ABSTRACT
Title of dissertation: CFD/CSD STUDY OF INTERACTIONAL AERODYNAMICS
OF A COAXIAL COMPOUND HELICOPTER IN HIGH-SPEED
FORWARD FLIGHT
Vera Klimchenko, Doctor of Philosophy, 2020
Dissertation directed by: Professor James Baeder
Department of Aerospace Engineering
This work presents a computational study of the aerodynamic interactions that
arise between the components of a high-speed lift-offset coaxial compound helicopter
in forward flight. The objective of this study is to develop a computational method-
ology that would enable fundamental understanding of the complex aeromechanics
of a modern lift-offset coaxial compound rotorcraft configuration in it?s entirety.
The modeling of a helicopter is a coupled aeroelastic problem, in which the aerody-
namics is highly dependent on the structural dynamics, and vice versa. Therefore,
the prediction of the rotorcraft airloads and blade deformations must be performed
with sufficient fidelity to accurately model both aspects of the problem.
A high-fidelity computational fluid dynamics framework, HPCMP CREATETM -
AV Helios, was used in conjunction with an in-house comprehensive analysis solver,
to simulate a lift-offset coaxial compound helicopter in forward flight. A notional
X2TD helicopter consisting of a lift-offset coaxial rotor, airframe and an aft-mounted
propeller, was modeled in this work. An in-house comprehensive analysis solver,
PRASADUM, performed trim calculations and the structural modeling using low
order aerodynamics.
Conventionally, the comprehensive analysis rotor airloads that are computed
from the built-in low order aerodynamic models, would be corrected with the high-
fidelity CFD airloads using delta coupling procedure. In this study, the conventional
rotor delta coupling methodology was used to study the interactional aerodynamics
of a coaxial rotor system in forward flight at a range of flight speeds (50 knots
to 225 knots). This study also focused on extending this methodology to perform
high-fidelity airloads corrections for airframe and the propeller. The low order rotor,
airframe and propeller aerodynamic loads were corrected with the high-fidelity CFD
airloads, using a full vehicle loose delta coupling methodology. The two CFD/CSD
coupling approaches, rotor and full vehicle, were compared. The results showed that
correcting the low fidelity CSD airframe airloads with high-fidelity CFD airloads
affects the rotor trim solution.
The converged trim state from the full vehicle delta coupling procedure was
utilized to study the fundamental interactional aerodynamics between various com-
ponents of the coaxial compound helicopter. The CFD simulations were performed
for isolated helicopter components and component combinations.
CFD/CSD STUDY OF INTERACTIONAL AERODYNAMICS OF
A COAXIAL COMPOUND HELICOPTER IN HIGH-SPEED
FORWARD FLIGHT
by
Vera Klimchenko
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
2020
Advisory Committee:
Professor James Baeder, Chair/Advisor
Professor Anubhav Datta
Professor Inderjit Chopra
Professor Alison Flatau
Professor Kenneth Kiger
?c Copyright by
Vera Klimchenko
2020
For Mom, Dad and Mike.
ii
Acknowledgments
Foremost, I would like to express my deep appreciation and gratitude to my
family and my dearest friends. Thank you for supporting me on this wonderful
journey. Your overwhelming support and love sustained me throughout the years.
I am sincerely thankful for each and every one of you.
I am grateful to my Ph.D. advisor, Dr.James Baeder, for graciously granting
me the opportunity to perform research in his group and introducing me to the
complex world of computational fluid dynamics.
I would like to extend a heartfelt thank you to Dr.Anubhav Datta for his
guidance, motivation and support during the final stages of my graduate studies.
His constructive criticism and mentoring have been invaluable. He never ceased to
believe in me and my abilities, I will be forever grateful to him.
I would like to thank Dr.Alison Flatau for allowing me the opportunity to
conduct undergraduate research in her laboratory. It was a gateway to the world
of research and graduate studies. I would like to show my deep appreciation to
Dr.Anya Jones, my M.S. advisor, for teaching me the essential skills that I would
need to succeed as a graduate student. Also, I would like to thank Dr.Inderjit
Chopra for encouraging me to take the Helicopter Design course. This course was
truly a rewarding experience which changed my academic and research perspectives.
Finally, I would like to give my appreciation to the VLRCOE technical men-
tor, Dr.Mahendra Bhagwat, and the VLRCOE committee for supporting my Ph.D.
project and providing valuable constructive criticism.
iii
Table of Contents
List of Tables vii
List of Figures viii
Nomenclature xii
1 Introduction 1
1.1 Background and Motivation . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Summary of Previous Work . . . . . . . . . . . . . . . . . . . . . . . 9
1.2.1 Experimental Studies . . . . . . . . . . . . . . . . . . . . . . . 10
1.2.2 CFD/CSD Simulations - SMR Configurations . . . . . . . . . 13
1.2.3 CFD/CSD Simulations - Coaxial Rotor Configurations . . . . 16
1.3 Contributions of Present Research . . . . . . . . . . . . . . . . . . . . 20
1.4 Scope and Organization of Thesis . . . . . . . . . . . . . . . . . . . . 22
2 Notional High-Speed Coaxial Compound Helicopter 24
2.1 Coaxial Rotor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.2 Auxiliary Propulsor . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.3 Airframe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3 Comprehensive Analysis 37
3.1 Rigid Body Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.2 Aerodynamic Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.2.1 Fuselage Airloads . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.2.2 Empennage Airloads . . . . . . . . . . . . . . . . . . . . . . . 41
3.2.3 Auxiliary Propeller Airloads . . . . . . . . . . . . . . . . . . . 42
3.2.4 Coaxial Rotor System Airloads . . . . . . . . . . . . . . . . . 43
3.3 Structural Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.4 Rotor Controls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.5 Trim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.6 Trim Solution Method . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.7 Validation of the Notional X2TD Comprehensive Analysis Model . . 56
iv
4 Computational Fluid Dynamics 59
4.1 Governing Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.2 Reynolds Averaged Navier-Stokes Equations . . . . . . . . . . . . . . 62
4.3 CFD Solvers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.3.1 Coaxial Main Rotor - OVERFLOW . . . . . . . . . . . . . . . 65
4.3.2 Airframe and Propeller - FUN3D . . . . . . . . . . . . . . . . 66
4.3.3 Off-body - SAMCart . . . . . . . . . . . . . . . . . . . . . . . 69
4.4 Blade Motion and Deformation . . . . . . . . . . . . . . . . . . . . . 70
5 CFD/CSD Coupling Methodology 72
5.1 Rotor CFD/CSD Coupling . . . . . . . . . . . . . . . . . . . . . . . . 72
5.2 Full Vehicle CFD/CSD Coupling . . . . . . . . . . . . . . . . . . . . 74
5.3 CFD/CSD Coupling Validation . . . . . . . . . . . . . . . . . . . . . 77
6 Results Part I: Coaxial Rotor CFD/CSD Coupling 79
6.1 Main Rotor Controls and Vehicle Pitch Attitude . . . . . . . . . . . . 81
6.1.1 Rotor Collective (?0) and Fuselage Pitch . . . . . . . . . . . . 81
6.1.2 Cyclic Pitch ?1s and Cyclic Pitch ?1c . . . . . . . . . . . . . . 84
6.2 Blade Pitch and Flap . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
6.3 Rotor Airloads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
6.4 Coaxial Rotor Interactional Aerodynamics - 50 Knots . . . . . . . . . 93
7 Results Part II: Vehicle CFD/CSD Coupling 104
7.1 Trim Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
7.2 Main Rotor Blade Pitch and Flap . . . . . . . . . . . . . . . . . . . . 111
7.3 Main Rotor Airloads . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
7.3.0.1 Normal Force - Upper and Lower Rotor . . . . . . . 116
7.3.0.2 Chordwise Force - Upper and Lower Rotor . . . . . . 122
7.3.0.3 Pitching Moment - Upper and Lower Rotor . . . . . 124
7.4 Structural Blade Loads . . . . . . . . . . . . . . . . . . . . . . . . . . 130
7.5 Pusher Propeller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
8 Results Part III: Fundamental Understanding of Interactional Aero-
dynamics of Compound Coaxial Helicopter 136
8.1 Interactional Aerodynamics Affecting the Upper Rotor . . . . . . . . 138
8.2 Interactional Aerodynamics Affecting the Lower Rotor . . . . . . . . 143
8.3 Interactional Aerodynamics Affecting the Airframe . . . . . . . . . . 148
8.4 Interactional Aerodynamics Affecting the Auxiliary Propeller . . . . . 159
9 Conclusions 162
9.1 Summary of Research . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
9.2 Key Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
9.2.1 Coaxial Rotor CFD/CSD Coupling . . . . . . . . . . . . . . . 164
9.2.2 Results Part II: Vehicle CFD/CSD Coupling . . . . . . . . . . 165
v
9.2.3 Results Part III: Fundamental Understanding of Interactional
Aerodynamics of Compound Coaxial Helicopter . . . . . . . . 167
9.3 Recommendations for Future Work . . . . . . . . . . . . . . . . . . . 168
B Coordinate Systems 170
B Flow Visualization for Results Part I 172
C Flow Visualization for Results Part III 174
D Collective Sweep for Isolated Auxiliary Propeller and Airframe-
Propeller Combination 176
Bibliography 177
vi
List of Tables
2.1 The X2TD rotor system parameters . . . . . . . . . . . . . . . . . . . 25
2.2 The notional X2TD auxiliary propeller parameters [1]. . . . . . . . . 33
4.1 Grid spacing per level in terms of root chords for the off-body Carte-
sian mesh. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
6.1 Coaxial CFD/CSD coupling forward flight speeds. . . . . . . . . . . . 80
6.2 The final coaxial CFD/CSD controls and vehicle pitch attitude at
various speeds. The control angles and the vehicle pitch attitude are
shown in degrees. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
6.3 The final coaxial CFD/CSD controls and vehicle pitch attitude at
50 knots with interactional effects (Case 1) and without interactional
effects (Case 2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
7.1 CFD interactional aerodynamics case . . . . . . . . . . . . . . . . . . 105
7.2 Comparison between final coaxial CFD/CSD and full vehicle CFD/CSD
coupling at 150 knots. . . . . . . . . . . . . . . . . . . . . . . . . . . 107
7.3 Comparison between final coaxial CFD/CSD and full vehicle CFD/CSD
pitch deflection coupling at 150 knots. . . . . . . . . . . . . . . . . . 112
8.1 CFD interactional aerodynamics case . . . . . . . . . . . . . . . . . . 138
8.2 Mean auxiliary propeller thrust and power for three configurations at
150 knots. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
vii
List of Figures
1.1 A high-speed coaxial compound helicopter, Sikorsky-Boeing SB>1
DEFIANT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 A conventional single main rotor helicopter, Sikorsky UH-60 Black
Hawk. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 The limitations on a helicopter rotor which effect forward flight speed. 4
1.4 An example of edgewise velocity distribution around the rotor disk. . 4
1.5 Evolution of the Sikorsky coaxial aircraft. . . . . . . . . . . . . . . . . 7
1.6 Experimental testing of coaxial rotor configurations. . . . . . . . . . . 11
1.7 Hart II CFD/CSD study presented in Ref. [2] . . . . . . . . . . . . . 15
1.8 The iso-surfaces of vorticity from the CFD and VVPM simulations
presented by Jacobellis et al. in Ref. [3]. . . . . . . . . . . . . . . . . 18
2.1 A flight test of the Sikorsky X2 Technology Demonstrator Ref. [4]. . . 25
2.2 Sikorsky X2TD and XH59-A main rotor blade thickness distribution [5]. 27
2.3 Notional X2TD rotor blade. . . . . . . . . . . . . . . . . . . . . . . . 27
2.4 Notional X2 rotor blade parameters. . . . . . . . . . . . . . . . . . . 29
2.5 Main rotor RPM ratio for X2TD obtained from Ref. [5] and lateral
LOS obtained from Ref. [6]. . . . . . . . . . . . . . . . . . . . . . . . 31
2.6 Auxiliary propeller power required at 4K density altitude, obtained
from flight tests [6]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.7 Notional X2TD auxiliary propeller twist and chord distribution. . . . 34
2.8 Notional X2TD airframe. . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.9 Sikorsky X2TD during it?s first flight on August 27, 2008 [6]. . . . . . 36
3.1 The power validation for the notional X2TD. . . . . . . . . . . . . . . 57
3.2 The fanplot validation for the notional X2TD. . . . . . . . . . . . . . 58
4.1 Helicopter mesh system information. . . . . . . . . . . . . . . . . . . 64
4.2 Main rotor blade mesh. . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.3 Airframe near-body surface mesh. . . . . . . . . . . . . . . . . . . . . 68
4.4 Notional X2TD auxiliary propeller near-body surface mesh. . . . . . . 68
4.5 Mesh domain viewed from port side of the helicopter. . . . . . . . . . 69
5.1 Conventional, rotor CFD/CSD coupling schematic. . . . . . . . . . . 73
viii
5.2 Full vehicle CFD/CSD coupling schematic. . . . . . . . . . . . . . . . 75
5.3 Comparison of predicted CFD/CSD airloads with the wind tunnel
test data for UH-60A rotor. . . . . . . . . . . . . . . . . . . . . . . . 78
6.1 The coaxial CFD/CSD coupling mesh system and Q-criterion flow
visualization for coaxial rotor at 50 knots. . . . . . . . . . . . . . . . 80
6.2 The final coaxial CFD/CSD main rotor controls (a) and vehicle pitch
attitude (b) at various speeds. . . . . . . . . . . . . . . . . . . . . . . 82
6.3 Upper rotor and lower rotor tip pitch deflections for coaxial and full
vehicle CFD/CSD coupling at a range of forward flight speeds. . . . . 86
6.4 Upper rotor and lower rotor tip flap deflections for coaxial and full
vehicle CFD/CSD coupling at a range of forward flight speeds. . . . . 86
6.5 The upper rotor airloads for a range of speeds. . . . . . . . . . . . . . 88
6.6 The lower rotor airloads for a range of speeds. . . . . . . . . . . . . . 89
6.7 The upper(a) and lower(b) rotor sectional normal force for a range of
speeds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
6.8 The upper (a) and lower rotor (b) sectional pitching moment for a
range of speeds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
6.9 The upper and lower rotor normal force at 50 knots for interactional
and non-interactional case utilizing deflections from CSD0. . . . . . . 95
6.10 The upper and the lower rotor tip pitch and flap deflections for in-
teractional and non-interacting cases at 50 knots. . . . . . . . . . . . 97
6.11 The upper (a) and lower (b) rotor normal force at 50 knots for in-
teractional and non-interactional case at final CFD/CSD coupling
iteration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
6.12 The upper (a) and lower (b) rotor sectional normal force at 50 knots
for interactional and non-interactional case. . . . . . . . . . . . . . . 101
6.13 The upper and lower rotor pitching moment at 50 knots for interac-
tional and non-interactional case. . . . . . . . . . . . . . . . . . . . . 102
6.14 The upper (a) and lower (b) rotor sectional normal force at 50 knots
for interactional and non-interactional case. . . . . . . . . . . . . . . 103
7.1 Rotor controls and fuselage attitude convergence history for coax and
full vehicle CFD/CSD coupling at 150 knots. . . . . . . . . . . . . . . 108
7.2 Convergence of airframe loads at CG at 150 knots. . . . . . . . . . . 109
7.3 Pusher propeller thrust convergence at 150 knots. . . . . . . . . . . . 109
7.4 Upper rotor and lower rotor tip pitch deflections for coaxial and full
vehicle CFD/CSD coupling at 150 knots. . . . . . . . . . . . . . . . . 114
7.5 Upper rotor and lower rotor tip flap deflections for coaxial and full
vehicle CFD/CSD coupling at 150 knots. . . . . . . . . . . . . . . . . 114
7.6 Upper and lower rotor tip flap and pitch deflections for coaxial and
full vehicle CFD/CSD coupling at 150 knots. . . . . . . . . . . . . . . 115
7.7 Non-dimensional normal force distribution for upper rotor, rotating
counter-clockwise. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
7.8 Comparison of upper rotor sectional normal force at 150 knots. . . . . 119
ix
7.9 Non-dimensional normal force distribution for lower rotor, rotating
clockwise. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
7.10 Comparison of lower rotor sectional normal force at 150 knots. . . . . 121
7.11 Non-dimensional chordwise force distribution for upper rotor, rotat-
ing counter-clockwise. . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
7.12 Comparison of upper rotor sectional chordwise force at 150 knots. . . 124
7.13 Non-dimensional chordwise force distribution for lower rotor, rotating
clockwise. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
7.14 Comparison of lower rotor sectional chordwise force at 150 knots. . . 126
7.15 Non-dimensional pitching moment distribution for upper rotor, ro-
tating counter-clockwise. . . . . . . . . . . . . . . . . . . . . . . . . . 127
7.16 Comparison of upper rotor sectional chordwise force at 150 knots. . . 128
7.17 Non-dimensional pitching moment distribution for lower rotor, rotat-
ing clockwise. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
7.18 Comparison of lower rotor sectional pitching moment force at 150 knots.130
7.19 Upper and lower rotor flap bending moment obtained using coaxial
and full vehicle CFD/CSD coupling at 150 knots. . . . . . . . . . . . 131
7.20 Upper and lower rotor chord bending moment obtained using coaxial
and full vehicle CFD/CSD coupling at 150 knots. . . . . . . . . . . . 131
7.21 Time history of the upper and lower rotor torsion bending moment
obtained using coaxial and full vehicle CFD/CSD coupling at 150 knots.132
7.22 Convergence history for propeller power and collective. . . . . . . . . 135
8.1 Helicopter components and isolated parts interactional aerodynamic
study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
8.2 Aerodynamic interactions effects on the upper rotor. . . . . . . . . . 141
8.3 Pressure above the lower rotor at the disk plane of the upper rotor
at 150 knots. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
8.4 Upper rotor hubloads for various configurations shown in Fig. 8.2(a)
at 150 knots. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
8.5 Aerodynamic interactions effects on the lower rotor at 150 knots. . . . 145
8.6 The difference between the coaxial rotor system and the lower rotor,
the coaxial airframe combination and coaxial rotor system, helicopter
and coaxial airframe combination at 150 knots. . . . . . . . . . . . . 146
8.7 Lower rotor hubloads for various configurations shown in Fig. 8.5(a)
at 150 knots. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
8.8 Effect of blade passage on the pressure over the airframe 150 knots. . 152
8.9 The time-series and harmonic amplitudes of the airframe spanwise at
150 knots. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
8.10 The time-series and harmonic amplitudes of the airframe side force
at 150 knots. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
8.11 The time-series and harmonic amplitudes of the airframe normal force
at 150 knots. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
8.12 The time-series and harmonic amplitudes of the airframe roll moment,
positive starboard side up, about the center of lower hub at 150 knots.156
x
8.13 The time-series and harmonic amplitudes of the airframe pitching
moment, positive nose up, about the center of lower hub at 150 knots. 157
8.14 The time-series and harmonic amplitudes of the airframe yaw mo-
ment, positive counter-clockwise, about the center of lower hub at
150 knots. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
8.15 Auxiliary propeller airloads at 150 knots. . . . . . . . . . . . . . . . . 161
B.1 CSD body-axis frame of reference used for trim procedure. . . . . . . 170
B.2 CFD global axis, utilized for describing CFD airframe airloads. . . . . 170
B.3 Reference frame utilized for the non-dimensional deformed airloads,
used for delta coupling. . . . . . . . . . . . . . . . . . . . . . . . . . . 171
B.1 Iso-surfaces of q-criterion, shown for q = 6e?4, colored by the non-
dimensional vertical velocity, for 50 knot forward flight case. . . . . . 172
B.2 Iso-surfaces of q-criterion, shown for q = 6e?4, colored by the non-
dimensional vertical velocity. The right column shows the view of
from the top, while the left column shows the view from the starboard
side. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
C.1 Iso-surfaces of q-criterion, shown for q = 6e?4, colored by the non-
dimensional vertical velocity. . . . . . . . . . . . . . . . . . . . . . . . 174
C.2 Top view of the iso-surfaces of q-criterion, shown for q = 6e?4, col-
ored by the non-dimensional vertical velocity. . . . . . . . . . . . . . 175
D.1 Auxiliary propeller collective sweep for isolated and installed propeller
at various forward flight speeds. . . . . . . . . . . . . . . . . . . . . . 176
xi
Nomenclature
UT tangential velocity
r dimensional radial position
? rotor azimuth, degrees
V? Free-stream velocity
C M2n non dimensional deformed frame normal force
CmM
2 non dimensional deformed frame pitching moment
C 2cM non dimensional deformed frame chordwise force
nP Per rotor revolution
r/R Non dimensional blade radial station
? Density
?0, ?1c, ?1s Main rotor collective and cyclic pitch controls
Nb Number of rotor blades (per rotor)
R Rotor radius
M? Free-stream Mach number
xB, yB, zB Body frame axes
? Efficiency factor
AR Aspect ratio
a0 Lift curve slope
CD Lift induced dragi
E,F,G Flux Vectors
u, v, w Flow velocity components
? Ratio of specific heats
p Pressure
e Total energy
List of Abbreviations
CA Comprehensive Analysis
CCW Counter Clockwise Rotation
CW Clockwise Rotation
CFD Computational Fluid Dynamics
CSD Computational Structural Dynamics
RANS Reynolds-Averaged Navier-Stokes
SA Spalart-Allmaras
X2TD X2 Technology Demonstrator
GRP Sikorsky Generalized Rotorcraft Performance Methodology
LOS Lift-Offset
RPM Revolutions per minute
CG Center of gravity
SMR Single main rotor
xii
1 Introduction
1.1 Background and Motivation
The objective of this research is to expand the fundamental understanding
of the interactional aerodynamics of a high-speed coaxial compound helicopter. A
fundamental understanding of the interactional aerodynamics is critical for the de-
sign of the next generation vertical lift vehicles. The next generation multi-role
aircraft designs, such as the coaxial compound configurations shown in Fig.1.1 and
tilt-rotors, consist of various components that function together to achieve high-
maneuverability, high-speed cruise and efficient hover. A typical single main rotor
helicopter, shown in Fig.1.2, is not capable of achieving forward flight speeds ex-
ceeding 170 knots due to various limitations that arise during the high-speed flight
regime [7].
The two dominant limitations that prevent single main rotor helicopters from
achieving high-speed flight are the compressibility effects on the advancing side and
the reverse flow region on the retreating side, shown in Fig.1.3. The edgewise velocity
at a blade cross-section can be described using equation Eq.1.1. The edgewise
velocity at the blade is a function of the rotational speed of the rotor and the free-
stream velocity. The rotational speed of the rotor increases towards the tip. On
1
Figure 1.1: A high-speed coaxial compound helicopter, Sikorsky-Boeing SB>1 DE-
FIANT.
Figure 1.2: A conventional single main rotor helicopter, Sikorsky UH-60 Black Hawk.
2
the advancing side, the blades are advancing into the free stream, resulting in the
addition of vehicle airspeed and rotor rotational speed.
