2.16: Pitching moment distribution for µ=0.15,CT/σ=0.14
Angle of attack for static stalled(C ) region: µ=0.15, C /σ=0.14
m T
 
90
  1 15
120 60
150   0.5 30
10
180 0
5
210 330
240 300
270
 0
Figure 2.17: Angle of attack for static Cm stall;µ=0.15,CT/σ=0.14
42
Angle of attack distribution : µ=0.3, C /σ=0.12
T
 20
90
  1
120 60
0
150   0.5 30
−20
180 0
−40
−60
210 330
−80
240 300
270
 
Figure 2.18: Angle of attack distribution for µ=0.3,CT/σ=0.12
Pitching moment coefficient : µ=0.3, C /σ=0.12
T −4x 10
 
90
  1
120 60
1
150   0.5 30
0
−1
180 0
−2
210 330
−3
240 300
−4
270
 
Figure 2.19: Pitching moment distribution for µ=0.15,CT/σ=0.12
Angle of attack for static stalled(C ) region: µ=0.3, C /σ=0.12
m T
 20
90
  1
120 60
0
150   0.5 30
−20
180 0
−40
−60
210 330
−80
240 300
270
 
Figure 2.20: Angle of attack for static Cm stall for µ=0.3,CT/σ=0.12
43
2.2 Analytical Model:TEFs
Performance gains with active control surfaces are expected to be largest at
high speeds and high thrust levels, where a small redistribution of loading can
result in significant gains. Parametric sweeps of TEF actuations were carried out to
determine suitable combinations of steady, 1/rev and 2/rev TEF inputs that yield
overall power reductions. Different combinations of steady plus 2/rev TEF inputs
were prescribed, in order to obtain the trends of the actuations that had the best
impact on performance.
The basic rotor and flap data, TEF geometry and standard flight conditions
used in this study are listed in Table 2.1.The TEF geometry was prescribed based
on sizing studies performed at Sikorsky Aircraft per Hoerner ( [85]).
44
2.3 TEF blade section aerodynamic characteristics
The two-dimensional (2D) airfoil characteristics (Cl , Cd , Cm) in the C-81
table look-up format for the TEF sections were generated using an in-house CFD
analysis TURNS ( [86]) for the baseline SC1094R8 airfoil and for TEF deflections
of ±2.5◦, ±5◦ , ±10◦ , ±15◦ and a range of operational Mach numbers (0.3 to 0.8)
and angles of attack (-20◦ to +20◦ in steps of 2.5◦).The aerodynamic characteristics
of the TEF section, at a representative Mach number (with the TEF midspan blade
section at 65%R) of 0.5 are shown in the figure[ 2.21] for the baseline SC1094R8
airfoil and TEF deflections of -5◦ and 5◦. A downward (positive) TEF deflection
increases the lift, increases drag at positive angles of attack and decreases drag at
negative angles of attack, and increases nose-down pitching moments. Overall, a
positive TEF deflection improves section L/D at small angles of attack.
2.4 Multicyclic Controller for TEFs
For the vibration reduction studies, earlier results were obtained by exploring
the contours of the vibratory hub loads for a wide range of flap inputs to detect
the points of minima. A table of the results (Table . 2.2 and Table . 2.3) for
3, 4 and 5/rev TEF actuations and blade stiffness of (100%GJ) and (75%GJ) for
simultaneous reduction of different loads, is given below.
45
1.5  0.2  
C  : M = 0.5 C  : M = 0.5
l d Baseline
°
δ = −5
1
°
0.15 δ = 5
0.5
0.1
0
Baseline 0.05
−0.5 °
δ = −5
°
δ = 5
−1 0 
−10 −5 0 5 10 −10 −5 0 5 10
α α
(a) (b)
80  0.1  
C /C  : M = 0.5 C  : M = 0.5
l d m
60
0.05
40
20 0
0
Baseline −0.05
Baseline
−20 °
δ = −5 °
δ = −5
°
δ = 5 °
δ = 5
−40 −0.1 
−10 −5 0 5 10 −10 −5 0 5 10
α α
(c) (d)
Figure 2.21: 2D CFD-generated airfoil characteristics (SC1094R8) with −5◦ and 5◦
TEF deflections at M = 0.5
46
Properties Value
UH-60A rotor data
Rotor type Articulated
Number of blades Nb 4
Radius R 26.83 ft.
Chord c 1.73 ft.(nominal)
Rotor speed Ω 258 RPM
Solidity σ 0.0832
Lock number γ 6.33
Trailing-edge flap data
Length 10%R
Chord 15%c
Midspan location 65%R
Hinge location Flap leading-edge
Leading-edge slat data
Length 40%R
Chord 15%c
Midspan location 70%R
Baseline airfoil SC2110
Slat orientations S0,S1,S6
Table 2.1: Basic rotor,flap and slat data
47
Blade natural frequencies (/rev)
1 2 3
Flap 1.04 2.84 4.69
Lag 0.28 12.4 -
Torsion 4.3 13.5 -
Flight conditions
C8534 µ = 0.368, CW/σ = 0.0783
C9017 µ = 0.237, CW/σ = 0.1325
48
Table 2.2: 3/rev and 4/rev TEF actuations for minimization of diferent loads
49
Table 2.3: 5/rev TEF actuations for minimization of diferent loads
50
It may be observed that it is not easy to predict actuations for simultaneous
reduction of different loads,and so an algorithm for multicyclic control was developed
and implemented for use with UMARC to determine the optimal TEF actuation
schedule and the flap inputs necessary for vibration reduction.This algorithm is
based on a linear, quasi-static representation of the rotor hub vibration response to
TEF inputs ( [90]).
1. This algorithm estimates the Jacobian for the hub loads with respect to flap
inputs and uses this to calculate the inputs for minimizing a vibration objective
function that is a suitably weighted combination of the hub loads ( [87]).
2. The results from the multicyclic controller are compared to previously reported
results to validate the accuracy of the prediction of optimal TEF inputs.
3. Vibration data for reduction of the 3 hub loads Fz ,Mx and My were obtainedh h h
from the controller.
Validation of multicyclic controller for TEFs
The reductions in the three hub loads from the baseline value and the com-
bination of flap amplitudes found to achieve maximal reduction were compared for
the ‘Brute Force’ method i.e. identification of optimal actuations from the load
reduction contours, and the Multicyclic Controller method. It was found that the
controller predicts the minima with good accuracy. This means that the linear,
quasi-static model of helicopter vibration with respect to trailing-edge flap inputs
51
( [87]), constructed about an operating condition corresponding to a vector of flap
inputs and resulting hub loads, is valid.
A scalar vibration objective function J1 was defined to minimize the target
hub loads and, optionally, the TEF deflections.
J1 = z
T
n Wzzn + θ
T
nWθθn (2.1)
Here zn is a vector containing the cosine and sine components of the non-
dimensional Nb/rev fixed system hub loads Fx, Fy, Fz, Mx and My, and θn is a
vector containing the harmonics of the flap control inputs at a time step n. The
shear and moment hub loads are respectively non-dimensionalized by the quantities
m0(ΩR)
2 and m0(ΩR)
2R. For the reduction of Nb/rev hub loads, the flap actuations
consist of (Nb − 1, Nb, Nb + 1)/rev components. The matrices Wz and Wθ contain
weighting functions for the vibration harmonics and control inputs respectively.
Choosing the weights suitably enables targeting specific loads and using specific
input flap harmonics.
The system vibration response zn is linearized about the current control state
using the sensitivity matrix T calculated once at the uncontrolled operating condi-
tion using a forward difference method.
zn = zn−1 + T (θn−1 − θn) (2.2)
Minimizing J1 by solving ∂J/∂θn = 0 yields the algorithm for updating the
control input vector θn
52
∆θn = Czn−1 − Cθθn−1 (2.3)
In Eq. 2.3,
C = −DT TWz
Cθ = DWθ (2.4)
D = (T TW T +W )−1z θ
In the present study, the diagonal weighting matrix Wz was assumed to have
the form
 
