High Resolution Methods for the Aerodynamic Design of Helicopter Rotors by Alan Brocklehurst

369 Pages·2013·29.91 MB·English

High Resolution Methods for the
Aerodynamic Design of Helicopter Rotors
by
Alan Brocklehurst
June 6, 2013
This Thesis is submitted in fulfillment
of the requirements for
the degree of
Doctor of Philosophy
CFD Laboratory
School of Engineering
Faculty of Science and Engineering
University of Liverpool
i
Dedication
This thesis is dedicated to my wife and family
who I thank for their patience, support and understanding.
ii
Declaration
I hereby declare that this thesis is a record of my own work and was undertaken on a part-
time basis from 2003 to 2005 in the Department of Aerospace Engineering at the University
of Glasgow, and from 2006 to 2013 in the School of Engineering, Faculty of Science and
Engineering at the University of Liverpool. This thesis is original in content except where
otherwise indicated.
Alan Brocklehurst
March 2013
iii
Abstract
The research reported here was driven by a desire to obtain a prediction method for helicopter rotor
performance that would have sufficient resolution to evaluate changes to the design of the blade tip. This
thesis examines the effectiveness of Computational Fluid Dynamics (CFD) methods to solve this problem.
An accurate, high-fidelity prediction is essential to quantify the performance of a new rotor tip shape
which hitherto could not be properly assessed by a traditional approach. The CFD method lends itself to
the resolution of the compressible, viscous flow around the helicopter blade tip. Starting from the surface
shape required to generate a grid, together with the flow conditions, the flowfield naturally evolves from the
numericalsolutionofthe Navier-Stokesequations,basedon the principles ofconservationofmass,momentum
and energy. Thus both the flow physics and the geometry of the tip are fully modelled by this technique.
In order to demonstrate the process, the Helicopter Multi-block solver (HMB) is used to predict the per-
formance of a series of example tail rotor configurations. The various tip shapes are evaluated and compared,
initially using an Euler approach to economically cover a wide range of designs, before going on to apply the
Navier-Stokes method. The concepts behind each of the tail rotor blade (TRB) tip designs are explained in
the thesis. As further computational resources became available, the datum blade, and the down-selected
Ku¨chemann-like and anhedral-Ku¨chemann tip blades were the subject of Navier-Stokes predictions. Early in
thiswork,thenumericalmethodwasvalidatedagainstpublisheddata,andwasalsocomparedtoexistingmodel
tailrotortestdataforbladeshavingdifferenttwist. Inthecentralpartofthisthesis,thecomputationalresults
are further analysed to reveal the influence of blade design changes on the time-averagedinduced flow, and to
extract more familiar aerodynamic parameters such as the angle of attack from the 3D rotor computations.
Steady Navier-Stokes predictions were obtained over a range of pitch angles such that the induced power
factor could be reliably determined and the trends on profile power could also be established for the selected
tip shapes. The research reported in this thesis has established that this numerical approach provides a good
prediction of rotor performance, adequately resolving the flow-field and tip aerodynamics.
Sincetheassessmentofhelicopterrotorsmayinvolveadditionalinteractionaleffects,oradegreeofunsteady
flow due to operating at high pitch angles near the onset of stall, an unsteady case was also demonstrated for
a tail rotor blade adjacent to a fin.
It is concluded that only by using a CFD approach can a sufficiently high-fidelity prediction be obtained
for helicopter rotor aerodynamics to allow progressiveenhancements of future helicopter blade designs.
iv
Acknowledgements
The writer wishes to thank his employers,Westland Helicopters Ltd (now partof AgustaWestland), andin
particular, Rob Harrisonand Bob Hansford, for their help and support, and for giving permission to use data
from the model rotor tests. More recently, Pierre Abdel-Nour, Antonio Saporiti, and Andrea D’Andrea have
also given their support to this research, prior to my retirement on 6th April 2011. The assistance of Richard
Markiewicz of DSTL is also gratefully acknowledgedfor helping to release data into the public domain for the
Twisted Model Tail Rotor experiments which were carried out in the 1980’s with MoD funding.
Special thanks are due to Professor George Barakos for his supervision, help and encouragement, and his
valuable time which was so freely given throughout the course this research. His enthusiasm for this subject
is infectious and has sustained me through this part-time PhD programme. I have benefited greatly from our
many discussions.