UT (r, ?) = ?r + V? cos(?S) sin(?) (1.1)
V? cos(?S)
? = (1.2)
?R
As the flight airspeed increases the addition of the rotational speed and the
vehicle speed leads to the development of localized regions of transonic flow near the
tip of the advancing blades. The compressibility effects include formation of shocks,
resulting in loss of lift and increase in drag. On the retreating side, the blade
advances with the free-stream resulting in the subtraction of the airspeed from the
rotational velocity. On the inboard stations of the retreating blades the free-stream
velocity is greater than the rotational velocity and the flow travels from the trailing
edge to the leading edge of the blade. This phenomena is called reverse flow and the
region on the blade where the flow is traveling from the trailing edge to the leading
edge is called reverse flow region. Further along the blade, the rotational velocity
becomes greater than the free-stream velocity and the flow travels in the nominal
direction from the leading edge to the trailing edge. The radius of the reverse flow
region is directly dependent on the advance ratio. The advance ratio of a helicopter
is given in Eq.1.2. Thus, as the flight speed increases the advance ratio increases
and the reverse flow region grows.
Inside the reverse flow region there is negative thrust and substantial drag
increase. In order for the retreating side to produce thrust, the sectional blade
3
Figure 1.3: The limitations on a helicopter rotor which effect forward flight speed.
Figure 1.4: An example of edgewise velocity distribution around the rotor disk.
4
angle of attack must increase. However, substantial increase in the sectional angle
of attack leads to stall and flow separation. Thus, there is a limit on the available
thrust produced by the retreating side of the rotor disk. The equilibrium of the
roll moment, for a single main rotor helicopter, is enforced from the balance of the
advancing side and retreating side roll moments. Therefore, the thrust produced by
the advancing side is limited by the the thrust capabilities of the retreating side.
The need for high-speed helicopters and the limitations of the conventional sin-
gle main rotor helicopters led to the innovation and the development of various viable
multi-rotor, compound options including a coaxial compound helicopter. Over the
past few decades substantial research was performed to realize the full potential of
the coaxial compound helicopters as means of increasing the speed envelope of the
rotary wing vehicles. The Sikorsky Advancing Blade Concept (ABCTM), discussed
in Ref. [8], was developed to maximize the lift of the advancing side of the rotor disk
and offload the retreating side by utilizing two, rigid counter-rotating coaxial rotors
with lift-offset. High flap stiffness allows for the reduction of the rotor separation
distance and maintenance of the required blade clearance. Unlike a single rotor
configuration, where roll moment is achieved by the advancing and retreating sides
of the rotor disk, the ABCTM configuration achieves the roll moment equilibrium by
utilizing the advancing sides of both rotors. For an ABCTM rigid helicopter rotor,
the thrust requirement is met while simultaneously maintaining vehicle rolling mo-
ment balance by exploiting the increased dynamic pressure on the advancing sides of
each rotor to produce lift. Thus, most of the lift can be carried on the advancing side
of the rotor, offloading the retreating side, and reducing the severity of retreating
5
blade stall.
The Sikorsky X2 Technology Demonstrator (X2TD) successfully utilized the
ABCTM concept and other design methodologies to reach speeds beyond 200 knots.
In Ref. [5], Bagai discusses the methodology used for the design of the X2TD main
rotor blades and the improvements that the new design had on the aerodynamic
efficiency of the rotor at high speeds. The new design attributes included modern
airfoils, non-uniform planform, variable twist gradients and thickness. An external
auxiliary propeller provides the required propulsive force at high speeds, allowing for
the decrease in main rotor RPM and alleviation of the compressibility effects on the
advancing side [5]. The development of the Sikorsky X2TM Technology Demonstrator
(X2TD) showed that a coaxial helicopter has a capability to achieve higher maximum
forward flight speeds, while still maintaining hover and low speed efficiencies [1, 5,
6]. Further modifications and improvements to the Sikorsky X2TD coaxial aircraft
have led to the evolution and the new development of the Sikorsky S-97 Raider
Demonstrator and the Sikorsky-Boeing SB>1 DEFIANT, shown in Figs.1.5(b), (c)
and (d), respectively.
The flow field around the helicopter is complex due to the aerodynamic inter-
actions between various components and their wakes. The addition of the second
rotor and the auxiliary propeller further increases the complexity of the flow field
around the vehicle. Similarly to a conventional single main rotor helicopter, there
exist aerodynamic interactions between the rotor and the fuselage as well as the
blades and the trailing vortices. Additional interactions arise between the stacked
rotors. The performance of the empennage and the auxiliary propeller is affected
6
(a) Sikorsky S-69/XH-59A. (b) Sikorsky X2 Technology Demonstrator.
(c) Sikorsky S-97 Raider Demonstrator. (d) Sikorsky-Boeing SB>1 DEFIANT.
Figure 1.5: Evolution of the Sikorsky coaxial aircraft.
7
by the fuselage and rotor wake. Often times these components require additional
modifications in order to function in the complex environment. Thus, thorough
understanding of these interactions and their implications on the performance and
the vibrations is crucial for the design and the testing of the aircraft. The interac-
tional aerodynamics between the vehicle components must be considered in order
to accurately predict the rotor performance, vehicle vibrations and aeroelastic blade
response. Advanced simulations and experimental techniques are necessary to accu-
rately model the interactional aerodynamics and predict stability and performance
of the next generation vehicles.
The prediction of rotorcraft loads is inherently an coupled aeroelastic problem
that requires precise modeling of the aerodynamics and structural dynamics of the
vehicle, which are interdependent [9]. The trim solution and the modeling of the
rotor blade structural dynamics is performed in a comprehensive analysis (CA)
solver.
Numerous comprehensive analysis solvers as well as other special purpose
codes have been developed over the years in industry, government and academia to
study rotorcraft systems: CAMRAD [10], RCAS [11], DYMORE [12], UMARC [13],
CHARM [14], PRASADUM [15], etc. A typical comprehensive analysis solver relies
on the low-fidelity aerodynamic models to predict the blade sectional aerodynamic
loads. These low-order aerodynamic models are incapable of accurately predicting
the dynamic stall effects on the retreating side and 3D compressibility effects on the
advancing side. The inaccuracies in the predictions of the airloads tend to propa-
gate into the calculation of the structural blade loads [16]. The correction of the
8
CSD airloads with the high-fidelity CFD airloads, known as the CFD/CSD cou-
pling, improves airloads prediction which improves the accuracy of the structural
blade loads. Over the past few decades the CFD/CSD coupling methodology has
become a trusted tool in the rotorcraft community for the analysis of the complex
rotorcraft problems.
1.2 Summary of Previous Work
Numerous efforts have been made to analyze and understand the high-speed
coaxial compound helicopter design and the influence of aerodynamic interactions
on the blade loads, the performance and the vibrations. Quite a few experimental
studies were performed to analyze the performance of coaxial configurations in hover
and level flight. However, the experimental studies do not provide detailed infor-
mation regarding unsteady sectional airloads. Various studies focused on studying
the rotor-rotor aerodynamics utilizing CFD/CSD coupling methodology to correct
the low order rotor airloads within the comprehensive analysis solvers. Often times
these studies only included isolated coaxial rotor system in the CFD simulations,
without the airframe. Other studies focused on simulating full vehicle in the CFD
and exchanging only the rotor airloads in the CFD/CSD coupling procedure. This
work focuses on extending the CFD/CSD methodology to correct the airframe and
auxiliary propeller airloads in the CSD solver, as well as to trim the auxiliary pro-
peller. The objective of the extended methodology is to obtain high-fidelity full
vehicle trim solution and to gain fundamental understanding of the full vehicle
9
interactional aerodynamics for a high-speed coaxial helicopter. The following sub-
sections will present selected prior works related to the experimental studies and
modeling of interactional aerodynamics on in the rotary-wing vehicles as well as the
high-fidelity numerical studies pertaining high-speed coaxial compound helicopters.
1.2.1 Experimental Studies
Numerous experimental studies have been performed to investigate the effi-
ciency of the coaxial rotor system in hover. Most of these experimental studies
focused on quantifying the performance of the coaxial rotors in hover. Harrington
(1951) performed wind tunnel tests in the Langley full-scale wind tunnel to inves-
tigate the static-thrust performance of a coaxial rotor system in hover [17]. The
results from the wind tunnel tests compared well with the theoretical calculations
for a single main rotor of equivalent solidity. McAlister and Tung (2006) measured
the hover performance of a small-scale coaxial rotor, varying the rotor separation
distance and the proximity to the ground [18]. In 2014, Cameron et al. built and
conducted hover experiments for a Mach-scaled rigid coaxial rotor system. The dy-
namic hub loads and the pushrod loads were compared for a single rotor, two-bladed
and four-bladed coaxial rotor configurations [19].
Limited number of experiments have been performed for coaxial rotors in for-
ward flight and only few experiments included the full vehicle. Dingeldein (1954)
performed wind tunnel tests and quantified the power requirements of coaxial and
tandem rotor systems in static thrust and level flight conditions [20]. The per-
10
(a) Full-scale Harrington coaxial rotor in the Lan- (b) Full-scale rigid (ABC) coaxial rotor system
gley wind tunnel [17] in NASA Ames 40- by 80-Foot wind tunnel [21]
(c) Rigid two-bladed coaxial rotor in the Glenn (d) A 1/5 scale compound coaxial helicopter
L. Martin wind tunnel [19] tested in the NFAC wind tunnel [26]
Figure 1.6: Experimental testing of coaxial rotor configurations.
11
formance of the multi-rotor configurations was compared with an equivalent single
rotor and theoretical calculation. The experiments showed that the coaxial rotor
in forward flight required more power than a single rotor with equivalent solidity.
Performance data was obtained for an ABC coaxial rigid rotor system during the
wind tunnel tests at the 40- by 80-Foot NASA Ames wind tunnel [21], [22]. Felker
(1981) described the testing of the full-scale coaxial compound X-H59A helicopter
in the 40- by 80-Foot NASA Ames wind tunnel [23]. The wind tunnel tests were
performed for the full vehicle configuration as well as the isolated components and
the component combinations. Cameron and Sirohi (2016) performed wind tunnel
tests in the Glenn L. Martin wind tunnel for a rigid untwisted two-bladed coaxial
rotor [24]. The blade clearance, steady and vibratory hubloads were measured in
that experiment. Lorber et al. presented results from a wind tunnel test of a scaled
compound coaxial helicopter [25]. The forces and moments on various helicopter
components were measured. Figure 1.6 shows various experiments performed for a
coaxial rotor configurations.
Only limited information is available regarding the flight tests performed for
coaxial compound helicopters. Most of the data from the flight tests has not been
publicly released. The XH-59A flight test program, spanning from 1973 to 1981,
was focused on demonstrating the feasibility of the XH-59 coaxial compound heli-
copter configuration [27]. The Ka-32 helicopter flight tests were conducted by the
to investigate the coaxial rotor wake using smoke flow visualizations and high-speed
imagery [28]. The Sikorsky X2 Technology Demonstrator flight tests, conducted
between 2008 and 2011, showed that the high-speed limitations can be overcome
12
with a compound coaxial helicopter [6].
The aforementioned wind tunnel and flight tests provide useful knowledge re-
garding the performance of the coaxial rotor system and the time-averaged loads
experienced by the vehicle. However, substantial instrumentation and complex se-
tups are required to obtain the unsteady loads, aerodynamic as well as structural,
along the rotor blade span at various azimuthal locations.
1.2.2 CFD/CSD Simulations - SMR Configurations
Extensive work has been performed in the area of CFD/CSD coupling applied
to single main rotor configurations [29]. The availability of flight test data and ex-
perimental data for the UH-60A and HART-II configurations allowed for validation
of the CFD/CSD coupling methodologies and expansion of these methodologies to
other single main rotor configurations. Coupling high-fidelity rotor CFD and CSD
significantly improved predictions of the airloads and structural loads for a single
main rotor configurations for a range of operating conditions.
Datta et al. showed that CFD/CSD coupling improved the prediction of the
unsteady transonic pitching moment at high forward flight speeds for a UH-60A
rotor [30]. Improvement in the UH-60A torsional load predictions, using CFD was
also observed [16]. Potsdam showed that CFD/CSD accurately capture blade-vortex
interactions for UH-60A in a low speed flight [9]. However, these rotor CFD/CSD
studies included only the rotor in the CFD simulations and neglecting the airframe.
Over time the capabilities of the CFD/CSD coupling methodologies have increased
13
dramatically to include the whole vehicle in the CFD simulations utilized for the
CFD/CSD studies. Numerous attempts have been made to perform full vehicle
CFD/CSD coupling studies of single main rotor helicopters.
Various researchers have successfully studied the acoustics and interactional
aerodynamics of the HART-II configuration using CFD/CSD coupling methodology
[2], [31], [32], [33]. The HART-II case consists of a single main rotor mounted
on top of a fuselage-shaped fairing supported by a sting, shown in Fig.1.7(a). A
typical mesh used in the CFD simulations, representing the HART-II configuration,
is shown in Fig.1.7(b). For the HART-II configuration, the presence of the fuselage
effected the blade vortex interactions on the advancing side of the rotor disk. The
UH-60A simulations have also increased in complexity. The CFD/CSD simulations
were modified to include the UH-60 airframe and in some cases the tail rotor [34].
Embacher et al. (2010) performed a helicopter CFD/CSD feasibility study,
coupling in the time-averaged airframe airloads in addition to the unsteady rotor
airloads for the Eurocopter EC145 helicopter [35]. The EC145 helicopter consisted
of a single main rotor, a tail rotor, airframe and skids. Embacher et al. showed that
there were significant fluctuations in airframe pitching moment and lateral force,
which affected the final trim state of the helicopter.
Lorber, Min and Zhao (2019) analyzed the unsteady tail interactions and the
rotor-fuselage flow field, on the S-92 helicopter configuration, using STAR-CCM+
and CREATE-AV Helios CFD simulations [26]. The rotor was trimmed, using
RCAS, to match the rotor flapping from the experiments. The authors showed that
the blade tip vortices and the retreating blade stall vortices introduce additional
14
(a) Hart II experiment.
(b) Hart II mesh.
Figure 1.7: Hart II CFD/CSD study presented in Ref. [2]
15
harmonics into the empennage loads. This study did not couple the high-fidelity
CFD airframe airloads back into the CSD solver.
Roget et al. (2019) studied the effect of performing full vehicle CFD/CSD
coupling for a single main rotor helicopter, UH-60A, using CREATE-AV Helios and
RCAS [36]. Roget demonstrated the feasibility of performing full vehicle CFD/CSD
coupling and correcting the low order airframe airloads with high-fidelity CFD re-
sults.
1.2.3 CFD/CSD Simulations - Coaxial Rotor Configurations
The high-fidelity CFD/CSD coupling studies pertaining to lift-offset coax-
ial rotors, especially in high-speed forward flight, are not as common as the SMR
CFD/CSD studies described above. Only limited experimental data is available for
the lift-offset coaxial rotor making it more challenging to validate the CFD/CSD
coupling methodologies for coaxial rotors. The complexity that arises from the ad-
dition of multiple rotors in both the CFD and CSD simulations also play a factor.
Nevertheless, in the past few years various CFD/CSD studies were performed to
study the aerodynamics of coaxial rotors.
Passe (2015) conducted a CFD/CSD study, utilizing CREATE-AV Helios and
an in-house comprehensive analyzing code PRASADUM, to study interactional aero-
dynamics of a notional X2TD coaxial rotor system at 55, 100 and 150 knots [37].
Passe showed that CFD/CSD captured an 8P impulsive change in normal force and
pitching moment caused by the blade crossings. In this study the coaxial rotor was
16
trimmed using propulsive trim methodology in PRASADUM and only the coaxial
rotor was present in the CFD simulations. The CSD low order aerodynamic airloads
were corrected using the high-fidelity CFD airloads. Klimchenko (2017) expanded
this work to higher forward flight speeds, 200 and 225 knots [38].
Jacobellis et al. (2018) used a dynamic inflow model, Viscous Vortex Particle
Method (VVPM) and the high-fidelity CFD/CSD coupling to predict the airloads
on the coaxial rotor at a high-advance advance ratio of ? = 0.66 [3]. A wind tunnel
trim of the coaxial rotor was performed using RCAS. The iso-surfaces of vorticity
from the CFD and the VVPM simulations are shown in 1.8. The physics-based
models, VVPM and high-fidelity CFD, were able to captured the 8P blade-blade
interactions. However, VVPM and dynamic inflow model rely on the tabulated 2D
airfoil data and are unable to accurately predict the aerodynamic phenomena in the
reverse flow region. The CFD simulations captured the effects of the reverse flow
region on the airloads.
Jia and Lee (2019) utilized high-fidelity CFD/CSD coupling, CREATE-AV
Helios coupled with RCAS, to study the acoustic signature of the coaxial helicopter
at 100, 150 and 200 knots [39]. The study showed that there is an increase in
impulsive sound-pressure level for coaxial rotor with lift-offset. Authors noted that
the shaft angle was fixed at zero for this study and there may be variations in
impulsive acoustics with different shaft angles.
Additional studies were performed using CFD/CSD methodology which in-
cluded the full vehicle geometry in the CFD, without coupling in the airframe air-
loads into the CSD, applied to multi-rotor vehicles. Bhagwat et al.(2008) studied
17
(a)
Figure 1.8: The iso-surfaces of vorticity from the CFD and VVPM simulations
presented by Jacobellis et al. in Ref. [3].
airloads, blade loads and vehicle performance of a duel-rotor CH-47 helicopter us-
ing CFD/CSD coupling methodology [40]. The vehicle fuselage was modeled in the
CFD simulations. Trim calculations and structural modeling was performed using
RCAS, while the fluid dynamic simulations were performed using OVERFLOW.
The comprehensive analysis airframe airloads were not corrected with the airloads
from CFD solution.
Zhao, Brigley and Modarres (2019) compared high fidelity CFD/CSD vibra-
18
tory hub loads and blade loads of the S-97 RAIDER, in low speed transition flight, to
2016 and 2017 flight test data [41]. The propeller was not operation and the propul-
sive force was generated by the rotors during these flight tests. The blade deflections
were modeled using the Rotorcraft Comprehensive Analysis System (RCAS) [11].
Both rotors were trimmed to time-averaged vertical force and pitch/roll moments
obtained from the actual flight test. Since previous studies showed that the flexibil-
ity of the airframe did not have significant effect on the vibratory loads, flexibility
of the airframe was ignored and rotor hubs were independently connected to the
ground. The CFD simulations included coaxial rotor system, rotor hubs and the
fuselage (excluding the empennage and the pylon). Only airloads from the coaxial
rotor were coupled with CSD. The authors correctly predicted the upper and lower
rotor 3P blade normal bending moments but underpredicted the 5P blade normal
bending which lead to the underprediction of the peak 4P hub moment.
Bowles et al. (2019) studied interactional aerodynamics of a full-vehicle, S-97
RAIDER aircraft, using a commercial unstructured solver (STAR-CCM+) [42]. The
main rotor and the auxiliary propeller blades were modeled using the Virtual Blade
Model (VBM) which is an embedded blade-element method model in STAR-CCM+.
The simulation results were compared with wind-tunnel and flight test data. The
presence of spinning hubs results in large increase in the unsteady yaw moment due
to the coupling of lower rotor hub wake with pylon wake structures.
Anusonti-Inthra (2019) studied the effects of the fuselage on the performance of
a conceptual coaxial compound rotorcraft at two moderate advance ratios, ? = 0.234
and ? = 0.0.292, using loose CFD/CSD coupling methodology [43]. The CFD
19
simulation included coaxial rotor system, rotor hubs, fuselage, canards, stabilizers
and ducted fan shrouds. Rotor structural dynamics were modeled with RCAS.
The rotor blade airloads from Helios/FUN3D were coupled to RCAS, airloads from
the fuselage were not coupled between CFD and CSD. The study found that the
presence of the fuselage significantly effected the lower rotor flap bending moment
on the retreating side as well as the blade vertical load harmonics. However, the
presence of the fuselage did not have significant effects on the final trim parameters.
The coaxial vehicle CFD/CSD studies mentioned above included the airframe
geometry in the CFD simulations but did not correct the CSD airframe airloads with
the high-fidelity airframe airloads from CFD. In 2016 Passe et al. performed a unique
CFD/CSD study focused on studying the effect of the rotor-airframe interactional
aerodynamics for a coaxial compound helicopter [44]. His objective was to couple
in the time-averaged airframe airloads into the CSD. This CFD/CSD study showed
that correcting the CSD airframe airloads with CFD airloads changed the final trim
state of the coaxial rotor due to additional moments produced on the airframe by
interactional aerodynamics. This study did model the auxiliary propeller in the
CFD and neglected the auxiliary propeller in the CFD/CSD coupling.
1.3 Contributions of Present Research
The literature survey of the previous work shows that there is a substantial lack
of high-fidelity CFD/CSD studies pertaining to the high-speed coaxial compound
helicopter with lift-offset. Most of the studies discussed did not utilize full vehicle
20
CFD/CSD methodology to predict the trim state and the performance of the vehicle.
Only one study, Ref. [44], corrected the coaxial helicopter airframe CSD airloads with
high-fidelity CFD airframe airloads. However, this CFD/CSD study did not account
for interactional aerodynamics on auxiliary propeller. The present research will show
the importance of correcting both, the airframe and propeller CSD airloads, with
the high-fidelity CFD airloads and the effect of inter-component aerodynamics on
the final trim state of the vehicle.
The objective of the present research is to extend the full vehicle CFD/CSD
coupling procedure to a high-speed coaxial helicopter and to fill in the gap that exists
in literature that pertains to interactional aerodynamics of the coaxial compound
helicopter using high fidelity full vehicle CFD/CSD coupling procedure.
1. Develop full vehicle CFD/CSD coupling methodology for a high-speed coax-
ial compound helicopter. Include the correction of time-averaged airframe
airloads and auxiliary propeller power in the comprehensive analysis. Simul-
taneously trim the propeller to mandatory power, correcting CSD propeller
power with CFD power. Identify and analyze the effect of the interactional
aerodynamics on the final trim state of the vehicle, structural blade deforma-
tion and hub loads.
2. Develop a fundamental understanding of interactional aerodynamics of a high-
speed coaxial compound helicopter. Systematically compare the vehicle com-
ponent airloads, in isolation and in installed configuration, to identify and
analyze the effects of components on one another.
21
3. Characterize the lift-offset high-speed coaxial rotor propulsive trim variable
trends, airloads and structural deformation for a range of advance ratios. Un-
derstand the effect of lift-offset on the airloads and structural blade deforma-
tions.
The intent of this study is to develop the computational tools and gain fundamental
insights into the complex aeromechanics of a modern lift-offset coaxial compound
rotorcraft.
1.4 Scope and Organization of Thesis
The current chapter focused on giving the reader an overview of the limita-
tion of a high-speed single main rotor helicopter and convincing the reader that the
coaxial compound helicopter can overcome these limitation. The complex interac-
tional aerodynamic environment that arises in the vicinity of the coaxial compound
helicopter components was described. The high-fidelity numerical methodologies
that are needed to accurately simulate the compound helicopter were introduced.
Prior work which utilized the high-fidelity methodologies for single main rotor and
a coaxial rotor was discussed.
Following this introduction, the second chapter describes the notional heli-
copter studied in the present research and gives physical description of the helicopter.