/F 2
 x0 



/F 2y0 
Wz = (1− β) 1/F 2  (2.5) z0  1/M2x0 
1/M2y0
Wθ = βI (2.6)
In the present study, β = 0 was used, so the controller attempts to minimize
the hub loads without constraining the amplitude of the flap motion.
The reductions in target hub loads,using the TEF multicyclic controller,at the
flight condition C8534,for the blade torsional stiffness of 100%,75%,60% and 50%,are
given in Table . 2.4 and Table . 2.5 . The TEF optimal actuations are graphically
53
shown in Fig.2.22.The reduction of the target hub loads,at various advance ratios,for
forward flight CW/σ = 0.08,is shown in Table.2.6.
Figure 2.22: Multicyclic control of three hub forces for optimal TEF actuations for
various GJ: C8534
54
Table 2.4: Multicyclic control for mini5m5ization of 4/rev vibratory loads:C8534
Table 2.5: Multicyclic control for minimization of J :C8534
56
Table 2.6: Multicyclic control for minimization of J : CW/σ = 0.08,at various forward
flight speeds
57
2.5 Analytical Model: LES
2.5.1 Leading-edge slat structural model
Previously, the slat motion was modeled as a combination of 2 prescribed
rotations (see Fig. 2.23), one about the blade elastic center (denoted by χb) and the
other about its hinge (denoted by χs). The separation Rs was assumed constant.
The local (deformed blade) coordinate system is centred at the blade elastic center
and the coordinate directions are along {iξ, jη,kζ}. The local slat coordinate system
is defined by {is, js,ks}, centred at the slat hinge.
0.15
0.1 kξ
k
s
0.05
χ R
s χ s
b
0
j j
e.a.
s η
−0.05 Blade
−0.1
−0.1 −0.05 0 0.05 0.1 0.15 0.2 0.25
Figure 2.23: 2 degree-of-freedom slat model
58
The fidelity of the model with respect to the experimental slat positions S1-
S6 as described in [75] was investigated using suitable combinations of χb and χs.
While it is possible to approximate to some extent the translation-rotation of the
slat by means of 2 rotations, it was determined that a more accurate description of
the actual motion of the slat will require an additional degree of freedom.
To this end, a 3 degree-of-freedom model has been developed, the 3 degrees
being the 2 coordinates of the slat hinge (denoted by ηh and ζh), and the rotation
of the slat about the hinge (χs), maintaining the length of the strut connecting
the slat to the hinge (Rs) and the angle between the strut and the slat local axes
(χ0) constant.(Fig. 2.24). The attached animations illustrate that the new model
captures any given actuation schedule corresponding to the experimental setup,
exactly.
Also,in Fig.2.25,both the 2 and 3 DOF models of the slat motion are given to
illustrate the differences.
From the data corresponding to the experimental setup, the following charac-
teristics were extracted (note that lengths are non-dimensionalized with respect to
the baseline blade chord, taken to be 24′′) :
1. Baseline blade airfoil SC2110; slat airfoil supplied was designed for constant
area flow between slat and baseline blade
2. For attachment to the quarter-chord position of the slat section, Rs = 0.075;
3. Coordinates of the experimental hinge positions in the blade coordinates (jη,kζ)
: S1 = (0.21,0.06) ; S6 = (0.23,0.04)
59
0.15
0.1 kHinge line ξ
k
s
0.05 χ
s R (η ,ζ )
χ s h h
0 0
j e.a.j
s η
−0.05 Blade
−0.1
−0.1 −0.05 0 0.05 0.1 0.15 0.2 0.25
Figure 2.24: 3 degree-of-freedom slat model
Figure 2.25: 2 and 3 degrees of freedom slat models
60
4. Angle between slat local axes and strut , χ ◦0 = 14.76
Enhancements were made to the baseline blade analysis in the University of
Maryland Advanced Rotor Code (UMARC) for the integration of the complete
structural, inertial and aerodynamic contributions of leading-edge slats to model
its’ benefits.The slat airfoil is modeled as an additional element on the baseline
blade(same geometry as the UH-60A blade). The slat motion is modeled with 3 ad-
ditional degrees of freedom to improve conformity of the slat airfoil with the blade
airfoil and to capture the experimental translation-rotation actuation methodol-
ogy.The quasi-steady aerodynamic effects are being modeled using 2D table lookup
for section aerodynamic coefficients as a function of angle of atttack,Mach number
and slat orientation.
The inertial contributions of the leading-edge slat to the baseline blade equa-
tions of motion have been formulated and incorporated in the finite-element model
in UMARC, with 3 additional global degrees of freedom.
The aerodynamic forces in the presence of the slat are calculated by an airfoil
table-lookup process, with section aerodynamic coefficients obtained from 2-D CFD
analysis for different blade angles of attack, local Mach number and slat position.
The motion of the slat is from S1 on the advancing blade to S6 on the retreating
blade in a 1/rev fashion, i.e.
√
• ηh(ψ) = ηS1 + d(ψ)/ 2
√
• ζh(ψ) = ζS1 + d(ψ)/ 2
• χs(ψ) = θ(ψ)
61
where the hinge distance from S1 on the hinge line S1-S6 (negative toward S6)
is given by
d(ψ) = −0.32′′ + 0.32′′sin(ψ)
normalized with respect to the blade chord; and the rotation of the slat from the
blade axis is given by
θ(ψ) = −23.75◦ + 3.75◦sin(ψ)
The slat geometry used in this study and the definition of ’effective chord’ are
shown in Fig. 2.26 and Fig. 2.27.
0.15
0.1 Slat S1
0.05 Main element
 SC2110
0 Slat S6
−0.05
−0.1
−0.1 −0.05 0 0.05 0.1 0.15 0.2 0.25
Figure 2.26: Slat configurations with respect to baseline airfoil
2.5.2 Description of slat motion
The equations of motion governing the slat are given below.The final equations
of motion governing the extension, torsion and the slat motion can be obtained using
62
0.2
0.15
0.1 Slat airfoil
Base airfoil
0.05 To T.E.
’Effective’ 1/4c
0
’Effective’ chord line
−0.05
Base airfoil 1/4c
−0.1
−0.1 −0.05 0 0.05 0.1 0.15 0.2 0.25
Figure 2.27: Definition of ’effective’ chord
63
the expression for Hamilton’s Variational Principle and the equations for the con-
tributions from the slat and blade(and/or TEF and work done by external forces).
As shown in Fig. 2.28, the slat motion is modeled as a combination of 2
prescribed rotations, one about the blade elastic center (denoted by χb) and the
other about its hinge (denoted by χs). The separation Rs is assumed constant. The
local (deformed blade) coordinate system is centred at the blade elastic center and
the coordinate directions are along {iξ, jη,kζ}. The local slat coordinate system is
defined by {is, js,ks}, centred at the slat hinge.
k
χ ζ
s
k
s
slat
R
s
j
s χ
b blade
j e.a.
η
Figure 2.28: Definition of slat degrees of freedom
2.5.3 Hamilton’s principle
The finite element energy expressions for the elastic model are derived using
the generalized Hamilton’s principle, given as :
64
∫ t2
(δU − δT − δW )dt = 0 (2.7)
t1
where δU , δT and δW are the virtual work contributions of conservative forces
(variation of potential energy), inertial forces (variation of kinetic energy) and non-
conservative forces. In the following sections, the incremental contributions of the
slat to the total energy are given, without ignoring any terms based on ordering
schemes.
2.5.4 Strain Energy
(a)Section properties
Slat section properties
η1 = ηscosχs +Rscosχb
ζ1 = ηss∫inχ∫s +Rssinχb
∫ ∫ dηdζ = Ass
∫ηsd∫ηdζ = A eas Ass
∫ ∫ ζsdηdζ = 0s
∫ ∫η2sdηdζ = IaZss
∫ ∫ ζ2sdηdζ = 0s
∫ ∫ (η2 + ζ2s s )2dηdζ = Ba1ss
η (η2 + ζ2 2s s s ) dηdζ = B
a
2s
s
65
Derived slat section properties
∫ ∫
∫ ∫ η1dηdζ = AseAss
∫ ζ∫1dηdζ = AsdAss
∫ ∫ η21dηdζ = IZss
∫ ∫ ζ21dηdζ = IY ss
(η21 + ζ
2
1 )∫dηd∫ζ = IY s + I 2Zs = AskAss
∫ ∫ (η2 + ζ2)21 1 dηdζ = B1ss
∫ ∫ η1(η21 + ζ2 21 ) dηdζ = B2ss
∫ ∫ ζ (η2 + ζ2)21 1 1 dηdζ = B3ss
∫ ∫ η (η2 21 1 + ζ1 )dηdζ = D1ss
ζ 21(η1 + ζ
2
1 )dηdζ = D2s
s
(b)Expression for strain energy The potential energy for the rotor is the
sum of blade and slat contributions.
δU = δUb + δUs
The contribution of the deformation of the blade itself to δUs is given by
∫ ∫ ∫
(Exxxδxx +Gxηδxη +Gxζδxζ)dηdζdx
s
where the integration is carried out over the slat spanwise limits.
66
In addition, the slat motions themselves give rise to
∆δUs = kχ χbδχb + kχsχsδχb s
where kχ , kχs are the equivalent springs located at the origins of the slat motions,b
i.e. the blade elastic center and the slat hinge. Thus
∫
δUs
δUs = = (Uu′eδu
′ ′ ′
e + Uv′δv + Uw′δw + U
′′
v′′δv + U
′′
w′′δw (2.8)
m 2 30Ω R s
+Uφ̂δφ̂+ Uφ̂′δφ̂
′ + U ′′φ̂′′δφ̂ + Uχ δχb + Ub χsδχs)dx
(c)Slat contributions
′2 ′2 ′′2
Uu′e = EA [u
′ + k2 (θ′φ̂′s e As + θ
′w′v′′ + φ̂ + w v + φ̂′w′v′′)]
2 2
−EAseAs[v′′(cosθ − φ̂sinθ) + w′′(sinθ + φ̂cosθ)]
−EAsdAs[w′′(cosθ − φ̂sinθ)− v′′(sinθ + φ̂cosθ)]
Uv′ = 0
67
U ′ = GJ (φ̂′v′′ + w′v′′2) + EA [k2 (θ′v′′u′ + φ̂′v′′w s s As e u
′ ′ ′ ′′2
e + u ew v )
−(θ′v′′2 + φ̂′v′′2 + w′v′′3){eAs(cosθ − φ̂sinθ) + dAs(sinθ + φ̂cosθ)}
−(θ′v′′w′′ + φ̂′v′′w′′ + w′v′′2w′′){dAs(cosθ − φ̂sinθ) + eAs(sinθ + φ̂cosθ)}
+EB1s(θ
′2φ̂′v′′ + 3θ′φ̂′2v′′ + 2θ′φ̂′w′v′′2 + 2θ′2w′v′′2 + 3θ′w′2v′′3+
2 2
1 φ̂′3v′′ + 3 φ̂′2w′v′′2 + θ′φ̂′w′v′′2 + 3 φ̂′w′2v′′3 + 1w′3v′′4)
2 2 2 2
U ′′ = GJ (φ̂′w′ + v′′w′2v s ) + EAs[u
′
e{−eAs(cosθ − φ̂sinθ) + dAs(sinθ + φ̂cosθ)}]
+v′′{EI 2Zscos θ1 + EI 2Y ssin θ1 − 2EIZY scosθ1sinθ1}
+w′′{(EIZs − EIY s)cosθ1sinθ1 + EIZY scos2θ1}
′2 ′2 ′′2
+[sinθ(EB − φ̂EB ) + cosθ(φ̂EB − EB )](θ′φ̂′ + θ′w′v′′ + φ̂ + w v3s 2s 3s 2s + φ̂′w′v′′)2 2
Uw′′ = −EA ′s[u e{dAs(cosθ − φ̂sinθ) + eAs(sinθ + φ̂cosθ)}]
w′′{EI sin2θ + EI cos2Zs 1 Y s θ1 + 2EIZY scosθ1sinθ1}
+v′′{(EIZs − EIY s)cosθ1sinθ1 + EIZY scos2θ1}
−[sinθ(EB2s −
′2 ′2 ′′2
φ̂EB3s) + cosθ(φ̂EB2s + EB3s)](θ
′φ̂′ + θ′w′v′′ + φ̂ + w v + φ̂′w′v′′)
2 2
68
Uφ = EA
′ ′′
su e[v {dAs(cosθ − φ̂sinθ) + eAs(sinθ + φ̂cosθ)}
−w′′{eAs(cosθ − φ̂sinθ)− dAs(sinθ + φ̂cosθ)}]
+E(θ′φ̂′ + θ′w′v′′ + φ̂
′2 ′2
+ w v
′′2
+ φ̂′w′v′′)[(v′′sinθ ′′
2 2 1
− w cosθ1)D1s
+(v′′cosθ + w′′1 sinθ1)D2s]
+w′′2[(EIZs − EIY s)cosθ1sinθ1 + EIZY scos2θ1]
−v′′2[(EIZs − EIY s)cosθ1sinθ1 + EIZY scos2θ1]
+v′′w′′[(EIZs − EIY s)cos2θ1 − 2EIZY ssin2θ1]
Uφ′ = GJs(φ̂
′ + w′v′′) + EAsk
2
As(θ
′ + φ̂′ + w′v′′)u′e
+EB (θ′2φ̂′ + θ′2w′v′′ + 3θ′φ̂′2 + 3θ′φ̂′w′v′′ + 3θ′w′2v′′2 + 1 φ̂′31s 2 2 2
+3 φ̂′2w′v′′2 + 3 φ̂′w′2v′′2 + 1w′3v′′3)
2 2 2
−EB (θ′ + φ̂′2s + w′v′′){v′′(cosθ − φ̂sinθ) + w′′(sinθ + φ̂cosθ)}
+EB3s(θ
′ + φ̂′ + w′v′′){v′′(sinθ + φ̂cosθ) + w′′(cosθ − φ̂)}
Uφ′′ = 0
69
Uχ = k
a
χ χb +GAsRseAssin(χs − χb)(φ̂′2 + φ̂′w′v′′ + w′2v′′2)b b
+EAsu
′ ′′
e[v (Rs{sinχbcosθ1 + cosχbsinθ1})− w′′(Rs{cosχbcosθ1 − sinχbsinθ1})
− ′2 ′2 ′′22R ea sin(χ − χ )(θ′φ̂′ + θ′w′v′′ + φ̂ + w v + φ̂′w′v′′s As b s )]2 2
+w′′2[EA 2sRssin(χb + θ1)cos(χb + θ1) + EA
a
sRseAscos(χb + θ1)sin(χs + θ1)]
−v′′2[EAsR2ssin(χ + θ )cos(χ + θ ) + EA R eab 1 b 1 s s Assin(χb + θ1)cos(χs + θ1)]
+v′′w′′[EA 2 asRscos2(χb + θ1) + EAsRseAscos(χb + χs + 2θ1)]
′2 ′2 ′′2
+2E(θ′φ̂′ + θ′w′v′′ + φ̂ + w v + φ̂′w′v′′)[{v′′cos(χb + θ2 2 1)
+w′′sin(χb + θ1)}AsR2 aseAssin(χb − χs)
+{v′′cos(χ + θ ) + w′′sin(χ + θ )}R Ias 1 s 1 s Zssin(χb − χs)]
+E[{R3sAs + AsR Ia 2 as Zs + 2AsRseAscos(χb − χs)}
(θ′φ̂′ + θ′w′v′′ φ̂
′2 w′2v′′2+ +∫ ∫ + φ̂
′w′v′′){v′′sin(χb + θ )− w′′1 cos(χb + θ1)}2 2
−2{R3A ea 3 2 as s As +Rs ηsdηdζ + 2RsIZscos(χs b − χs)}sin(χb − χs)
′2 ′2 ′′2
(θ′φ̂′ + θ′w′v′′ + φ̂ + w v + φ̂′w′v′′)2]
2 2
70
Uχs = kχsχs +GAsR
a
seAssin(χb − χs)(φ̂′2 + φ̂′w′v′′ + w′2v′′2)
+EAsu
′
e[v
′′(eaAs{sinχscosθ1 + cosχssinθ1})− w′′(eaAs{cosχscosθ1 − sinχssinθ1})
− ′2 ′2 ′′22R aseAssin(χ ′ ′ ′ ′ ′′
φ̂ w v ′ ′ ′′
b − χs)(θ φ̂ + θ w v + + + φ̂ w v )]2 2
+w′′2[EA asRseAssin(χb + θ1)cos(χs + θ1) + EI
a
Zscos(χs + θ1)sin(χs + θ1)]
−v′′2[EAsR eas Assin(χs + θ1)cos(χb + θ1) + EIaZssin(χs + θ1)cos(χs + θ1)]
+v′′w′′[EA R eas s Ascos(χb + χs + θ1) + EI
a
Zscos2(χs + θ1)]
− ′ ′ ′ ′ ′′ φ̂′2 w′2v′′22E(θ φ̂ + θ w v + + + φ̂′w′v′′)[{v′′cos(χb + θ1)2 2
+w′′sin(χb + θ1)}A 2 asRseAssin(χb − χs)
+{v′′cos(χs + θ ) + w′′1 ∫ ∫ sin(χs + θ1)}RsI
a
Zssin(χb − χs)]
+E[{R2sAsea + η3As sdηdζ + 2RsIaZscos(χb − χs s)}
′ ′ ′2 ′2 ′′2(θ φ̂ + θ′w′v′′ + φ̂ + w v + φ̂′w′v′′){v′′∫ ∫ sin(χ + θ )− w
′′cos(χ + θ )}
2 2 s 1 s 1
+2{R3A ea +R η3dηdζ + 2R2Ias s As s s s s Zscos(χb − χs)}sin(χb − χs)
′ ′ ′ ′ ′′ φ̂′2 w′2 ′′2(θ φ̂ + θ w v + + v + φ̂′w′v′′)2]
2 2
2.5.5 Kinetic Energy
(a) Section properties
Slat section properties
71
∫ ∫
∫ ∫ ρdηdζ = mss
∫ρη∫sdηdζ = m eas ss
∫ ∫ ρζsdηdζ = 0s
ρη2sdηdζ = I
a
Zs
s
Derived slat section properties
∫ ∫ ∫ ∫
∫ ∫ ρη1dηdζ = mses ∫ ∫ ρζ1dηdζ = msds ss
∫ ∫ ρη21dηdζ = msk2m2s ∫ ∫ ρζ
2
1dηdζ = m
2
s s
km1s
s
ρ(η∫2 +∫ζ21 1 )dηdζ = m k2 2s mss ∫ ∫ρη1ζ1dηdζ = m ks s m3s
∫ ∫ ρη̇1dηdζ = msės ∫ ∫ ρζ̇1dηdζ = msḋs ss
∫ ∫ ρη̈1dηdζ = msës ∫ ∫ ρζ̈ dηdζ = m d̈s 1 s ss
∫ ∫ ρηsη1dηdζ = m 2 2sesη ∫ ∫ ρηs sζ1dηdζ = msdsηs
∫ ∫ ρη 2 2sη̇1dηdζ = msėsη ρηsζ̇1dηdζ = ms sḋsηs ∫ ∫
∫ ∫ ρη η̈ dηdζ = m ë2s 1 s sη ∫ ∫ ρηsζ̈1dηdζ = m d̈
2
s s sη
s
∫ ∫ ρζ1η̇1dηdζ = m k2 2s m4s ∫ ∫ ρη1ζ̇1dηdζ = ms skm5ss
∫ ∫ ρη1η̇1dηdζ = m 2skm6s ∫ ∫ ρζ1ζ̇1dηdζ = m k
2
s s m7s
s
∫ ∫ ρζ1η̈1dηdζ = msk2m8s ∫ ∫ ρη1ζ̈1dηdζ = m
2
s s
km9s
s
ρη η̈ dηdζ = m k2 21 1 s m10s ρζs 1ζ̇1dηdζ = mskm11s
s
(b)Expression for kinetic energy The potential energy for the rotor is the
72
sum of blade and slat contributions.
δT = δTb + δTs
where ∫
δTs = ρvs.δvsdηsdζsdx
s
where the integration is carried out over the slat spanwise limits. Thus
∫
δT xfs
δTs = = (Tueδu
′
e + Tvδv + Twδw + Tv′δv + Tw′δw
′ (2.9)
m Ω2R30 xi
+Tφ̂δφ̂+ Tχ δχb + Tχsδχs)dxb
(c)Slat contributions
Tue = ms[x+ (∫−(βp + 2θ̇)es − 2ḋ∫s)sinθ + (−(βp + 2θ̇)ds − 2ės)cosθ
−1 x ′2 ′2 x ′2 ′ ′ ′2(v + w )dx+ (v̇ + v v̈ + ẇ + w′ẅ′)dx
2 0 0
+ue − üe + 2v̇ − wβp + v′{〈ds(1 + θ̇2)− 2ėsθ̇ − esθ̈ − d̈s〉sinθ
+〈−es(1 + θ̇2)− 2ḋsθ̇ − dsθ̈ + d̈s〉cosθ}+ 2v̇′{〈−esθ̇ − ḋs〉sinθ + 〈−dsθ̇ + ės〉cosθ}
+v̈′{escosθ − dssinθ}+ w′{〈−es(1 + θ̇2)− 2ḋsθ̇ − dsθ̈ + ës〉sinθ
+〈−ds(1 + θ̇2) + 2ėsθ̇ + esθ̈ + d̈s〉cosθ}+ 2ẇ′{〈−dsθ̇ + ės〉sinθ + 〈esθ̇ + ḋs〉cosθ}
+ẅ′{essinθ + dscosθ}+ φ̂{〈−esβp − 2esθ̇ − 2ḋs〉cosθ + 〈dsβp + 2dsθ̇ − 2ės〉sinθ}
˙̂
+2φ{−dscosθ − essinθ]
73
∫ x
Tv = ms[2 (v
′v̇′ + w′ẇ′)dx+ {−d 2s(1 + θ̇ + 2βpθ̇) + 2(βp + θ̇)ės + esθ̈ + d̈s}sinθ0
+{es(1 + θ̇2 + 2βpθ̇) + 2(βp + θ̇)ḋs + dsθ̈ − ës}cosθ
−2u̇ + v − v̈ + 2ẇβ + v′e p {−2〈esθ̇ + ḋs〉sinθ + 2〈−2dsθ̇ + ės〉cosθ}
+v̇′{−2dssinθ + 2escosθ}+ w′{2〈−2dsθ̇ + ės〉sinθ + 2〈esθ̇ + ḋs〉cosθ}
+ẇ′{2essinθ + 2dscosθ}+ φ̂{〈−d 2s(1 + θ̇ + 2βpθ̇) + 2(βp + θ̇)ės + esθ̈ + d̈s〉cosθ
−〈es(1 + θ̇2 + 2βpθ̇) + 2(βp + θ̇)ḋs + dsθ̈ − ës〉sinθ}
˙̂
+φ{2〈es(βp + θ̇) + ḋs〉cosθ + 2〈−ds(βp + θ̇) + ės〉sinθ}
¨̂
+φ{essinθ + dscosθ}]
74
∫ x ∫ x 2 2
Tv′ = ms[(escosθ − dssinθ){1 (v′2 + w′2)dx− x− (v̇′ + v′v̈′ + ẇ′ + w′ẅ′)dx}2 0 0
+sinθcosθ{(k2 − k2 2 2m2s m1s)(βp + θ̇) + 2(km4s + km5s)}
+cos2θ{2(βp + 2θ̇)k2 2 2 2 2m3s + 2(km7s − km6s)} − ((βp + 2θ̇)km3s + 2km7s)
+ue{dssinθ − escosθ}+ üe{−dssinθ + escosθ}+ 2v̇{dssinθ − escosθ}
+wβp{−dssinθ + escosθ}
+v′{cosθsinθ〈−2k2 2m3s(1 + θ̇ )
−2(k2 − k2m7s m6s)θ̇ + (k2m2s − k2 2 2m1s)θ̈ + (km8s + km9s)〉
+cos2θ〈(1 + θ̇2)(k2 − k2 2 2 2 2 2m2s m1s) + 2(km4s + km5s)θ̇ + 2km3sθ̈ + (km11s − km10s)〉
+〈(1 + θ̇2)k2 2 2 2m1s − 2km4sθ̇ − km3sθ̈ − km10s〉}
+v̇′{2cosθsinθ〈(k2 2 2 2m2s − km1s)θ̇ + (km4s + km5s)〉
+2cos2θ〈2k2 2 2m3sθ̇ + (km7s − km6s)〉 − 2〈k2 2m3sθ̇ + km7s〉
+v̈′{2cosθsinθk2m3s − cos2θ(k2 2 2m2s − km1s)− km1s}
+w′{cosθsinθ〈(k2 − k2 )(1 + θ̇2) + 2(k2 2m2s m1s m4s + km5s)θ̇
+2k2 θ̈ + (k2 − k2m3s m11s m10s)〉
+cos2θ〈2(1 + θ̇2)k2 2m3s + 2(km7s − k2 )θ̇ − (k2 2 2 2m6s m2s − km1s)θ̈ − (km8s + km9s)〉
−〈(1 + θ̇2)k2m3s + 2k2m7sθ̇ + k2m1sθ̈ − k2m8s〉}
+ẇ′{2cosθsinθ〈2k2 2 2m3sθ̇ + (km7s − km6s)〉
+2cos2θ〈−(k2m2s − k2m1s)θ̇ − (k2m4s + k2m5s)〉+ 2〈−k2 2m1sθ̇ + km4s〉}
+ẅ′{−cosθsinθ(k2 − k2 )− 2cos2∫ m2s m1s ∫ θk
2
m3s + k
2
m3s}
x x 2 2
+φ̂{(dscosθ + essinθ)〈−1 (v′2 + w′2)dx+ x+ (v̇′ + v′v̈′ + ẇ′ + w′ẅ′)dx〉2 0 0
−4cosθsinθ〈k2 (β + 2θ̇) + (k275 − k2 )〉+ cos2θ〈(k2 − k2m3s p m7s m6s m2s m1s)(βp + 2θ̇)
+2(k2 + k2
˙̂
m4s m5s)〉+ φ〈sin2θ(k2 2m2s − km1s) + 2cos2θk2m3s〉]
∫ x
T = m [β (1 (v′2 + w′2w s p )dx− x) + sinθ{es(θ̇2 + 2βpθ̇) + 2(βp + θ̇)ḋs + dsθ̈ − ës}2 0
+cosθ{ds(θ̇2 + 2βpθ̇)− 2(βp + θ̇)ės − esθ̈ − d̈s}
−βpue − 2v̇βp − ẅ + v′{βp(escosθ − dssinθ)}
+w′{βp(essinθ + dscosθ)}+ φ̂{−sinθ〈d 2s(θ̇ + 2βpθ̇)− 2(βp + θ̇)ės − esθ̈ − d̈s〉
+cosθ〈es(θ̇2 + 2βpθ̇) + 2(βp + θ̇)ḋs + dsθ̈ − ës〉}
˙̂
+φ{2sinθ〈es(βp + θ̇ + ḋs)〉+ 2cosθ〈ss(βp + θ̇ − ės)〉}
¨̂
+φ{dssinθ − escosθ}]
76
∫ x
T ′ = m [(e sinθ + d cosθ){1 (v′2 + w′
∫
2 − − x ′2 ′ 2w s s s )dx x (v̇ + v v̈′ + ẇ′ + w′ẅ′)dx}2 0 0
+sinθcosθ{2k2m3s(β 2 2p + 2θ̇) + 2(km7s − km6s)}
+cos2θ{−(βp + 2θ̇)(k2m2s − k2 2 2 2 2m1s)− 2(km4s + km5s)}+ km2s(βp + 2θ̇) + 2km5s)
+ue{−essinθ − dscosθ}+ üe{essinθ + dscosθ}+ 2v̇{−dscosθ − essinθ}
+wβp{e ′ 2ssinθ + dscosθ}+ v {cosθsinθ〈(km2s − k2m1s)(1 + θ̇2) + 2(k2 2m4s + km5s)θ̇
+2k2 2 2m3sθ̈ + (km11s − km10s)〉
+cos2θ〈2(1 + θ̇2)k2m3s + 2(k2 2 2 2 2 2m7s − km6s)θ̇ − (km2s − km1s)θ̈ − (km8s + km9s)〉
+〈−(1 + θ̇2)k2m3s + 2k2 θ̇ + k2 θ̈ + k2m6s m2s m9s〉}
+v̇′{2cosθsinθ〈2k2 2 2m3sθ̇ + (km7s − km6s)〉
−2cos2θ〈(k2 − k2m2s m1s)θ̇ − (k2 2m4s + km5s)〉+ 2〈k2m2sθ̇ + k2m5s〉
+v̈′{−cosθsinθ(k2m2s − k2m1s)− 2cos2θk2m3s + k2m3s}
+w′{cosθsinθ〈2k2m3s(1 + θ̇2) + 2(k2 2m7s − km6s)θ̇
−(k2m2s − k2m1s)θ̈ − (k2 2m8s + km9s)〉
+cos2θ〈−(k2 − k2 )(1 + θ̇2)− 2(k2 2 2 2 2m2s m1s m4s + km5s)θ̇ − 2km3sθ̈ − (km11s − km10s)〉
+〈(1 + θ̇2)k2 + 2k2 2 2m2s m5sθ̇ + km3sθ̈ − km10s〉}
+ẇ′{2cosθsinθ〈−(k2 2 2m2s − km1s)θ̇ − (km4s + k2m5s)〉
+2cos2θ〈−2k2m3sθ̇ − (k2 2 2 2m7s − km6s)〉+ 2〈km3sθ̇ − km6s〉}
+ẅ′{−2cosθsinθk2 + cos2θ(k2 − k2 )− k2∫ m3s m2s m1s m2s}
{ − 〈1 x ′ ′
∫
2 2 x 2 2+φ̂ (escosθ dssinθ) (v + w )dx− x− (v̇′ + v′v̈′ + ẇ′ + w′ẅ′)dx〉2 0 0
+2cosθsinθ〈2(k2m2s − k2m1s)(βp + 2θ̇) + 4(k2m4s + k2m5s)〉
+cos2θ〈2k2 77 2 2m3s(βp + 2θ̇) + 2(km7s − km6s)〉
˙̂
+φ〈2sin2θk2m3s − 2cos2θ(k2 2 2m2s − km1s) + 2km2s〉]
Tφ̂ = ms[−2(k2m6s + k2∫m7s)(βp + θ̇)− k
2
msθ̈ + (k
2 2 2
m8s∫− km9s)− km3scos2θ
+cosθ〈 x xesβp(1 ′2 ′2∫ (v + w )dx− x)− 2d
′
s ∫ (v v̇
′ + w′ẇ′)dx〉
2 0 0
+sinθ〈− xd β (1 (v′2 xs p + w′2)dx− x)− 2es (v′v̇′ + w′ẇ′)dx〉2 0 0
−cosθsinθ(k2m2s − k2m1s) + ue{βp(dssinθ − escosθ)}+ 2u̇e{essinθ + dscosθ}
−v{essinθ + dscosθ}+ 2v̇{βp(dssinθ − escosθ)}
+v̈{essinθ + dscosθ} −∫ 2ẇ{βp(essinθ + dscos∫θ)}+ ẅ{dssinθ − escosθ}x x 2 2
+v′{(e sinθ + d cosθ)(−1 (v′2 + w′2)dx+ x+ (v̇′ + v′v̈′ + ẇ′ + w′ẅ′s s )dx)2 0 0
−2sin2θβpk2 2 2m3s + βpcos2θ(km2s − km1s)}
+v̇′{−∫2sin2θ(k
2 2
m2s − km1s)− ∫2k
2
m3scos2θ}
+w′{(escosθ − d sinθ)(1
x x 2 2
s (v
′2 + w′2)dx− x− (v̇′ + v′v̈′ + ẇ′ + w′ẅ′)dx)
2 0 0
+cos2θ〈2β 2pkm3s − 2(k2 + k2m6s m7s)〉+ βpsin2θ(k2 2m2s − km1s)}
+ẇ′{−2sin2θk2 + 2cos2θ(k2 − k2 )− 2k2m3s ∫m2s m1s m2s}
+φ̂{ x(essinθ + dscosθ)β (−1 (v′2p ∫ + w
′2)dx+ x)
2 0
x
+2(dssinθ − escosθ) (v′v̇′ + w′ẇ′)dx0
−cos2θ(k2 2 2m2s − km1s) + 2sin2θkm3s}
˙̂
+φ{−2(k2 + k2m6s m7s)} −
¨̂
φk2ms]
78
∫ x ∫ x
T = m R [β cos(θ + χ )(1 (v′2 + w′2)dx− x)− 2sin(θ + χ ) (v′v̇′ + w′ẇ′χ s s p b b )dxb 2 0 0
+(2βp + θ̇)θ̇(dscosχb − essinχb)− 2(βp + θ̇)(ḋssinχb + ėscosχb)
−(escosχb + dssinχb)θ̈ + (ëssinχb − d̈scosχb) + dscosχb
−cos2θ(dscosχb + essinχb) + sinθcosθ(dssinχb − escosχb)
+ue{−cos(θ + χb)βp}+ u̇e{2sin(θ + χb)} − v{sin(θ + χb)}
−v̇{2βpcos(θ + χb)}+ v̈sin(θ + χb)
+ẇ{∫−2βpsin(θ + χb)}+ ẅ{∫−cos(θ + χb)}′{ x x 2 2+v sin(θ + χb)(−1 (v′2 + w′2)dx+ x+ (v̇′ + v′v̈′ + ẇ′ + w′ẅ′)dx)2 0 0
+cosθsinθ〈−2βp(essinχb + dscosχb)〉
+cos2θ〈βp(escosχb − dssinχb)〉}
+v̇′{sin2θ(dssinχb∫− escosχb)− 2cos
2θ(es∫sinχb + dscosχb) + 2dscosχb}
+w′{ x x 2 2cos(θ + χ 1 ′2 ′2 ′ ′ ′ ′ ′ ′b)( (v + w )dx− x− (v̇ + v v̈ + ẇ + w ẅ )dx)2 0 0
+sin2θ〈β 2p(escosχb − dssinχb)〉+ 2cos θ〈βp(dscosχb + essinχb)〉
−2βpessinχb + 2(dscosχb − essinχb)θ̇ − 2(ḋssinχb + ėscosχb)}
+ẇ′{−sin2θ(dscosχb +∫essinχb) + 2cos
2θ(escosχb − dss∫inχb)− 2escosχb}x x
+φ̂{sin(θ + χ )(x− 1 (v′2 + w′2b )dx)− 2cos(θ + χ ) (v′v̇′b + w′ẇ′)dx2 0 0
+sin2θ(essinχb + dscosχb) + cos2θ(dssinχb − escosχb)}
˙̂
+φ{2(βp + θ̇)(dscosχb − essinχb)− 2(ḋssinχb + ėscosχb)}
− ¨̂φ{escosχb + dssinχb}]
79
∫ x
Tχs = m
a
s[βpescos(θ + χ )(
1 (v′2s ∫ + w
′2)dx− x)
2 0
−2ea xssin(θ + χ ) (v′v̇′s + w′ẇ′)dx0
+(2βp + θ̇)θ̇(d
2
sηcosχ − e2s sηsinχs)− 2(β 2 2p + θ̇)(ḋsηsinχs + ėsηcosχs)
−(e2sηcosχs + d2 2sηsinχs)θ̈ + (ësηsinχs − d̈2sηcosχs) + d2sηcosχs
−cos2θ(d2sηcosχs + e2sηsinχs) + sinθcosθ(d2 2sηsinχs − esηcosχs)
+ue{−cos(θ + χs)β eap s}+ u̇ ae{2essin(θ + χs)}
−v{eassin(θ + χs)} − v̇{2β a apescos(θ + χs)}+ v̈essin(θ + χs)
+ẇ{−2β ea∫ p ssin(θ + χs)}+ ẅ{−∫ e
a
scos(θ + χs)}
+v′{easin(θ + χ )(−1 x x 2 2s s (v′2 + w′2)dx+ x+ (v̇′ + v′v̈′ + ẇ′ + w′ẅ′)dx)2 0 0
+cosθsinθ〈−2β (e2p sηsinχs + d2sηcosχs)〉+ cos2θ〈β 2p(esηcosχs − d2sηsinχs)〉}
+v̇′{sin2θ(d2sηsinχ − e2 cosχ )− 2cos2s ∫ sη s θ(e
2
sη∫sinχ + d
2
s sηcosχ ) + 2d
2
s sηcosχs}
x x 2 2
+w′{eascos(θ + χ )(1 (v′2 + w′2s )dx− x− (v̇′ + v′v̈′ + ẇ′ + w′ẅ′)dx)2 0 0
+sin2θ〈βp(e2sηcosχ 2s − dsηsinχs)〉+ 2cos2θ〈βp(d2sηcosχ 2s + esηsinχs)〉
−2β 2pesηsinχs
+2(d2sηcosχ − e2s sηsinχs)θ̇ − 2(ḋ2sηsinχ + ė2s sηcosχs)}
+ẇ′{−sin2θ(d2sηcosχ + e2s ∫sηsinχ
2
s) + 2cos θ(e
2 cosχ − d2sη s sηs∫inχs)− 2e
2
sηcosχs}
x x
+φ̂{eassin(θ + χ 1 ′2 ′2 a ′ ′ ′ ′s)(x− (v + w )dx)− 2escos(θ + χs) (v v̇ + w ẇ )dx2 0 0
+sin2θ(e2 2 2 2sηsinχs + dsηcosχs) + cos2θ(dsηsinχs − esηcosχs)}
˙̂
+φ{2(βp + θ̇)(d2sηcosχs − e2sηsinχ 2 2s)− 2(ḋsηsinχs + ėsηcosχs)}
− ¨̂φ{e2sηcosχ 2s + dsηsinχs}]
80
2.5.6 Non-conservative forces - virtual work
This is expressed as :
∫
δW R
δW = = (Luδu+Lvδv+Lwδw+Mφ̂δφ̂+Mχ δχb +Mχsδχs)dx (2.10)m Ω2R3 b0 0
where the slat contributions are only across its physical spanwise and chordwise
limits.
The airloads Lu, Lv, Lw in the x,y,z directions and the aerodynamic moments
about the elastic axis and slat hinges Mφ̂,Mχ ,Mχs are calculated from unsteadyb
theory or using look-up tables for the airfoil with slat attached, for different angles
of attack, slat positions and local Mach number.
2.5.7 Assembly of final equations of motion
Hence, using the expression for Hamilton’s variational principle, Eqn. 2.7
and the separate contributions from the slat (Eqns. 2.8-2.10) and blade (and/or
trailing-edge flaps) and the work done by external forces Eqn. 2.10, we can obtain
the governing equations for extension (ue), bending (v, w), torsion (φ̂), and the slat
motions (χb, χs) by setting the coefficients of the variations in the following equation
to zero.
∫ t2
{(....)δu+ (....)δv + (....)δw + (....)δφ̂+ (....)δχb + (....)δχs}dt = 0 (2.11)
t1
81
2.6 Slatted airfoil characteristics:
The slat configurations explored were proposed by Lorber et al.( [75]).Figure
1(a) shows slat configurations S0, S1 and S6. Configuration S1 is a compromise
between high lift and low drag, while S6 (which has the slat element deployed
further forward) provides still higher maximum lift, with higher drag (at small angles
of attack) as well. S0 is a baseline position with a low drag penalty. The slatted
blade sections had the SC2110 baseline/slatted airfoils in place of the baseline UH-
60A airfoils: SC1095 and SC1094R8. The slat configurations were designed for
optimum channeling of the flow near the leading-edge of the SC2110 airfoil, hence
the replacement of the baseline UH-60A airfoils in the slat sections.
The correlations between the slat configurations used by Lorber et al.( [75])
and the slat motion prescribed in this study are given in Fig.2.29.
2.7 Validation of the leading-edge slat model
The purely aerodynamic effect of slats was examined by fitting the baseline
rotor with slatted airfoils, without any modifications to the rotor dynamics due to
slats. Fig.2.31 shows the predicted hover performance (FM vs. CT/σ) of the UH-
60A rotor fitted with the SC2110/S1/S6 airfoils in place of the SC1094R8( [88]).
The two-dimensional(2D) airfoil characteristics (Cl, Cd, Cm) in the C-81 ta-
ble look-up format for the slatted sections were generated using CFD analysis
82
TURNS( [89]) for the SC2110 airfoil section as well as the slat orientations S1 and
S6. Dynamic slat actuations were simulated by a look-up table scheme interpolating
between different orientations across azimuth, identified by the rotation angle of the
slat element with respect to the baseline profile. Note that the slatted sections are
assumed to move such that the offset between the elastic axis and effective quarter
chord is invariant at any radial location. The aerodynamic characteristics of the
SC2110 and the S1 and S6-slatted airfoil sections were obtained at steps of 0.1 in
Mach number between 0.3 and 0.7 and 2◦ in angle of attack from about -15◦ to
25◦.The 4 coefficients, namely Cl,Cd, Cl/Cd and Cm are plotted against angle of
attack(α)(deg) at a representative Mach number as shown in Fig.2.30. All coeffi-
cients are referenced to the ’effective’ airfoil chord (and pitching moments defined
about the ’effective quarter-chord point’), as defined in Fig. 2.27. In general, the
slat elements improve the maximum lift characteristics of the blade section, while
imposing a drag penalty at small angles.
The slat dynamics model in UMARC was evaluated for various flight con-
ditions of interest, especially high thrust and forward flight conditions.The val-
idation of the baseline UH-60A forward flight performance with flight test data
from the Airloads Programme( [79]) was carried out for two weight coefficients of
CW/σ=0.0783(flight 85) and CW/σ=0.0891(flight 84).The break-up of the power
into different components,namely the profile,parasite and induced/propulsive power
was carried out for the purpose of performance evaluation. Figs. 2.32 and 2.33 show
the various components of the main rotor power coefficient as a function of advance
ratio,respectively for CT/σ=0.0783 and CT/σ=0.0891.
83
The correlation of predictions with test data is quite satisfactory.
84
Figure 2.29: Correlation between experiments and slat motion
85
Figure 2.30: 2D CFD-generated airfoil characteristics
86
0.8  
0.75
0.7
0.65
0.6
0.55
baseline UH−60A test
0.5 baseline UH−60A
SC2110
0.45 SC2110−S1
SC2110−S6
0.4 
0.05 0.1 0.15
C /σ
T
Figure 2.31: Hover performance with slatted airfoils
87
FM
Power curve − C /σ = 0.0783
W
0.015  
Total power
Induced+propulsive
Profile
0.01 Parasitic
Total − test
0.005
0 
0.05 0.1 0.15 0.2 0.25 0.3 0.35
µ
Figure 2.32: UH-60A main rotor power in forward flight(flight 85)
88
C /σ
P
Power curve − C /σ = 0.0891
W
0.015  
Total power
Induced+propulsive
Profile
0.01 Parasitic
Total − test
0.005
0 
0.05 0.1 0.15 0.2 0.25 0.3 0.35
µ
Figure 2.33: UH-60A main rotor power in forward flight(flight 84)
89
C /σ
P
 