Sincere thanks are also due to Professor Ken Badcock for his help and support throughout this period of
study, and to Rene Steijl and Mark Woodgate for their patience and assistance. The opportunity to meet and
discuss many aspects of rotor aerodynamics with other researchers in the CFD lab, both in the early days at
Glasgow and subsequently at Liverpool, is also much appreciated.
v
CONTENTS CONTENTS
Contents
1 Introduction 1
1.1 Motivation and Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.4 Literature Survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.4.1 Review of Fixed-Wing Tip Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.4.2 Review of Helicopter Tip Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
1.4.3 Conclusions from Literature Survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
2 Numerical Methods 93
2.1 Helicopter Multiblock Solver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
2.2 Grid Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
2.3 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
2.4 Wake Visualisation and Vortex Criterion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
2.5 2D Aerofoil Code - MSES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
3 Validation 100
3.1 Aerofoils . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
3.1.1 NACA 23012,M=0.2, Re=3 million . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
3.1.2 NACA 0012, M=0.5, Re=5 million . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
3.1.3 NACA 0012, M=0.5, Effect of Reynolds Number . . . . . . . . . . . . . . . . . . . . . . 111
3.1.4 NACA0012, M=0.5, Re=1 million, Unsteady Stall . . . . . . . . . . . . . . . . . . . . . 114
3.2 Grid Sensitivity Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
3.2.1 Model Tail Rotor - Hover - Euler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
3.3 UH60A Model Rotor with Swept Back Tip in Hover . . . . . . . . . . . . . . . . . . . . . . . . 122
3.3.1 Rotor Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
3.3.2 Aerofoils, and Smoothing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
3.3.3 Blade Drafting and Mesh Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
3.3.4 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
3.3.5 Comparison with Measured Pressure Distributions . . . . . . . . . . . . . . . . . . . . . 125
3.4 WHL Model Tail Rotor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
3.4.1 Geometry and Grid for Model Tail Rotor Comparisons . . . . . . . . . . . . . . . . . . . 134
3.4.2 Performance Comparisons (Zero Twist) . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
3.4.3 Predicted and Measured Vortex Locations (Zero Twist) . . . . . . . . . . . . . . . . . . 137
3.4.4 Further Performance Comparisons (0, 8, 16 degrees Twist) . . . . . . . . . . . . . . . . 145
3.4.5 Comparison of Predicted Loading and Effect of Twist . . . . . . . . . . . . . . . . . . . 147
4 Tip Design 154
4.1 Design Aims. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
4.2 Tip Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
4.2.1 Datum Blade, TRB-000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
4.2.2 TRB-001, Ku¨chemann-Type Tip (0.25c Wide) . . . . . . . . . . . . . . . . . . . . . . . 159
4.2.3 TRB-002, Ku¨chemann-Type Tip (0.5c Wide) . . . . . . . . . . . . . . . . . . . . . . . . 160
4.2.4 TRB-003, 70-degree Swept-Edge Tip . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
4.2.5 TRB-004, Rectangular Tip with 20 degrees of Anhedral . . . . . . . . . . . . . . . . . . 161
4.2.6 TRB-005, Ku¨chemann-Type Tip (0.25c Wide) with Anhedral . . . . . . . . . . . . . . . 162
4.2.7 TRB-006, Rectangular with Volume-of-Revolution Tip Cap . . . . . . . . . . . . . . . . 162
4.2.8 TRB-007, Parabolic Tip . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
4.2.9 Thoughts for a Final Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
4.3 Tip Design Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
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CONTENTS CONTENTS
5 Euler Evaluation 166
5.1 Comparison of Tip Shapes in Hover . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
5.1.1 Thrust and Induced Power Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
5.1.2 Loading Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
5.1.3 Vortex Trajectories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
5.2 Selection of Tip Shapes for Further Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
5.3 Forward Flight Comparisons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
5.4 Summary of Euler Evaluations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204
6 Navier-Stokes Hover 206
6.1 Tip Shapes and Grid Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
6.2 Navier-Stokes Evaluation at Low-to-Moderate Pitch . . . . . . . . . . . . . . . . . . . . . . . . 211
6.2.1 Performance Predictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
6.2.2 Loading Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218
6.2.3 Vortex Trajectories - Comparisons of Euler and Navier-Stokes . . . . . . . . . . . . . . . 218
6.2.4 Vortex Trajectories - Navier-Stokes - Effect of Tip Shape . . . . . . . . . . . . . . . . . 223
6.3 Flowfield Variations at High Pitch Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229
6.4 Performance Comparisons at High Pitch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242
6.4.1 Performance Near Stall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242
6.4.2 Loading and Pressure Distributions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244
6.4.3 Stall Monitors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260
7 Further Analysis of CFD solutions 263
7.1 Angle of Attack from Time AveragedDownwash . . . . . . . . . . . . . . . . . . . . . . . . . . 264
7.2 Angle of Attack from Stagnation Point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272
7.3 Angle of Attack from Cp Matching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279
7.4 Surface Pressures at Tip . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282
8 Application of Unsteady Navier-Stokes 286
8.1 Tail Rotor Fin Blockage Test Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287
8.2 Unsteady Isolated Rotor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297
8.3 Unsteady Navier-Stokes - Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299
9 Conclusions and Outlook 300
A 2D Euler Grid Sensitivity 319
B 3D Wing Exploratory Study 324
C Further Model Rotor Validation (R/c=13.7) 329
D Smoothed Co-ordinates for SC1095 and SC1095R8 334
E Co-ordinates for NACA 23012 with Sharp T.E. 337
F Co-ordinates for NACA 0012 with Sharp T.E. 339
G Rotor-Analyser Fortran Program Listing 341
vii
CONTENTS CONTENTS
Nomenclature
Latin
A Area of rotor disk
AR Aspect ratio
AoA Angle of Attack
b wing span
c chord
C Chordwise Force Coefficient
c
C Drag Coefficient
D
C Sectional Drag Coefficient
d
C Lift Coefficient
L
C Sectional Lift Coefficient
l
C , C Moment Coefficient
M m
C Normal Force Coefficient
n
C Rotor Thrust Coefficient, Non-dimensional ratio of thrust to rotor disk area, density and
T
tip-speed squared, T
12ρS(RΩ)2
C /s Blade Loading Coefficient, Thrust Coefficient divided by Solidity
T
C Pressure Coefficient
p
C Power Coefficient
P
C Torque Coefficient, Non-dimensional ratio of torque to rotor disk area, density, tip-speed
Q
squared and length, Q
12ρSR(RΩ)2
e Internal energy of fluid element
E Total Energy per unit volume
f Rotation frequency
FoM FigureofMerit,Ratioofpowerrequiredtoproducethrust,P tototalpowerrequired,P+P
p
C3/2
where Pp is the profile power to overcome aerodynamic drag of blades, 2CTQ.