The third chapter discusses the in-house computational structural dynamics solver,
PRASADUM. The coaxial compound helicopter trim equations and the modeling
of the structural blade dynamics are also discussed. The third chapter examines
22
the computational fluid dynamics framework, CREATE-AV Helios, and discusses
the individual solvers used in this study. It also gives a brief overview of the fun-
damental fluid dynamics equations that are solved. The fourth chapter discusses
the conventional and the full vehicle CFD/CSD coupling methodology used for the
research and provides validation for the CFD/CSD methodology using a well known
UH-60A rotor case which was part of the UH-60A Airloads Workshop efforts.
The results are presented in three chapters, chapter five through chapter seven.
The first part of the results, chapter five, focuses on studying the individual com-
ponents of the vehicle at various speeds. The coaxial rotor system is analyzed at
various speeds using conventional rotor CFD/CSD coupling methodology. The con-
verged trim states, airloads and blade deformations are analyzed and compared for
various speeds. The vehicle airframe is also analyzed at various speed and the force
breakdown on various components of the airframe is shown. The next chapter, chap-
ter six, focuses on comparing the full vehicle CFD/CSD coupling methodology with
the rotor CFD/CSD coupling methodology. The final trim variables and rotor air-
loads are compared. The CSD predicted airframe airloads are also compared to the
CFD predicted airframe airloads. The last results chapter, chapter eight, focuses on
systematically increasing the complexity of the simulations to understand the funda-
mental aerodynamic interactions that occur between different vehicle components.
Chapter nine summarizes the research, provides key conclusions and recommends
future work.
23
2 Notional High-Speed Coaxial Compound Helicopter
This chapter describes the helicopter configuration modeled in this work. The
helicopter modeled in this study is a Sikorsky X2 Technology Demonstrator (X2TD),
shown in Fig.2.1. The X2TD is a 6000-lb class compound coaxial helicopter designed
to operate at high forward flight speeds greater than 200 knots. This helicopter
configuration consists of a coaxial rotor system, airframe and an auxiliary propeller.
The parameters for the notional X2TD coaxial rotor system and the airframe used
for this study were approximated by Passe in Ref. [45] to closely match the publicly
available data from flight tests in Refs. [1], [5], [6]. Because the helicopter parameters
modeled in this study were estimated from publicly available data, the helicopter is
referred to as ?notional? X2TD. The rotor swashplate, rotor hub fairings and the
blade root cutout regions are not modeled in this study. The following sections will
describe the components of the notional X2TD helicopter utilized in this study.
2.1 Coaxial Rotor
The X2TD coaxial rotor system consists of eight blades, four blades per rotor,
with upper rotor rotating counter-clockwise and the lower rotor rotating clockwise.
All eight blades are identical. The rotor parameters are given in the Table 2.1. The
24
Figure 2.1: A flight test of the Sikorsky X2 Technology Demonstrator Ref. [4].
Table 2.1: The X2TD rotor system parameters
Parameter Value Units
Number of rotors 2
Number of blades per rotor 4
Radius 13.2 ft
Rotor Vertical Separation 1.5 ft
Root chord 0.687 ft
Rotation Speed - Hover to 200 knots 446 RPM
Rotation Speed - 280 knots 360 RPM
25
radius of the main rotor is 13.2 feet with root cutout of 1.5 feet. The rotor blades
of the Sikorsky X2TD rotor were designed, using the Sikorsky Generalized Rotor
Performance (GRP) methodology, to improve rotor aerodynamic performance at
high-speeds without compromising hovering efficiency or low speed cruise charac-
teristics [5].
The names of the airfoil sections utilized for the actual X2TD blade were
not publicly released. Thus, only limited information is available about the X2TD
airfoils and their selection. Reference [5] briefly discusses the airfoil selection process
and compares the thickness of the X2TD rotor blade to the XH-59A rotor blade,
shown in Fig.2.2. The airfoil cross-sections along the notional X2TD blade, shown
in Fig.2.3(a), were selected in Ref. [45] to closely resemble the actual X2TD blade
and to satisfy the blade design requirements discussed in Ref. [5]. The notional
X2TD rotor blade, utilized in this study and shown in Fig.2.3(a), was assembled by
Passe in Ref. [45].
The actual X2TD rotor blade consists of proprietary thick double-ended airfoil
on the inboard sections of the blade [5]. At high-speeds, there is a large reverse flow
region on the retreating side of the X2TD rotor disk, where the air travels from
the trailing edge to the leading edge of the airfoil, resulting in separation and an
increase in drag. Compared to a sharp trailing edge airfoil, the double-ended airfoil
sees reduced reverse flow separation which minimizes the reverse flow penalties. A
double-ended Sikorsky DBLN-526 rotorcraft airfoil was selected and modified for the
in-board sections of the notional X2TD rotor blade. The modified DBLN-526 airfoil
26
Figure 2.2: Sikorsky X2TD and XH59-A main rotor blade thickness distribution [5].
(a) Notional X2TD airfoil profiles.
(b) Airfoil distribution.
Figure 2.3: Notional X2TD rotor blade.
27
extends from the root to 33%R of the rotor blade. An unspecified conventional
sharp trailing edge airfoil was incorporated in transition from the double-ended
airfoil at the root to the advanced transonic airfoils on the outboard stations of the
actual X2TD rotor blade. The blade tip on the advancing side of the rotor disk
operates in transonic flow during high-speed flight, which results in compressibility
effects and performance penalties. A choice of airfoil cross-section is crucial in this
region of the blade. An advanced transonic airfoil, Sikorsky SSC-A09, was chosen for
the tip of the notional X2TD rotor blade, while a Sikorsky SC1012-R8 was selected
for the transition region of the notional X2TD rotor to ensure smooth blend between
the blunt and the sharp trailing edge airfoil profiles near the midspan.
Take note that Fig. 2.3(a) shows the start of true airfoil sections of the no-
tional X2TD blade described above. In between the demarcation lines the airfoils
are automatically interpolated, in the blade mesh generator, for smooth transition
between the adjacent airfoil profiles, as shown in Fig.2.3.
Figure 2.4(b) shows the non-linear chord distribution along the span of the
notional X2TD rotor blade. The rotor blade chord increases towards the outboard
stations of the blade for 70%R. The studies of the XH-59A blades have shown
that the 2:1 taper ratio resulted in the high retreating blade drag on the inboard
stations of the retreating blades. Therefore, the X2TD blades were designed with
a non-linear taper and the redistribution of the blade area towards the outboard
sections.
Figure 2.4(c) shows the bi-linear twist distribution of the notional X2TD rotor
blade. The positive twist gradient, on the inboard stations the blade, reduces the
28
(a) Notional X2TD blade planform
(b) Notional X2TD blade chord
(c) Notional X2TD blade twist
Figure 2.4: Notional X2 rotor blade parameters.
29
negative lift on the in-board sections of the retreating blade by aligning the inboard
sections with the local incident velocity. The twist slope transitions from positive
to a conventional negative slope near 40%R.
In addition to the advanced blade design, main rotor RPM and LOS schedul-
ing were implemented on the X2TD main rotor to improve the high-speed cruise
efficiency. The main rotor RPM remained constant up to flight speeds of 200 knots.
Beyond flight speeds of 200 knots the main rotor RPM was reduced such that 20%
reduction was achieved at 280 knots and the advancing tip Mach number remained
below 0.9. Figure 2.5(a) shows the rotor RPM ratio for a range of cruise speeds.
The rotor RPM ratio data was digitized from Ref. [5]. The RPM of the main rotor
is reduced with increase in advance ratio to reduce the compressibility effects on
advancing blade tip.
Figure 2.5(b) shows the LOS data as a function of flight speed. The LOS data
shown in Fig.2.5(b) in blue was digitized from X2TD flight tests discussed in detail
in Ref. [6]. The high levels of scatter are present in the test data, which may be due
to different flight conditions and regimes discussed in Ref. [6]. A linear line of fit was
used to approximate the LOS data, which is consistent with how other researchers
have treated this data [46]. The LOS scheduling is utilized to take advantage of the
full potential of the advancing side of the rotor disk. The LOS is a measure of the
displacement of thrust vector from the center of rotation.
30
(a) Main rotor RPM ratio for various cruise speeds.
(b) Main rotor lateral LOS for various cruise speeds.
Figure 2.5: Main rotor RPM ratio for X2TD obtained from Ref. [5] and lateral LOS
obtained from Ref. [6].
31
2.2 Auxiliary Propulsor
This section discusses the notional auxiliary propeller utilized in this work. A
six bladed auxiliary propeller, with a radius of 3.33 feet, provides the propulsive force
for the X2TD helicopter traveling at high cruise speeds. There is limited informa-
tion available to the public regarding the geometry of the X2TD auxiliary propeller.
Table 2.2 shows the propeller parameters given in Ref. [1] as well as assumed param-
eters. The propeller and the main rotor operate on a common drivetrain, therefore
the RPM of the propeller is also reduced at high speeds, similarly to the main rotor.
The required auxiliary propeller power, at 4000 feet density altitude, was digitized
from Ref. [46] and is shown in Fig.2.6.
The photographs of the X2TD helicopter show the propeller to have high non-
linear twist and variable planform. However, due to lack of information regarding the
exact blade geometry, various assumptions had to be made to model the propeller
in the simulations. The notional pusher propulsor was modeled in this study as a
six bladed propeller, with linear twist, constant chord and NACA0012 airfoil along
the span. A linear twist for the notional X2TD propeller is shown in Fig.2.7. The
propeller was designed with high twist to increase the angle of attack on the inboard
stations of the blade. The angle of attack on the inboard stations of the propeller
blade in high-speed cruise condition is reduced due to high inflow velocity. The radial
chord distribution is shown in Fig.2.7(b). A simple constant chord distribution was
chosen for the notional X2TD auxiliary propeller. The blades are treated as rigid
without any elastic deformations.
32
Figure 2.6: Auxiliary propeller power required at 4K density altitude, obtained from
flight tests [6].
Table 2.2: The notional X2TD auxiliary propeller parameters [1].
Parameter Value Units
Number of blades 6
Radius 3.33 ft
Root chord (notional) 0.50 ft
Root-cutout (notional) 0.67 ft
Rotation Speed - Hover to 200 knots 2529 RPM
Rotation Speed - 280 knots 2041 RPM
33
(a) Auxiliary propller twist distribution.
(b) Auxiliary propller chord distribution.
Figure 2.7: Notional X2TD auxiliary propeller twist and chord distribution.
2.3 Airframe
This section describes the airframe of the notional X2TD helicopter utilized
in this study. The airframe of the notional X2TD helicopter resembled the actual
34
Sikorsky X2TD, shown in Fig, with few exceptions. The notional airframe consists
of a cigar shaped fuselage, empennage, mast and pylon, shown in Fig.2.8. All of
the airframe components are very smooth, without any protrusions. The rotor hub
fairings and rotor hubs not modeled in this study. The airframe CAD was assembled
by Passe in [45].
The fuselage, shown in gray in Fig.2.8, is modeled as a smooth surface without
any protrusions. The fuselage is 30.6 feet long. At it?s maximum thickness, near
the cockpit of the vehicle, the fuselage has a height of 4.9 feet. The flat plate drag
area for the fuselage, given in Ref. [46], is 4.6 feet squared. The rotor shaft, shown
in green in Fig.2.8, is modeled as a cylindrical non-rotating mast with diameter of
0.9 feet. It extends from the top of the pylon to the upper rotor hub plane.
The empennage is composed of two horizontal stabilizers, shown in red in
Fig.2.8, and a vertical tail, shown in blue. The horizontal tails of the notional
X2TD resemble the horizontal tails on the actual X2TD helicopter during it?s first
flight shown in Fig. [6]. The equivalent flat plate surface area of the combined hor-
izontal tails is 34 feed squared [37]. The actual aircraft included ground adjustable
horizontal tail pitch incidence, as described in Ref. [1], however in this study the
horizontal tail pitch incidence was fixed at +5 degrees with respect to the horizon-
tal. The vertical tail also resembles that of the actual X2TD during early flight
tests. An additional horizontal tail was installed near the bottom of the vertical tail
following 12th flight test. However, the additional horizontal tail was not modeled
in this study. The equivalent flat plate surface area of the vertical tail is 15.4 feet
squared [37].
35
Figure 2.8: Notional X2TD airframe.
Figure 2.9: Sikorsky X2TD during it?s first flight on August 27, 2008 [6].
36
3 Comprehensive Analysis
This chapter describes a comprehensive analysis (CA) methodology utilized in
modeling the high-speed coaxial compound helicopter described in previous chap-
ter. An in-house University of Maryland rotorcraft comprehensive analysis tool,
PRASADUM, was utilized to perform trim and to model elastic blade deflections
of the rotor blades. The in-house comprehensive analysis tool, PRASADUM, was
developed by Sridharan, in Ref. [15], as part of a doctoral thesis. PRASADUM has
been used for multiple CFD/CSD coupling studies by various researchers at Uni-
versity of Maryland, Ref.Ref. [38], [45], Ref. [47], as well as in the UH-60 Airloads
workshop.
3.1 Rigid Body Dynamics
This section describes the rigid body dynamics of a coaxial compound heli-
copter modeled in PRASADUM. The Newton?s second law is applied to the heli-
copter, modeled as a rigid body in space. The helicopter non-linear, rigid body
equations of motion include force and moment equilibrium equations, shown in
Eqs.3.1 - 3.3 and Eqs.3.4 - 3.6. A comprehensible, detailed derivation of the force
and moment equations, as well as the specific variables, can be found in Ref. [48].
37
The right hand side of the equations represents the inertial loads acting on the heli-
copter at CG, which depends, directly and indirectly, on the nine rigid body states.
The nine rigid body states are three linear and three angular body-axis velocities at
CG, as well as the three Euler angles that define the orientation of the helicopter
with respect to the earth fixed axis. The body-axis coordinate system is shown in
B. It is assumed that the center of gravity lies on the shaft, some distance below
the rotor. The left-hand side of Eqs.3.1 - 3.3 and Eqs.3.4 - 3.6, accounts for the
aerodynamic loads on the airframe (empennage and fuselage), rotor system as well
as the propeller.
The force equilibrium equations in the body-axis frame:
X = m (u? + q w ? r v + g sin ? ) (3.1)
F F F F F F F
Y = m (v? + r u ? p w ? g sin? cos ? ) (3.2)
F F F F F F F F
Z = m (w? + p v ? q u ? g cos? cos ? ) (3.3)
F F F F F F F F
The moment equilibrium equations in the body-axis frame:
L = Ixxp? ? Ixy(q? ? p r )? Ixz(r? + p q )? Iyz(q2 ? r2)? (Iyy ? Izz)q rF F F F F F F F F F F
(3.4)
M = Iyy q? ? Iyz(r? ? q p )? I 2yx(p? + q r )? Izx(r ? p2 )? (Izz ? I )r pF F F F F F F F F xx F F
(3.5)
N = Izz r? ? Izx(p? ? r q )? Izy(q? + r p )? Ixy(p2 ? q2)? (IF F F F F F F F F xx ? Iyy)p qF F
(3.6)
38
The aerodynamic force and moment contributions from various components of a
coaxial compound helicopter in the body-axis frame:
X = X + X +X + X + X + X
F HT VT PP UR LR
Y = Y + Y + Y + Y + Y
F HT VT UR LR
Z = Z + Z + Z + Z + Z
F HT VT UR LR
L = L + L + L + L + L
F HT VT UR LR
M = M + M + M + M + M
F HT VT UR LR
N = N + N + N + N + N
F HT VT UR LR
The presence of the auxiliary propeller is accounted for in the X force equation,
which contains the contribution of the propulsive thrust from the auxiliary propeller.
The thrust from the auxiliary propeller is assumed to act along the X body axis,
thus it does not impart any moments about the CG. The roll moment produced
by the auxiliary propeller rotation is also neglected in this study, (LPP=0). Some
additional assumptions, applicable to cases without airframe CFD/CSD coupling,
are described below:
1. The fuselage normal force, side force, roll, pitch and yaw moments are zero,
(YF = 0, ZF = 0, LF = 0, MF = 0, NF = 0).
2. The horizontal tail axial force, side force, roll and yaw moments are zero,
(XHT = 0, YHT = 0, LHT = 0, NHT = 0).
If the full vehicle CFD/CSD coupling procedure is performed, the above assumptions
are relaxed and all of the CFD aerodynamic forces and moments are included as
39
corrections to these equations.
3.2 Aerodynamic Model
This section describes the calculation of the aerodynamic forces and moments
on the helicopter components needed to satisfy Eqs.3.1 - 3.3 and Eqs.3.4 - 3.6. The
calculation of the airframe aerodynamic forces and moments is subdivided into three
parts: fuselage, horizontal tail and vertical tail. In this study the flexibility of the
airframe is neglected, the airframe is modeled as a rigid entity.
3.2.1 Fuselage Airloads
This subsection discusses the calculation of the aerodynamic forces on mo-
ments on the fuselage of the notional X2TD in the CA. The fuselage aerodynamic
forces and moments are calculated from the fuselage aerodynamic coefficients given
in the input lookup-tables. The first look-up table provides the lift, flat plate drag
area and pitching moment as a function of angle of attack of the fuselage. The
comprehensive analysis assumes that the flat plate drag area does not change with
varying angles of attack. The fuselage look-up table assumes the fuselage lift and
pitching moment are zero. In Ref. [46], Johnson reports the X2TD to have flat plate
drag area of 4.6 feet squared. It was assumed that the flat plate drag area was
defined using the maximum frontal area of the actual X2TD aircraft, it is unknown
whether the flat plate drag area includes the frontal area of the rotor hubs and the
mast pylon.
40
Various CFD studies of the isolated airframe were conducted to verify that the
flat plate drag area of the CFD model matched the number provided in Ref. [46].
The CFD model fuselage flat plate drag area was determined to be half of the
reported one. It was assumed that the discrepancy was due to the missing hubs and
the lack of protrusions in the CFD simulations. The second look-up table provides
the fuselage side force, roll moment and yaw moment as functions of sideslip angle.
All of the values in the second look-up table are assumed to be zero. Thus, the only
force acting on the fuselage, in the CA, is the drag force. The equation for the flat
plate drag area is as follows:
D
f = CDSref = 1??V2 ?
3.2.2 Empennage Airloads
This subsection describes the calculation of the horizontal tail and vertical tail
airloads in the CA code. The horizontal and vertical tail aerodynamic forces and
moments are calculated from the lift and drag coefficients provided in the input
look-up tables. Both, horizontal and vertical tails are treated as low aspect ratio
symmetric wings.
The lift coefficient in the look-up table, Eq.3.7, was calculated from Prandtl?s
lifting-line theory, shown in Eq.3.8, where a0 is the airfoil lift curve slope, AR is the
aspect ratio, ? is the efficiency factor. The efficiency factor was assumed to be 0.85
for both horizontal and vertical tails. The airfoil curve slope of 2? was assumed for
41
both tails.
CL = CL?? (3.7)
ao
CL? = 1 + a
(3.8)
0
?AR?
The tabulated drag coefficient in the look-up tables is the lift induced drag co-
efficient calculated using Eq.3.9, where CL is the lift coefficient calculated from
Prandtl?s lifting line theory in Eq.3.7.
C2
C LD = (3.9)i ??AR
The two horizontal tails are modeled as a single wing with aspect ratio equal to
3.5. The angle of attack which is used to determine the lift and drag coefficients from
the horizontal tail look-up table is calculated based on the aircraft pitch attitude
as well as the incidence angle of the horizontal tail. The vertical tail was modeled
to have an aspect ratio of 1.2. The angle of attack used to determine lift and drag
coefficients from the vertical tail look-up table is a function of the sideslip angle.
3.2.3 Auxiliary Propeller Airloads
This subsection explains the calculation of the notional X2TD auxiliary pro-
peller airloads in the CA. As previously shown in Eqs.3.1 - 3.3 and Eqs.3.4 - 3.6,
only the propeller axial force is accounted for in the force and moment equations. It
is assumed that the propeller thrust vector acts along the CG axis, therefore there
is no pitching moment about the vehicle CG due to the propeller thrust. Also, the
42
roll moment about the CG produced by the propeller is neglected. For the notional
X2TD helicopter cases the auxiliary propeller thrust is tabulated in a speed schedule
look-up table. The notional X2TD propeller thrust was calculated from the power
curve shown in Fig.2.6 using a simplified expression from the momentum theory
formulation for a propeller in climb, P = TV . In this expression P is power, T is
thrust and V is flight velocity. The power expression is purely induced. Later, the
CFD simulations are used to correct the simplified expression.
3.2.4 Coaxial Rotor System Airloads
This section discusses the procedure used to calculate the rotor airloads needed
for Eqs.3.1 - 3.3 and Eqs.3.4 - 3.6. The rotor airloads in these equations are the rotor
forces in body frame and rotor moments about the CG of the vehicle. These forces
and moments are calculated from the sectional rotor blade airloads. The rotor
blade sectional airloads were calculated using a uniform inflow model, 2D steady
airfoil tables and unsteady aerodynamics. The rotor blade properties discussed in
the previous section are implemented in the CA model of the notional X2TD. The
2D airfoil look-up tables contain the steady lift, drag and pitching moment airfoil
coefficients as a function of angle of attack and Mach number for airfoils shown in
Fig.2.3(a). The data in the 2D airfoil look-up tables was compiled by Passe using
a UMD unsteady RANS CFD code, TURNS [45]. For this study, the low angle of
attack Cl data, for all of the notional X2TD airfoils, was replaced with a linear Cl
curve slope of 2?, which resulted in an improved trim convergence.
43
Only the steady component, ?o, of the three state Peters-He dynamic inflow
model, given in Eq.3.10, was used to compute the induced velocity at the rotor disk
[49]. This low order assumption implies that the inflow is independent of the radial
and azimuthal location. Since airloads were later corrected with high-fidelity CFD
airloads, the use of uniform inflow was deemed sufficient. The detailed calculation
of the dynamic inflow coefficients, including the ?o, is provided in Ref. [49].
?(r, ?) = ?o + ?1cxcos? + ?1sxsin? (3.10)
The sectional lift and pitching moment, in the airfoil frame, were calculating using
Eqs.3.11 and 3.12, respectively [50]. The calculation of the lift and pitching moment
can be partitioned into circulatory and non-circulatory components.
L = LC + LNC (3.11)
M = MC + MNC (3.12)
The sectional circulatory and non-circulatory lift per unit span on the rotor blade are
given by Eq.3.11 [50]. The circulatory lift, given in Eq.3.13, depends on the airfoil lift
coefficient at a given rotor blade section [50]. The sectional lift coefficient at a given
angle of attack and Mach number is obtained from a look-up table provided by the
user as an input. The blade sectional angle of attack, ? , is obtained using Eq.3.14.
The UP velocity includes the induced inflow velocity calculated using Eq.3.10 [50].
The magnitude of the free-stream velocity at the elastic axis was calculating using
44
Eq.3.15 [50]. In this study, the elastic axis coincided with the quarter chord line on
the rotor blade.
LC = 1/2 ? V
2
? c Cl(?,M) (3.13)
? = tan?1 ? UP (3.14)
? U2 + U2T P
V? = U2 + U2 + U2 (3.15)T P R
The non-circulatory lift per unit span can be partitioned into two parts, shown in
Eq.3.16, due to the pitching and plunging motion of the blade section. The first part
is produced due to the plunging acceleration, h? of the blade section. The second
part is produced due to the pitching of the blade section, ?.