fixed S6
Actuation − 1
°
ψ=90 Actuation − 2
°
ψ=0
°
ψ=180
°
ψ=270
 
(a) Slat deployment across azimuth
S
6
Actuation − 1
Actuation − 2
S
1
S
0
0 90 180 270 360
ψ (deg)
(b) Dynamic actuations 1 and 2
Figure 2.34: Slat actuations.Actuation 1 passes through S1 at ψ = 90◦ and S6 at ψ
= 270◦, and Actuation 2 passes through S0 at ψ = 90◦ and S6 at ψ = 270◦
90
Slat rotation angle 
(relative to baseline airfoil)
Chapter 3: Trailing-Edge Flaps
3.1 Results and discussion
In this chapter, the presentation of the results is organized so as to system-
atically build on the objectives of the study, namely, the effects of active control
with TEFs on performance in terms of power consumption, vibration, and dynamic
stall. First, hover performance is considered. Next, the level high speed, high vi-
bration, moderate thrust flight condition C8534 from the UH-60A airloads program
(Ref.( [83])) is explored for vibration reduction and power reduction, and finally
for simultaneous power and vibration reduction with TEFs. Next, the standard
high altitude, high thrust flight condition C9017 is explored for power reduction,
stall alleviation and vibration reduction with TEFs. This chapter concludes with a
summary of key observations from the study.
The rotor properties,TEF geometry and standard flight conditions used in this
study are listed in Table 2.1.
The UH-60A performance data shown here are computed by the University of
Maryland Advanced Rotor Code (UMARC - Ref. [80]) and the results are validated
with the available flight data from the UH-60 Airloads Program.
The validation of the baseline UH-60A hover performance with flight test data
91
from the airloads program was carried out with the shaft angles fixed to zero. Fig.
3.1 presents the main rotor figure of merit as a function of blade loading (CT/σ).
0.8  
Test data
0.75
UMARC
0.7
0.65
0.6
0.55
0.5
0.45
0.4 
0.02 0.04 0.06 0.08 0.1 0.12 0.14
C /σ
T
Figure 3.1: Baseline UH-60A hover performance
3.2 Blade torsional stiffness and TEF effectiveness
The TEF used in this study is a ’moment flap’.It operates by modifying the sec-
tion pitching moments and inducing blade elastic twist in response to the moments.
92
FM
A parameter that directly affects the blade twist, and therefore, the effectiveness of
the TEF, is the torsional stiffness(GJ of the blade).As part of this study, the tor-
sional stiffness of the blade was reduced by upto 50% to investigate any performance
benefits from torsional softening of the blade. The rotor fan plots for the baseline
blade and the soft blade(50% of the baseline blade GJ)are shown in Fig. 3.2. The
effect of torsional stiffness is primarily on the blade first torsional mode:the 1st tor-
sion frequency reduces from 4.3/rev for the baseline blade to 3.3/rev for the 50%
stiff blade.This will be shown later to influence the vibratory loads.
6/rev 6/rev
30 8/rev 7/rev 6/rev 30 8/rev 7/rev 6/rev
F
5 5/rev F F 5/revF
4 5 4
25 25
F F
3 4/rev 3 4/rev
20 T 20
1
3/rev 3/rev
T
15 15 1
F
2 F
2
2/rev 2/rev
10 10
F F
1 1/rev 1 1/rev
5 5
L L
1 1
0 0
0.2 0.4 0.6 0.8 1 1.2 0.2 0.4 0.6 0.8 1 1.2
Normalized Rotor Speed Normalized Rotor Speed
(a) Baseline (100%GJ) blade (b) Baseline (50%GJ blade
Figure 3.2: Uh-60A rotor blade frequencies in vacuo;F:Flap, L:Lead-Lag,T:Torsion
3.3 Hover performance with TEFs
The impact of TEFs on hover performance was examined by estimating the
UH-60A rotor figure of merit(FM) with different steady flap deflections (−5◦, 0◦, 5◦,
10◦). The results with TEFs and/or hypothetical blade torsional stiffnesses indicate
93
Natural frequency, Hz
Natural frequency, Hz
the predicted trends only. UMARC FM changes should be considered qualitative
only, as the flowfield model does not fully capture vortex interaction effects.
Fig. 3.3 compares the rotor figure of merit for the baseline blade with different
steady flap deflections. A positive (downward) flap deflection improves the rotor
performance, especially at higher thrust levels. The percent changes in power and
the induced and profile power components from the no-flap condition are given in
Fig. 3.4. A negative value indicates a reduction in the component of power from the
corresponding value for the baseline blade at the same thrust level.
The effect of positive (downward)TEF deflections is to increase the nose-down
elastic twist of the blade from root to tip, thus making the peak of the spanwise
loading move inboard and hence reducing induced power. The power reductions
with flap deflections is therefore largely attributable to the induced power. Since the
flap analyzed(Table 1)operates by inducing blade twist,the effectiveness of the TEF
with variation in blade torsional stiffness was also investigated.The rotor figure of
merit for the baseline and 75% torsional stiffness blades without TEFs is compared
in Fig. 3.5.The combined effect of reduced stiffness and steady flap deflections is
illustrated in Fig. 3.6 which shows the improved figure of merit for the rotor with
the 75% stiff blade and with 10◦ TEF deflections.
As an illustration of the benefits of both TEF deflections and softer blades,
the spanwise elastic twist and loading of the blade are shown in Fig. 3.7, for the
baseline (100% GJ) blade, 75% GJ blade and the 100% and 75% GJ blades with
TEF deflection of 10◦. Hence, there is a net increase in the blade elastic twist
response as a result of either reduced stiffness or a positive TEF deflection, and the
94
0.8  
0.7
0.6 °−5
Baseline
°
5
°
0.5 10
 
0.04 0.06 0.08 0.1 0.12
C /σ
T
Figure 3.3: Effect of TEF (10%R, 15%c, midspan location at 65%R) deflection on
baseline UH-60A rotor figure of merit; hover
95
Figure of Merit
15    15
10 10
5 5
0 0
−5 −5
°
−5
−10 Baseline −10
°
5
−15 −15
°
10
−20   −20
0.06 0.08 0.1 0.12 0.06 0.08 0.1 0.12 0.06 0.08 0.1 0.12
C /σ C /σ C /σ
T T T
(a) Induced power (b) Profile power (c) Total power
Figure 3.4: Percent change in induced, profile and total power for UH-60A rotor in
comparison to baseline for different TEF deflections; hover
spanwise loading gets redistributed inboard compared to the baseline blade. The
integrated induced losses are thus reduced.
The improvements in FM are appreciable at high thrusts, both due to a re-
duction in torsional stiffness and TEF deflections. For instance, there is an increase
of about 24% in figure of merit over the baseline blade when a 10◦ downward de-
flected TEF is used on a 75% torsionally stiff blade operating at a thrust level of
CT/σ = 0.12.
3.4 Rotor performance in high speed forward flight with TEFs
TEFs deployed at 1 or 2/rev are capable of redistributing the aerodynamic
loads across the rotor disk, so that net performance gains can be realized. In general,
the gains are attributed to the alleviation of the negative loading on the advancing
blade, caused by the high negative pre-twist. Deflections of TEFs induce blade
twisting, which in turn redistributes disk loads and minimizes negative loading. In
this section, actuation requirements to achieve this objective are investigated.
96
∆ C /C  (%)
P P
i noTEF
∆ C /C  (%)
P P
0 noTEF
∆ C /C  (%)
P P
notef
0.9  
0.8 75%GJ
0.7 100%GJ
0.6
0.5
 