k Turbulent kinetic energy in k ω model
−
k constant
k Fin Blockage Ratio, k =(Fin Force)/(Tail Rotor Shaft Thrust
B B
k Induced power factor
i
M Mach number
N Number of blades
b
P Power
p Pressure
q Heat flux
r Radial station along blade
R Length of blade, radius of rotor, Residual
Re Reynolds number, =U.c/ν
S Area
s rotor solidity, ratio of nominal blade area to rotor-disc area, Nbc.
πR
T Temperature
t time
U Velocity in a generic direction
u Flow velocity in x-direction
V Tip speed
tip
v Flow velocity in y-direction
v Induced velocity
i
w Flow velocity in z-direction
X A generic direction
x x direction, or fractional distance along rotor blade, x=r/R
y y direction
z z direction
viii
CONTENTS CONTENTS
Greek
α Angle of attack
β Rotor Blade Flapping Angle (Coning angle, β )
o
γ Lock number, or Shaft Tilt Angle
∆ Anhedral Angle
µ Advance Ratio, Ratio of forward velocity to blade tip velocity
ξ Vorticity
ρ Density
λ Induced inflow ratio
ν Kinematic Viscosity
τ Viscous stress tensor
σ Relative Density, also used for Rotor Solidity when used to divide USA CT (ie without the
1/2), CT/σ
θ Local pitch angle, θ referenced to rotor centre
o
ψ Azimuth angle
Ω Angular Velocity
ω Specific Dissipation (defines scale of turbulence), ν =k/ω)
T
Gradient
∇
Subscripts and Superscripts
avg Average
c Average value of c
c Cosine term
s Sine term
o Constant term
B Blockage
F Fin
MR Main Rotor
p Profile Drag or Power
T, TR Tail Rotor
tip Blade tip conditions
W, WT Wind or wind tunnel
Freestream conditions
∞
ix
CONTENTS CONTENTS
Acronyms and Definitions
AHS American Helicopter Society
AIAA American Institute of Aeronautics and Astronautics
AW AgustaWestland (part of the Finemecanica Group)
AW (Yeovil) Formerly Westland Helicopters Ltd, Yeovil, Somerset.
BERP British Experimental Rotor Programme
BET Blade ElementTheory - considering the spanof the blade as sep-
arate strips.
B´ezier curves Usuallydefinedby4 controlpoints,locatedatthe endpoints and
with 2 intermediate points to define the gradient at the ends.
B-splines Basis-splines are a more general form of B´ezier curves, allowing
local knots to have more weight to control the curve.
BVI Blade Vortex Interaction
CFD Computational Fluid Dynamics
CFL Courant-Friedrichs-Lewycondition
DARP UK Defence Applied Research Programme
Disk loading Thrust divided by rotor-disk area
ERF European Rotorcraft Forum
FoM Figure of Merit
GOAHEAD EuropeanresearchprogrammefortheGenerationOfanAdvanced
Helicopter ExperimentalAerodynamicDatabasefor CFDValida-
tion
HART Higher harmonic control Aeroacoustics Rotor Test
HB Harmonic Balance
HMB Helicopter Multiblock Solver
LE Leading Edge
MoD Ministry of Defence
N-S Navier-Stokes
NURBS Non-Uniform Rational B-Splines
PIV Particle Image Velocimetry
RAE Royal Aircraft Establishment
REACT Rotor Embedded Active Control Technology
SST Shear Stress Transport
TE Trailing Edge
TM Time Marching
TRB Tail Rotor Blade
US, USA United States of America
Vorticity Ameasureoftherotationoffluidelementsinfluidflow. Givenas
ξ = V =2ω
∇×
WHL Westland Helicopters Limited, Yeovil, Somerset.
x