? ?
L 2NC = ?c h? + ?c
2V??? (3.16)
4 4
The sectional pitching moment per unit span, about the elastic axis, can also be
decomposed into the circulatory and non-circulatory pitching moments, as shown
in Eq.3.12 [50]. The circulatory pitching moment is given by Eq.3.17. The first
portion of the circulatory pitching moment depends on the sectional angle of attack
and the pitching moment coefficient obtained from the airfoil look-up tables. The
second portion of the circulatory pitching moment depends on the circulatory lift
obtained from Eq.3.13 and the distance from the elastic axis to the aerodynamic
center of the airfoil section. The third portion of the circulatory pitching moment
depends on the time rate of change of the angle of attack.
45
?
MC = 1/2 ? V
2 c2? Cm(?,M) + xac LC + ? ?? ? V 3? c (3.17)16
The non-circulatory pitching moment is given by 3.18.
?
M = ?c2
?
NC h? xmc + ?c
2V??? x0.75c (3.18)
4 4
The rotor blade sectional drag per unit span is a function of the sectional angle
of attack and the Mach number. The airfoil drag coefficient is obtained from the
look-up table discussed above.
D = 1/2 ? V 2? c(r) Cd(?,M) (3.19)
The lift, drag and moment coefficients along the rotor blade are then used
to calculate the sectional force and moment components in the rotating deformed
airfoil frame. The sectional airloads are converted to the rotating undeformed airfoil
frame. The rotor hubloads in the rotating frame are calculated by integrating the
airloads along the span and finally, the rotating hubloads in the fixed frame are
calculated. The hub forces can then be used in Eqs.3.1 - 3.3. The hub moments are
transferred to the vehicle CG to satisfy Eqs.3.4 - 3.6.
3.3 Structural Model
The rotor airloads described in previous subsection are highly dependent on
the deformations of the rotor blade through UP and UT . The blade deformations
are influenced by the aerodynamic and inertial forces, as well as the blade structural
46
properties and control inputs. Therefore, the problem is aeroelastically coupled and
in order to obtain a representative airloads it is important to correctly model the
deformation of the rotor blades.
The rotor blades modeled in the CA are geometrically exact representations
of the notional X2TD rotor blades discussed in 2.1. The blade twist, chord and
airfoil sections are specified in the input files. In this study, the main rotor blades
are modeled as one dimensional isotropic Euler-Bernoulli beams, undergoing flap,
lag and torsion. The Euler-Bernoulli assumption states that upon deformation, the
plane cross-sections normal to the beam elastic axis remain plane and normal to
the deformed elastic axis. The shear deformations of the beam are neglected. The
translation of the elastic axis and the rotation of the cross-section can be used to
calculate the deflection of any point on the cross-section.
The blade structural equations of motion are non-linear coupled partial dif-
ferential equations. In order to obtain the structural deformations of the rotor
blades, the structural equations of motion must be solved. The structural forces
and moments are related to the external forces acting on the beam. A finite ele-
ment discretization is used to eliminate the spatial coordinates and transform the
PDEs into a system of non-linear coupled ordinary differential equations in time.
Ten finite elements are used to discretized the blades in this study. Modal reduction
was performed to reduce the number of equations, using rotating natural vibration
modes. Six modes were used in this analysis. An in-depth development of the struc-
tural equations of motion and the solution methodology is presented by Sridharan
in PRASADUM theory manual [50].
47
3.4 Rotor Controls
This section discusses the calculation of the main rotor pitch control angles.
A pilot desired vehicle state results from the orientation of the rotor blades as they
travel around the azimuth. The pilot provides the pitch control inputs which are
transferred to the swashplate resulting in the re-orientation of the blades to a desired
state. The pitch control angle is shown in Eq.3.20. For an articulated rotor, there
is a phase delay between the pilot control inputs and the blade response, 80 to
90 degrees for hover. The phase delay, shown in Eq.3.21, depends on the blade
flap frequency and the Lock number. The pilot controls are: ?0, ?1s and ?1c. The
collective control angle, ?0, has an effect on the thrust and the yaw moment of the
helicopter. For a conventional rotor with phase-offset of roughly 90 degrees, the
longitudinal cyclic pitch, ?1s, affects the pitching moment while the lateral cyclic
pitch, ?1c, controls the roll moment. For moderately stiff rotors, with high flap
frequency, the phase delay is shorter, roughly 40 to 50 degrees.
?C = ?0 + ?1c cos(?) + ?1s sin(?) (3.20)
?/8
? = tan?1 (3.21)
?2? ? 1
The CA utilized for this study assumes that the notional X2TD rotor is mod-
erately stiff, and neglects the phase delay between the pilot controls and the blade
response. Therefore, the formulation assumes that the ?1s controls the roll moment
while ?1c controls the rotor pitch moment.
48
For a coaxial rotor system, upper and lower rotor have their own set of control
angles. The collective angles for the upper and lower rotor, ?U0 and ?
L
0 , are computed
using Eqs.3.22 and 3.23, where the ?0 is a mean collective and ??0 is the differential
collective. The negative sign in Eqs.3.23 and 3.23 accounts for the direction of the
rotation of the lower rotor.
?U0 = ?0 + ??0 (3.22)
?L0 = ?0 ? ??0 (3.23)
The cyclic pitch angles, ?U1c and ?
L
1c, for the upper and lower rotor are computed
using Eqs.3.24. The longitudinal lift-offset angle is assumed to be zero, the cyclic
pitch angle ?1c is the same for both rotors.
?U1c = ?
L
1c = ?1c (3.24)
The cyclic angles, ?U1s and ?
L
1s, for the notional X2TD coaxial rotor were calculated
using Eqs.3.25 and 3.26. As previously stated, the notional X2TD rotor was assumed
to be moderately stiff and the phase delay between the control inputs and blade
response was neglected. Therefore, the lateral lift-offset angle was included in the
computation of the ?1s control because ?1s effects the roll moment when phase delay
is zero. The swashplate phase offset angle is also neglected.
?U1s = ?1s + ?LOS (3.25)
?L1s = ?1s ? ?LOS (3.26)
The total pitch control angle for upper and lower rotor is given by Eqs.3.27 and
3.28. The azimuth, ?, shown in Eqs.3.27 and 3.28 is the global azimuth angle,
49
corresponding to a counter-clockwise rotation with zero over the tail of the vehicle.
The blades cross-over the tail and every 90 degrees.
?UC = ?
1
0 + ?1c cos(?) + ?
1
1s sin(?) (3.27)
?LC = ?
2
0 + ?1c cos(?) + ?
2
1s sin(?) (3.28)
3.5 Trim
The objective of this section is to describe the trim procedure and it?s imple-
mentation in the in-house CA solver, PRASADUM. The goal of the trim procedure
is to determine the trim state of a helicopter for a given flight condition. In this
study, the vehicle is undergoing a steady, level flight. Trim can be defined as a bal-
ance of forces and moments on an aircraft. When the vehicle is trimmed, the main
rotor blade dynamics are periodic and the inflow at the main rotor does not vary
with consecutive revolutions. The concept of trim can be expressed as a coupled
non-linear algebraic system of equations, given by Eq.3.29 [51]. The vector, F (x),
represents a set of equations that must be satisfied for helicopter to be in trim.
There exists a corresponding solution vector, x, given in Eq.3.31, which solves this
algebraic system of equations for a given flight condition. The solution vector, x,
is unknown. Therefore, the objective of the trim procedure is to find vector x that
solves the non-linear algebraic system of equations. Both, vectors, x and F (x),
consist of the rigid body, inflow and main rotor components [51]. The rest of this
section is dedicated to describing the components of vectors F and x.
50
F (x) = 0 (3.29)
F = [F TB F I FR] (3.30)
x = [xB xI xR]
T (3.31)
Vector, FB, represents the rigid body dynamic equations of the vehicle, shown
in Eqs.3.1 through 3.6. The definition of trim implies that the vehicle translation and
angular accelerations, along the body axes, are zero. The translation accelerations
(u?, v?, w?) and angular accelerations (p?, q?, r?) can be calculated from Eqs.3.1 through
3.6. Extending this definition to rotorcraft application requires that the summation
of forces and moments over one rotor revolution is equal to zero, which can be shown
with an equivalent condition in Eqs. 3.32 through 3.37 Ref. [50].
? T
? u? dt =  = 0 (3.32)F RB10 T
? v? dt =  = 0 (3.33)F RB20T
? w? dt =  = 0 (3.34)F RB30 T
? p? dt =  = 0 (3.35)F RB40 T
? q? dt =  = 0 (3.36)F RB50T
r? dt =  = 0 (3.37)
F RB6
0
51
The vector xB, representing the rigid body unknowns, is given in Eq.3.38. The
vector of the rigid body unknowns consists of trim control angles ( ?0, ?1c, ?1s and
??0), fuselage angle of attack (?F ) and the lift-offset angle (?LOS).
x TB = [?0 ?1c ?1s ??0 ?F ?LOS] (3.38)
Equation 3.32 is an equivalent representation of the force equilibrium in the
X direction, given by Eq.3.1. The unknown trim variable from vector xB, corre-
sponding to Eq.3.32 is ?F . The propulsive force produces by the auxiliary propeller
is assigned by the user in a look-up table, based on the speed of the vehicle and
the power given in Ref. [46]. The propulsive force, is counteracted by the vehicle H
force. Therefore, the angle of attack of the vehicle, ?F , must be solved for in order
to counteract the propeller propulsive force resulting in the vehicle pitch attitude
being an unknown trim control for this equation.
The trim parameters, ?1s and ?LOS, shown in Eq.3.38, affect the side force
represented by Eq.3.33 and roll moment represented by Eq.3.35. The LOS angle
depends on the LOS requirement identified by the user in the inputs. The LOS
requirement is specified in a lookup-table and was obtained from linear interpolation
of the available test data given for the X2TD rotor in Ref. [5]. During the propulsive
trim, the Eq.3.39, must satisfy the LOS given in the lookup-table. The ?LOS is
calculated based on the given LOS value.
?Mx
LOSreq = (3.39)
TR
52
(3.40)
The trim parameters, ?0 and ??0, govern the vertical force equation, Eq.3.34,
and the yaw moment equation Eq.3.37. Equation 3.36 is an equivalent representation
of the pitching moment equilibrium about the vehicle CG. For the notional X2TD
the horizontal tails produce significant pitch down moment about the vehicle CG.
The main rotor counteracts the pitch-down moment produced by the horizontal
tails. The trim parameter for this equation is the cyclic pitch angle, ?1c.
The inflow trim equations are given by Eqns.3.41-3.43 [51]. These equations
enforce the conditions that the inflow does not change between consecutive itera-
tions. The inflow is described by Eqn.3.10. The main rotor inflow unknowns, xI ,
are given by Eq.3.44. However, components ?1c and ?1s of Eq.3.44 are neglected for
this study because only the uniform inflow component was considered.
? T
? ??0dt = 0 (3.41)0T
? ??1cdt = 0 (3.42)0T
??1sdt = 0 (3.43)
0
x TI = [?o ?1c ?1s] = [?0]
T (3.44)
The ordinary differential equations of motions governing the structural dy-
namics of a single rotor blade, expressed in generalized coordinates, are given by
53
Eq.3.45 [51]. The helicopter rotor blade response and blade deformations are peri-
odic if the helicopter is in a trim condition. Therefore, the blade motions can be
approximated using Fourier Series truncation given in Eq.3.46 [51].
q? = fq(q, q?) (3.45)
?Nh
qk(?) ? qkappx(?) = qk0 + (qkjc cos j? + qkjs sin j?) (3.46)
j=1
In Eq.3.46, qk(?) represents the generalized coordinates of kth blade modes. Because
the x is no longer exact but approximate, there will exist a residual such as shown
in Eq. 3.47 [51].
(?) = q?appx ? fq(qappx, q?appx) (3.47)
In order for the residual, shown in Eq.3.47, to be minimized, Eqs.3.48 through 3.50
must be enforced if the Galerkin method is used [51]. The generalized coordinates of
the Nm blades modes that satisfy Eqs.3.48 through 3.50 are given in xR in Eq.3.51.
? 2?
? k(?)d? = 0 (3.48)02?
? k(?) cos(j?)d? = 0 (3.49)0 2?
k(?) sin(j?)d? = 0 (3.50)
0
xR = [q
1
0 q
1 1 1 1 1 1
1c q1s q2c q2s . . . qN c qN s . . . q
Nm qNm qNm . . . qNm Nm T
h h 0 1c 1s N
q
hc N
]
hs
(3.51)
54
3.6 Trim Solution Method
This section will describe the method utilized to solve the system of alge-
braic equations given in Eq.3.29. A non-linear equation solver, HYBRD1 from
the MINPACK-1 library, Ref. [52], solves this system of non-linear equations in
PRASADUM.
( )
fi = x , x , ..., x = 0, 1 6 i 6 n (3.52)1 2 n
In the context of this work, the values x1, x2, ..., xn represent the trim pa-
rameters, discussed in previous section, which include rotor control angles, vehicle
attitude angles, inflow constants and blade modes. In the coaxial helicopter propul-
sive trim, lift-offset and propeller thrust are also trim variables. Trim enforces that
the user specified lift-offset and the propeller thrust are satisfied.
The functions, f1, f2, ..., fn, relate the trim parameters to the force and moment
equilibrium of the vehicle, the rotor inflow states, and beam deformations. The user
provides an initial approximations x to the solution of the functions f1, f2, ..., fn.
Usually, the initial guess does not solve the system of equations, there exists a
residual. The solution algorithm determines a correction to the initial guess which
minimizes the residual. The updated guess is then used as a new starting point to
evaluate the functions f1, f2, ..., fn.
55
3.7 Validation of the Notional X2TD Comprehensive Analysis Model
The in-house comprehensive solver, PRASADUM, utilized for this study has
been widely used within the UMD rotorcraft community [45], [44], [38], [47], [53],
[54], [55]. Thus, the validation focused on verifying the notional X2TD model, as
well as the main rotor structural properties, implemented in the CA instead of the
implementation of the CA.
The notional X2TD power obtained with the CA was compared with the rotor
power given in Ref. [6]. Figure 3.1 compares the rotor power from flight data and
the CA, as well as the data fit line for the flight data. The CA utilized 6 blade modes
and 4 harmonics, as well as a free-wake methodology to for the validation case [56].
It can be observed that the predicted power matches well with the digitized power
from Ref. [6].
Figure 3.2 shows the notional X2TD fanplot. A notional X2TD fanplot, calcu-
lated using the in-house CA, is compared with the digitized data from the Sikorsky
X2TD fanplot obtained from Ref. [1]. The notional X2TD main rotor blade mass
and stiffness properties in the CA, were parametrically derived and scaled from the
Sikorsky XH-59A main rotor blades by Passe in Ref. [45] to closely match the fanplot
data from Ref. [1]. Passe also compared the derived frequencies to those obtained
by Johnson using CAMRAD II [10] in Ref. [46].
There is good agreement between the first flap, first chordwise, second flap and
first torsional frequencies predicted using CA and those given in Ref. [1]. However,
there is a large disparity between the notional X2TD and the actual X2TD third
56
Figure 3.1: The power validation for the notional X2TD.
flapwise and the second chordwise frequencies, Ref. [1]. Nevertheless, the third flap-
wise and second chordwise frequencies match well with those obtained by Johnson
in Ref. [46] and were deemed sufficient for this study.
57
Figure 3.2: The fanplot validation for the notional X2TD.
58
4 Computational Fluid Dynamics
This chapter discusses the fundamental equations of fluid motion and the
computational approach used to solve these equations. The fundamental equations
of the fluid motion, that are solved in the computational codes used for this study,
are the three dimensional, unsteady, compressible Navier-Stokes equations. The
Navier-Stokes equations are mathematical laws that enforce the conservation of
mass, momentum and energy. The two near-body solvers which were chosen for this
study are OVERFLOW and FUN3D, as part of the CREATE-AV Helios framework.
The off-body is solved using a Cartesian flow solver, SAMCart. The objective of the
CFD in this work is to solve for flow variables and obtain high-fidelity aerodynamic
loads on the helicopter components.
4.1 Governing Equations
This section discusses the three dimensional, unsteady Navier-Stokes equa-
tions utilized for this study. The three-dimensional Navier-Stokes equations may be
written in a strong conservation form, shown in Eq. 4.1 [57].
?Q ?Ec ?Fc ?Gc ?Ev ?Fv ?Gv
+ + + = + + (4.1)
?t ?x ?y ?z ?x ?y ?z
59
The vector Q is a vector of conserved variables given by Eq.4.2, where the variables
?, u, v, w and e denote the local flow density, the three velocity components and
the total energy, respectively. ?? ??? ?? ??? ?
?
? ?u ????
Q = ??? ?v
???? ?
??? (4.2)
? ?w ????
e
The vectors Ec, Fc and Gc, given in Eq. 4.3, are the inviscid fluxes in the x, y, z
directions.
?? ? ? ? ? ??
???
?u
? ?? ?
?v ? ?w
? ?u2 + p ????
? ???? ???? ?uv ???? ??
??? ?? ?? ??uw ????
E ? ?c = ??? ?uv ??? Fc = ???? ?v2 + p ???? Gc =? ? ? ? ?? ? ? ? ?
?? ?vw ? (4.3)?? ?uw ?? ?? ?vw ?? ???
???
? ?w2 + p ????
u(e+ p) v(e+ p) w(e+ p)
The pressure, denoted by p, in the Eq.4.3 can be obtained by using the equation of
state applied to calorically perfect gas, Eq.4.4. The ratio of specific heats, ?, was
assumed to be 1.4.
1
p = (? ? 1)[e? ?(u2 + v2 + w2)] (4.4)
2
60
The vectors Ev, F v and Gv, given in Eq.4.5, are the viscous fluxes in the x, y, z
directions.
?? ? ? ? ? ??
???
0 0 0
? ??? ??? ??? ??? ???
??
? ? ? ? ? ?xx ??? ??? ?? ? xy ?? ? ? ?? ??
? ?xz ??
Ev = ?? ? ?
?
? Fv = ?? ? ???? Gv = ???? ? ??? (4.5)? yx yy ? yz??? ? ? ? ?zx ??? ??? ?zy ??? ??? ?zz ??
?
??
Ev5 Fv5 Gv5
where
Ev5 = u?xx + v?xy + w?xz ? qx (4.6)
Fv5 = u?yx + v?yy + w?yz ? qy (4.7)
Gv5 = u?zx + v?zy + w?zz ? qz (4.8)
The stress tensor, denoted by ? , is obtained using the Stokes? hypothesis, assuming
Newtonian fluid [58]. The ? and ? = ?2?/3 are the first and second coefficients
of viscosity. The Sutherland?s formula, Eq.4.10, can be used to calculate the first
coefficient of viscosity, ?, where C1 and C2 are constants for air. The temperature, T ,
can be calculated using the perfect gas law, Eq.4.11. The Kronecker delta function
is denoted by ?ij, shown in Eq.(4.12. ) ( )
?ui ?uj ?ui
?ij = ? + + ? ?ij (4.9)
?xj ?xi ?xj
C1T
(3/2)
? = (4.10)
T + C2
P
T = (4.11)
?R
61
?????
?ij = ?0, i =6 j??? (4.12)1, i = j
The qx, qy and qz components of the vector q present in Eqs.4.6-4.8, represent
the rates of thermal conduction. The rates of thermal conduction, obtained us-
ing the Fourier?s Law of heat conduction shown in Eq.4.13, are dependent on the
temperature and the thermal conductivity of the fluid Ref. [59].
?dT
qj = k j = x, y, z (4.13)
?xj
4.2 Reynolds Averaged Navier-Stokes Equations
The flow field surrounding a helicopter is inherently turbulent, containing a
wide range of length and time scales. An extremely fine grid and a very small
time step is required to properly resolve the smallest length and time scales in
the flow field, making the solution process infeasible for practical applications. A
workaround involves solving only for the mean flow quantities while modeling tur-
bulent fluctuations, which can be done using the Reynolds Averaged Navier-Stokes
(RANS) Equations .
The instantaneous flow variables (ui, ?, p, T,), denoted by ? in Eq.4.14, can
be decomposed into the mean, ??, and fluctuating, ??, quantities using Reynolds
decomposition [60].
? = ?? + ?? (4.14)
62
The Reynolds decomposition of the flow variables is substituted into the instan-
taneous governing equations shown in Eq.4.1. The modified equations are then
averaged resulting in cancellation and simplification of numerous terms based on
the mathematical identities for averaged and fluctuating quantities. An in-depth
derivation of the RANS equations can be found in Ref. [60] and Ref. [61]. The
Reynolds Stress Tensor, given in Eq.4.15, is one of the key differences between the
original governing equations and the averaged governing equations. The Reynolds
Stress Tensor depends on the turbulent fluctuating quantities, u?i and u
?
j.
(?? ) = ??u?u?ij turb i j (4.15)
The Boussinesq eddy viscosity hypothesis, given in Eq.4.16, can be used to
obtain the Reynolds Stress Tensor [62]. A turbulence closure model is then used to
determine the turbulent viscosity, ?turb. In this study, Spalart-Allmaras (SA), a one
equation turbulence model is utilized [63]. Spalart-Allmaras has been validated and
extensively used for practical helicopter simulations.
( )
?ui ?uj 2 ?ui
(??ij)turb = ?turb + + ?ij (4.16)
?xj ?xi 3 ?xj
4.3 CFD Solvers
This section describes the CFD framework utilized for this study. A CFD
framework, CREATETM -AV Helios (version 9.1), was used to perform the CFD
simulations [64]. The CREATETM -AV Helios has developed over the years into a so-
63
phisticated rotorcraft analysis tool which utilizes multi-mesh, multi-solver paradigm
to perform high-fidelity rotorcraft flow simulations [65], [66], [67]. The overset do-
main connectivity within Helios, between the near-body and off-body solvers, is
performed by the PUNDIT software [68]. A Mesh Motion Loading and Displace-
ment Interface (Melodi), within the Helios framework, oversees the fluid structure
interaction coupling, including the application of the prescribed elastic blade deflec-
tions to the blade mesh [69].
Various near-body solvers were used for the study, including OVERFLOW
and FUN3D. Figure 4.1 shows an overview of the mesh system and the dedicated
solvers, as well as the number of grid points in each mesh body. The CFD simulations
were run in a fully turbulent mode using the Spalart-Allmaras turbulence model for
Figure 4.1: Helicopter mesh system information.
64
OVERFLOW and FUN3D near-body solvers, as well as for the off-body SAMCart
solver. The simulations were run using a main rotor quarter degree time step.
4.3.1 Coaxial Main Rotor - OVERFLOW
The structured CFD solver, OVERFLOW (version 2.2n) developed at NASA,
was used for the main rotor blades [70]. OVERFLOW was initially developed as a
finite difference CFD solver which over time evolved to include finite volume capabil-
ities. The OVERFLOW code solves the unsteady RANS equations. The formulation
for the unsteady RANS equations is discussed in the previous section. Numerous
spatial and temporal discretization schemes are available in OVERFLOW.