0.06 0.08 0.1 0.12
C /σ
T
Figure 3.5: Effect of GJ with no TEF on baseline UH-60A rotor figure of merit;
hover
Parametric sweeps of TEF actuations were carried out to determine suitable
combinations of steady, 1/rev and 2/rev TEF inputs that yield overall power re-
ductions. Actuation schedules were of the form δ = δsteady + δ1pcos(ψ + φ1p) +
δ2pcos(2ψ + φ2p), for varying amplitudes δsteady, δ1p, δ2p and phase angles φ1p, φ2p.
The cases were developed in the following stages:
1. δ = δsteady + δ2pcos(2ψ + φ2p): Different combinations of steady and 2/rev
TEF inputs were prescribed, in order to obtain the trends of the actuations
that had the best impact on performance. Two advance ratios, µ = 0.3 and
0.4, were chosen for the study, and different thrust levels (in terms of CW/σ)
were investigated.
2. δ = δsteady + δ1pcos(ψ+ φ1p) + δ2pcos(2ψ+ φ2p): Different 1/rev TEF inputs
97
Figure of Merit
0.9  
75%GJ,
°
δ=10
0.8
100%GJ
0.7
0.6 75%GJ
0.5
 
0.06 0.08 0.1 0.12
C /σ
T
Figure 3.6: Effect of a 25% reduction in GJ and 10◦ TEF deflection on UH-60A
rotor figure of merit; hover
−2 0.3
100%GJ
75%GJ
0.2 75%GJ, 
−4 °
δ=10
100%GJ,
° 0.1
δ=10
75%GJ, 
−6 ° 100%GJ
δ=10
0
0.2 0.4 0.6 0.8 1 0.2 0.4 0.6 0.8 1
r r
(a) Elastic twist (b) Normal force C M2n
Figure 3.7: Effect of a 25% reduction in blade GJ and 10◦ TEF deflection on the
spanwise variation of UH-60A rotor blade elastic twist and section normal force;
hover, CT/σ=0.12
98
φ
Figure of Merit
2
C  M
n
° °
δ  = 0 ° ° ° δ  = 0 ° ° °
steady 2.5 5 7.5 steady 2.5 5 7.5
10 10
8 8
6 6
°
4 ° 4 δ = 0δ = 0 2p
2p °δ = 7.5
2p
2 2
°
δ = 5 °δ = 7.5
2p 2p
0 ° 0
δ = 2.5 °
2p ° δ = 5
δ = 2.5 2p
2p
−2 −2
0 90 0 90 0 90 0 90 0 90 0 90 0 90 0 90
φ φ φ φ φ φ φ φ
2p 2p 2p 2p 2p 2p 2p 2p
(a) CW /σ = 0.06 (b) CW /σ = 0.08
°
δ  = 0 ° ° °
steady 2.5 5 7.5
10
8
6 °δ = 7.5
2p
4
°
δ = 0
2p
2
0
° °
δ = 2.5 δ = 5
−2 2p 2p
0 90 0 90 0 90 0 90
φ φ φ φ
2p 2p 2p 2p
(c) CW /σ = 0.1
Figure 3.8: Effect of 2/rev phasing of TEF (10%R, 15%c, midspan location at
65%R) inputs δ = δsteady + δ2pcos(2ψ + φ2p) on UH-60A rotor power for different
weights; µ = 0.3
were directly superimposed on specific steady plus 2/rev inputs from stage (i),
that were most beneficial to power.
99
% power
% power
% power
4
4
°
δ = 7.5
1p
2 2 °° δ = 5
δ = −2.5 , 1p
steady
° ° °
δ  = 5 , φ = 30 δ = 7.5
2p 2p 1p
°
δ = 2.5
0 0 1p
°
δ = 5
1p °
δ = 0 ,
steady
° °
δ  = 5 , φ = 45
−2 −2 2p 2p
°
δ = 2.5
1p
0 90 180 270 360 0 90 180 270 360
φ φ
1p 1p
(a) CW /σ = 0.08; (b) CW /σ = 0.1;
Figure 3.9: Effect of 1/rev phasing of TEF (10%R, 15%c, midspan location at
65%R) inputs δ = δsteady + δ1pcos(ψ + φ1p) + δ2pcos(2ψ + φ2p) on UH-60A rotor
power for different weights; µ = 0.3
3.4.1 Case I: Advance ratio µ = 0.3
Steady plus 2/rev TEF input: Fig. 3.8 shows the percentage change in power for
the flapped rotor operating at µ of 0.3 and weight coefficient CW/σ between 0.06
and 0.1, from the respective baseline case (no flaps), with different combinations
of steady and 2/rev inputs of amplitudes from 0◦ to 7.5◦, in steps of 2.5◦. Each
column in the plot corresponds to a specific steady TEF input δsteady, and each
curve represents a 2/rev input of a specific amplitude δ2p and varying phase φ2p. A
negative value is beneficial while a positive value means more power requirement.
The best gains are obtained with no steady input, and a phase φ2p between
0◦ and 30◦. This corresponds approximately to a negative TEF deflection on the
100
% power
% power
advancing and retreating sides, and a positive deflection on the front and rear. There
is a nose-up pitching moment induced by the TEFs on the advancing side, increasing
the lift by reducing the negative angles of attack. Consequently, the front and rear
parts of the disk are offloaded due to smaller angles of attack, resulting in net power
reduction.
Steady plus 2/rev plus 1/rev TEF input: Fig. 3.9 shows the percentage change in
power for the flapped rotor operating at µ = 0.3 and weight coefficient CW/σ of 0.8
and 0.1 ,from the baseline case (no flaps), with different 1/rev inputs of amplitudes
2.5◦, 5◦ and 7.5◦ and varying phase angles φ1p, imposed on an actuation from Fig. 3.8
that yielded benefits with an addition of 1/rev inputs. The broken horizontal line
indicates the power reduction for the baseline with steady+2/rev input in each case.
The 1/rev actuations with the best gains are at a phase φ1p between 30
◦ and
90◦. This corresponds approximately to a negative TEF deflection on the advancing
side and positive on the retreating side, inducing pitching moments that increase
the angles (reduce negative angles) on the advancing blade while reducing them on
the retreating blade. Overall, there is a modest benefit in combining TEF inputs at
different frequencies at this speed. Power reductions of 2.6% at CW/σ of 0.08 and
1.7% at CW/σ of 0.1 were observed with the above parametric study.Also, reductions
of 1.6% at CW/σ of 0.07 and 1.3% at CW/σ of 0.09 (not shown) were observed.
101
°
δ  = 0 ° ° ° °
steady 2.5 5 7.5 δ  = 0 ° ° °steady 2.5 5 7.5
8 8
6 6
4 °
δ = 0 4
2p °δ = 0
° 2p
2 δ = 2.52p 2
0 0
−2 °−2 δ = 7.5
2p
° °
δ = 7.5 δ = 2.5 °° δ = 5
−4 δ = 5 2p −4 2p 2p
2p
0 90 0 90 0 90 0 90 0 90 0 90 0 90 0 90
φ φ φ φ φ φ φ φ
2p 2p 2p 2p 2p 2p 2p 2p
(a) CW /σ = 0.07 (b) CW /σ = 0.085
Figure 3.10: Effect of 2/rev phasing of TEF (10%R, 15%c, midspan location at
65%R) inputs δ = δsteady + δ2pcos(2ψ + φ2p) on UH-60A rotor power for different
weights; µ = 0.4
 90
 
90 90
 
0.01
0.025 0.005
0 0
0
180 0
180 0 180 0
−0.025 −0.01
−0.005
−0.05
−0.02
−0.01
  270 270  270
(a) Normal force CnM
2 (b) Power −r ∗ CcM2 (c) Pitching moment CmM2
Figure 3.11: Change in UH-60A rotor disk loading from baseline rotor, due to 2/rev
TEF (10%R, 15%c, midspan location at 65%R) input δ = 2.5◦ + 5◦cos(2ψ + 30◦);
µ = 0.4, CW/σ = 0.085; Blue-decrease, Red-increase
102
% power
% power
8
8
6 °
δ = 7.5 6
1p
°
δ = 7.5
4 °δ = 0 , 1p
steady 4
° °
δ  = 7.5 , φ = 15
2 2p 2p °2 δ = 5
1p
0 °δ = 5 0
1p °δ = 2.5
1p
−2 −2 °
° δ = 2.5 ,
δ = 2.5 steady
1p ° °
−4 −4 δ  = 5 , φ = 302p 2p
−6 −6
0 90 180 270 360 0 90 180 270 360
φ φ
1p 1p
(a) CW /σ = 0.07; δ
◦ ◦
steady=0 ,δ2p=5 ,φ2p=15
◦ (b) CW /σ = 0.085; δsteady=2.5
◦,δ2p=5
◦,φ ◦2p=30
Figure 3.12: Effect of 1/rev phasing of TEF (10%R, 15%c, midspan location at
65%R) inputs δ = δsteady + δ1pcos(ψ + φ1p) + δ2pcos(2ψ + φ2p) on UH-60A rotor
power for different weights; µ = 0.4
   
90 90 90
0.02
0.03 0.004
0.015
0.015
0
0.01
180 0 180 0 180 0
0
0.005
−0.004
−0.015
0
−0.03 −0.008 −0.005
 270  270  270
(a) Normal force CnM
2 (b) Power −r ∗ C M2c (c) Pitching moment C M2m
Figure 3.13: Change in UH-60A rotor disk loading due to 1/rev TEF (10%R, 15%c,
midspan location at 65%R) input 5◦cos(ψ + 30◦) superimposed on 2/rev input δ =
2.5◦ + 5◦cos(2ψ + 30◦); µ = 0.4, CW/σ = 0.085; Blue-decrease, Red-increase
3.4.2 Case II: Advance ratio µ = 0.4
Steady plus 2/rev TEF input: Fig. 3.10 shows the percentage change in power for
the flapped rotor operating at µ = 0.4 and weight coefficient CW/σ between 0.07
103
% power
% power
and 0.085 (close to the lift boundary at this speed), from the respective baseline
case (no flaps), with different combinations of steady inputs between -2.5◦ to 7.5◦
and 2/rev inputs of amplitudes from 0 ◦ to 7.5◦, in steps of 2.5◦. Each column in the
plot corresponds to a specific steady TEF input δsteady, and each curve represents a
2/rev input of a specific amplitude δ2p and varying phase φ2p.
The actuations with the best gains are with a phase φ between 0◦2p and 30
◦,
as can be seen from Fig. 3.10, but an additional small positive steady deflection is
seen to reduce power slightly by reducing the angles further on the front and rear
parts of the disk. Negative steady deflections (flap deflected upward) are seen to
worsen performance at this speed.
At this high speed condition, the advancing blade is negatively loaded, while
the majority of the thrust is generated on the front and rear, which consequently
also dominate the contributions to the shaft torque.
The effect of the TEF deployment δ = 2.5◦ + 5◦cos(2ψ + 30◦) is illustrated
as the changes in section aerodynamic loads from the baseline rotor, in Fig. 3.11.
There is a nose-up pitching moment induced by the TEFs on the advancing side
(Fig. 3.11c), increasing the lift (Fig. 3.11a) by reducing the negative angles of attack.
Consequently, the front and rear parts of the disk are offloaded due to smaller angles
of attack, resulting in net power reduction (Fig. 3.11b).
Steady plus 2/rev plus 1/rev TEF input: Fig. 3.12 shows the percentage change
in power for the flapped rotor operating at µ = 0.4 and weight coefficients CW/σ of
0.07, 0.08 and 0.085, from the baseline case (no flaps), with different 1/rev inputs of
104
amplitudes 2.5◦, 5◦ and 7.5◦ and varying phase angles δ1p, imposed on the best case
actuations from Fig. 3.10. The broken horizontal line indicates the power reduction
with the base steady+2/rev input in each case. Power reductions of 5.2% at CW/σ
of 0.07, 3.7% at CW/σ of 0.085 were observed with the above parametric study.
The 1/rev actuations with the best gains are at a phase φ1p between 0
◦ and
30◦to target the negative loading peak located in the ψ = 90-180◦ quadrant. The
effects of the 1/rev TEF deployment 5◦cos(ψ + 30◦) superimposed on the 2/rev
deployment δ = 2.5◦+ 5◦cos(2ψ+30◦) (from Fig. 3.11) are illustrated as the changes
in section aerodynamic loads, in Fig. 3.13. There is a nose-up pitching moment
induced by the TEFs on the advancing side, increasing the lift by reducing the
negative angles of attack. Consequently, the other parts of the disk are offloaded
due to smaller angles, resulting in net power reduction.
Fig. 3.14 shows the percentage change in power with steady, 1 and 2/rev TEF
inputs at advance ratios of 0.3 and 0.4, and weight coefficients CW/σ of 0.08. For
example, a flap input of 2.5 + 5◦ cos(ψ +30◦) + 7.5◦ cos(2 ψ+15◦) reduces power
requirement by about 3.4% at µ of 0.4 and CW/σ of 0.08.
However,the same actuation that yields performance benefits also leads to a
significant increase in vibration levels,i.e., about 70% in the vibration index J1, as
shown if Fig.3.15 for the same cases as above.J1 is defined as J1 =z
T Wz z, where z
is a vector containing the cosine and sine components of the non dimensional 4/rev
fixed system hubloads Fx, Fy ,Fz,Mx, and My,and weighting matrix Wz is defined
as follows:
105
The diagonal weighting matrix Wz was assumed to have the form
 1/F 2 x0 

 1/F 2 y0 
Wz = (1− β) 1/F 2  (3.1) z0 1/M2 x0 
1/M2y0
in order to target the hub Fx, Fy, Fz, Mx and My. The first three elements are
weights for both components of the 3 hub shears and the final two elements are
weights for both components of the hub moments. Wθ was assumed to be of the
form Wθ = βI.
Wθ = βI (3.2)
In the present study, β = 0 was used, so the controller attempts to minimize
the hub loads without constraining the amplitude of the flap motion.
Fig. 3.16 shows the percentage change in effective rotor L/D due to a combi-
nation of steady, 1/rev and 2/rev TEF inputs at advance ratios of 0.3 and 0.4, and
weight coefficient CW/σ of 0.08. Rotor L/D is defined as the ratio of rotor thrust
to rotor drag,
T
L/D =
P/V∞ −Dv
Dv being the vehicle drag. For example, a flap input of 2.5
◦+ 5◦cosψ+ 7.5◦cos(2ψ+
15◦) improves rotor L/D by about 6.9% at µ of 0.4 and CW/σ of 0.08.
106
8  8
6 δ1p 6
°
0
4 °2.5 4
°
5
2 ° 2
7.5
0 0
−2 −2
−4 −4
0 90 180 270 360 0 90 180 270 360
φ  (deg) φ  (deg)
1p 1p
(a) µ = 0.3; δ ◦steady = −2.5 , δ2p = 5◦, φ = 30◦2p (b) µ = 0.4; δ ◦ ◦ ◦steady = 2.5 , δ2p = 7.5 , φ2p = 15
Figure 3.14: Effect of 1/rev phasing of TEF (10%R, 15%c, midspan location at
65%R) inputs δ = δsteady + δ1pcos(ψ + φ1p) + δ2pcos(2ψ + φ2p) on UH-60A rotor
power for CW/σ = 0.08.
 
150 150
δ
1p
°
0
°
100 2.5 100
°
5
°
7.5
50 50
0 0
0 90 180 270 360 0 90 180 270 360
φ  (deg) φ  (deg)
1p 1p
(a) µ = 0.3; δ ◦steady = −2.5 , δ2p = 5◦, φ2p = 30◦ (b) µ = 0.4; δsteady = 2.5◦, δ2p = 7.5◦, φ2p = 15◦
Figure 3.15: Effect of 1/rev phasing of TEF (10%R, 15%c, midspan location at
65%R) inputs δ = δsteady + δ1pcos(ψ + φ1p) + δ2pcos(2ψ + φ2p) on vibration index
J1 for UH-60A rotor; CW/σ = 0.08.
107
% J (vibration index) % power
% J (vibration index) % power
3.5 Rotor vibration reduction with TEFs : High speed flight condi-
tion (C8534) - µ=0.368, CW/σ=0.0783
This is a high speed, moderate thrust condition, characterized by high vibra-
tion levels.
Results obtained for vibration reduction investigated for this flight using TEFs
are presented here. The target hub loads were the 4/rev hub longitudinal, lateral
and vertical shears, rolling moment and pitching moment (Fx, Fy, Fz, Mx and My).
The analysis used free-flight trim.
°
δ = 0 , °
steady δ = 2.5 ,
5 ° °
steady
δ  = 5 , φ = 30 5 ° °
2p 2p δ  = 7.5 , φ = 152p 2p
°
δ = 2.5
°
2.5 1p0 0
°
δ = 5
1p °
δ = 5
° 1p
−5 δ = 7.51p −5
−10 −10 °δ = 7.5
1p
0 90 180 270 360 0 90 180 270 360
φ φ
1p 1p
(a) µ = 0.3; δsteady=0
◦,δ ◦2p=5 ,φ2p=30
◦ (b) µ = 0.4; δ ◦steady=2.5 ,δ2p=7.5
◦,φ2p=15
◦
Figure 3.16: Effect of 1/rev phasing of TEF (10%R, 15%c, midspan location at
65%R) inputs δ = δsteady + δ1pcos(ψ + φ1p) + δ2pcos(2ψ + φ2p) on UH-60A rotor
L/D for CW/σ = 0.08
108
% L/D
e
% L/D
e
3.5.1 Contours of vibratory loads:
The TEF input harmonics used for 4/rev vibration control are 3–5/rev, since
these are the frequencies of the rotating frame loads that contribute to the hub
loads. Initially, open loop vibration characteristics of the blade with TEFs were
examined in order to gain insight into the sensitivity of vibration to various TEF
input harmonics, amplitudes and phases. Any one harmonic has different effects
−7
5
100 100
002 22 2
0
2 0
0 20
0
10
1 11 1 00 00
−50 0
1
−25
−25 −25 0
0 0 0
0
0
−1 −1 −50 −1
50
−25
−2 −2 −2 100
50 0 200
−2 −1 0 1 2 −2 −1 0 1 2 −2 −1 0 1 2
4/rev cosine TEF input (deg) 4/rev cosine TEF input (deg) 4/rev cosine TEF input (deg)
(a) Fx (b) Fy (c) Fz
5
−25 −7
2 2
−50
− −502
1 1 5
−7
5 0 −25 0
0 − 0 050
50
−1 − −125 50
50
−2 0 −1020
−2 −1 0 50 1 2 −2 −1 0 1 2
4/rev cosine TEF input (deg) 4/rev cosine TEF input (deg)
(d) Mx (e) My
Figure 3.17: UH-60A 4/rev hub loads with 4/rev TEF inputs; high speed forward
flight (C8534: µ=0.368, CW/σ=0.0783). Values shown are % changes in vibratory
amplitude relative to the baseline (no flaps). The highlighted region corresponds to
reduction of the respective vibratory load.
109
4/rev sine TEF input (deg)
4/rev sine TEF input (deg)
100 −25
50 −50
4/rev sine TEF input (deg)
0 −75
−25
4/rev sine TEF input (deg)
−25
4/rev sine TEF input (deg)
−50
−25
−50
0
100
0
20
0
001
200
50−
0
100
0
50
0
10
0
50
0
10
2 0
4
200 00
40 2
50
200
1 1
0
0 0 0
0 0
−1 −1 0
200
−2 40 200 −20 50
800
−2 −1 0 1 2 −2 −1 0 100 1 2
4/rev cosine TEF input (deg) 4/rev cosine TEF input (deg)
(a) Vibration objective function J1 (b) Vibration Intrusion Index
Figure 3.18: Vibration objective function J1 and Vibration Intrusion Index with
4/rev TEF inputs; UH-60A rotor in high speed forward flight (C8534). Values
shown are % changes relative to the baseline (no flaps). The highlighted regions
correspond to reduction of the respective vibratory index.
on the different vibratory loads. This is illustrated in Fig. 3.17, which maps the
% changes in each of the 5 hub loads from the baseline values, as a function of
4/rev sine and cosine TEF deflections. Deflections with sine and cosine components
upto ±2.5◦ are shown. Each point corresponds to a particular 4/rev cosine and
sine deflection, or equivalently, a particular amplitude and phase of actuation. Each
contour line corresponds to a specific value of the % change in the vibratory load
from its baseline value, as a result of 4/rev TEF deflections.
It is clear that the specific actuations that cause the largest reductions in any
particular load are quite different, and could even lead to an increase in the other
loads. Contours of 2 consolidated vibration indices are also plotted in Fig. 3.18 as
a % change from the baseline value, due to 4/rev TEF deflections. The indices are
as follows:
110
4/rev sine TEF input (deg)
80
60 00
200
−25
0
4/rev sine TEF input (deg)
150
100
50
−25
50
0
10
0
15
150
−2
5
0
400
600
1. Index J1:
J1= z
T Wz z
2. Index J2: A load-based Vibration Intru√sion Index, defined only using the 4/rev
non-dimensional vibratory shears, a (0.5 Fx)2 + (0.75 F )2y + F 2z , assigning
weights to the 3 shears as per the ADS-27A standard,
where z is a vector containing the cosine and sine components of the non-
dimensionalNb/rev fixed system hub loads Fx, Fy, Fz, Mx andMy, and the weighting
matrix Wz is defined in Equation (1).
This procedure was used to estimate the actuations at individual harmon-
ics for reduction of different target loads, and the multicyclic feedback controller
methodology was validated by comparing its predictions with those obtained from
the parametric studies. All subsequent results for vibration reduction were obtained
by applying the multicyclic control algorithm.
111
F F F M M M
x y z x y z
(lb) (lb) (lb) (lb−ft) (lb−ft) (lb− ft)1500
M
y
Case − I II III IV V
M
x
1000
F
x
(baseline)
500
F
y
F
z
M
0 z
Fz Mx My Fz, Mx, My J
Target for reduction
Figure 3.19: UH-60A rotor baseline (no flap) and reduced 4/rev vibratory loads for
different targets for reduction using the multicyclic control algorithm; high speed
forward flight (C8534). Fx: longitudinal shear, Fy: lateral shear, Fz: vertical shear,
Mx: rolling moment, My: pitching moment, J : target Fx, Fy, Fz, Mx and My. The
horizontal lines indicate the baseline vibratory hub loads (uncontrolled).
3.5.2 Multicyclic Controller - different targets:
It was possible to reduce the vibration objective function by upto 80% using
a combination of 3–5/rev flap inputs. As an illustration of the working of the
multicyclic algorithm, four cases were considered. The first three cases used the
algorithm to minimize a single load (Fz - case 1, Mx - case 2, My - case 3), the fourth
case targeted Fz, Mx and My alone and the fourth case targeted all three hub shears
and rolling and pitching moments, corresponding to the objective function J defined
earlier, simultaneously. Figure 3.19 shows the changes obtained in the six hub loads
112
4/rev hubload
2000  2000  
In−plane shear (lbs)
Vertical shear (lbs)
1500 In−plane moment (ft−lbs) 1500
1000 1000
500 500
0 0 
0 0.1 0.2 0.3 0.4 0 0.1 0.2 0.3 0.4
Advance ratio Advance ratio
(a) Baseline 4/rev hub loads (b) Reduced(with TEFs) 4/rev hub loads
10  
3/rev
4/rev
7.5 5/rev
5
2.5
0 
0 0.1 0.2 0.3 0.4
Advance ratio
(c) HPP optimal TEF deflections for vibration
reduction
Figure 3.20: UH-60A rotor baseline (no flap) vibratory loads and optimal TEF
actuation amplitudes for various speeds; moderate thrust forward flight (Flight 85),
CW/σ=0.0783
Fx, Fy, Fz, Mx, My and Mz in each of these five cases. The horizontal lines represent
the levels of the baseline vibratory hub loads. The five targets of reduction, namely
Fz, Mx, My, all three and vibration objective function J , are along the x-axis, and
the values of the six vibratory hub loads with the optimal actuation in each case
113
4/rev hub loads
HPP amplitude (deg)
4/rev hub loads
constitute the five bars.
This figure shows that a reduction in a particular hub load may be accompanied
with an increase in the other hub loads. For instance, targeting only My (case 3)
resulted in near-100% reduction of My, but there were only modest reductions in
the levels of Fy, Fz and Mx. It also indicates that some loads are more sensitive
to small TEF deflections than others. The results that follow target the vibration
index J (hub loads Fx, Fy, Fz, Mx and My) for reduction.
3.5.3 Vibration reduction at various speeds:
The TEF is capable of vibration suppression at different flight speeds, requir-
ing higher deflections in the high vibration regimes. The highest vibrations occur
at transition speeds and at high spee√ds, as shown in the overall vibratory levels
indicated √by the hub in-plane shear ( F 2x + F 2y ), vertical shear Fz and in-plane
moment ( M 2x +M
2
y ), as shown in Fig. 3.20a, for a constant weight coefficient
CW/σ=0.0783 (termed Flight 85). Flight C8534 corresponds to the highest speed in
this case. High-speed vibration is due to unsteady pitching moments, which cause
large elastic twist deformations. Low speed vibration, on the other hand, is caused
by blade-vortex interactions. Figure 3.20c shows the flap actuation amplitudes re-
quired to suppress combined Fx, Fy, Fz, Mx and My at different forward speeds.
The fractions of the actuations corresponding to the individual frequencies (3, 4 and
5/rev) are indicated as well.
114
High thrust flight condition (C9017): µ=0.237, CW/σ=0.1325
This is a high altitude, high thrust flight condition used to study dynamic stall
events. First, vibration reduction for C9017 flight condition using TEFs is addressed.
Then, the effect of 1 and 2/rev TEF inputs on power is discussed, and inputs for
dynamic stall alleviation are presented. Finally, the possibility of combining benefits
in vibration, power and stall is explored.
Vibration reduction
Figure 3.21: UH-60A rotor baseline (no flap) and reduced vibratory loads; high
thrust forward flight (C9017: µ=0.237, CW/σ=0.1325). Fx: longitudinal shear, Fy:
lateral shear, Fz: vertical shear, Mx: rolling moment, My: pitching moment. The
loads targeted for reduction were Fz, Mx and My.
The target hub loads were, as before, the 4/rev hub vertical shear, rolling
moment and pitching moment (Fz, Mx and My). Fig. 3.21 shows a comparison of
the baseline and reduced vibratory load levels. The optimal HPP TEF amplitude
115
for vibration reduction was 3◦.
3.5.4 Effect of torsional stiffness on vibration reduction:
A torsionally softer blade was earlier shown to improve performance at hover.
In order to determine if reducing the blade torsional stiffness leads to smaller flap
actuation requirements for vibration suppression at C8534, the torsional stiffness of
the blade was reduced by up to 50% and the optimal actuation requirements in each
hypothetical case were estimated.
Fig. 3.22 shows the baseline loads and reductions obtained with the optimal
flap actuations, for blades of different torsional stiffnesses. The baseline vibrations
(uncontrolled) increase steadily with a reduction in blade stiffness. This can be
explained by examining the rotating and fixed frame loads, and the natural response
characteristics of the blade, as stiffness is reduced. Fig. 3.23 shows the 3, 4 and
5/rev components of the blade root shears fx, fy and fz, and torsion and flapwise
bending moments mx and my. The 3/rev component is clearly the most dominant
one, and increases as the torsional stiffness is reduced. Indeeed, the blade response,
particularly the elastic twist, contains a large 3/rev component which increases for
the softer blades. The blade 1st torsion frequency approaches 3/rev as the torsion
stiffness is reduced. Consequently, the 3/rev components of the blade response and
section loads increase rapidly, resulting in larger 4/rev hub loads (Fig. 3.22).
116
Baseline With flaps
1,000
0
1,000
0
1,000
0
2,000
0
2,000  
0 
100 75 50
Torsional stiffness (%)
Figure 3.22: UH-60A rotor baseline (no flap) and reduced vibratory loads for differ-
ent blade torsional stiffnesses (GJ); high speed forward flight (C8534). Fx: longitu-
dinal shear, Fy: lateral shear, Fz: vertical shear, Mx: rolling moment, My: pitching
moment. The loads targeted for reduction were Fx, Fy, Fz, Mx and My.
117
M     M     
y x
(lb−ft) F  (lb) F  (lb)
F  (lb)
(lb−ft) z y x
100% 75% 50%
200
0
500
0
1,000
0
 
100
0 
1,000
0
3/rev 4/rev 5/rev 3:5/rev
Frequency
Figure 3.23: Components of UH-60A rotor baseline (no flap) HPP blade root loads
for different blade torsional stiffnesses (GJ); high speed forward flight (C8534). fx:
lateral shear, fy: longitudinal shear, fz: vertical shear, mx: torsion bending moment,
my: flapwise bending moment
118
m f
y m z f f
x y x
GJ
 
100%
75%
50%
15
10
5
0 
3/rev 4/rev 5/rev HPP
Harmonic
Figure 3.24: Flap deflection amplitudes for UH-60A vibration reduction for different
blade torsional stiffnesses (GJ); high speed forward flight (C8534). HPP: half peak-
to-peak amplitude of optimal actuation
119
HPP amplitude (deg)
Hence, any improvements in the effectiveness of the flap at altering the twist
response with torsionally softer blades were offset by the increase in the baseline
vibratory loads themselves, resulting in larger flap deflection requirements for vi-
bration control. Milgram and Chopra ( [91]) also reported a decrease in vibration
reduction effectiveness with a reduction in blade torsional stiffness. Fig. 3.24 com-
pares the TEF amplitudes of the 3–5/rev and combined HPP (Half Peak-to-Peak)
flap deflections obtained from the optimization procedure, for blades of different
torsional stiffnesses. These are the optimal actuations used to obtain the vibration
reduction shown in Fig. 3.22. The 3/rev deflection component is the largest, due to
the frequency distribution of the blade loads.
120
3.5.5 Effect of not using 5/rev TEF inputs for vibration reduction:
The 5/rev component of the actuation is small compared to 3 and 4/rev for
the baseline (100% GJ) blade. It is desirable to avoid high frequency actuations
from a practical standpoint. Therefore, the potential vibration reduction with only
3 and 4/rev deflections was determined using the multicyclic control methodology.
Figure 3.25 shows the baseline and reduced vibratory loads and optimal control
actuations for vibration control with 3–5/rev and only 3 and 4/rev inputs. The
target loads were Fz, Mx and My. From Fig. 3.25a, the reductions in the target
loads were still appreciable (99% in Fz, 85% in Mx and 91% in My), although the
hub moments were reduced to a slightly smaller extent. This is expected, since
the 3 and 5/rev components of the root bending moments contribute to the 4/rev
vibratory hub moments, and the 5/rev TEF input is necessary to target the 5/rev
blade loads. Nevertheless, this demonstrates that it is possible to achieve large
reductions in vibration without the high frequency 5/rev TEF inputs.
3.5.6 Stall alleviation with TEFs - ‘down-only’ 1/rev TEF inputs
TEFs excited at a suitable phasing and amplitude can reduce the magnitude
of dynamic stall events occurring in high thrust forward flight. Thus, it is possible to
push the rotor operational envelope to higher operational thrust levels using trailing-
edge flaps. To this end, 1/rev flap inputs (hereafter referred to as “down-only” 1/rev
inputs) were prescribed to the TEF, chosen so that the flap deflection is maximum
on the retreating side, ensuring reductions in section angles of attack due to the
121
increased nose-down pitching moment, and as small as possible on the advancing
side, for minimum drag penalties. The general form of the actuation was δ =
δ0 +δ0 cos(ψ−φ). Note that an actuation of this type attains its maximum positive
(downward) TEF deflection at an azimuth equal to φ. It was found that with such
a deployment, it is possible to reduce the stall loads and achieve power reductions
simultaneously. Fig. 3.26a shows the normal force and pitching moment at select
radial sections for the baseline C9017 case and with actuations of 3◦+3◦cos(ψ−270◦)
and 5◦ + 5◦cos(ψ − 270◦). The pitching moment stall events outboard of 80%R are
reduced with the down-only TEF deployment (see Fig. 3.26b).
The metric used to quantify the stall level, CTors, is defined as the HPP higher
harmonic (≥4/rev) blade root torsional moment (mx), since dynamic stall is char-
acterized by a sudden increase in airfoil nose-down pitching moment, affecting the
lb lb−ft
1000  2000 6  
Baseline With 3,4,5/rev TEF
With 3,4,5/rev TEF
With 3,4/rev TEF
With 3,4/rev TEF
750 1500
4
500 1000
2
250 500
0  0 0  
Fx Fy Fz Mx My 3/rev 4/rev 5/rev HPP
4/rev hub shears 4/rev hub moments Harmonic
(a) Baseline (no flap) and reduced 4/rev hub loads (b) Optimal TEF deflections for vibration re-
duction
Figure 3.25: Comparison of UH-60A vibration reduction obtained with 3–5/rev TEF
deflections and only 3 and 4/rev deflections; high speed forward flight (C8534)
122
HPP amplitude (deg)
blade torsional loads. Fig. 3.26 shows the reduction in the rotor power and stall
loads, with down-only 1/rev TEF inputs of amplitudes 1◦, 3◦ and 5◦, from the base-
line C9017 value. The inputs are shown in terms of the azimuth φ at which the
maximum downward flap deflection is attained. In general, the inputs phased to
attain their peak downward deflections on the retreating side yield the best reduc-
tions in the stall metric, while power reductions of the order of 7-8% were achievable
with a HPP amplitude of 5◦. For example, a down-only TEF input of amplitude 5◦
and attaining a maximum at 270◦ azimuth, reduces the stall metric by about 45%,
power by about 7.6% and allows the rotor to operate at a 5% higher thrust, which
would normally not be achievable due to stall-related losses.
Fig. 3.28 shows the vibratory hub loads with down-only 1/rev TEF inputs
of amplitudes 1◦, 3◦ and 5◦. These inputs do not affect vibration adversely, even
causing reductions in the vibratory loads.
3.6 Simultaneous power, vibration and stall reduction with ’down-
only’ 1/rev TEF inputs: High thrust flight condition(C9017)
Fig. 3.27a shows the actuations required for vibration and power reduction,
with a down-only 1/rev input amplitude of 5◦, at the optimum phase of 270◦. The
HPP actuation requirement for vibration reduction is 3.0◦ for the baseline case and
2.5◦ with the 1/rev input. The net actuation HPP amplitude is 6.6◦, yielding a 7.5%
reduction in power and 42% in CTors/σ from baseline C9017, in conjunction with
reductions in all three 4/rev hub shears and the hub 4/rev roll and pitch moments
123
(31% in Fx, 82% in Fy, 83% in Fz, 87% in Mx and 83% in My). The amplitudes of
each of the input harmonics: 1, 3, 4 and 5/rev, are shown in Fig. 3.27b.
This demonstrates that the TEF is capable of vibration control as well as
performance improvement, combining stall mitigation and power reduction at high
thrust conditions.
r=0.67R r=0.77R r=0.86R r=0.67R r=0.77R r=0.86R
0
0.2
−0.02
0.1
−0.04
0
r=0.92R r=0.96R r=0.99R r=0.92R r=0.96R r=0.99R
0
0.2
−0.02
0.1
−0.04
0
0  180 0 180 360 180 360 0  180 0 180 360 180 360
ψ ψ
(a) Section normal force (b) Section pitching moment
124
2
C  M  (undef)
n
2
C  M  
m
0  0  
power reduction °δ =1
0
°
δ =1 −10
−2 0
−20
°
δ =3
−4 0
°
δ =3 −30
0
°
−6 δ =50
−40
°
δ =5
0
−8 −50 
0 90 180 270 360 0 90 180 270 360
φ φ
(a) Power (b) CTors/σ
Figure 3.26: Effect of phasing of down-only 1/rev TEF inputs δ = δ0 +δ0 cos(ψ−φ)
on UH-60A rotor power and stall metric CTors; high thrust forward flight (C9017).
φ is thus the azimuth for maximum positive (downward) TEF deflection.
12  
Total
10 1/rev 8
Power
8
6
6
4
4 Vibration : components
2 2
0
0
1/rev 3/rev 4/rev 5/rev 3:5/rev HPP
vibration only vibration & power
−2
Vibration optimization including 1/rev
Vibration optimization only
−4  (b) TEF amplitudes
0 90 180 270 360
ψ
(a) TEF actuations
Figure 3.27: TEF actuation combining inputs for UH-60A power, vibration and
stall reduction; high thrust forward flight (C9017). The individual components for
vibration reduction and power/stall reduction are also shown.
125
% power change from baseline
TEF actuation (deg)
% C  change from baseline
Tors
HPP TEF actuation (deg)
lb lb lb−ft
  2000  
600 600
1500
Baseline
Baseline °
400 400 δ =10
° 1000
δ =3 °
° 0 δ =3
δ =1 Baseline 0
0
°
δ =3 ° °
200 0 δ =5 δ =5200 0 0
500
°
δ =5 °
0 δ =1
0
0 0 0 
0 90 180 270 360 0 90 180 270 360 0 90 180 270 360
φ φ φ
(a) 4/rev hub in-plane shear (b) 4/rev hub vertical shear (c) 4/rev hub in-plane moment
Figure 3.28: Effect of phasing of down-only 1/rev TEF inputs δ = δ0 +δ0 cos(ψ−φ)
on UH-60A vibratory loads; high thrust forward flight (C9017). φ is thus the azimuth
for maximum positive (downward) TEF deflection.
   