A fourth order central differencing scheme with a stabilizing fifth order ar-
tificial dissipation was used for the discretization of the inviscid fluxes in this
study [71]. The usage of central differencing scheme is common for rotorcraft appli-
cations [39], [40], [72], [73], . The Roe flux splitting scheme [74] was also tested for
this study but the convergence was slower than that of the central scheme, for the
same number of sub-iterations. This may be attributed to the stiffness of the prob-
lem due to the low Mach number flow near the reverse flow region. A second order
central differencing was used for the viscous fluxes. The second order backwards
differencing formula (BDF2) was utilized for the temporal discretization [75], [76].
The initial studies were performed using 20 Newton sub-iteration but later increased
to 40 to improve the convergence at high forward flight speeds.
The structured near-body notional X2TD blade meshes utilized in this study
65
Figure 4.2: Main rotor blade mesh.
were generated by Passe in Ref. [45] using an in-house algebraic O-O grid generator.
A single blade mesh, shown in Fig.4.2, consists of 0.88 million grid points: 125 in
wrap around direction, 129 in spanwise direction and 55 in the vertical direction.
The eight near-body meshes have a total of 7.1 million grid points. The height of
the first wall spacing was chosen such that the y+ = 1 is satisfied at a Reynolds
number of 2.6 million based on the main rotor root chord and the rotor tip speed.
4.3.2 Airframe and Propeller - FUN3D
An unstructured CFD solver FUN3D (version 13.3) [77], developed by NASA,
was chosen to solve the flow equations for the notional X2TD airframe and the
propulsor. The FUN3D solver is a finite volume solver that utilizes unstructured
66
meshes and solves the unsteady RANS equations. Numerous spatial and temporal
schemes are available within FUN3D. In this study, the second order Roe upwinding
scheme was utilized to solve the inviscid fluxes. FUN3D was run in a fully turbulent
mode with Spalart-Allmaras turbulence model.
An airframe CAD geometry obtained from Passe in Ref. [45] was modified to
reflect the five degree positive incidence angle of the horizontal stabilizers. An un-
structured meshing technique was chosen for the notional airframe of the X2TD due
to geometric complexity. The airframe containing various regions of high curvature
as well as convex and concave junctions. The unstructured airframe mesh, shown in
Fig.4.3 was generated using CREATETM - GENESIS Capstone software [78]. The
airframe surface grid consists of triangular elements. Fifty prism layers were grown
from the surface to capture the boundary layer on the airframe. The thickness of
the first prism layer is 7e?5 grid units. The airframe near-body mesh contains 15.6
million grid points.
The unstructured blade grid, shown in Fig.4.4, for the propeller was gener-
ated from blade CAD using the CREATETM - GENESIS Capstone software. The
propeller consists of six blades, with 2.2 million grid points per blade, resulting in
total of 13.2 million grid points. The first layer thickness was chose to be 7e? 5 to
ensure that y+ < 1 is satisfied. For consistency, one grid unit, in the airframe and
propeller mesh, is equal to one root chord of the main rotor blade.
67
Figure 4.3: Airframe near-body surface mesh.
Figure 4.4: Notional X2TD auxiliary propeller near-body surface mesh.
68
4.3.3 Off-body - SAMCart
SAMCart, a high-order Cartesian flow solver native to the Helios framework,
was used to solve the flow equations in the off-body region [79]. The off-body domain
extended eight rotor radii around the center of the lower rotor hub. Figure 4.5 shows
a view of the mesh domain extents, from the port side of the aircraft, as well as
the close up of the fixed refinement region near the aircraft. The off-body region
was refined using seven nested levels, such that the finest level was ten percent of
the main rotor root chord. Table 4.1 gives the grid spacing for of each refinement
level. The finest region extended behind the center of the rotor shaft to capture the
rotor wake structures downstream. The coarsest level defines the outer boundary
Figure 4.5: Mesh domain viewed from port side of the helicopter.
69
of the computational domain. A fifth order central differencing scheme was used
for the calculations of the inviscid fluxes. The viscous fluxes were discretized using
the fourth order central differencing scheme. The turbulence was modeled using the
Spalart-Allmaras turbulence model with the default settings. Eight sub-iterations
were used for SAMCart to achieve a drop of roughly 2 orders. A total of 115 million
mesh points made up the off-body Cartesian domain.
Table 4.1: Grid spacing per level in terms of root chords for the off-body Cartesian
mesh.
Off-Body Refinement Level Grid Spacing
Level 1 6.55
Level 2 3.27
Level 3 1.63
Level 4 0.819
Level 5 0.409
Level 6 0.205
Level 7 0.102
4.4 Blade Motion and Deformation
This section describes the blade deformation within the CFD solver. The main
rotor blades elastically deform as they travel around the azimuth. The main rotor
blades deform according to the blade elastic deformations, obtained from the com-
70
prehensive analysis solver. These blade deformations include three translational and
three rotational transformations around the elastic axis of the blade. For the no-
tional X2TD the elastic axis coincides with the quarter chord line. Within the Helios
framework, the Melodi module enforces the blade motions and deformations [69].
There exists a capability to transfer the blade deformations directly and automati-
cally from the comprehensive analysis solvers to Melodi, however, only RCAS and
CAMRAD comprehensive analysis solvers are currently interfaced with Helios frame-
work. Therefor, the azimuthal distribution of the spanwise elastic deformations and
the quarter chord definition, from PRASADUM, were transferred to Melodi as pre-
scribed deformations by the way of file IO.
Unlike the main rotor blades, the propeller blades were treated as rigid blade
entities in the Melodi module. The propeller collective obtained from CSD, was
applied to the propeller blade using the Melodi xml input, not the prescribed defor-
mation file. For both, the main rotor system and the propeller, the twist and the
chord files were provided to Melodi to obtain the non-dimensional sectional airloads
in the deformed airfoil frame.
71
5 CFD/CSD Coupling Methodology
This chapter discusses the coaxial rotor and full vehicle CFD/CSD coupling
procedures used in this study. The prediction of rotorcraft airloads is a multi-
disciplinary task that requires the knowledge of structural dynamics of the rotor
blades as well as the aerodynamics of the operational flow field [80]. Various types of
CFD/CSD coupling approaches are possible including tight and loose coupling [81].
In a tight coupling, the exchange of information between the CFD and the CSD
solvers occurs every time step. While, in a loose coupling approach the exchange
of information occurs periodically. A loose CFD/CSD coupling approach is utilized
for this study. Because this study is performed for steady level flight, it was deemed
acceptable to use the loose CFD/CSD coupling approach. For flight regimes where
the state of the aircraft is highly coupled to time, a tight coupling approach is
recommended.
5.1 Rotor CFD/CSD Coupling
This section provides an overview of the conventional, loosely coupled CFD/CSD
approach utilized in this study to obtain results for the isolated coaxial rotor shown
in Chapter 6. This coupling approach follows the methodology described in Refs. [9]
72
Figure 5.1: Conventional, rotor CFD/CSD coupling schematic.
and [16]. Because this conventional approach transfers the information pertaining
only to the main rotor between the CFD and CSD solvers, from here on out it
will be referred to as a ?rotor? CFD/CSD coupling approach. Figure 5.1 shows
the schematic of the rotor CFD/CSD coupling approach. At the beginning of the
procedure, a propulsive trim, described in Chapter 3, is performed using an in-house
comprehensive analysis solver.
The trim procedure solves for the main rotor elastic blade deformations at
specified locations along the blade. The elastic blade deformations and the pitch
attitude of the vehicle are the inputs into the CFD simulations. Because the CSD
and the CFD codes are not directly interfaced, the data transfer is done using manual
file IO method. The main rotor elastic deformations from the CSD are manually
transferred to the location of the CFD simulation. Once the CFD simulation has
73
completed 2 revolutions, the non-dimensional airloads in deformed airfoil frame, are
manually transferred back from the CFD to the location of the CSD solver. A delta
coupling procedure, given in Eqn.5.1, is utilized to obtain the difference between the
CFD airloads and the low order CSD airloads.
CSDi+1 = LOi+1 + (CFDi ? LOi) = LOi+1 + ?i (5.1)
The difference between the high-fidelity CFD airloads and the low order CSD
airloads is treated as a correction which is applied to the next trim iteration. Once
a new trim state is obtained using the delta correction, the new CSD elastic blade
deformations are manually transferred back to the location of the CFD code. A new
CFD simulation is performed. It was decided not to restart from an old CFD solution
due slower convergence which stems from initial transients. Thus, a completely new
CFD cycle was started after every CFD/CSD coupling exchange. Take note, for this
study only the main rotor system is present in the CFD simulations for this type of
coupling. However, it is common to also include the airframe and/or prop in CFD,
as shown in Ref. [82].
5.2 Full Vehicle CFD/CSD Coupling
The rotor CFD/CSD methodology, described in previous section, was utilized
for the coaxial rotor portion of the results, presented in Chapter 6. This section dis-
cusses the full vehicle CFD/CSD coupling procedure utilized for the full vehicle and
the interactional aerodynamic portions of the results, discussed in Chapters 7 and 8,
respectively. Figure 5.2 shows the schematic of the full aircraft trim procedure. The
74
key difference between the rotor CFD/CSD coupling procedure, shown in Fig.5.1,
and the full vehicle CFD/CSD coupling approach is the trimming of the auxiliary
propeller and the presence of the airframe and propeller in the CFD simulations.
The full vehicle CFD/CSD coupling procedure is performed as follows. First,
a wind tunnel trim was performed for the isolated notional X2TD auxiliary propeller
to obtain the propeller collective for a given flight condition. The three targets for
the wind tunnel trim are the propeller power, pitching moment and roll moment.
The wind tunnel target propeller power was determined from the power curve for
the actual X2TD propeller given in the Ref. [46]. Both, the pitching moment and
the roll moment targets were assumed to be zero for the wind tunnel trim. The
auxiliary propeller collective resulting from the wind tunnel trim was retained for
Figure 5.2: Full vehicle CFD/CSD coupling schematic.
75
CFD simulations. Second, a propulsive trim was performed to obtain main rotor
elastic blade deflections and pitch attitude for the notional X2TD vehicle. The
propulsive trim included the full notional X2TD vehicle, as described in Chapter
3. Note that in the first trim iteration, the propeller thrust in the lookup-table is
obtained from a simplified expression, P = TV . However, for all of the consecutive
iterations the propeller thrust is obtained from the CFD simulations. Then, the
main rotor blade elastic deformations, vehicle pitch attitude and propeller collective
are incorporated into the CFD simulations.
Once the CFD simulations has completed 2 main rotor revolutions the main
rotor sectional airloads, mean airframe airloads and the mean propeller yaw hub
moment are transferred to CSD solver. The mean propeller power is extracted from
the CFD propeller yaw moment. A cumulative delta difference, starting at the initial
coupling cycle is calculated and applied to the CSD propeller airloads, the propeller
is then re-trimmed to the target power and a new propeller collective is obtained.
The full aircraft speed schedule mean propeller thrust from the most recent CFD
run is entered into the propeller speed schedule for the full aircraft trim. The delta
correction discussed in previous section and given by Eq.5.1, was utilized to correct
the CSD low order main rotor airloads. A propulsive trim is once again performed
with the delta correction. Then the main rotor deflections, fuselage pitch attitude
and propeller collective are manually transfered back to the CFD solver. The data
transfer between CFD and CSD solvers continues until convergence is achieved for
the rotor controls, sectional airloads and propulsor power.
76
5.3 CFD/CSD Coupling Validation
The rotor CFD/CSD coupling procedure discussed in this chapter was vali-
dated using the existing full scale UH-60A rotor wind tunnel test data, obtained
May 2010 in the 40-by-80-Foot NFAC wind tunnel Ref. [83]. An in-depth discussion
of the wind tunnel test and the results is given in Ref. [83]. One of the four UH-60A
rotor blades was instrumented with 235 pressure transducers, distributed along the
chord at the nine spanwise locations. The sectional normal force, chordwise force
and pitching moment along the blade were integrated from the chordwise pressure
distributions. The wind tunnel case, 5240, is representative of a high-speed level
flight condition with advance ratio of ? = 0.3, blade loading of CT/? = 0.09 and ad-
vancing tip Mach number MAdv.T ip = 0.65. The Helios/OVERFLOW CFD solvers
were coupled with the in-house comprehensive analysis solver. Wind tunnel trim
was performed with four harmonics and eight blade modes, trimming the rotor to
target thrust, rolling and pitching moments. Figure 5.3 shows the sectional normal
force and pitching moment at two spanwise stations along the blade, r/R = 0.225
and r/R = 0.865. The CFD/CSD predicts reasonably well the normal force trends.
There is negative loading on the outboard stations of the blade, in the second quad-
rant, due to decreased angle of attack resulting from the the need to maintain equi-
librium of the roll moments. However, the magnitude of the negative normal force
peek is under-predicted. The normal force trends on the retreating side, quadrants
3 and 4, matches reasonably well to the test data. These results were approved for
public release and presented at the 2017 UH-60A Airloads workshop [84].
77
(a)
(b)
Figure 5.3: Comparison of predicted CFD/CSD airloads with the wind tunnel test
data for UH-60A rotor.
78
6 Results Part I: Coaxial Rotor CFD/CSD Coupling
This chapter discusses the results from the coaxial rotor CFD/CSD coupling
study. In this study, the CFD simulations included only the coaxial rotor system,
consisting of an upper rotor, rotating counter-clockwise, and the lower rotor, rotating
clockwise. Figure 6.1 shows the coaxial rotor system utilized for this study. Take
note that the airframe and pusher propeller were not present in the CFD simulations.
However, a full vehicle propulsive trim was performed in the CSD and a delta
coupling procedure was used to correct the low order rotor CSD airloads. The results
shown in this section are from converged coaxial CFD/CSD coupling iterations.
The first objective of the coaxial rotor CFD/CSD coupling study was to iden-
tify and explain the effect of forward flight speed on the trim parameters, blade
deflections and airloads. Table 6.1 shows the five forward flight speeds that were
investigated. The LOS value for the each flight condition was obtained from a lin-
ear interpolation of the flight test data presented in Ref. [5]. The second objective
was to analyze the rotor-rotor interactions at 50 knots and explain the interactional
effects on the trim parameters and performance of the rotor. The same CFD/CSD
coupling procedure, as above, was performed. However, for the non-interactional
case the CFD runs were performed with isolated rotors.
79
Figure 6.1: The coaxial CFD/CSD coupling mesh system and Q-criterion flow vi-
sualization for coaxial rotor at 50 knots.
Table 6.1: Coaxial CFD/CSD coupling forward flight speeds.
V? (knots) ? MR RPM MADV LOS(%R)
50 0.14 446 0.64 3.75
100 0.27 446 0.71 7.50
150 0.41 446 0.79 11.3
200 0.55 446 0.87 15.0
225 0.65 423 0.88 16.9
80
6.1 Main Rotor Controls and Vehicle Pitch Attitude
This section discusses the effect of flight speed on the trim configuration of the
vehicle. The control angles and the vehicle pitch attitude are examined at various
flight speeds given in the Table 6.1. Figure 6.2 and Table 6.2 show the coaxial rotor
controls and fuselage pitch attitude. The following sections will analyze and explain
the trends shown in Fig.6.2(a) and (b).
6.1.1 Rotor Collective (?0) and Fuselage Pitch
This subsection examines the upper and lower rotor collective and vehicle
pitch attitude as a function of flight speed for final CFD/CSD coupling iterations.
Between 50 and 100 knots, the vehicle pitch attitude changes from a tilt fore to a
tilt aft orientation. The pusher propeller begins to contribute a substantial amount
of the propulsive thrust to counteract the vehicle drag. This results in a decrease
of the collective angle, since the rotor does not need to provide both the propulsive
thrust and the lifting force. Note that in the CSD, the pusher propeller thrust is
prescribed in a look-up table and the vehicle is trimmed to account for the pusher
propeller thrust, as described in the Methodology section.
From 100 knots to 150 knots, the rotor collective decreases and the vehicle
pitch attitude also slightly decreases. The collective decreases because the rotor is
offloaded since the pusher propeller is providing the propulsive thrust to counteract
the vehicle drag. However, the vehicle does not need to tilt back as much compared
to 100 knots, to counteract the propulsive force from the pusher prop in the trim
81
(a) (b)
Figure 6.2: The final coaxial CFD/CSD main rotor controls (a) and vehicle pitch
attitude (b) at various speeds.
Table 6.2: The final coaxial CFD/CSD controls and vehicle pitch attitude at various
speeds. The control angles and the vehicle pitch attitude are shown in degrees.
V (knots) ? ?CCW ?CW CCW? F 0 0 ?1c ?
CW ?CCW1c 1s ?
CW
1s
50 -0.42 9.58 9.86 3.61 3.61 -3.15 2.70
100 2.37 5.99 5.95 2.15 2.15 -3.85 3.40
150 2.00 5.59 5.56 0.94 0.94 -5.10 4.81
200 1.88 5.84 5.80 0.11 0.11 -6.62 6.40
225 2.90 5.44 5.09 -0.92 -0.92 -7.16 6.65
82
process, because the drag on the rotor is substantially high.
Fromm 150 knots to 200 knots, the rotor collective slightly increases. At
200 knots, the rotor wake is convected straight back thus each rotor is forced to
operate in it?s own wake. The wake-rotor interactions result in decrease of rotor
thrust, therefore the rotor collective needs to be increased at this operational speed.
From 200 knots to 225 knots, the rotor wake is convected through the upper rotor,
reducing the downwash.
There is less than one percent difference between the upper and the lower
rotor collectives for the 100, 150 and 200 knots, shown in Fig.6.2(a). However, at
flight speeds of 50 knots and 225 knots, the difference between the upper and the
lower collective increases to more than three percent. At 50 knots, the lower rotor
is trimmed to a higher collective than the upper rotor and the vehicle has a forward
tilt, as shown in Fig.6.2(b). The wake from the upper rotor is convected down and
backwards, through the aft portion of the lower rotor disk, as shown in Fig.6.1. The
wake from the upper rotor impinges on the lower rotor, causing lower rotor to loose
thrust, which in turn is forces the lower rotor to trim to higher collective in order to
maintain the required thrust. A similar but opposite scenario occurs at 225 knots.
At 225 knots, the upper rotor collective is higher than the lower rotor collective and
the vehicle is titled aft. The backward tilt of the vehicle forces the wake of the lower
rotor to be ingested into the upper rotor, causing the upper rotor to loose lift and
needing to operate at a higher collective.
83
6.1.2 Cyclic Pitch ?1s and Cyclic Pitch ?1c
Rotor control, ?1s, is associated with lift-offset, shown in Table 6.1. Lift-offset
is a measure of the displacement of the thrust vector from the center of the hub. In an
SMR configuration, the roll moment balance is achieved from the equilibrium of the
thrust on advancing and retreating sides of the disk. The time-averaged thrust acts
at the center of the rotor hub. The thrust produced on the advancing side is limited
by the amount of thrust produced on the retreating side. In a coaxial configuration,
the roll moment equilibrium is achieved from the balance of roll moments of each
rotor. This offloads the retreating side and allows the advancing side to produce
more lift. As the speed increases, the LOS also increases, resulting in an increase
in the ?1s. An independent CSD study was conducted to observe the effect of LOS
at various speeds. Without lift offset, thrust vector acts at the axis of rotation,
the pitch angle on the advancing side was minimum. As the lift offset increased
the pitch angle on that advancing side also increased. The cyclic control, ?1c, is
associated with the control of the pitch on the fore and the aft of the rotor disk.
As the speed increases, the ?1c decreases, which is indicative of a shift in pitch bias
towards the advancing side of the rotor disk
6.2 Blade Pitch and Flap
This section shows the effect of the forward flight speed on the blade tip pitch
and blade tip flap angles. It follows as an extension of the previous section where
the collective and the cyclic pitches were given in the Table 6.2 and Fig.6.2(a).
84
The five forward flight speeds discussed in this section are shown in Table 6.1. A
positive blade pitch is defined as a pitch-up rotation about the blade quarter chord.
A positive flap is defined as a flap-up motion of the blade.
Figure 6.3 shows the time-history of the elastic blade tip pitch deflection for
the speeds given in Table 6.1. The upper rotor blade tip pitch is shown in Fig.
6.3(a), while the lower rotor blade tip pitch is shown in Fig.6.3(b). An increase
in forward flight speed results in a decrease of the minimum blade pitch on the
advancing side. This is due to an increase in the LOS and the decrease in the ?1s,
as shown in Fig.6.2(a) The location of the minimum blade pitch on the advancing
side shifts to an earlier azimuthal location as the speed increases. This is a result
of the decrease in the ?1c, Fig.6.2(a). At the 50 knots speed, the blade pitch on
the advancing side differs significantly compared to the rest of the speeds, which
is a reflection of the trim state at that speed. The pusher propeller only provides
roughly 18 pounds of thrust at 50 knots, therefore the rotor needs to provide enough
thrust to counteract the weight from the vehicle as well as the drag of the vehicle,
resulting in a high collective.
Figure 6.4 shows the time-history of the rotor elastic blade tip flap deflection
for the speeds given in the Table 6.1. The upper rotor, Fig.6.4(a), experiences an
increase in the flap-down motion on the aft portion of the rotor disk as a result of
increase in speed.
The flap-up motion on the advancing and retreating sides, at ? = 90 and
? = 270, is predominantly associated with roll moment of the rotors. For a single
main rotor, the roll moment equilibrium is achieved by utilizing both, the advancing
85
(a) (b)
Figure 6.3: Upper rotor and lower rotor tip pitch deflections for coaxial and full
vehicle CFD/CSD coupling at a range of forward flight speeds.
(a) (b)
Figure 6.4: Upper rotor and lower rotor tip flap deflections for coaxial and full
vehicle CFD/CSD coupling at a range of forward flight speeds.
86
and the retreating side. In contrast, for the coaxial rotor configuration, the roll
moment equilibrium can be achieved by utilizing the advancing sides of the upper
and the lower rotors using lift-offset. As previously mentioned, lift-offset is a measure
of displacement of the thrust vector from the rotational axis of the rotor. At 50
knots, the lift-offset is relatively small, LOS = 3.75%R, resulting in the advancing
and the retreating sides of the rotors are producing roughly similar roll moments,
as shown in Fig.6.4(a) and Fig.6.4(b). As flight speed increases so does the LOS,
resulting in higher flap-up and more roll moment on the advancing side.
6.3 Rotor Airloads
This section presents the airloads for various speeds and conditions given in
Table 6.1. Figure 6.5 shows contour plots of the non-dimensional normal force,
pitching moment and chordwise force distributions on the upper rotor, rotating
counter-clockwise. The airloads for the lower rotor, rotating clockwise, are shown
in Fig. 6.6. The airloads presented in this section are shown in the deformed airfoil
frame. The normal force is positive up, pitching moment is positive for pitch-up
and chordwise force is positive from the trailing edge to the leading edge.
The upper and lower rotor normal force distribution for forward flight speeds
of 50 ? 225 knots are shown in the Fig. 6.5(a) and Fig. 6.6(a), respectively. A
redistribution of normal force over the rotor disk is observed from the comparison
of the normal force contours across the range of forward flight speeds. At the lowest
speed, 50 knots, the normal force is distributed around the rotor disk, with highest
87
(a)
(b)
(c)
(d)
Figure 6.5: The upper rotor airloads for a range of speeds.
88
(a)
(b)
(c)
(d)
Figure 6.6: The lower rotor airloads for a range of speeds.