90 90 90
120 60 120 60 120 60
0.05 0.03
0.005
150   0.5 30 150   0.5 30 150   0.5 30
0.02
0
0
0.01
180 0 180 0 180 0
−0.05
−0.005 0
210 330 210 330 210 330
−0.1 −0.01
240 300 240 300 −0.01 240 300
270 270 270
   s
(a) Lift (b) Drag (c) Pitching moment (positive
nose up)
Figure 3.29: Change in UH-60A rotor disk loading from baseline, due to 2/rev
TEF input δ = 5◦cos(2ψ + 15◦); high speed forward flight (C8534); Blue-decrease,
Red-increase
126
F
x,y:4/rev
F
z:4/rev
M
x,y:4/rev
lb−ft
lb  lb  4000  
1500 ° 1500
δ =5 ° Baseline
0 3000 δ =30
° °
δ =3 δ =5
0 0
°
δ =1
0
1000 1000
2000
°
° δ =1
δ =1 0°
500 Baseline 500 Baseline
0 δ =3
0 1000
°
δ =5
0
0  0  0  
0 90 180 270 360 0 90 180 270 360 0 90 180 270 360
φ φ φ
(a) 4/rev hub in-plane shear (b) 4/rev hub vertical shear (c) 4/rev hub in-plane moment
Figure 3.30: Effect of phasing of 1/rev TEF inputs δ = δ0 cos(ψ + φ) on UH-60A
vibratory loads; high speed forward flight (C8534)
127
F
x,y:4/rev
F
z:4/rev
M
x,y:4/rev
3.7 Power reduction with 1,2/rev TEF inputs:High speed flight con-
dition (C8534)
Fig. 3.29 shows the rotor disk loading with the flap actuated at δ = 5◦cos(2ψ+
15◦), in terms of the change in the section aerodynamic loads from the baseline
C8534 condition. The baseline condition has the advancing blade operating at
negative angles of attack. The TEF causes nose-up pitching moments and twist
on the advancing blade, increasing the angles of attack in the sections producing
negative lift. Thus the advancing side produces more lift without an associated drag
penalty. The other parts of the disk are offloaded slightly and their drag contribution
is reduced.
lb−ft
lb  lb  4000 °  
° δ =5
δ =5 0
0
1500 ° 1500
°
δ =3
δ =3 0
0 3000 Baseline °
° Baseline δ =1
δ =1 0
0
1000 1000
2000
°
Baseline δ =5
0
500 500 °
δ =3 1000
0
°
δ =1
0
0 0 0 
0 90 180 270 360 0 90 180 270 360 0 90 180 270 360
φ φ φ
(a) 4/rev hub in-plane shear (b) 4/rev hub vertical shear (c) 4/rev hub in-plane moment
Figure 3.31: Effect of phasing of 2/rev TEF inputs δ = δ0 cos(2ψ + φ) on UH-60A
vibratory loads; high speed forward flight (C8534)
Note that the 1/rev inputs with power benefits do not have a significant adverse
effect on the vibratory loads (4/rev hub in-plane and vertical shears, and in-plane
moment), as seen in Fig. 3.30. The baseline vibration levels are indicated by the
128
F
x,y:4/rev
F
z:4/rev
M
x,y:4/rev
6  6  6  
°
δ =5
4 ° ° 0δ =5 4 δ =5 4
0 0
°
δ =3 ° °
0 power increase δ =30 δ =32 2 2 0
°
° δ =1
δ =1 0 °
0 δ =10
0 0 0
−2 −2 power −2
reduction
   
0 90 180 270 360 0 90 180 270 360 0 90 180 270 360
φ φ φ
(a) µ = 0.1 (b) µ = 0.2 (c) µ = 0.3
Figure 3.32: Effect of phasing of 2/rev TEF inputs δ = δ0 cos(2ψ + φ) on UH-60A
rotor power (% change from baseline); moderate thrust forward flight (Flight 85),
CW/σ=0.0783
horizontal lines. However, the 2/rev deflections that result in performance gains
affect the vibration levels adversely, as seen in Fig. 3.31. Of the target loads, Fz in
particular increases by a large fraction of the baseline value.
Therefore, 2/rev TEF deployment has power benefits at the C8534 condition.
However, it also has a negative effect on the vibration levels. A performance im-
provement that worsens vibration is less desirable, hence one of the goals of this
study is to ascertain if the TEF is capable of yielding a net performance improve-
ment while also reducing vibration. This shall be discussed in the following section.
The mechanism for power reduction with 2/rev TEF inputs at high forward speeds
is to affect the loading on the advancing disk producing negative lift. However, at
lower speeds, there is little or no negative loading, so the mechanism of any power
reductions effected by the TEF is expected to be different. Figure 3.32 shows the %
change in power from the respective baselines, for the rotor operating at a weight
coefficient CW/σ of 0.0783 (termed Flight 85), and advance ratios of 0.1, 0.2 and
129
% power change from baseline
% power change from baseline
% power change from baseline
0.3. At lower forward speeds, the optimum phasing of the TEF input moves towards
increasing the loading on the front and rear parts of the disk i.e. towards a phase
of φ = 180◦.
Power reduction with 1, 2/rev harmonic TEF inputs
C9017 was investigated for possible power reductions using 1 and 2/rev TEF
deflections. Actuation schedules of the form δ = δ0 cos(nψ+φ), n = 1, 2, for varying
amplitudes and phases φ were prescribed to the flap defined in Table 2.1. Fig. 3.33
shows the percent change in power for the flapped rotor operating at C9017, from
the baseline case (no flaps), with 1 and 2/rev inputs, respectively. It is clear that
the performance gains with flap amplitudes upto 5◦ are less than half (maximum
gains of the order of 1% reduction in power) compared to the high speed C8534
condition. This is because there are no sections of the disk producing negative lift,
hence the power reductions (with 2/rev TEF inputs) occur due to offloading of the
advancing and retreating blades and there is not a significant improvement in the
section L/Ds on the advancing side, as was identified for high-speed flight.
The 1/rev inputs with power benefits do not have a significant adverse effect on
the vibratory loads (4/rev hub in-plane and vertical shears, and in-plane moment),
as seen in Fig. 3.34. The baseline vibration levels are indicated by the horizontal
lines. However, the 2/rev deflections that result in performance gains affect the
vibration levels adversely, as seen in Fig. 3.35.
130
A=1
1.5  1.5  
°
δ =5
0
1 1 °δ =5
0
°
δ =3 power increase
0 °
0.5 0.5 δ =30
°
δ =1 °
0 δ =10
0 0
−0.5 −0.5
power reduction
−1 −1
−1.5 −1.5 
0 90 180 270 360 0 90 180 270 360
φ φ
(a) 1/rev TEF inputs (n = 1): δ = δ0 cos(ψ + φ) (b) 2/rev TEF inputs: δ = δ0 cos(2ψ + φ)
Figure 3.33: Effect of phasing of 1 and 2/rev TEF inputs on UH-60A rotor power;
high thrust forward flight (C9017)
lb lb lb−ft
  2000  
600 600
1500 °
Baseline δ =1 Baseline0
400 ° 400
δ =1
0 1000
Baseline
°
°
° δ
δ =5
=5
° 0
δ =3 δ =3 0 °
200 δ =30 200 0 0
500
°
δ =5
0
°
δ =1
0 0 0 0 
0 90 180 270 360 0 90 180 270 360 0 90 180 270 360
φ φ φ
(a) 4/rev hub in-plane shear (b) 4/rev hub vertical shear (c) 4/rev hub in-plane moment
Figure 3.34: Effect of phasing of 1/rev TEF inputs δ = δ0 cos(ψ + φ) on UH-60A
vibratory loads; high thrust forward flight (C9017)
3.8 Simultaneous power and vibration reduction with TEFs : High
speed flight condition (C8534)
It was observed that it was possible to reduce vibratory loads with suitable
3–5/rev TEF deflections, while suitable combinations of steady, 1/rev and 2/rev
131
F
x,y:4/rev
% power change from baseline
F
z:4/rev
% power change from baseline
M
x,y:4/rev
lb lb−ft lb  2000  
° °
δ =5 δ =5
0 0
600 600
° °
δ =3 1500 δ =30 0
Baseline
°
° Baseline
δ =1
0
400 δ =1 400
0
° 1000
δ =3
0 Baseline
°
δ =1
° 0
δ =5
200 200 0
500
0 0 0 
0 90 180 270 360 0 90 180 270 360 0 90 180 270 360
φ φ φ
(a) 4/rev hub in-plane shear (b) 4/rev hub vertical shear (c) 4/rev hub in-plane moment
Figure 3.35: Effect of phasing of 2/rev TEF inputs δ = δ0 cos(2ψ + φ) on UH-60A
vibratory loads; high thrust forward flight (C9017)
deflections yielded power reductions. However, a reduction of power consumption
is accompanied by an increase in vibration, while the flap actuations for vibration
reduction increase the power requirements. Hence, revised actuations are necessary
for reducing the vibration that comes with power benefits.
For the purpose of this discussion, the C8534 high speed flight condition is con-
sidered. From a parametric sweep of different steady and 2/rev inputs, the actuation
3◦ cos(2ψ + 30◦) was chosen and 1/rev inputs of amplitude 3◦ were superimposed
on this actuation for further power reduction.
Figs. 3.36 and 3.37 summarize the power and vibration benefits as a function of
the phase φ1p of the 1/rev input. Fig. 3.36 shows the changes in power effected by (i)
only 1/rev inputs of amplitude 3◦ superimposed on the actuation 3◦ cos(2ψ+30◦), (ii)
superimposition of 1, 2/rev inputs on the baseline optimal actuation for vibration
reduction only and (iii) combination of 1, 2/rev inputs and the revised optimal
actuation for vibration reduction. The actuation for vibration reduction only results
132
F
x,y:4/rev
F
z:4/rev
M
x,y:4/rev
4
power increase Vibration optimization
including 1,2/rev
2
vibration 
optimum
0
Only 1+2/rev
−2 Vibration optimization
power reduction only
−4
0 90 180 270 360
Phase φ  (deg)
1p
Figure 3.36: Separate and combined effects of 1 plus 2/rev TEF input δ = 3◦cos(ψ+
φ1p) + 3
◦cos(2ψ + 30◦) on UH-60A rotor power, for three cases: (i) only 1, 2/rev,
(ii) only vibration optimization and (iii) vibration optimization including 1, 2/rev;
high speed forward flight (C8534); vibration objective function: J1.
in 1.5% higher power requirement. The best power reduction using 1, 2/rev inputs
only was 2.3% at a phase of 60◦. Superimposing 1, 2/rev inputs on the optimal
vibration actuation yielded a maximum power reduction of 1.5% at a phase of 90◦.
Fig. 3.37 shows that of the resultant vibratory hub loads, the vertical shear loads
increase by up to 50% even though the inplane shear and moment were still reduced
by about 50%. The controller predicted a revised actuation for vibration control
at this stage, with the final power requirement nearly the same as the baseline
condition. This means that it was possible to reduce vibration levels with a net
power reduction.
133
% Power (relative to baseline)
lb lb
1200  1200  lb − ft
2500  
Only 1+2/rev
2000
800 800 Baseline
1500 Vibration optimization
including 1,2/rev
400 400 1000 Vibration optimization
only
500
0 0 0 
0 90 180 270 360 0 90 180 270 360 0 90 180 270 360
Phase φ  (deg) Phase φ  (deg) Phase φ  (deg)
1p 1p 1p
(a) In-plane shear (b) Vertical shear (c) In-plane moment
Figure 3.37: Separate and combined effects of 1 plus 2/rev TEF input δ = 3◦cos(ψ+
φ )+3◦ ◦1p cos(2ψ+30 ) on UH-60A vibratory hub shears and moments, for three cases:
(i) only 1, 2/rev, (ii) only vibration optimization and (iii) vibration optimization
including 1, 2/rev; high speed forward flight (C8534); vibration objective function:
J1.
134
In−plane shear
Vertical shear
In−plane moment
3.9 Concluding remarks
The rotor performance was improved in hover with a combination of torsion-
ally softer blades and positive TEF deflections which contribute to a favorable elastic
twist response and reduced induced losses. In high-speed forward flight(C8534),a
combination of steady,1 and 2/rev inputs reduced the negative loading on the ad-
vancing blade and thus off-loaded the front and rear parts of the disk,improving
performance.
2/rev TEF inputs were shown to alter the disk loding to reduce power con-
sumption at high speed (C8534)without significantly altering the trim control set-
tings. A 2.73% power reduction was obtained with a TEF actuation δ = 5◦cos(2ψ+
15◦),which reduces the negative loading on the advancing blade.
The loads were redistributed for power benefits using HPP deflections of about
10◦. Softening the blades in torsion to improve the effectiveness of the TEF increases
the vibratory loads at high speeds,resulting in larger flap actuation requirements for
vibration reduction.
Targeting both vibration and power reduction was made possible by a com-
bination of 2,3,4 and 5/rev TEF inputs,resulting in a reduction of power of 1.9%
and in-plane vibratory loads of more than 70% at high speed(C8534).The deflection
requiements were higher than for separate reductions in power or vibration.
A TEF, with a 1/rev actuation, with a constant downward deflection, was
shown to be effective at altering the section angles of attack so as to reduce the
severity of retreating blade stall at high thrust (C9017) and in the process reduced
135
power consumption.The optimal phasing was the one that resulted in maximum
downward deflection on the retreating blade and zero deflection on the advancing
blade.A combination of 1,2,3, and 5/rev inputs resulted in a power reduction of
7.5%,while also reducing the vibratory loads by 80%,and the severity of the dynamic
stall. The 1/rev deflections did not affect the vibration adversely.
136
Chapter 4: Leading-Edge Slats
4.1 Results and discussion
The effect of leading-edge slats on rotor maximum lift, power requirement and
vibratory hub loads is examined in the following sections. The study uses propulsive
free flight trim. Vehicle weight and speed are prescribed and the rotor control angles,
tail rotor collective and fuselage attitude angles are obtained to maintain force and
moment equilibrium about three axes.
4.2 Lift Boundary
Leading-edge slats help increase the maximum lift generated by airfoil sections
and are thus capable of pushing the rotor maximum lift boundary above the baseline
level for the rotor without slats. Additionally the dynamic behavior of slatted
airfoils, in terms of delaying boundary layer separation from the airfoil surface, is
better than airfoils without slats. The current results include unsteady corrections
to the airloads due to airfoil dynamic properties, as modelled by Leishman and
Beddoes. The parameters for the Leishman-Beddoes dynamic stall model (used in
UMARC) were modified for the slatted airfoils using the static data obtained from
137
2D-CFD calculations.
Mishra et al.7 showed by means of coupled CFD-CSD simulations (without
modifications to the baseline structural dynamics) that both static and dynamic
stall actuations on a slatted UH-60A blade are highly effective in mitigating the
severity of the dynamic stall at the high speed flight condition C9017. This is
accompanied by a significant reduction in the peak-to-peak pitch link loads. The
improved performance of the blade sections in dynamic stalled flight conditions
contributes to an effective increase in the maximum rotor lifting capability in forward
flight.
The slat positions used in the analysis are S0, S1 and S6. S0 is a low drag
position that is approximated by using the S1 lift and moment characteristics, and
the SC1094R8 drag characteristics. The ’no slats’ baseline case has the SC2110
airfoil section in place of the UH-60A airfoil sections in the corresponding radial
positions. Dynamic actuations considered are :
I. Actuation - 1: a 1/rev motion that passes through S1 at ψ = 90◦ and S6 at
ψ= 270◦.
II. Actuation - 2: a combination of a 1/rev and 3/rev motion that passes
through SI, S0 at ψ = 90◦ and S6 at ψ = 270◦.
Figure 2.34a is a graphic of the slat orientation across azimuth in comparison
to the fixed S6 case, and figure 2.34b shows the variation of the orientation of the
slat element with respect to the main element, as a function of azimuth for each of
these dynamic actuations.
Figure 4.1 shows the maximum lift boundary of the rotor without and with
138
static slats SI and S6 spanning 50-90% R. The McHugh’s lift boundary was obtained
for a model rotor from wind tunnel testing. The high-lift slatted airfoils S6 increase
the maximum rotor CT/σ by about 15− 30% at moderate to high speeds, with the
low drag airfoils SI providing about 10− 20% more lift than unslatted blades.
0.2  
0.15
0.1
McHugh boundary
UH−60A baseline
0.05
Baseline − no slats
S1 airfoils (50−90%R)
S6 airfoils (50−90%R)
0 
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
µ
Figure 4.1: UH-60A rotor lift boundary with and without fixed (S1,S6) slats from
50-90%R
In the following sections, the benefits of prescribing dynamic slat actuations to
power requirements will be discussed. The dynamic actuations are chosen to retain
the high lift benefits of the slats while seeking to minimize profile drag penalties
over regions of the rotor disk operating at lower angles of attack i.e. the advancing
side.Fig. 4.2 shows the rotor maximum lift boundary with the active slat actuations
1 and 2. Because these configurations pass through the maximum lift position on
the retreating side, where the slats have the best benefits, the maximum rotor thrust
139
C /σ
T max
0.2  
0.15
0.1
UH−60A baseline
S1 airfoils (50−90%R)
0.05
S6 airfoils (50−90%R)
Actuation 1 (50−90%R)
Actuation 2 (50−90%R)
0 
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
µ
Figure 4.2: UH-60A rotor lift boundary with and without active slats from 50-90%R
; Actuations 1 & 2: dynamic actuations between low drag positions on advancing
side and high lift position on retreating side
140
C /σ
T max
achievable with them is close to that of the static S6 case, which is highly desirable
when combining the benefits in performance and rotor lifting capability.
The effects of accounting for the dynamic properties of airfoil sections are illus-
trated in Fig.4.3, which shows the maximum predicted rotor thrust from UMARC
assuming fully attached flow versus dynamic stalled flow wherever applicable. Thus,
the maximum lifting capabilities of the rotor are enhanced when accounting for dy-
namic characteristics of the airfoil sections. As an example, the predicted maximum
lift of the baseline UH-60A rotor is about 15-20% higher with dynamic stall effects.
0.2  
0.15
0.1
McHugh boundary
UH−60A baseline− attached
0.05
UH−60A baseline− dynamic stall
S6 airfoils (50−90%R) − attached
S6 airfoils (50−90%R)− dynamic stall
0 
0.1 0.15 0.2 0.25 0.3 0.35
µ
Figure 4.3: UH-60A rotor lift boundary with attached flow assumption and dynamic
stall model: baseline rotor and with fixed S6 slats from 50-90%R
141
C /σ
T max
4.3 Visualising maximum lift flight condition
Identifying stall is a key step to defining the aerodynamic capability of a rotor.
Determination of the maximum achievable thrust numerically requires the use of
performance metrics that capture the essence of the rotor loading in high thrust
conditions. To this end, two stall-based metrics were considered and monitored to
evaluate whether the numerical limit was indeed a satisfactory prediction of the
maximum rotor lift limit:
1. A static indicator, namely the extent of static airfoil pitching moment stall.
2. A dynamic indicator - Cmx/σ. The higher harmonic (≥ 4/rev) torsion mo-
ment at the blade root, mx, in non-dimensional form, Cmx, is defined as HPP
moment/(m0)(ΩR)
2R). Lorber et al.6 used this definition for a quantitative
measure of the strength of the retreating blade stall.
1. Static indicator:
One method of capturing the limit of the rotor’s lifting ability is to examine the
extent of the rotor disk that is stalled as the operating thrust level increases.
Fig.4.4 shows the areas of the baseline UH-60A rotor disk where blade sections
are operating at angles beyond the values for (2-D) pitching moment stall
at the corresponding local Mach numbers. The flight conditions considered
for this purpose are µ = 0.3 and weight coefficients from 0.07 through the
maximum achievable value at this forward speed. The sections below the
local stall angle are white, while the stalled sections are denoted by black.
142
It can be seen that blade sections are likely to stall even before the lift limit is
actually reached and the ’stalled’regions of the rotor disk gradually increase in
size as the maximum lift limit is approached. In this case, in going from Cw/σ
of 0.08 to the maximum thrust condition at this speed i.e. Cw/σ of 0.1325
(Fig.4.5e), the percentage of the rotor with stalled blade sections increases
from 2.5% to 20.2%.
143
90 90 90 90
120 60 120 60 120 60 120 60
150 30 150 30 150 30 150 30
180 0 180 0 180 0 180 0
210 330 210 330 210 330 210 330
240 300 240 300 240 300 240 300
270 270 270 270
(a) CW /σ = 0.08 (b) CW /σ = 0.1 (c) CW /σ = 0.12 (d) CW /σ = 0.1325
(limit)
Figure 4.4: Baseline UH-60A rotor: stalled blade sections for different operating
thrust levels, µ = 0.3
90 90 90 90 90
120 60 120 60 120 60 120 60 120 60
150 30 150 30 150 30 150 30 150 30
180 0 180 0 180 0 180 0 180 0
210 330 210 330 210 330 210 330 210 330
240 300 240 300 240 300 240 300 240 300
270 270 270 270 270
(a) CW /σ = 0.08 (b) CW /σ = 0.1 (c) CW /σ = 0.12(d) CW /σ = 0.14(e) CW /σ = 0.16
(limit)
Figure 4.5: UH-60A rotor with fixed S6 slats from 50-90%R: stalled blade sections
for different operating thrust levels, µ = 0.3
The effect of having the S6 slats from 50-90% R on rotor blade stall is shown in
figure 4.5. In this case, going from Cw/σ of 0.08 (figure 4.5a) to the maximum
thrust condition at this speed i.e. Cw/σ of 0.16 (figure 4.5e), the percentage
of the rotor with stalled blade sections increases from 2.5% to 13.7%. As com-
pared to the baseline UH-60A rotor, the slatted rotor achieved 21% increase
in maximum thrust capability. The stalled regions of the disk are smaller at
144
the same operating weight.
Fig. 4.6 shows the percentage of the rotor disk that is stalled, as a function
of operating thrust (CT/σ) for the UH-60A baseline rotor and with fixed slats
from 50-90% R, at advance ratios of 0.2 and 0.3. Slatted blade sections need to
operate at lower angles of attack to achieve the same thrust, due to increased
lifting characteristics. They are also able to operate till higher angles of attack
before the onset of flow separation and stall. These factors contribute to the
higher achievable maximum rotor lift with leading-edge slats.
2. Dynamic indicator:
The choice of this metric is motivated by the increase in torsion loads as a
result of pitching moment stall. Since the 1/rev as well as higher frequency
content (due to the stall spike) of the loads increase with thrust, only the
higher harmonics (≥ 4/rev) are retained. Fig. 4.9 shows the variation of the
dynamic indicator Cmx/σ as a function of blade loading/thrust level CT/σ for
two forward flight advance ratios, 0.2 and 0.3. There is a steep rise in the
moment loads as thrust is increased, and again with the slatted sections, the
metric is lower than for the baseline rotor at high speed and high thrust levels.
145
  
15 15
10 10
5 5
UH−60A baseline
Baseline − no slats
S1 airfoils (50−90% R)
S6 airfoils (50−90% R)
0 0 
0.1 0.12 0.14 0.16 0.18 0.2 0.1 0.12 0.14 0.16
C /σ C /σ
T T
(a) µ = 0.2 (b) µ = 0.3
Figure 4.6: UH-60A rotor without and with fixed slats from 50-90%R: % of rotor
disk with stalled airfoil sections
146
% of rotor disk stalled
% of rotor disk stalled
−4 −4
x 10 x 10
 9  
UH−60A baseline
9
Baseline − no slats
S1 airfoils (50−90%R)
S6 airfoils (50−90%R)
6
6
3
3
  
0.1 0.12 0.14 0.16 0.18 0.2 0.1 0.12 0.14 0.16
C /σ C /σ
T T
(a) µ = 0.2 (b) µ = 0.3
Figure 4.7: UH-60A rotor without and with fixed slats from 50-90%R: dynamic
indicator of rotor stall Cmx/σ
4.4 Power requirement with Leading-Edge Slats
In the previous sections, the lift-enhancing benefits of leading-edge slats were
discussed. In addition to these benefits, it may be possible to achieve a decrease
in power requirement by prescribing dynamic actuations that take advantage of the
lift-enhancing properties of the slat on the retreating side, while trying to minimize
the drag penalty on the advancing side by means of low-drag slat configurations.
Figs. 4.10-4.13 show the power requirement and break-up of power (induced
and profile) with increasing thrust at advance ratios of 0, 0.1, 0.2 and 0.3, for the
rotor without and with slats fitted to the blades from 50-90% R. The cases considered
are fixed S1 and S6 slats, and dynamic actuations 1 and 2 from 50-90% R. In hover
(µ = 0), the induced power is a dominant component, and therefore, the slat has a
147
C /σ
mx
C /σ
mx
0.015   
UH−60A baseline
Baseline − no slats
S1 airfoils (50−90%R) 0.002
S6 airfoils (50−90%R)
Actuation 1 (50−90%R)
Actuation 2 (50−90%R)
0.01
0.0015
0.005
 0.001 
0.08 0.1 0.12 0.14 0.08 0.1 0.12 0.14
C /σ C /σ
T T
(a) Induced power (b) Profile power
 
 
0.015
0
0.01
−5
0.005
  
0.08 0.1 0.12 0.14 0.08 0.1 0.12
C /σ C /σ
T T
(c) Total power (d) % change in power from baseline
Figure 4.8: UH-60A components of rotor power vs thrust at µ = 0, without and
with slats from 50-90%R ; Actuations 1 & 2: dynamic actuations between low drag
positions on advancing side and high lift position on retreating side
smaller effect on total power. On the other hand, at higher speeds, the slat plays
a more important role. For example, figure 4.12d shows that at µ = 0.3, static
S6 deployed from 50-90% R reduces power consumption for CT/σ > 0.12, while
dynamic actuation 2 reduces power consumption for CT/σ > 0.105. The benefits
148
C / C /σσ Pi
P
Power (% change) C /σP0
−4 −4
x 10 x 10
 9  
UH−60A baseline
9
Baseline − no slats
S1 airfoils (50−90%R)
S6 airfoils (50−90%R)
6
6
3
3
  
0.1 0.12 0.14 0.16 0.18 0.2 0.1 0.12 0.14 0.16
C /σ C /σ
T T
(a) µ = 0.2 (b) µ = 0.3
Figure 4.9: UH-60A rotor without and with fixed slats from 50-90%R: dynamic
indicator of rotor stall Cmx/σ
are seen in both induced power and profile power. At lower thrust levels, where
the operating angles of attack are low, blades with slats do not benefit from the
lift-enhancing properties of slats and high profile power penalties are incurred. This
leads to increased power requirements at low thrust levels and low advance ratios.
The performance benefits of leading-edge slats are most appreciable at high thrust
flight conditions. The active deployments 1 and 2 perform better than the fixed
slats (S6) at low thrusts because the slat is retracted back over the baseline airfoil
on the advancing side (positions S0 and S1). Using actuation 2, power reductions
of about 10-15% are predicted at the maximum baseline rotor operating thrust at
different forward speeds.
149
C /σ
mx
C /σ
mx
0.015   
UH−60A baseline
Baseline − no slats
S1 airfoils (50−90%R)
0.002
S6 airfoils (50−90%R)
Actuation 1 (50−90%R)
Actuation 2 (50−90%R)
0.01
0.0015
0.005
 0.001 
0.08 0.1 0.12 0.14 0.08 0.1 0.12 0.14
C /σ C /σ
T T
(a) Induced power (b) Profile power
  
0.015
0
0.01
−5
0.005
  
0.08 0.1 0.12 0.14 0.08 0.1 0.12
C /σ C /σ
T T
(c) Total power (d) % change in power from baseline
Figure 4.10: UH-60A components of rotor power vs thrust at µ = 0, without and
with slats from 50-90%R ; Actuations 1 & 2: dynamic actuations between low drag
positions on advancing side and high lift position on retreating side
150
C /σ C /σ
P Pi
Power (% change) C /σ
P0
0.015  0.003  
UH−60A baseline
Baseline − no slats
S1 airfoils (50−90%R)
S6 airfoils (50−90%R)
Actuation 1 (50−90%R)
0.01
Actuation 2 (50−90%R)
0.002
0.005
 0.001 
0.08 0.1 0.12 0.14 0.16 0.08 0.1 0.12 0.14 0.16 0.18
C /σ C /σ
T T
(a) Induced power (b) Profile power
  
0.015
0
0.01
−5
0.005
 −10 
0.08 0.1 0.12 0.14 0.16 0.18 0.08 0.1 0.12 0.14
C /σ C /σ
T T
(c) Total power (d) % change in power from baseline
Figure 4.11: UH-60A components of rotor power vs thrust at µ = 0.1, without and
with slats from 50-90%R ; Actuations 1 & 2: dynamic actuations between low drag
positions on advancing side and high lift position on retreating side
151
C /σ C /σ
P Pi
C /σ
Power (% change) P0
0.012  0.005  
UH−60A baseline
Baseline − no slats
S1 airfoils (50−90%R)
0.004
S6 airfoils (50−90%R)
Actuation 1 (50−90%R)
0.008
Actuation 2 (50−90%R)
0.003
0.004 0.002
 0.001 
0.08 0.1 0.12 0.14 0.16 0.18 0.08 0.1 0.12 0.14 0.16 0.18
C /σ C /σ
T T
(a) Induced power (b) Profile power
 25  
20
0.015
15
10
0.01 5
0
−5
0.005
−10
 −15 
0.08 0.1 0.12 0.14 0.16 0.18 0.08 0.1 0.12 0.14
C /σ C /σ
T T
(c) Total power (d) % change in power from baseline
Figure 4.12: UH-60A components of rotor power vs thrust at µ = 0.2, without and
with slats from 50-90%R ; Actuations 1 & 2: dynamic actuations between low drag
positions on advancing side and high lift position on retreating side
152
C /σ C /σ
P Pi
Power (% change) C /σ
P0
  
UH−60A baseline
Baseline − no slats
0.006 0.004
S1 airfoils (50−90%R)
S6 airfoils (50−90%R)
Actuation 1 (50−90%R)
Actuation 2 (50−90%R)
0.004 0.003
0.002 0.002
  
0.08 0.1 0.12 0.14 0.16 0.08 0.1 0.12 0.14 0.16
C /σ C /σ
T T
(a) Induced power (b) Profile power
 20  
15
0.012
10
0.01 5
0
0.008
−5
−10
0.006
 −15 
0.08 0.1 0.12 0.14 0.16 0.08 0.1 0.12
C /σ C /σ
T T
(c) Total power (d) % change in power from baseline
Figure 4.13: UH-60A components of rotor power vs thrust at µ = 0.3, without and
with slats from 50-90%R ; Actuations 1 & 2: dynamic actuations between low drag
positions on advancing side and high lift position on retreating side
153
C /σ
C /σ Pi
P
Power (% change) C /σP0
0.02  0.007  
UH−60A baseline
Baseline − no slats
S1 airfoils (50−90%R)
0.016 S6 airfoils (50−90%R)
Actuation 1 (50−90%R) 0.006
Actuation 2 (50−90%R)
0.012
0.005
0.008
0.004
0.004  
0.08 0.1 0.12 0.14 0.16 0.18 0.08 0.1 0.12 0.14 0.16 0.18
C /σ C /σ
T T
(a) In-plane shear (b) Vertical shear
0.0016   
75
0.0012
50
25
0.0008
0
0.0004  
0.08 0.1 0.12 0.14 0.16 0.18 0.08 0.1 0.12 0.14
C /σ C /σ
T T
(c) In-plane moment (d) Vibration index J
Figure 4.14: UH-60A hub vibratory loads vs thrust at µ = 0.1, without and with
slats from 50-90%R ; Actuations 1 & 2: dynamic actuations between low drag
positions on advancing side and high lift position on retreating side
154
In−plane shear
In−plane moment
F
J (% change) z
 0.003  
UH−60A baseline
0.009 Baseline − no slats
S1 airfoils (50−90%R)
S6 airfoils (50−90%R)
Actuation 1 (50−90%R)
Actuation 2 (50−90%R)
0.002
0.007
0.005
0.001
0.003  
0.08 0.1 0.12 0.14 0.16 0.18 0.08 0.1 0.12 0.14 0.16 0.18
C /σ C /σ
T T
(a) In-plane shear (b) Vertical shear
0.0008   
125
100
0.0006
75
50
0.0004
25
0
0.0002  
0.08 0.1 0.12 0.14 0.16 0.18 0.08 0.1 0.12 0.14
C /σ C /σ
T T
(c) In-plane moment (d) Vibration index J
Figure 4.15: UH-60A hub vibratory loads vs thrust at µ = 0.2, without and with
slats from 50-90%R ; Actuations 1 & 2: dynamic actuations between low drag
positions on advancing side and high lift position on retreating side
155
In−plane moment In−plane shear
J (% change) F
z
0.014   
UH−60A baseline
Baseline − no slats
S1 airfoils (50−90%R) 0.005
S6 airfoils (50−90%R)
Actuation 1 (50−90%R)
0.01 Actuation 2 (50−90%R)
0.003
0.006
0.002 0.001 
0.08 0.1 0.12 0.14 0.16 0.08 0.1 0.12 0.14 0.16
C /σ C /σ
T T
(a) In-plane shear (b) Vertical shear
 50  
0.0009
25
0.0006
0
0.0003 −10 
0.08 0.1 0.12 0.14 0.16 0.08 0.1 0.12
C /σ C /σ
T T
(c) In-plane moment (d) Vibration index J
Figure 4.16: UH-60A hub vibratory loads vs thrust at µ = 0.3, without and with
slats from 50-90%R ; Actuations 1 & 2: dynamic actuations between low drag
positions on advancing side and high lift position on retreating side
156
In−plane shear
In−plane moment
J (% change) Fz
In the following sections, the benefits of prescribing dynamic slat actuations to
power requirements will be discussed. The dynamic actuations are chosen to retain
the high lift benefits of the slats while seeking to minimize profile drag penalties over
regions of the rotor disk operating at lower angles of attack i.e., the advancing side.
Figure 4.2 shows the rotor maximum lift boundary with the active slat actuations 1
and 2. Because these configurations pass through the maximum lift position on the
retreating side, where the slats have the best benefits, the maximum rotor thrust
achievable with them is close to that of the static S6 case, which is highly desirable
when combining the benefits in performance and rotor lifting capability.
The effects of accounting for the dynamic properties of airfoil sections are illus-
trated in figure 4.3, which shows the maximum predicted rotor thrust from UMARC
assuming fully attached flow versus dynamic stalled flow wherever applicable. Thus,
the maximum lifting capabilities of the rotor are enhanced when accounting for dy-
namic characteristics of the airfoil sections. As an example, the predicted maximum
lift of the baseline UH-60A rotor is about 15-20% higher with dynamic stall effects.
4.5 Vibratory hub loads with Leading-Edge Slats
Figs.( 4.14-4.16) show the 4/rev vibratory hub loads with increasing thrust
at advance ratios of 0.1, 0.2 and 0.3, for the rotor without and with slats fitted
to the blades from 50-90% R The shear and moment hub loads are respectively
non-dimensionalized by the quantities (m0ΩR)
2 and (m0ΩR)
2R. The vibratory load
metrics compared here are:
157
1. 4/rev hub in-plane shear
2. 4/rev hub vertical shear
3. 4/rev hub in-plane moment
4. Vibration index J, defined as
√
J = (F /F 2 2 2 2 2x x,0) + (Fy/Fy,0) + (Fz/Fz,0) + (Mx/Mx,0) + (My/My,0)
where the subscript ’0’ denotes the quantities for the corresponding baseline
(UH-60A) case.
In general, the vibratory hub loads are seen to increase from the baseline
levels in the presence of leading-edge slats, particularly the in-plane shear loads
(Figs. 4.14a,4.15a,4.16a). It is observed that the dynamic active deployments 1
and 2 (50-90% R) perform better than the fixed slats S1 and S6 [Fig.4.14a] and
the increase in in-plane shear loads at µ = 0.1 and CT/σ = 0.12 and CT/σ = 0.14
is in the range of 10-15%. At higher forward speeds, there is a reduction in the
hub vertical shear and in-plane moments at high thrust levels (Figs. 4.16b-4.16c).
Comparison of the vibration index J with the baseline UH-60A rotor shows that up
to 75% increase in vibration results from the use of leading-edge slats. The penalties
are less severe at low speeds and thrust levels.
Overall, the dynamic actuations appear to be a good compromise between en-
hancing performance and impacting vibration the least. The possibility of vibration
reduction using higher frequency actuation (2-5/rev) of leading-edge slats is a topic
of future studies.
158
4.6 Varying span-size of Leading-Edge Slats
The spanwise extent of the leading-edge slats used earlier, namely 50-90%, was
chosen to completely replace the SC1094R8 airfoil sections on the UH-60A blade. In
this section, trade-offs in power requirement and vibratory hub loads with varying
spanwise lengths are examined. The different leading-edge slat sizes used are:
I 20% R : 50-70% R, 60-80% R, 70-90% R
II. 30% R : 40-70% R, 50-80% R, 60-90% R
III. 40% R : 40-80% R, 50-90% R
The dynamic slat actuation Actuation 2 is chosen for this parametric study,
because it has been shown to offer the best compromise in enhanced lift, reduction
of power requirement and changes in vibratory load levels.
Fig. 4.17 shows the power requirement, break-up of power (induced and pro-
file) , and rotor lift-to-drag ratio L/De (L/De = T/(P/V∞- Dv), Dv being the vehicle
drag at an operating weight coefficient Cw/σ of 0.08 and as a function of advance
ratio, for the rotor without and with slats of varying lengths fitted to the blades
and actuated as per the previously defined Actuation 2. Fig. 4.18 shows the effect
of the varying span lengths on the vibratory hub loads. Figs. 4.19 and 4.20 show
the same quantities at an operating weight coefficient of 0.1.
From a performance standpoint, the slats are less effective when located out-
boards (70-90% R, 60-90% R, 50-90% R) where the dynamic pressure is higher,
because blade angles of attack are lower and profile drag penalties are higher due
to slats, as shown in figures 4.17b and 4.19b for the two weights. The rotor L/De
159
is lower and power requirement is consequently higher, as shown in figures 4.17d ,
4.19d and 4.17c , 4.19c respectively.
At the lower weight,the slats are seen not to offer much benefit and in fact
impact the performance (upto 10% decrease in L/De) and vibration adversely (upto
25%) at high speeds, but at the higher weight, an improvement of up to 14% in
maximum L/D with the 40% span slats is predicted with an accompanied penalty
of nearly 30% in vibratory hub loads, while a modest 10% improvement in L/D with
a smaller increase (20% at high speeds) or decrease in the vibratory loads is seen
with the 20% span slat from 70-90%R.
4.7 Forward flight speed limit with Leading-Edge Slats
Having pushed the maximum lift of the rotor at all forward speeds with
leading-edge slats, it is expected that the vehicle with a slatted rotor ought to
be able to operate at higher speeds than the baseline. To this end, the slatted ro-
tor was trimmed at a nominal thrust level CT/σ of 0.08 to determine the highest
forward speeds the rotor could operate at.
Fig. 4.21 shows the power requirement, break-up and rotor L/D for the rotor
without and with slats fitted to the blades from 50-90% R. Fixed slats S1 and S6
as well as dynamic actuations 1 and 2 are considered here. The highest advance
ratio the baseline UH-60A rotor could be trimmed to was 0.45, while the slatted
rotors could be trimmed up to an advance ratio of 0.49. As expected, the power
requirement is generally higher with slats at this moderate thrust level, although
160
−3 −3
x 10 x 10
  