89
(a) Upper Rotor
(b) Lower Rotor
Figure 6.7: The upper(a) and lower(b) rotor sectional normal force for a range of
speeds.
90
(a) Upper Rotor
(b) Lower Rotor
Figure 6.8: The upper (a) and lower rotor (b) sectional pitching moment for a range
of speeds.
91
normal force along the outer portion of the blade. At the highest speed, most of
lift is distributed on the fore and aft portions of the rotor disk, biased toward the
advancing side. The redistribution of lift towards the fore and aft of the rotor disk
observed at the intermediate speeds, 100 ? 200 knots, is related to the decrease in the
cyclic pitch ?1c, which causes a shift in the minimum pitch towards the advancing
side as shown in Fig.6.3. Starting at a 100 knots, decrease in normal force on
the advancing blade tip, is observed in the first quadrant. This region of negative
normal force on the advancing side, grows in both azimuth and span, with increased
speed. This is a consequence of the increase of the cyclic pitch ?1s, which increases
with forward flight speed. Even though there is an increase in the lift-offset and an
offloading of the retreating side, the cyclic pitch ?1s is still substantially high. The
magnitude of the ?1s and the negative twist on the tip of the blade cause a negative
angle of attack on the outboard portions of the blade on the advancing side.
Figures 6.5(b) and 6.6(b) show the contours of the pitching moment at various
forward flight speeds for upper and lower rotors. There is an increase in the negative
pitching moment on the advancing side, roughly ? = 45 to ? = 135 degrees, on
the outboard regions. On the retreating side, there is an increase in magnitude
of the nose-up pitching moment and an increase in spanwise extent of this region,
characteristic of the reverse flow region. At the two higher speeds, there is an
isolated region of negative pitching moment, in the third quadrant, which may be
indicative of dynamic stall. On the aft of the rotor disk, ? = 0 degrees, increase in
positive pitching moment can be observed close to the tip of the blade due to the
blade vortex interactions. The magnitude of the pitching moment due to the 8P
92
blade passage also increases with forward flight speed.
Figure 6.5(c) and 6.6(c) show the chordwise force distribution on the upper
rotor for a range of forward flight speeds. The distribution of the chordwise force
on the rotor disk significantly changes as a function of forward flight speeds. At low
speeds, 55 and 100 knots, the positive chordwise force is observed over the majority
of the rotor disk, with coon the outer portions of the blade on the front half of
the disk, ? = 90 to ? = 270 degrees. The contour levels show that the highest
positive chordwise force is located on the outboard stations of the retreating blade,
? = 225 to ? = 270 degrees, at 55 knots. At 225 knots, the contour levels show that
the highest positive chordwise force is observed on the midspan at ? = 90 degrees.
Relatively low chordwise force is observed inboard at the front of the disk. With an
increase in forward flight speed, the distribution of the positive chordwise force in
this region moves inward.
The sectional normal force, shown in Fig.6.7, and the pitching moment, shown
in Fig.6.8, show the vortex induced loading at low speeds as well as the dynamic
stall phenomena at the highest speed. At the lowest flight speed, the interactions
between the blades and the trailing vortices from the previous blades result in vortex
induced loading at in the third quadrants, shown in Fig.6.8(b).
6.4 Coaxial Rotor Interactional Aerodynamics - 50 Knots
The objective of this section is to examine the interactional aerodynamics
between the upper and the lower rotors of a coaxial rotor system. In previous
93
section it was observed that at the lowest speed, 50 knots, there was a substantial
difference in the upper and the lower collectives. The difference in the collectives was
deemed to be a result of the interactional aerodynamics. This theory was tested out
by running an additional CFD/CSD case, isolating upper and lower rotor in CFD
but re-coupling forces from both rotors in CSD. This additional case isolated the
interactional effects and showed effect of rotor-rotor interactions on the final trim
solution. This latter case was initialized with the same initial CSD trim solution
as in the coaxial CFD/CSD coupling 50 knot case discussed in previous section,
where aerodynamics depend purely on the low order aerodynamic model and no
CFD/CSD coupling has been performed.
Figure 6.9 shows the upper and the lower rotor normal force distribution,
utilizing initial CSD deflections, for interactional (Case 1) and non-interactional
(Case 2) cases. Take note that the CFD/CSD coupling procedure has not been
performed yet and the objective of analyzing this set of airloads is to understand
the effect of the interactional aerodynamics on the airloads. Also, the deflections for
the upper and the lower rotor, for initial CSD, are almost identical. For the given
deflections, there is a significant loss in normal force produced in the 3rd quadrant
for the lower rotor, when the lower rotor is operating below the upper rotor. The
induced velocity from the upper rotor wake decreases the sectional angle of attack,
reducing the lift on the lower rotor. The lower rotor does not produce the same
amount of normal force as the upper rotor at the given collective. Therefore in
order for the lower rotor to produce the required normal force it needs to operate
with higher collective. The isolated lower rotor, operating with the same deflection
94
(a) Upper rotor (b) Lower rotor
(c) Upper rotor
(d) Lower rotor
Figure 6.9: The upper and lower rotor normal force at 50 knots for interactional
and non-interactional case utilizing deflections from CSD0.
95
as the lower rotor in the coaxial rotor system does not see the extreme drop in lift
in the first quadrant. The lower rotor and the upper rotors, in isolation, produce
higher normal force compared to the rotors operating in the coaxial rotor system.
The difference in the normal force for the rotors operating in isolated and coaxial
configuration foreshadows the difference in the final trim state of the vehicle at these
two different configurations.
Table 6.3 shows the initial and the converged coaxial CFD/CSD control angles
and the vehicle pitch attitude at 50 knots for the two cases. The interactional case
(Case 1) results in the upper and the lower rotor being trimmed to different final
collectives, whereas, the non-interacting case (Case 2) results in the same collective
for the upper the lower rotors. The final upper and the lower rotor, for Case 1, are
trimmed to a higher collective than the initial CSD collectives, while the rotors in
Case 2 were trimmed to lower collectives than the initial CSD. It was observed, in
Fig.6.9(c) and (d), that the normal force for the upper and the lower rotor in Case 2
was very similar. Thus, it is of no surprise that without any interactions the upper
and the lower rotor were trimmed to similar values. It was also observed that in the
interactional case the lower rotor produced less normal force than the upper rotor.
Therefore the final collective of the lower rotor is slightly higher than that of the
upper rotor, for the interactional case. The difference plot showed that the rotors in
isolation produced more normal force than those in the coaxial configuration, which
explains the change in the final collectives for both cases compared to the initial
predictions.
For both cases, the rotors were trimmed to a higher final cyclic pitch ?1c
96
Table 6.3: The final coaxial CFD/CSD controls and vehicle pitch attitude at 50
knots with interactional effects (Case 1) and without interactional effects (Case 2).
?CCW ?CW ?CCW ?CW ?CCW0 0 1c 1c 1s ?
CW
1s ?F
Initial 8.12 8.12 0.25 0.25 -1.99 1.99 -0.38
Case 1 9.58 9.86 3.61 3.61 -3.15 2.70 -0.42
Case 2 7.46 7.46 2.48 2.48 -1.81 1.74 -0.68
(a) (b)
Figure 6.10: The upper and the lower rotor tip pitch and flap deflections for inter-
actional and non-interacting cases at 50 knots.
97
compared to the initial prediction. The tip pitch deflection is shown in Fig.6.10(a).
The initial CSD prediction trimmed the rotors to very low cyclic pitch ?1c as shown
in Table 6.3. The low ?1c resulted in similar blade pitch on the fore and the aft of
the rotor disk which produced a significant imbalance of normal force on the rotor
disk, especially for the lower rotor in Case 1. Thus, the final cyclic pitch ?1c was
increased to lower the blade pitch over the nose of the aircraft, where high normal
force concentration was observed, and increase the blade pitch over the tail.
Figure 6.11 shows the contour plots of the normal force distribution, on the
upper and the lower rotors, for the final CFD/CSD iteration of the interactional
and non-interactional case at 50 knots. The CFD/CSD coupling procedure was
performed until the trim solution did not vary significantly. The difference between
Case 2 and Case 1 normal force is also shown in Fig. 6.11. The sectional normal
force at two radial locations, 45%R and 98%R, is shown in Fig. 6.12 (a) and (b).
The non-interactional case, Case 2, shows the upper and the lower rotor to have
almost identical normal force distribution, which is a result of similar blade pitch
distribution. The difference plots, for the upper and the lower rotors, show that
Case 1 has higher normal force distribution on the outboard stations, at the front
of the rotor disk. In these regions of the rotor disk, the Case 1 blade pitch is higher
than for Case 2. It can also be said that the tip vortices are stronger for Case 1. In
both cases, upper and lower rotor have very high normal force on outboard sections
of the blades in 2nd and 3rd quadrants. Blade vortex interactions are responsible
for the high normal force. The tip vortices from previous blades are staggered above
98
the blade at 180 degrees from the retreating blade is traveling above the blade in
these quadrants.
For the upper rotor and the lower rotor, the non-interactional case shows a
loss in normal force in the first quadrant and third quadrants near the tip of the
blade as shown in Fig.6.12(b). The upper and the lower rotor in the interactional
case also experience a drop in the normal force in the first and third quadrants. This
drop in the normal force in the first and the third quadrants are due to the tip of
the blade passing through the coalescence of the tip vortices from previous blades.
Figures 6.13 and 6.14 show the pitching moment contour plots for the upper
and the lower rotors, for interactional and non-interactional cases. The interactional
case exhibits strong 8P impulses in the pitching moment every 45 degrees which are
absent from the non-interactional case. The impulses are due to the blade crossings.
The 8P impulses are stronger for the upper rotor in the interactional case.
99
(a) Upper rotor (b) Lower rotor
(c) Upper rotor
(d) Lower rotor
Figure 6.11: The upper (a) and lower (b) rotor normal force at 50 knots for inter-
actional and non-interactional case at final CFD/CSD coupling iteration.
100
(a) Upper Rotor
(b) Lower Rotor
Figure 6.12: The upper (a) and lower (b) rotor sectional normal force at 50 knots
for interactional and non-interactional case.
101
(a) Upper rotor (b) Lower rotor
(c) Upper rotor
(d) Lower rotor
Figure 6.13: The upper and lower rotor pitching moment at 50 knots for interactional
and non-interactional case.
102
(a) Upper Rotor
(b) Lower Rotor
Figure 6.14: The upper (a) and lower (b) rotor sectional normal force at 50 knots
for interactional and non-interactional case.
103
7 Results Part II: Vehicle CFD/CSD Coupling
This chapter examines the effect of the full vehicle CFD/CSD coupling on the
final trim parameters, elastic blade deflections, aerodynamic and structural loads.
The results from the full vehicle CFD/CSD coupling and the coaxial rotor CFD/CSD
coupling are compared. Some of the results described in the following chapter were
briefly discussed in Ref. [85]. The full vehicle CFD/CSD coupling simulations are
more expensive than the coaxial rotor CFD/CSD coupling simulations; an addi-
tion of the unstructured helicopter airframe and unstructured propeller to the CFD
increases the CFD computation time by a factor of five. Thus, it is important to
demonstrate the effects that the full vehicle CFD/CSD coupling has on the final trim
state of the vehicle. Each vehicle CSD iteration involves a auxiliary propeller wind
tunnel trim and a separate full vehicle trim. There are various differences between
the isolated coaxial CFD/CSD trim procedure and a full helicopter configuration
procedure:
1. The addition of the airframe and the auxiliary propeller in the CFD simula-
tions.
2. The input of the time-averaged airframe loads and time-averaged auxiliary
propeller power from the CFD into the comprehensive analysis.
104
3. The auxiliary propeller is trimmed for the target power obtained from the
literature [6], while accounting for the installation effects.
The results in this section are shown for a forward flight speed of 150 knots, with
case parameters given in Table 7.1.
Table 7.1: CFD interactional aerodynamics case
V?(knots) ? MR RPM Madv.tip LOS(%) Blade Modes Harmonics
150 0.41 446 0.79 11.3 6 8
7.1 Trim Parameters
This section examines the effects of the full vehicle CFD/CSD coupling on the
control angles of the coaxial rotor system and the attitude of the airframe, as well
as the propeller collective. The rotor deflections from an isolated coaxial CFD/CSD
simulations were used as a starting point for the full vehicle CFD/CSD coupling
process. However, it is not necessary to start the full vehicle CFD/CSD coupling
process from an isolated coaxial rotor cases. Nine coupling iterations were performed
for the full CFD/CSD coupling case, ensuring that the trim parameters did not vary
significantly with consecutive iterations.
Understanding of the mechanisms responsible for the differences between the
final trim controls, of the coaxial CFD/CSD and the full vehicle CFD/CSD, can
be achieved by analyzing the force and moment equilibrium of the vehicle. For the
vehicle to be in trim, the force and moment equilibrium must be enforced at CG,
105
for every rotor revolution. The force and moment contributions are closely tied to
the rotor trim controls and the vehicle attitude. Thus, this subsection will focus
on relating the changes in the vehicle forces/moments to the main rotor controls
and airframe attitude. The forces and moments described in this section are along
an axis where xCG points towards the tail, the yCG points starboard, and the zCG
points upward. The center of this axis lies at the CG of the aircraft.
Figure 7.1 shows the convergence of main rotor control angles and the fuselage
pitch attitude over various trim iterations (CFD/CSD coupling cycles) at 150 knots.
The trim iterations 0 through 4, shown in the green section of Fig. 7.1, represent the
coaxial rotor system CFD/CSD coupling procedure. The trim iterations 5 through
13, shown in the yellow section of Fig. 7.1, represent the full vehicle CFD/CSD
coupling. There is a difference between the two cases, predominantly due to the in-
teractional aerodynamic effects on the airframe and coupling of the airframe airloads
from CFD into CSD.
Figure 7.1(a) shows the convergence of the collective angle for the upper and
the lower rotors, for coaxial rotor system alone as well as for vehicle CFD/CSD
coupling. The collective angles for the upper and the lower rotor, from the coaxial
CFD/CSD coupling, trimmed to similar values. After the inclusion of the airframe
and the auxiliary propeller in the CFD simulations (trim iteration 5 and greater),
the upper rotor collective was reduced while the lower rotor collective was increased.
The differential in the collective can be explained from comparing the airframe
yaw moments at CG from 4th and 13th trim iterations. Figures 7.2(d-f) show the
airframe aerodynamic roll, pitch and yaw moments at CG at 4th and 13th trim
106
Table 7.2: Comparison between final coaxial CFD/CSD and full vehicle CFD/CSD
coupling at 150 knots.
150 Knots Coax CFD/CSD Full Vehicle CFD/CSD
6.02 (CCW) 5.76 (CCW)
Collective (deg)
5.95 (CW) 7.04 (CW)
0.96 (CCW) 2.43 (CCW)
Cyclic ?1C (deg)
0.96 (CW) 2.43 (CW)
-5.49 (CCW) -5.63 (CCW)
Cyclic ?1S (deg)
5.16 (CW) 6.54 (CW)
Fuselage Pitch (deg) 2.01 2.85
107
(a) (b)
(c) (d)
Figure 7.1: Rotor controls and fuselage attitude convergence history for coax and
full vehicle CFD/CSD coupling at 150 knots.
108
(a) (b) (c)
(d) (e) (f)
Figure 7.2: Convergence of airframe loads at CG at 150 knots.
Figure 7.3: Pusher propeller thrust convergence at 150 knots.
109
the clockwise moment from the airframe.
Figure 7.1(b) compares the convergence of the ?1s control angle between the
coaxial and the full vehicle CFD/CSD coupling. There is a difference between the
final trimmed coaxial CFD/CSD and the final full vehicle CFD/CSD ?1s control
angle, for both the upper and the lower rotor. For the final full vehicle CFD/CSD
coupling, the lower rotor ?1s trimmed to a higher value than the upper rotor, provid-
ing excessive roll moment starboard side down. This can be explained by analyzing
the difference in the roll moment on the airframe for the two different coupling
methodologies. There is also a negative aerodynamic roll moment, port side down,
at CG produced by the airframe, shown in Fig.7.2(d). In order for the system to
be in trim, the roll moment from the airframe needs to be compensated by the
differential roll moment from the rotors.
Figure 7.1(c) shows that there is an increase in the ?1c control angle from trim
iteration 4 (coaxial CFD/CSD) to trim iteration 13 (full vehicle CFD/CSD). The
increase in the ?1c control angle can be explained by analyzing the pitching moment
produced by the airframe. Figure 7.2(e) shows an increase in the nose-down airframe
pitching moment. The pitching moment produced by the rotors needs to increase
to counteract the nose down pitching moment produced by the airframe, resulting
in an increase of the ?1c.
The axial body force, Fx, equilibrium is related to the airframe pitch attitude
through the balance of the helicopter drag and the propeller thrust. The axial force
from the coaxial rotor system and the airframe must be counteracted by the auxiliary
propeller. The coaxial CFD/CSD coupling procedure assumes an approximation for
110
the prop thrust, calculated from a simple relation, P = TV , where P is the propeller
power for the X2TD given in Ref. [46]. Whereas, in the full vehicle CFD/CSD
coupling procedure, the propeller thrust is obtained from the propeller CFD airloads
for the propeller trimmed to the required power given in Ref. [46]. Figure 7.1(b)
shows an increase in the rearward tilt of the rotor disk, between trim iteration 4
and 13. The rotor disk is tilted rearward to counteract an increase in the propeller
thrust, shown in Fig. 7.3.
7.2 Main Rotor Blade Pitch and Flap
This section examines the effects of the full vehicle CFD/CSD coupling on the
upper and the lower rotor blade tip pitch and flap deflections. The pitch shown in
this section is a combination of the control pitch and the elastic twist, it does not
take into account the blade geometric twist angle.
Figure 7.4 shows the tip pitch angle of the main rotor blade, as the blade
travels around the azimuth. Take note that the azimuth is shown in the local rotor
reference frame where a positive pitch angle represents a pitch-up motion around
the quarter chord line while a negative pitch angle represents a pitch-down motion
around the quarter chord line. Figure 7.4(a) compares the upper rotor tip pitch
obtained from the final coaxial CFD/CSD trim (Trim 4) and the final full vehicle
CFD/CSD trim (Trim 13). The nomenclature for trim iterations is consistent with
the one shown in the previous section. A 1P pitch variation is observed for both
coaxial and full vehicle CFD/CSD coupling cases.
111
Table 7.3: Comparison between final coaxial CFD/CSD and full vehicle CFD/CSD
pitch deflection coupling at 150 knots.
150 Knots Coax CFD/CSD Full Vehicle CFD/CSD
5.83 (CCW) 5.61 (CCW)
Mean Pitch (deg)
5.76 (CW) 6.86 (CW)
5.72 (CCW) 6.31 (CCW)
1P Pitch Amplitude (deg)
5.39 (CW) 7.15 (CW)
The full vehicle CFD/CSD coupling approach resulted in a decrease of upper
rotor mean tip pitch and an increase in 1P pitch amplitude, shown in Fig.7.4(a) and
Table 7.3. The lower rotor experienced an increase in mean tip pitch, as well in an
increase in 1P amplitude, shown in Table 7.3 and Fig.7.4(b). The lower rotor mean
pitch increase and upper rotor mean pitch decrease is due to the need to counteract
the additional yaw moment from the airframe, as described in previous section.
An increase in the 1P variation reflects an increase in the roll moment needed to
counteract the additional airframe roll moment.
The coaxial CFD/CSD coupling approach resulted in the upper and the lower
rotors being trimmed to similar pitch deflections, with small differences on the ad-
vancing side near ? = 90 degrees and the retreating side near ? = 270 degrees,
shown in Fig.7.6(a). The upper and the lower mean tip pitch angle, obtained with
the coaxial CFD/CSD approach, shown in Table 7.2, differed by roughly 0.05 degrees
with less than 0.5 degree difference in the 1P amplitude. The small differences in
112
the upper and lower pitch can be attributed to interactional aerodynamics between
the rotors.
Figure 7.5(a) compares the upper rotor tip flap angle for the coaxial and the
full vehicle CFD/CSD coupling methods. The coaxial CFD/CSD coupling approach
trims the rotor to flap down over the vehicle tail and flap up over the nose. The full
vehicle CFD/CSD coupling approach results in a nearly zero upper rotor blade flap
over the tail of the vehicle, with small positive blade flap over the nose. Similarly for
the lower rotor, the coaxial CFD/CSD coupling results in the blades flap down over
the tail and flap up over the nose, as shown in Fig.7.5(b). However, the full vehicle
CFD/CSD coupling approach results in a nearly zero lower rotor blade flap over the
tail of the vehicle, with some positive blade flap over the nose. The flap over the
nose produces a cumulative rotor hub pitching moment to counteract the pitching
moment from the airframe and horizontal stabilizers. As discussed in the previous
section and as shown in 7.2(e), the pitching moment produced by the airframe was
lower for full vehicle CFD/CSD coupling approach, therefore the rotors did not
have to produce as much pitching moment as for the coaxial CFD/CSD coupling
procedure.
Figure 7.6(b) shows the lower and the upper rotor tip flap deflection, from
the coaxial and the full vehicle CFD/CSD approach, on the same plot. The coaxial
CFD/CSD coupling approach results in the upper and the lower rotor having indis-
tinguishable flap up deflection on the advancing side, ? = 90 degrees, as well as on
the retreating side, ? = 270 degrees. The full vehicle CFD/CSD approach results in
the lower rotor having larger flap angle than the upper rotor, on both the advancing
113
(a) (b)
Figure 7.4: Upper rotor and lower rotor tip pitch deflections for coaxial and full
vehicle CFD/CSD coupling at 150 knots.
(a) (b)
Figure 7.5: Upper rotor and lower rotor tip flap deflections for coaxial and full
vehicle CFD/CSD coupling at 150 knots.
114
Figure 7.6: Upper and lower rotor tip flap and pitch deflections for coaxial and full
vehicle CFD/CSD coupling at 150 knots.
and the retreating sides. The differential in flap angle for full vehicle CFD/CSD
coupling approach stems from the need to balance the port roll moment produced
by the airframe.
7.3 Main Rotor Airloads
This section examines the upper and lower rotor airloads at the final coaxial
CFD/CSD coupling iteration and full vehicle CFD/CSD coupling iteration. The
objective of the section is to identify and analyze the differences in the rotor airloads
resulting from the presence of the airframe and the auxiliary propeller and CFD as
well as in the CFD/CSD coupling exchange.
115
7.3.0.1 Normal Force - Upper and Lower Rotor
This subsection examines the effects of full vehicle CFD/CSD coupling and the
presence of the airframe/propeller in CFD simulations on the normal force produced
by the upper and the lower rotor. The azimuth convention for the upper rotor is
given in Fig.7.7(a), which shows a top view diagram of the upper rotor disk rotating
counter-clockwise. Figure 7.7(b) shows the upper rotor non-dimensional normal
force. The diagram labeled (1) in Fig.7.7(b) shows the normal force from the final
coax CFD/CSD coupling iteration, where the CFD simulations included only the
coaxial rotor system. The diagram labeled (2) in Fig.7.7(b) shows the normal force
from the full vehicle CFD simulations in which the rotor utilized the elastic blade
deflections from the final coaxial CFD/CSD coupling iteration. Therefore, the only
difference between the two data sets labeled (1) and (2) is the presence of the
airframe and the auxiliary propeller in CFD. The diagram labeled (3) in Fig.7.7(b)
shows the normal force from the final full vehicle CFD/CSD simulation. Figure
7.7(c) shows the difference between the normal force in datasets (1) through (3)
shown in Fig.7.7(b).