UH−60A baseline
Actuation 2: 50−70%R
5 60−80%R
70−90%R
40−70%R 3
50−80%R
60−90%R
40−80%R
4 50−90%R
2
3
2
 1 
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.05 0.1 0.15 0.2 0.25 0.3 0.35
µ µ
(a) Induced power (b) Profile power
 
 
6
0
4
2
0 −5
−2
−4 −10 
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.05 0.1 0.15 0.2 0.25 0.3 0.35
µ µ
(c) % change in power from baseline (d) % change in rotor L/De from baseline
Figure 4.17: UH-60A components of rotor power vs thrust at CW/σ = 0.08, without
and with slats of varying spanwise lengths; Actuation 2: dynamic actuation between
low drag positions on advancing side and high lift position on retreating side
161
Power (% change) C /σ
Pi
L/D  (% change) C /σ
e P0
−3 −3
x 10 x 10
10   
UH−60A baseline 6
Actuation 2: 50−70%R
8 60−80%R
70−90%R
40−70%R
50−80%R
60−90%R 4
6 40−80%R
50−90%R
2
4
2 0 
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.05 0.1 0.15 0.2 0.25 0.3 0.35
µ µ
(a) In-plane shear (b) Vertical shear
−4
x 10
10   
25
8
6
0
4
 −10 
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.05 0.1 0.15 0.2 0.25 0.3 0.35
µ µ
(c) In-plane shear (d) Vibration index J
Figure 4.18: UH-60A vibratory hub loads vs thrust at CW/σ = 0.08, without and
with slats of varying spanwise lengths; Actuation 2: dynamic actuation between low
drag positions on advancing side and high lift position on retreating side
162
In−plane moment In−plane shear
J (% change) F
z
−3 −3
x 10 x 10
  
UH−60A baseline
Actuation 2: 50−70%R
7
60−80%R
70−90%R
40−70%R 3
50−80%R
6 60−90%R
40−80%R
50−90%R
5
2
4
3
 1 
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.05 0.1 0.15 0.2 0.25 0.3 0.35
µ µ
(a) Induced power (b) Profile power
4  15  
2
10
0
−2 5
−4
0
−6
−8 −5 
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.05 0.1 0.15 0.2 0.25 0.3 0.35
µ µ
(c) % change in power from baseline (d) % change in rotor L/De from baseline
Figure 4.19: UH-60A components of rotor power vs thrust at CW/σ = 0.1, without
and with slats of varying spanwise lengths; Actuation 2: dynamic actuation between
low drag positions on advancing side and high lift position on retreating side
163
Power (% change) C /σ
Pi
L/D  (% change)
e C /σP0
−3 −3
x 10 x 10
14   
UH−60A baseline
6
12 Actuation 2: 50−70%R
60−80%R
70−90%R
10 40−70%R
50−80%R
60−90%R 4
8 40−80%R
50−90%R
6
2
4
2 0 
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.05 0.1 0.15 0.2 0.25 0.3 0.35
µ µ
(a) In-plane shear (b) Vertical shear
−4
x 10
  
10
25
8
6
0
4
 −10 
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.05 0.1 0.15 0.2 0.25 0.3 0.35
µ µ
(c) In-plane moment (d) Vibration index J
Figure 4.20: UH-60A vibratory hub loads vs thrust at CW/σ = 0.1, without and
with slats of varying spanwise lengths; Actuation 2: dynamic actuation between low
drag positions on advancing side and high lift position on retreating side
164
In−plane moment In−plane shear
J (% change) F
z
the fixed S1 slats appear to be a good compromise, offering some power reductions
even at this operating thrust.
Fig. 4.22 shows the power required to maintain trimmed flight between µ =0.4
and 0.5,for the baseline UH-60A and the slatted rotor.S6 and S1 fixed-slat configu-
rations could be trimmed upto µ =0.49,which is 20 knots faster than the maximum
trim speed of the baseline UH-60A rotor.The S6 fixed-slat configuration achieves an
incrementally higher trimmed Vmax than the corresponding S1 configuration with a
20% additional power penalty.
−3 −3 −3
x 10 x 10 x 10
  8  
UH−60A baseline
5 Baseline − no slats
6
S1 airfoils (50−90%R) 7
S6 airfoils (50−90%R)
Actuation 1 (50−90%R)
Actuation 2 (50−90%R)
4
6
4
5
3
4
2
2
  3 
0.1 0.2 0.3 0.4 0.5 0.1 0.2 0.3 0.4 0.5 0.1 0.2 0.3 0.4 0.5
µ µ µ
(a) Induced power (b) Profile power (c) Total power
  10  
6 10
0
4 0
−10
2 −10
0 −20 −20 
0.1 0.2 0.3 0.4 0.5 0.1 0.2 0.3 0.4 0.5 0.1 0.2 0.3 0.4 0.5
µ µ µ
(d) Rotor L/De (e) % change in power from(f) % change in rotor L/De
baseline from baseline
Figure 4.21: UH-60A components of rotor power vs thrust at CT/σ = 0.08, without
and with slats from 50-90%R ; Actuations 1 & 2: dynamic actuations between low
drag positions on advancing side and high lift position on retreating side
165
L/D
e C /σ
Pi
Power (% change)
C /σ
P0
L/D  (% change)
e C /σ
P
−3
x 10
8  
S6
Baseline
7
S1
6
Dynamic
5 actuation
 
0.4 0.5
µ
Figure 4.22: Effect of slats on rotor performance and rotor envelope;slats increase
Vmax by 20 knots,indicated by the double-ended horizontal arrows
4.8 Concluding remarks
Leading-edge slats with span 40% rotor radius, chord upto 15% blade chord
and nominal midspan located at 70 % R and at different orientations were investi-
gated for the purposes of improving the rotor maximum lift capability and reducing
power requirement from the baseline rotor values. From this study, the following
conclusions are drawn:
1. The maximum achievable rotor thrust was increased by about 15-30% at ad-
vance ratios greater than 0.2 using leading-edge slats. The slatted rotor had a
smaller portion of the rotor disk with stalled blade sections as compared to the
baseline rotor. Slatted blade sections need to operate at lower angles of attack
to achieve the same thrust, due to increased lifting characteristics. They are
166
Power(C /σ)
P
also able to operate till higher angles of attack before the onset of flow sepa-
ration and stall. These factors contribute to the higher achievable maximum
rotor lift with leading-edge slats.The high frequency content ( 4/rev) of the
blade torsional loads, an indicator of dynamic stall, was also smaller for the
slatted rotor at high speeds and high thrust levels.
2. At lower thrust levels, where the operating angles of attack are low, blades
with slats do not benefit from the lift-enhancing properties of slats and high
profile power penalties are incurred. This leads to increased power require-
ments at low thrust levels and low advance ratios. The performance benefits of
leading-edge slats are most appreciable at high thrust flight conditions. Power
reductions of the order of 10-15% at various speeds were achieved using dy-
namic slat actuations combining high-lift and low-drag orientations in a 1/rev
fashion across azimuth. The maximum slat rotation angle between different
orientations (relative to the baseline airfoil) was about 10◦.
3. The dynamic actuations still yielded nearly the same improvements in maxi-
mum rotor lift capability.
4. Leading-edge slats were in general found to affect vibratory hub loads ad-
versely, particularly at lower speeds. At higher forward speeds, there is a
reduction in the hub vertical shear and in-plane moments at high thrust lev-
els.The penalties are less severe at low speeds and thrust levels.Overall, the
dynamic actuations appear to be a good compromise between enhancing per-
formance while impacting vibration the least.
167
5. A 10% improvement in L/D accompanied with an increase of up to 20% (at
high speeds) or decrease in the vibratory loads was seen with a 20% span slat
located between 70-90% R.
6. The slatted rotor was trimmed at forward speeds not achievable by the baseline
rotor i.e. up to µ = 0.49, indicating that it is possible to push not just the lift
limits of the rotor, but also the forward speed limits with the use of leading-
edge slats.
168
Chapter 6: Summary and conclusions
Studies of active rotor TE flaps and LE slats in recent years have tended
towards methods of enhancing performance over a wide range of operating con-
ditions.Concepts such as fixed and dynamic slats, Variable Droop Leading-Edge
airfoils, circulation control and trailing-edge flaps have been considered for active
aerodynamic flow control, as opposed to passive designs involving blade geometry.
Of these, trailing-edge flaps (TEFs) and leading-edge slats are notable for their con-
ceptual simplicity and wide-ranging potential. Comprehensive rotor analyses appear
suited for evaluation of active control concepts through parametric studies to deter-
mine configurations that yield maximum benefits, and understand the mechanisms
of their operation.
The objective of this study has been to use a comprehensive analysis to
assess and quantify the capabilities of trailing-edge flaps and leading-edge slats for
performance improvement at high speeds, and recommend flap and slat configura-
tions for the UH-60A rotor blades that maximize performance benefits.
169
6.1 Summary
The University of Maryland Advanced Rotorcraft Code(UMARC) was mod-
ified to simulate the effects of trailing-edge flaps and leading-edge slats.The near-
wake model was modified to account for the effect of TEFs on the blade bound
circulation distribution.The structural, inertial and aerodynamic contributions of
TEFs and LESs were integrated into the baseline blade analysis in UMARC.The
TEF is modeled as a single additional degree of freedom and the motion of the flap
is prescribed in the analysis.The slat motion is modeled with 3 additional degrees
of freedom to improve conformity of the slat airfoil with the blade airfoil.The slat-
ted blade sections had the SC2110 baseline/slatted airfoils in place of the baseline
UH-60A airfoils:SC1095 and SC1094R8.The slat configurations were designed for
optimum channeling of the flow near the leading edge of the SC2110 airfoil, hence
the replacement of the baseline UH-60A airfoils in the slat sections.
The impact of TEFs on hover performance was examined with different steady
flap deflections and with a variation in the torsional stiffness. Performance gains
with active control surfaces are expected to be largest at high speeds and high thrust
levels, where a small redistribution of loading can result in significant reductions.
Rotor performance in high speed forward flight with TEFs is investigated by carry-
ing out parametric sweeps of TEF actuations to determine suitable combinations of
steady, 1 and 2/rev TEF inputs that can yield overall power reductions. Different
combinations of steady+2/rev TEF inputs were prescribed, in order to obtain the
trends of the actuations that had the best impact on performance. Two advance
170
ratios, µ = 0.3 and 0.4, were chosen for the study, and different thrust levels (in
terms of non-dimensional vehicle weight coefficient CW/σ) were investigated. Then,
a moderate thrust level condition (CW/σ = 0.09) at µ = 0.3, and an operating con-
dition close to the maximum lift boundary (CW/σ = 0.085) at µ = 0.4, were chosen
to further investigate the benefits of 1/rev inputs, strictly in an open-loop sense.
Rotor vibration reduction with TEFs was studied for high-speed flight conditions
along with the effect of torsional stiffness to estimate the optimal actuation require-
ments to get the best results.The possibility of simultaneous power and vibration
reduction with TEFs for high-speed flight conditions was explored with different
steady and 2/rev inputs superimposed on 1/rev inputs.Stall alleviation using TEFs
with down-only 1/rev inputs was studied to assess the scope for reduction of the
magnitude of dynamic stall events occurring in high thrust forward flight.
The maximum lift boundary of the rotor without and with static slats S1 and
S6 was obtained using UMARC and was compared with the McHugh’s lift boundary
obtained for a model rotor from wind tunnel testing to demonstrate that the high-lift
slatted airfoils S6 and the low drag airfoils S1 can increase the maximum rotor thrust
at moderate to high speeds and provide more lift than unslatted blades.Various dy-
namic actuations that take advantage of the lift enhancing properties of the slat
on the retreating side while trying to minimize the drag penalty on the advancing
side by means of low-drag slat configurations, were studied to identify a suitable
configuration that can result in lower power consumption.The vibratory hub load
levels in the presence of leading edge slats were studied at various speeds and low
and high thrust levels to determine when the penalties are less severe.The trade-
171
offs in power requirements and vibratory hub loads with varying spanwise lengths
were examined to arrive at the dynamic slat actuations that can offer the best com-
promise in enhanced lift, reduction of power requirement and changes of vibratory
loads.Having pushed the maximum lift of the rotor at all forward speeds with the
aid of leading-edge slats,it was also examined whether the vehicle with a slatted
rotor can be trimmed to attain forward speeds higher than the baseline.
The advantages of superimposition of TEFs and leading-edge slats were stud-
ied for 1/rev TEF actuations of the form δ = δ1pcos(ψ + φ1p), which were imposed
on the slatted rotor operating at µ=0.4,CW/σ=0.095,in an effort to improve the
power benefits by alleviating the negative loading on the advancing blade.The in-
crements in section aerodynamic properties due to TEFs were assumed to be generic
CFD-generated values obtained for the SC1094R8 airfoil.
6.2 Conclusions-TEFs
A trailing-edge flap with span of 10% rotor radius, chord of 15% blade chord
and its midspan located at 65%R was evaluated for performance improvement in
hover and high speed forward flight and reduction of 4/rev hub vibratory loads in
forward flight. From this study, the following conclusions are drawn:
(1) The rotor performance in hover was improved with a combination of torsionally
softer blades and positive flap deflections, which contribute to a favorable
elastic twist response and reduced induced losses.
(2) The rotor performance in high speed forward flight was improved by a suitable
172
combination of steady, 1/rev and 2/rev TEF inputs to reduce the negative
loading on the advancing blade and thus off-load the front and rear parts of
the disk.
(3) The 2/rev actuation phase for the best benefits lies between 0◦ and 30◦, while
the 1/rev actuation phase for the best benefits in conjunction with 2/rev input
lies between 0◦ and 90◦.
(4) Power reductions of the order of 2% at µ = 0.3 and 4-5% at µ = 0.4 were
observed using HPP actuation amplitudes of 5◦-10◦.
(5) The flap was shown to be capable of suppressing the target hub loads at a range
of forward speeds, using half peak-to-peak deflections of about 5◦. Softening
the blades in torsion in order to improve the effectiveness of the TEF was found
to increase the vibratory loads at high speed (C8534), resulting in larger flap
actuation requirements for vibration reduction.
6.3 Conclusions-LESs
Leading-edge slats with span 40% rotor radius, chord upto 15% blade chord
and nominal midspan located at 70 % R and at different orientations were investi-
gated for the purposes of improving the rotor maximum lift capability and reducing
power requirement from the baseline rotor values. From this study, the following
conclusions are drawn:
(1) The maximum achievable rotor thrust was increased by about 15-30% at ad-
173
vance ratios greater than 0.2 using leading-edge slats. The slatted rotor had a
smaller portion of the rotor disk with stalled blade sections as compared to the
baseline rotor. Slatted blade sections need to operate at lower angles of attack
to achieve the same thrust, due to increased lifting characteristics. They are
also able to operate till higher angles of attack before the onset of flow sepa-
ration and stall. These factors contribute to the higher achievable maximum
rotor lift with leading-edge slats.The high frequency content ( 4/rev) of the
blade torsional loads, an indicator of dynamic stall, was also smaller for the
slatted rotor at high speeds and high thrust levels.
(2) At lower thrust levels, where the operating angles of attack are low, blades
with slats do not benefit from the lift-enhancing properties of slats and high
profile power penalties are incurred. This leads to increased power require-
ments at low thrust levels and low advance ratios. The performance benefits of
leading-edge slats are most appreciable at high thrust flight conditions. Power
reductions of the order of 10-15% at various speeds were achieved using dy-
namic slat actuations combining high-lift and low-drag orientations in a 1/rev
fashion across azimuth. The maximum slat rotation angle between different
orientations (relative to the baseline airfoil) was about 10◦.
(3) The dynamic actuations still yielded nearly the same improvements in maxi-
mum rotor lift capability.
(4) Leading-edge slats were in general found to affect vibratory hub loads ad-
versely, particularly at lower speeds. At higher forward speeds, there is a
174
reduction in the hub vertical shear and in-plane moments at high thrust lev-
els .The penalties are less severe at low speeds and thrust levels.Overall, the
dynamic actuations appear to be a good compromise between enhancing per-
formance while impacting vibration the least.
(5) A 10% improvement in L/D accompanied with an increase of up to 20% (at
high speeds) or decrease in the vibratory loads was seen with a 20% span slat
located between 70-90% R.
(6) The slatted rotor was trimmed at forward speeds not achievable by the baseline
rotor i.e., up to µ = 0.49, indicating that it is possible to push not just the lift
limits of the rotor, but also the forward speed limits with the use of leading-
edge slats.
The superimposition of TEFs and leading-edge slats shows that for three dif-
ferent slat configurations from 50-90%:fixed slats S6,and dynamic slat actuations
1 and 2,an additional power reduction of about 2% was possible by suitable TEF
deployments superimposed on slat actuation 2, for a net reduction of about 15% at
this flight condition.Again, the 1/rev input of the form −δ1psin(ψ) increases the lift
on the advancing side while offloading other parts of the disk, which translates into
a net power reduction.Increasing the 1/rev amplitude beyond 5◦ begins to degrade
performance.
175
6.4 My publications
6.4.1 Journal papers
(1) Open-Loop Control of Performance And Vibratory Loads Using Leading Edge
Slats, with Chopra, Inderjit, submitted to the Journal of the American Heli-
copter Society 61, 0320032016.
(2) Trailing-Edge Flaps for rotor performance enhancement and vibration reduc-
tion, with Chopra, Inderjit and Wake, Brian and Hein, Benjamin, Journal of
the AHS, 58.022006(2013).
6.4.2 Conference Papers
(1) Active Rotor Controls for Vibration Reduction and Performance Enhancement,
with Ananthan, Shreyas and Chopra, Inderjit and Hein, Benjamin, 23-44, AHS
Aeromechanics Specialists Conference, San Francisco, 20-22 January 2010.
(2) Active Flaps and Slats for Rotor Performance Enhancement, with Chopra,
Inderjit and Wake, Brian and Hein, Benjamin, 188-204, 67th American He-
licopter Society International Annual Forum 2011, Virginia Beach, 3-5 May
2011
(3) Active Control of Performance and Vibratory Loads using Leading Edge Slats,
with Chopra, Inderjit, 53rd AIAA/ASME/ASCE/AHS/ASC Structures, Struc-
tural Dynamics and Materials Conference, 20th AI, 23-26 April 2012, Hon-
176
olulu, Hawaii.
6.5 Future areas of research
While the concept of active rotor control using trailing- edge flaps has been
explored for several years now, it has not yet reached the point of being validated
for in-flight primary and vibration control.
This study has shown that TEFs are capable of vibration reduction and perfor-
mance improvement.Leading-edge slats are also shown to enhance the rotor thrust
in moderate to high-speed flight conditions and reduce power requirements at high
thrust levels.Experimental testing of the active rotor concept is key to the validation
of the analysis employed. The most immediate areas of interest are:
• Systematic experiments need to be conducted under actual flight conditions
to validate these results.
• Parametric studies for primary control using leading-edge slats to improve the
flight envelope.
• Posssibility of vibration reduction using leading-edge slats.
In the long term, other possible areas of interest are:
• Relaxing the assumption of single-degree of freedom flaps/slats to model them
as flexible structures.
• Development of a more complex aerodynamic model for unsteady motion of
an airfoil with arbitrary geometry, fitted with flaps/slats.
177
• Validation of the trailing-edge flaps in unsteady flight conditions is impor-
tant,since they are likely to be more tested under such conditions. Current
work is focused on steady level flight.
• Vibration and noise analyses need a more elaborate study of the acoustics and
fuselage low harmonics, rather than the rotor.
178
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