The first diagram in Fig.7.7(c), labeled (2)?(1), is the difference in upper rotor
normal airloads between the (1) coaxial CFD/CSD simulation and (2) full vehicle
CFD simulation utilizing same deflections as (1). The difference plot shows that in
the presence of the airframe in the CFD, the normal force increases on the outboard
sections of the upper rotor, over the nose of the aircraft. There is an upwash over
the nose of the aircraft, decreasing the Up velocity at blade section, increasing the
116
(a)
(b)
(c)
Figure 7.7: Non-dimensional normal force distribution for upper rotor, rotating
counter-clockwise.
117
sectional angle of attack on the blade over the nose. In the presence of the airframe,
there is a decrease in rotor normal force over the tail due to the downwash produced
by the airframe and the wake from the mast.
The second diagram in Fig.7.7(c), labeled (3) ? (1), shows the difference be-
tween the upper rotor normal force obtained using the full vehicle CFD/CSD cou-
pling approach and the coaxial CFD/CSD coupling approach, see plots (3) and (1)
in Fig.7.7(b). The difference plot shows that the full vehicle CFD/CSD coupling
trimmed the rotor to produce higher normal force in the first quadrant and lower
normal force in the second quadrant. This can be correlated back to the blade pitch.
Figure 7.4(a) showed that the blade tip pitch obtained with full vehicle CFD/CSD
coupling was higher in the first quadrant and fourth quadrant but lower in the
second and third quadrants compared to the coaxial CFD/CSD coupling.
The upper rotor non-dimensional sectional normal force at selected radial sta-
tions is shown in Fig. 7.8). The plot compares the sectional normal force for three
datasets discussed above. The presence of the fuselage is observed over the nose
of the aircraft (around 180 degrees), resulting in an increase of the sectional nor-
mal force and over the tail (around 0 degrees) resulting in the decrease of sectional
normal force. The increase and decrease of normal force is more prominent on the
outboard stations of the blades and on lower rotor. Again, the differences between
the coaxial CFD/CSD coupling and the vehicle CFD/CSD coupling sectional nor-
mal force near the tip of the blade can be explained in terms of the blade tip pitch,
Fig. 7.4(a).
Figure 7.9(a) shows the azimuth convention for the lower rotor. Note the
118
Figure 7.8: Comparison of upper rotor sectional normal force at 150 knots.
change in the location of the advancing and the retreating sides. Since the lower
rotor is rotating clockwise, the advancing side of the lower rotor is on the port side
of the aircraft.
Figure 7.9(b) compares the lower rotor normal force for three data sets: (1)
final coaxial CFD/CSD coupling simulation, (2) vehicle CFD simulation utilizing the
elastic blade deformations from final coaxial CFD/CSD simulation and (3) final full
vehicle CFD/CSD coupling simulation. Figure 7.9(c) shows the difference between
the three data sets, (1) through (3). The first diagram in Fig.7.9(c) shows the
difference between dataset (2) and dataset (1). The presence of the airframe results
in higher normal force on the fore portion of the rotor disk, over the nose of the
aircraft, while the shedding from the mast and the downwash over the tail of the
aircraft result in lower normal force on the aft portion of the rotor disk. The second
diagram in Fig.7.9(c) shows the difference between lower rotor normal force predicted
119
(a)
(b)
(c)
Figure 7.9: Non-dimensional normal force distribution for lower rotor, rotating
clockwise.
120
with the full vehicle CFD/CSD coupled approach and the coaxial CFD/CSD coupled
approach. The final full vehicle CFD/CSD approach predicts higher lower rotor
normal force in the first quadrant over majority of the blade, as well as an increase in
normal force on the outboard stations of the blade on the retreating side, quadrants
3 and 4. The difference between the normal force predicted with the full vehicle and
the coaxial CFD/CSD approaches is due to the difference in the predicted blade
pitch Fig.7.4(b) and the need to counteract the airframe moments. Figure 7.10
shows the azimuthal distribution of the lower rotor sectional normal force at two
radial locations, 49%R and 98%R, to supplement the contour plots and provide the
reader with a more quantitative view of the normal force.
Figure 7.10: Comparison of lower rotor sectional normal force at 150 knots.
121
7.3.0.2 Chordwise Force - Upper and Lower Rotor
This subsection examines non-dimensional chordwise force on the upper ro-
tor and lower rotor, obtained using coaxial and full vehicle CFD/CSD coupling
methodologies. The non-dimensional chordwise force discussed in this section is in
the deformed airfoil frame, positive from the trailing edge to the leading edge.
Figure 7.11(a) shows the azimuthal sign convention for the upper rotor and
the nomenclature of the quadrants. Figure 7.11(b) shows the azimuthal distribution
of chordwise force for three datasets: (1) coaxial CFD/CSD, (2) vehicle CFD sim-
ulation utilizing main rotor elastic deflections from coaxial CFD/CSD simulation
and (3) full vehicle CFD/CSD simulation. It is difficult to recognize the dissimilar-
ities between these datasets, therefore a difference between the datasets is shown in
Fig.7.11(c). The first diagram in Fig.7.11(c) shows the difference between dataset
(2) and dataset (1) in Fig.7.11(b). The presence of the airframe in the CFD increases
the chordwise force on the fore region of the rotor disk, above the airframe, and de-
creases the chordwise force on the aft portion of the rotor disk. Re-trimming the
coaxial rotor with full vehicle CFD/CSD coupling methodology, decreases the blade
pitch over the front portion of the rotor disk which in turn decreases the chordwise
force. A quantitative view of the changes in chordwise force, over the upper rotor
disk, are shown for two radial stations in Fig.7.12.
The sign convention for the lower rotor chordwise force is the same as for the
upper rotor, with positive chordwise force from trailing edge towards the leading
edge. Again, take note of the direction of the rotation of the lower rotor and the
122
(a)
(b)
(c)
Figure 7.11: Non-dimensional chordwise force distribution for upper rotor, rotating
counter-clockwise.
123
Figure 7.12: Comparison of upper rotor sectional chordwise force at 150 knots.
locations of the advancing and retreating side with respect to the rotor disk, shown
in Fig.7.13(a). Figure7.13(b) shows the contours of the azimuthal distribution of
the lower rotor chordwise force, in the deformed airfoil frame, for various datasets
described above. It is difficult to analyze the differences between the datasets from
comparisons in Fig.7.13(b), therefore the differences between the datasets is shown
in Fig.7.13(c). The first diagram in Fig.7.13(c) shows the difference between chord-
wise force predicted (2) and (1), shown in Fig.7.13(b). The full vehicle CFD/CSD
coupling procedure predicts substantially higher chordwise force in the first, third
and fourth quadrants on the outboard stations, shown in Fig.7.13(b) and Fig.7.14.
7.3.0.3 Pitching Moment - Upper and Lower Rotor
The objective of this subsection is to identify and analyze the differences in
pitching moment that arise from full CFD/CSD coupling approach. The pitching
124
(a)
(b)
(c)
Figure 7.13: Non-dimensional chordwise force distribution for lower rotor, rotating
clockwise.
125
Figure 7.14: Comparison of lower rotor sectional chordwise force at 150 knots.
moment that will be shown in this section is a non-dimensional pitching moment
in the deformed airfoil frame. The pitching moment is positive for pitch up motion
around the quarter chord line. The pitching moment will be compared for three
datasets: (1) coaxial CFD/CSD coupling simulation, (2) vehicle CFD simulation
utilizing deflections from coaxial final CFD/CSD coupling simulation and (3) the
full vehicle CFD/CSD simulation.
Figure 7.15(b) shows the azimuthal distribution of the upper rotor pitching
moment for the three datasets, (1) through (3). Figure 7.15(c) shows the difference
between the pitching moment predicted in these datasets. The shedding from the
airframe mast in the full vehicle CFD simulation induces unsteady fluctuations in
the pitching moment on the aft of the rotor disk, shown in first diagram of Fig.7.15.
The full vehicle CFD/CSD simulations predict a decrease in the nose-down pitching
moment on the advancing side, shown in the second diagram of Fig.7.15(c) as well
126
(a)
(b)
(c)
Figure 7.15: Non-dimensional pitching moment distribution for upper rotor, rotating
counter-clockwise.
127
Figure 7.16: Comparison of upper rotor sectional chordwise force at 150 knots.
as in Fig.7.16.
Figure 7.17(b) shows the lower rotor pitching moment for the three datasets,
while Fig. 7.17(c) shows the difference in the lower pitching moment for the three
datasets. The difference between the lower rotor pitching moment predicted using
the full vehicle CFD/CSD coupling and the coaxial CFD/CSD coupling is shown
in the second diagram in 7.17(c). Majority of the differences occur on the aft
of the rotor disk, in the first and the second quadrants. In the first quadrant,
full vehicle CFD/CSD predicts lower nose down pitching moment compared to the
coaxial CFD/CSD prediction. In the second quadrant there is a nose down signature
which may be due to a vortex being pinched off of the retreating blade.
128
(a)
(b)
(c)
Figure 7.17: Non-dimensional pitching moment distribution for lower rotor, rotating
clockwise.
129
Figure 7.18: Comparison of lower rotor sectional pitching moment force at 150 knots.
7.4 Structural Blade Loads
This section compares the main rotor structural blade loads obtained with
the coaxial CFD/CSD coupling approach and the full vehicle CFD/CSD coupling
approach. The blade loads consist of the flap bending moment, chordwise bending
moment and torsional bending moment. The blade loads are obtained using the
force summation method, by integrating the aerodynamic, centrifugal and inertial
forces from the tip of the blade to the radial station of interest.
Figure 7.19 compares the flap bending moment obtained from the two CFD/CSD
coupling approaches. This figure shows the flap bending moment near the root of the
rotor blade, r/R = 18.6%R, as the blade travels around azimuth. The flap bending
moment is closely related to the normal force shown in Figs.7.7 and 7.9, as well as
the vertical components of the inertial and centrifugal forces acting on the blade.
130
(a) (b)
Figure 7.19: Upper and lower rotor flap bending moment obtained using coaxial
and full vehicle CFD/CSD coupling at 150 knots.
(a) (b)
Figure 7.20: Upper and lower rotor chord bending moment obtained using coaxial
and full vehicle CFD/CSD coupling at 150 knots.
131
(a) (b)
Figure 7.21: Time history of the upper and lower rotor torsion bending moment
obtained using coaxial and full vehicle CFD/CSD coupling at 150 knots.
A positive flap bending moment is defined with the upper surface in compression
(blade flapping up). Both CFD/CSD coupling approaches predict similar trends.
The maximum flap bending moment occurs on the advancing side of the rotor disk
due to high normal force distribution. The flap bending moment decreases as the
blade travels around the azimuth. The decrease is reflective of the normal force
decrease in the reverse flow region. However, the flap bending moment does not
become zero because there is a sufficient normal force on the outboard stations of
the blade on the retreating side. The flap bending moment does approach zero in
the third quadrant because there is a decrease in the normal force on the outboard
stations of the blades indicative of the dynamic stall vortex pinching off of the blade.
Both CFD/CSD approaches predicted very similar maximum flap bending moment
magnitudes. The full vehicle CFD/CSD approach predicts slightly higher flap bend-
132
ing moment on the aft portion of the rotor disk, as the blade travels through the
first and the third quadrants. The blade pitch in the first and third quadrant is
higher for the rotor trimmed with full vehicle CFD/CSD coupling procedure, shown
in Fig.7.4(a) and(b), producing more normal force in those quadrants. The full ve-
hicle CFD/CSD predicts lower flap bending moment on the fore portion the rotor
disk, as the blade travels through the second and the third quadrant. The blade
pitch in the second and the fourth quadrant is lower for the rotor trimmed with full
vehicle CFD/CSD coupling procedure, producing less normal force in these loca-
tions, therefore lower flap bending moment. The oscillatory nature of the flapping
moment is due to the high frequency content in the normal force.
Figure 7.20 shows the chordwise bending moment comparisons, at r/R =
18.6%R, for the coaxial and the full vehicle CFD/CSD coupling methodologies.
The chordwise bending moment is positive for blade lead. Both methods predict
the maximum chordwise bending moment to be located on the retreating side of
the rotor disk, a result of increased profile drag in the reverse flow region. Pro-
nounced differences in the sign of the chordwise bending moment are observed on
the advancing side of the rotor disk, with full vehicle CFD/CSD coupling predict-
ing upper rotor have negative chordwise bending moment in the first quadrant and
positive chordwise bending moment in the second quadrant. The coaxial CFD/CSD
coupling predicted the opposite to be true.
Figure 7.21 compares the torsion bending moment for coaxial and full vehicle
CFD/CSD coupling methodologies. The torsion bending moment is shown at 18.6%
radial location. A positive torsion bending moment is defined positive nose-up for
133
upper rotor and nose down for lower rotor. An 8P signature can be observed in the
time-history, with the high impulsive peaks being more prominent on the retreating
side. The 8P signature is an interactional aerodynamic phenomena, occurring at
blade crossings, which would not be evident in the structural blade loads without
the CFD/CSD coupling.
7.5 Pusher Propeller
The auxiliary propeller is treated as a rigid rotor with only a collective inputs.
Every coupling cycle the auxiliary propeller was trimmed in isolation using a climb
regime in the wind tunnel mode. The auxiliary propeller power, zero roll moment
and zero pitching moment are the trim targets. After the initial trim, a delta
coupling method was applied. The difference between the CFD auxiliary propeller
power and the target power is calculated and added on to the difference from the
previous iterations. The cumulative delta is then applied into the trim process. The
output of the auxiliary propeller trim is the collective and thrust. The propeller
thrust is an input into the full CFD/CSD coupling trim procedure, modifying the
speed schedule which specifies the thrust power at a specific speed. In the previous
section the auxiliary propeller thrust was calculated using momentum theory. The
propeller collective is an input into the CFD simulation.
Figure 7.22(a) compares the flight test auxiliary propeller power, published
in Ref. [6], and the predicted auxiliary propeller power obtained from full vehicle
CFD/CSD approach. Initially the CFD power is over-predicted. As the coupling
134
Figure 7.22: Convergence history for propeller power and collective.
cycles advance the predicted propeller power approaches the target propeller power.
At the third coupling cycle there was a sufficiently small difference between the
predicted and the flight test propeller power, therefore no further coupling itera-
tions were performed for the auxiliary propeller and the propeller was no longer
re-trimmed. The collective was kept constant, same collective as the third itera-
tion, for full configuration CFD/CSD coupling cycles. Even though the collective
remained constant, the propeller power went up due to the change in the fuselage
pitch attitude during the full CFD/CFD coupling. However, since this change in
power was relatively small and the CFD power closely matched the target power, it
was deemed acceptable not to re-trim the propeller any further.
135
8 Results Part III: Fundamental Understanding of Interac-
tional Aerodynamics of Compound Coaxial Helicopter
This chapter examines the aerodynamic interactions between various compo-
nents of the high-speed compound helicopter in steady level flight at 150 knots,
using Helios/OVERFLOW simulations. The objective of the chapter is to identify
the aerodynamic interactions between various components and determine their ef-
fect on the performance and the vibratory aerodynamic airloads. The components
that are investigated are coaxial rotor system, airframe and the auxiliary propeller.
CFD simulations were performed with individual components and component com-
bination, shown in Fig.8.1. The upper and lower rotor deflections from full vehicle
CFD/CSD coupling, discussed in previous chapter, were used for all simulations
that included the coaxial rotor system. The airframe includes the pylon, mast and
empennage. The pitch attitude of the helicopter was also obtained in the previous
section using full vehicle CFD/CSD coupling methodology and it did not change for
the interactional aerodynamic studies. The auxiliary propeller blade pitch was set
based on the final trim from full vehicle CFD/CSD simulations.
136
Figure 8.1: Helicopter components and isolated parts interactional aerodynamic
study
137
Table 8.1: CFD interactional aerodynamics case
V?(knots) ? MR RPM Madv.tip LOS(%) Blade Modes Harmonics
150 0.41 446 0.79 11.3 6 8
8.1 Interactional Aerodynamics Affecting the Upper Rotor
This section examines the aerodynamic interactions affecting the performance
of the upper rotor. CFD simulations of the upper rotor in isolations as well as in
conjunction with other helicopter components, shown in Fig.8.2(a), were performed
at 150 knots.
Figure 8.2(b) shows the normal force distribution for the geometries shown
in Fig.8.2(a). Isolated upper rotor results in fairly steady normal force around the
rotor azimuth, with significant amount of normal force produced over the aft of the
rotor disk. Including the lower rotor in the CFD simulations results in unsteadiness
in the normal force and drop off in normal force every 45 degrees, where blades
cross each other. Including the airframe in CFD simulations results in an upwash
over the aft portion of the airframe, decreasing the normal force over the aft of the
rotor disk. No significant change is observed in normal force with the addition of
the auxiliary propeller.
Figure 8.2(c) shows the chordwise force, in the airfoil frame, for the upper
rotor. The chordwise force is positive from the trailing to leading edge. CFD
simulation of isolated upper rotor results in high distribution of positive chordwise
force in the fourth quadrant, which decreases with the inclusion of the lower rotor
138
in the simulations. Periodic unsteadiness, which was observed in the normal force
distribution, is also observed in the chordwise force. This is due to the proximity
between the upper rotor blades and the wake of the lower rotor, note that at this
speed the rotor disk is tilted aft.
Figure 8.2(d) shows the upper rotor non-dimensional quarter-chord pitching
moment distribution, in the airfoil frame. Positive pitching moment for upper ro-
tor represents the airfoil section pitching up about the quarter chord of the blade.
Including the lower rotor in the CFD simulations introduces unsteadiness into the
pitching loads, as well as an 8P pitch-up impulsive spikes on the retreating side of
the disk.
The 8P impulsive changes in airloads originate when the blades of the upper
rotor cross with the blades of the lower rotor. During the crossing of the blades, the
upper rotor blades transverse through a low pressure region above the lower blades,
which reduces the pressure under the upper rotor blades resulting in a momentary
loss of lift.
Figure 8.4 shows the upper rotor aerodynamic hubloads in frequency domain,
for various configurations shown in Fig.8.2(a). The positive axial hub force is towards
the tail of the aircraft, the positive side hub force is starboard and the positive
vertical hub force is up. The positive hub roll moment is starboard side up, positive
pitching hub moment is nose up and positive yaw hub moment is clockwise.
For a coaxial configuration there is a significant increase in an 8P yaw moment,
shown in Fig.8.4(f), which is caused by the 8P periodic variation in both the lift
force and the drag force. The 8P yaw moment is a almost half of the steady yaw
139
moment. The addition of the airframe or the propeller did not have significant
effect on the 8P yaw moment. The 8P contribution to the roll moment, shown in
Fig.8.4(d), is also significant.
The steady side hub force, shown in Fig.8.4(b) and pitching hub moment,
shown in Fig.8.4(e), are strongly effected by the consideration of the lower rotor and
airframe. The steady negative side force (towards port side) increases with addition
of lower rotor and airframe, this is due to the proximity of lower rotor wake and the
mast wake to the upper rotor. The steady pitching hub moment changes sign and
significantly decreases in magnitude with addition of the airframe in the CFD. Take
note that the rotor blade deflections which are used for all the upper rotor cases,
Fig.8.2(a), were obtained using full vehicle CFD/CSD coupling discussed in previous
section. Therefore, these deflections do not represent trimmed state for the isolated
rotor and coaxial rotor system. Using the deflections from full vehicle CFD/CSD
coupling for an isolated rotor and coaxial rotor cases results in a nose down pitching
moment. However, when the airframe is included in the CFD simulations, there is an
upwash over the nose of the aircraft and a downwash over the tail, this phenomena
increases the nose up pitching moment hub and decreases the nose down pitching
moment.
140
(a) Geometries in CFD
(b) Normal force
(c) Chordwise force
(d) Pitching moment
Figure 8.2: Aerodynamic interactions effects on the upper rotor.
141
Figure 8.3: Pressure above the lower rotor at the disk plane of the upper rotor at
150 knots.
(a) (b) (c)
(d) (e) (f)
Figure 8.4: Upper rotor hubloads for various configurations shown in Fig. 8.2(a) at
150 knots.
142
8.2 Interactional Aerodynamics Affecting the Lower Rotor
This section examines the aerodynamic interactions affecting the performance
of the lower rotor. CFD simulations of the lower rotor in isolations as well as in
conjunction with other helicopter components, shown in Fig.8.5(a), were performed
at 150 knots.
Figure 8.5(b) shows the normal force azimuthal distribution, positive in the
upward direction, for the isolated lower rotor as well as in combination with other
helicopter components. Take note that the lower rotor rotates in the clockwise
direction. The addition of upper rotor into the CFD simulation introduces loss in
normal force every 45 degrees on the advancing side, starting at midspan of the blade
and extending to the tip. The difference between the normal force on the lower rotor
in the coaxial system and the lower rotor in isolation is shown in Fig.8.6(a), labeled
CRS-LR. This is due to the blade crossing, during which the lower rotor blades
pass under the upper rotor blades, the pressure on the top side of the lower rotor
blades increases. Including the airframe in the CFD, increases the normal force on
the front of the rotor disk due to the upwash from the airframe. The normal force
on the aft of the rotor disk decreases due to the downwash from the airframe. The
effect of the mast wake is also observed on the inboard sections of the blade at
? = 0 degrees, as loss in lift. The difference in normal force between coaxial rotor
system airframe combination and coaxial rotor system is shown in second column
of Fig.8.6(a), labeled CA-CRS.
Figure 8.5(c)shows the azimuthal distribution of the chordwise force on an
143
isolated lower rotor and lower rotor in combination with other helicopter compo-
nents, shown in Fig.8.5(a). For lower rotor the chordwise force, in an airfoil frame,
is positive towards the trailing edge. The addition of the airframe to the lower rotor
CFD simulations increases the chordwise force on the aft portion of the rotor disk
and introduces some unsteadiness, shown in Fig.8.6. The unsteadiness results from
the blades interacting with the mast wake.
Figure 8.5(d) shows the azimuthal distribution of the pitching moment, in
airfoil frame of reference, for lower rotor. The pitching moment, for lower rotor is
positive nose down and negative nose up. Inclusion of the airframe in the CFD
doesn?t introduce significant differences in terms of pitching moment on the lower
rotor, mostly unsteadiness at the rear of the rotor disk.
A significant difference which appears in normal force, chordwise force and
pitching moment, Fig.8.5 and Fig.8.6 is located in the third quadrant of the rotor
disk. For an isolated rotor there is a abrupt change in chordwise force and pitching
moment on the midspan of the retreating blade. This could be attributed to a
dynamic stall vortex pinching off of the retreating blade. This phenomena is reduced
when the upper rotor is included in the CFD. The increase in the pressure above the
lower rotor (due to the presence of the upper rotor), may attribute the attachment
of the vortex.
Figure 8.7 shows the aerodynamic hubloads for the lower rotor in isolation as
well as in combination with other helicopter components. Inclusion of the upper
rotor results in increased 8P harmonic for all hub forces and moments. The 8P
arises from the interactions of the lower and the upper rotor blades when they cross
144
over. There is an increase in the axial force with addition of the upper rotor and
the airframe. The unsteady wake from the mast contributes to the increase in drag
on the lower rotor.
(a) Normal force
(b) Chordwise force
(c) Pitching moment
Figure 8.5: Aerodynamic interactions effects on the lower rotor at 150 knots.
145
(a) Normal force
(b) Chordwise force
(c) Pitching moment
Figure 8.6: The difference between the coaxial rotor system and the lower rotor,
the coaxial airframe combination and coaxial rotor system, helicopter and coaxial
airframe combination at 150 knots.
146
(a) (b) (c)
(d) (e) (f)
Figure 8.7: Lower rotor hubloads for various configurations shown in Fig. 8.5(a) at
150 knots.
147
8.3 Interactional Aerodynamics Affecting the Airframe
The objective of this section is to examine the interactional aerodynamic effects
on the airframe resulting from the coaxial rotor and the propeller, at a flight speed
of 150 knots. The CFD airframe unstructured grid consists of smooth fuselage,
pylon, mast, vertical stabilizer and two horizontal stabilizers pitched at positive 5
degrees to the horizontal. The rotor hubs are not modeled in this work. The cases
considered in this study: (a) isolated airframe, (b) airframe + coaxial rotor, and (c)
full aircraft. The aerodynamic forces and moments are in the global CFD frame of
reference, centered at the lower hub. The axial force, Fx, is positive towards the tail
of the aircraft. The side force, Fy, is positive starboard. The vertical force, Fz, is
positive up.
Figure 8.9(a) shows the time-history of the airframe aerodynamic axial force,
from CFD simulations, with respect to azimuth angle in a rotor reference frame.
The presence the coaxial rotor system in the CFD introduces a periodic increase
in spanwise force every 90 degrees. The periodic increase in spanwise force occurs
when the rotor blades cross over the airframe. Figure 8.9(b)shows the harmonic
amplitudes of the spanwise force up to 8P, the 4P blade passage frequency is domi-
nant. Figures 8.9(d) and (e) show the harmonic contributions from various airframe
components, with the fuselage being the main source of the 4P and 8P harmonic
contributions. Figure 8.9(c) shows the mean spanwise force contributions from vari-
ous airframe components. For an isolated airframe, fuselage and mast were the main
contributers of spanwise force. The cylindrical mast is a bluff body which produces
148
significant amount of pressure drag. The presence of the rotor increased the fuselage
spanwise force. The addition of the propeller increased the airframe spanwise force.
Figure 8.10(a) shows the time-history of the airframe aerodynamic side force
for various configurations. The airframe in isolation experiences periodic fluctua-
tions that stem from the shedding off of the pylon and the mast. The presence of
the rotor induces additional frequencies and an increase in the mean of side force.
Figure 8.10(b) shows the harmonic amplitudes of the side force of the airframe. For
an isolated airframe, the 6P is dominant. The addition of the rotor and the auxil-
iary propeller introduced strong 4P and 8P. The fuselage and the pylon are the main
components that contributed to the 4P response, blade passage frequency. Figure
8.10(c) shows the steady side force contributions from various aircraft components
for the three configurations. There is an increase in the airframe side force in the
presence of the rotor and the auxiliary propeller. For an isolated airframe the hor-
izontal tails, produce roughly equal but opposite side force. The side force results
from the roll up and shedding of the tip vortices from the horizontal tail surfaces.
The presence of the coaxial rotor significantly reduces the side force on the port side
horizontal tail. The starboard horizontal tail side force is also reduced but not as
much as the port side, resulting in an imbalance The vertical tail also sees a non-zero
side force.
Figure 8.11(a) shows the time-history of the airframe aerodynamic vertical
force for configurations (a) through (c). The presence of the rotor introduces sig-
nificant loading peaks every 90 degrees, which are due to blade passage. Figure
8.11(b) quantifies the frequency of the loading peaks observed in Fig.8.11(a) to be
149
4P (dominant) and 8P. Figures 8.11(d) and (e) show that the 4P and 8P airframe
forcing comes from the fuselage and the horizontal tails. The steady normal force
for various airframe components, averaged over one rotor revolution, is shown in
Fig.8.11(c). In the presence of the rotor there is a negative download on the fuse-
lage. As the blades passover the airframe, the pressure on the top surface of the
fuselage increases as shown in Fig.8.8, creating a downward force on the fuselage.
Figure 8.11(c) also shows that the pylon and mast are creating upward normal force.
There is some negative pressure on the top of the pylon and the mast, which may
enable these parts to act as lifting surfaces.
The time-history of the airframe aerodynamic roll moment about the center of
the lower rotor hub is shown Figure 8.11(a) for configurations (a) through (c). For
an isolated airframe, there are low amplitude periodic fluctuations roughly about the
zero mean. An introduction of the rotor into the simulations results in higher, non-
zero, mean as well as additional frequency content. The presence of the auxiliary
propeller does not have significant effect on the mean or fluctuations of the roll
moment. Figure 8.12(b) compares the harmonic amplitudes of the roll moment for
various configurations. For an isolated airframe 6P harmonic dominates, whereas
4P and 8P harmonics dominate for the cases with coaxial rotor. The 6P is the
shedding frequency of the mast. The 4P is the blade passage frequency over the
airframe. The fuselage and the horizontal tails are the key airframe components that
produce the 4P and 8P roll moment. The total steady roll moment on the isolated
airframe is roughly zero as shown in Fig.8.12(c), equal and opposite roll moment is
produced by the horizontal tails without additional significant contributions from
150
other airframe components. However, in the presence of the rotor there is a positive
roll moment (starboard down) on the aircraft, with contributions from fuselage,
horizontal tails and vertical tail. The non-zero roll moment on the airframe is a
result of interactional aerodynamics and is an important factor to consider when
trimming the vehicle.
Figure 8.13(a) shows the time-history of the airframe aerodynamic pitching
moment about the center of the lower rotor hub. The pitching moment is positive
when the vehicle is pitching nose up. An isolated airframe experiences a relatively
steady, nose down pitching moment. The majority of the pitching moment is pro-
duced by the horizontal tail surfaces, shown in Fig.8.13(c). In the presence of the
rotor, the airframe experiences fluctuations in the pitching moment which arise from
interactional aerodynamics. The pitching moment harmonic amplitudes are shown
in Fig.8.13(b). The dominant harmonic is the 4P. An 8P is present but it?s ampli-
tude is roughly half of the 4P. The 4P harmonic stems from the fuselage, shown in
Fig.8.13(d), due to the blades passing directly over the fuselage. The 8P harmonic
is due to a combination of the horizontal tails and the fuselage, shown in 8.13(e).
The time-history of the aerodynamic airframe yaw moment, positive counter-
clockwise, about the center of the lower rotor hub is shown in Fig.8.14(a). An
isolated airframe sees a roughly steady yaw moment centered at zero. For an isolated
airframe, the horizontal tails produce equal and opposite yaw moments, shown in
Fig.8.14(c). The air flows from root to tip on the horizontal tails, creating an equal
and opposite radial force. In the presence of the rotor, the starboard horizontal tail
produces more yaw moment compared to the port horizontal tail. Compared to the
151
isolated airframe, where there was no significant yaw moment contributions from
other airframe components, in the presence of the rotor additional yaw moment is
produced by the vertical tail and the fuselage. In addition, in the presence of the
rotor, the airframe experiences a significant 4P yaw moment as well as a 8P, shown
in Fig.8.14(b), due to the interactional aerodynamics on the fuselage, 8.14(d) and
(e).
(a)
(b)
Figure 8.8: Effect of blade passage on the pressure over the airframe 150 knots.
152
(a) (b)
(c) (d) (e)
Figure 8.9: The time-series and harmonic amplitudes of the airframe spanwise at
150 knots.
153
(a) (b)
(c) (d) (e)
Figure 8.10: The time-series and harmonic amplitudes of the airframe side force at
150 knots.
154
(a) (b)
(c) (d) (e)
Figure 8.11: The time-series and harmonic amplitudes of the airframe normal force
at 150 knots.
155
(a) (b)
(c) (d) (e)
Figure 8.12: The time-series and harmonic amplitudes of the airframe roll moment,
positive starboard side up, about the center of lower hub at 150 knots.
156
(a) (b)
(c) (d) (e)
Figure 8.13: The time-series and harmonic amplitudes of the airframe pitching
moment, positive nose up, about the center of lower hub at 150 knots.
157
(a) (b)
(c) (d) (e)
Figure 8.14: The time-series and harmonic amplitudes of the airframe yaw moment,
positive counter-clockwise, about the center of lower hub at 150 knots.
158
8.4 Interactional Aerodynamics Affecting the Auxiliary Propeller
This section examines the effects of helicopter components on the performance
of the auxiliary propeller for the vehicle traveling at 150 knots. The collective of the
auxiliary propeller blades was obtained from the converged full vehicle CFD/CSD
coupling discussed in Chapter 7. The performance of the auxiliary propeller is an-
alyzed for three configurations shown in Fig.8.15(a); isolated propeller, propeller
airframe combination and helicopter configuration. The auxiliary propeller is rotat-
ing counter-clockwise, with ? = 0 degrees at the top and ? = 90 degrees on the
starboard side.
Figure 8.15(b) shows the azimuthal distribution of the propeller normal force
for the configurations shown in Fig.8.15(a). A propeller in isolation experiences
smooth normal force distribution over the propeller disk, with advancing side pro-
ducing less normal force than the retreating side. The imbalance in the normal force
is a consequence of the vehicle pitch attitude. At a flight speed of 150 knots, the
vehicle is trimmed nose up. Instead of flow coming in normal to the propeller disk,
the flow comes in at an angle. On the advancing side of the rotor disk, the edgewise
velocity at the propeller disk is subtracted from the rotational velocity, because of
the positive pitch attitude tilt. On the retreating side of the rotor disk, the edgewise
velocity at the propeller disk is compounded with the rotational velocity, resulting
in a higher normal force. The presence of the airframe increases the normal force on
the inboard stations. On an isolated propeller, the angle of attack on the inboard
stations of the blades is quite low due to the high inflow velocity, which is roughly
159
Table 8.2: Mean auxiliary propeller thrust and power for three configurations at 150
knots.
Iso. Prop Prop-Airframe Helicopter
Thrust (lb) 468.8 676.1 697.5
Power (hp) 293.8 393.5 400.7
the same as the forward flight speed of the vehicle. The wake from the airframe
reduces the inflow velocity at the rotor disk, increasing the sectional angle of attack
on the inboard stations of the propeller, and as a consequence, the normal force. It
is also observed that the normal force on the outer sections of the rotor increases in
the presence of the airframe, especially near ? = 0, ? = 90, ? = 180 and ? = 270
degrees, as shown in Fig.8.15(b). At these locations, there are strong interactions
between the propeller and the wake from the mast (near ? = 0 degrees), horizon-
tal tails (? = 90 and ? = 270 degrees) and the vertical tail (? = 180 degrees).
The increase in normal force and as a result the efficiency of the propeller, is a
consequence of a phenomena known as boundary-layer-ingestion, which has been
studied extensively by Min et al. in Ref. [86]. This phenomena is further explored
by performing a collective sweep using CFD simulations, for an isolated propeller
and airframe-propeller combination, shown in Fig.D.1.
160
(a) Configurations
(b) Auxiliary propeller normal force.
(c) Auxiliary propeller chordwise force.
Figure 8.15: Auxiliary propeller airloads at 150 knots.
161
9 Conclusions
9.1 Summary of Research
The future multi-role aircraft designs consist of various complex components
that aerodynamically interact with one another and each other?s wakes. The aero-
dynamic interactions may result in additional vibrations, as well as degradation of
the performance. Often times it is necessary to redesign the components as well as
their placement on the aircraft post-production. To avoid the costly redesign, it is of
paramount importance to fundamentally understand the source of the interactions
as well as their implications on the performance prior to production of the aircraft.
This work presented a numerical study of the fundamental aerodynamic inter-
actions between the components of a high-speed compound coaxial helicopter using
conventional and full vehicle CFD/CSD coupling approach. A high-speed compound
coaxial helicopter, notional X2TD, consisting of a coaxial rotor, airframe and an
aft-mounted propeller, was simulated in this study. A high-fidelity CFD framework,
HPCMP CREATETM -AV Helios, was used in conjunction with an in-house CSD
solver, to simulate helicopter in forward flight.
The results shown in this thesis are presented in three parts. The first part of
the results, discussed in Chapter 6, focused on studying the trends for a coaxial rotor
162
at a range of advance ratio, ? = 0.14 to ? = 0.65. A conventional rotor CFD/CSD
coupling methodology, where only the rotor airloads are transferred from the CFD
solver to the CSD solver, was utilized for the first part of the results. The CFD
simulations for this part of the results only included the coaxial rotor system. The
second part of the results, discussed in Chapter 7, focused on analyzing the effect of
the full vehicle CFD/CSD coupling on the trim parameters and airloads. The CFD
simulations included the coaxial rotor system, the airframe and auxiliary propulsor.
For this results section, the coaxial rotor airloads, time-averaged airframe airloads
and the pusher propeller thrust and power were transferred from the CFD solver
to the CSD solver. The final part of the results, presented in Chapter 8, focused
on the fundamental understanding of interactional aerodynamics of a high-speed
compound helicopter. The CFD simulations of components in isolation, in combi-
nation and in full configuration were performed. The unsteady coaxial rotor airloads
were compared for different configurations. The auxiliary propeller performance was
compared for an isolated as well as an installed propeller.
9.2 Key Conclusions
This section presents the key conclusions obtained from the results given in
Chapters 6, 7 and 8. Each chapter contains an in depth analysis and discussion of
the conclusions. The key conclusions are addressed in order, corresponding to their
respective chapters.
163
9.2.1 Coaxial Rotor CFD/CSD Coupling
This subsection summarizes the key results from Chapter 6. The results pre-
sented in Chapter 6 focused on characterizing the trim solution, airloads and struc-
tural deformation for a lift-offset coaxial rotor at five advance ratios ranging between
? = 0.14 and ? = 0.65 (50 knots and 225 knots). For these results, in Chapter 6, only
the coaxial rotor was present in the CFD simulations. A conventional CFD/CSD
coupling approach was utilized to correct the comprehensive analysis airloads.
A significant difference was observed between the upper and lower rotor col-
lectives at 50 knots and 225 knots, but not at other speeds. The lower rotor collec-
tive was 3% higher compared to the upper rotor collective for the 50 knot forward
flight condition. At 250 knots, the upper rotor collective was higher than the lower
collective by roughly 7%. At the intermediate speeds, the upper and lower rotor
collectives were within 0.6% of each other. For the 50 knot case, the combination
of the relatively low flight speed and the forward tilt of the rotor disks resulted
in the upper rotor wakes passing through the lower rotor. This caused a decrease
in the sectional angle of attack and the mean thrust of the lower rotor, which re-
sulted in the lower rotor trimming to a higher collective. To verify this phenomena
a CFD/CSD test case was run with the upper and the lower in isolation in CFD.
This test case showed that without the rotor-rotor interference, both rotors trim to
a roughly identical collectives.
The advance ratio sweep showed a significant increase in the negative loading
on the outboard stations of the rotor blade, on the advancing side. For 225 knots,
164
roughly 40% of the blade was negatively loaded at ? = 45 degrees azimuth. This
was due to the decrease in angle of attack on the outboard stations of the blade on
the advancing side.
The advance ratio sweep also showed that there is a pronounced redistribution
of the normal force over the rotor disk. At lower speeds the normal force was equally
distributed around the rotor disk. However, as the speed increased the fore and aft
portions of the rotor disk carried the majority of the normal force. This was a result
of the development of the negative loading on the advancing side, first quadrant, at
the outboard regions of the blade.
At low speeds a distinct 8P impulsive loading was observed every quarter
revolution due to blade-blade interactions. As the forward flight speed increased,
a decrease in the magnitude of the 8P blade-blade impulsive loading spikes on the
advancing side and an increase in magnitude of the 8P blade-blade loading spikes
on the retreating side was observed.
9.2.2 Results Part II: Vehicle CFD/CSD Coupling
This subsection summarizes the key findings from the full vehicle CFD/CSD
coupling study, presented in Chapter 7. The objective of Chapter 7 was to show
the effect of incorporating the airframe and propeller into the CFD/CSD coupling
methodology. The results from the full vehicle CFD/CSD coupling approach were
compared to those obtained with the rotor CFD/CSD coupling methodology. The
final trim solution, the main rotor airloads and the main rotor blade deformations
165
were compared.
The study showed that correcting CSD low order airframe airloads with high-
fidelity CFD airloads changed the final trim state of the vehicle. The CSD low
order aerodynamic model assumed zero roll and yaw moment on the fuselage. The
presence of the rotor above the airframe resulted in the nonzero airframe yaw and
roll moments, affecting the final trim state of the rotor. For 150 knots, the rotor
CFD/CSD coupling procedure predicted very similar upper and lower rotor collec-
tives. However, when performing the full vehicle CFD/CSD coupling procedure the
lower rotor collective increased by 16%, while the upper rotor collective decreased
by 4% . In addition, the presence of the airframe under the rotor system affected the
airloads on the main rotor which in turn also affected the final rotor trim solution.
Performing the full vehicle CFD/CSD coupling procedure also enabled a high-
fidelity prediction of the propeller thrust, accounting for the boundary-layer-ingestion
and rotor wake effects. The propeller thrust in the comprehensive analysis look-up
table was derived using simplified expression, P = TV , from momentum theory.
Correcting the table look-up propeller thrust, derived from simplified expression
P = TV , with high-fidelity CFD, also affected the final vehicle pitch attitude. The
rotor CFD/CSD coupling predicted a vehicle pitch attitude of 2 degrees, while the
full vehicle CFD/CSD coupling predicted a 2.8 degree pitch attitude.
166
9.2.3 Results Part III: Fundamental Understanding of Interactional
Aerodynamics of Compound Coaxial Helicopter
This subsection summarizes the key results from Chapter 8. The objective
of Chapter 8 was to identify the aerodynamic interactions between various compo-
nents of the notional coaxial compound helicopter and determine their effect on the
performance and the vibratory airloads at 150 knots. The CFD simulations were
performed with individual components and component combination.
The isolated upper and lower rotors experienced relatively smooth airloads
distribution. However, the presence of the lower rotor under the upper rotor in-
troduced a significant 8P loading, detectable as an 8P loss in normal force every
45 degrees. The magnitude of the 8P hub vertical force increased by 90% in the
presence of the lower rotor, resulting from blades of the upper rotor crossing with
the blades of the lower rotor. The 8P hub roll moment increased by 85%.
The presence of the rotor above the airframe, introduced significant 4P and
8P download, due to blade passage over the fuselage. Both, the magnitude of the
4P and 8P harmonics went up by roughly 100%. The presence of the propeller did
not have a significant effect on the airframe airloads.
The boundary-layer-ingestion effect increased the efficiency of the propeller in
an installed configuration. An isolated propeller produced a thrust equivalent 468
pounds, while an installed propeller produced a thrust of 698 pounds. As expected,
the required power also increased for an installed configuration. However, the overall
efficiency of the propeller increased. It was also observed that the rotor wake effected
167
the unsteady airloads on the propeller, increasing the normal force on the midspan
of the advancing side, while decreasing the normal force on the retreating side.
9.3 Recommendations for Future Work
This section provides the reader with suggestions for additional work which
may include but is not limited to the following items:
1. Expanding the simulated flight conditions to investigate the effect of advance
ratio on the interactional aerodynamics between the helicopter components.
The current study focused on understanding the interactional aerodynamics
of a helicopter at a cruise speed of 150 knots.
2. Expanding the simulated flight conditions for the rotor CFD/CSD study to
include speeds up to or beyond 250 knots. The future vertical lift rotorcraft
configurations promised to achieve speeds greater than 250 knots, therefore
simulating and understanding high-speed coaxial flight is in high demand.
The current study simulated a coaxial rotor at a range of flight speeds, 50
knots to 225 knots.
3. Performing an acoustics study to understand and show the effect of interac-
tional aerodynamics on the noise produced by each component.
4. The current work should be extended to include the upper and the lower rotor
hubs in the CFD simulations. Rotor hubs contribute substantial amount of
drag to the total drag of the helicopter, roughly 20% to 30% for a single main
168
rotor helicopter [87], which increases for a coaxial helicopter. In addition, the
hub way will affect the performance of the rotor blades. The hubs are not
present in the CFD simulations, in the current study.
5. Modifying the PRASADUM lift-offset implementation to account for a non-
zero phase offset between pilot controls and blade response. The current imple-
mentation assumes no phase delay between pilot controls and blade response
for a lift-offset coaxial rotor.
6. Including an option for longitudinal lift-offset in the trim equations. Currently,
only lateral lift-offset is implemented in the in-house comprehensive analysis.
7. Using the Adaptive Mesh Refinement [79] within Helios to refine and track
the vortices as they convent downstream, into the propeller.
8. Improving the main rotor structured blade geometry to have a smoother tran-
sition between the elliptical airfoils and the conventional airfoils, as well as a
better root and tip mesh quality.
9. Adjusting the time step and implementing a fixed refinement region near the
propeller to better capture the flow field near the propeller. The current CFD
simulation time step is a quarter degree of the main rotor, which is greater
than 1 degree for the propeller.
10. Modifying the geometry of the propeller to have non-linear twist and taper as
well as creating a structured O-O grid. The current work utilizes an unstruc-
tured grid for the notional propeller, which resulted in slow computations.
169
B Coordinate Systems
Figure B.1: CSD body-axis frame of reference used for trim procedure.
Figure B.2: CFD global axis, utilized for describing CFD airframe airloads.
170
Figure B.3: Reference frame utilized for the non-dimensional deformed airloads,
used for delta coupling.
171
B Flow Visualization for Results Part I
(a) Coaxial rotor System (Top View) (b) Coaxial rotor System (Starboard View)
(c) Isolated Lower Rotor (Top View) (d) Isolated Lower Rotor (Starboard View)
(e) Isolated Upper Rotor (Top View) (f) Isolated Upper Rotor (Top View)
Figure B.1: Iso-surfaces of q-criterion, shown for q = 6e?4, colored by the non-
dimensional vertical velocity, for 50 knot forward flight case.
172
Figure B.2: Iso-surfaces of q-criterion, shown for q = 6e?4, colored by the non-
dimensional vertical velocity. The right column shows the view of from the top,
while the left column shows the view from the starboard side.
173
C Flow Visualization for Results Part III
(a) Port View (b) Starboard View
(c) Port View (d) Starboard View
Figure C.1: Iso-surfaces of q-criterion, shown for q = 6e?4, colored by the non-
dimensional vertical velocity.
174
Figure C.2: Top view of the iso-surfaces of q-criterion, shown for q = 6e?4, colored
by the non-dimensional vertical velocity.
175
D Collective Sweep for Isolated Auxiliary Propeller and Airframe-
Propeller Combination
(a) Propeller thrust. (b) Propeller power.
Figure D.1: Auxiliary propeller collective sweep for isolated and installed propeller
at various forward flight speeds.
176
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