Helicopter Flight Dynamics Simulation With Refined Aerodynamic Modeling PHD Thesis

540 Pages·1988·5.95 MB·English

by  Alisse Theodore

HELICOPTER FLIGHT DYNAMICS SIMULATION WITH
REFINED AERODYNAMIC MODELING
by
Colin Rhys Theodore
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
2000
Advisory Committee:
Associate Professor Roberto Celi, Chair/Advisor
Professor Inderjit Chopra
Professor Sung W. Lee
Professor J. Gordon Leishman
Associate Professor Balakumar Balachandran, Dean’s Representative
Abstract
Title of Dissertation: HELICOPTER FLIGHT DYNAMICS SIMULATION
WITH REFINED AERODYNAMIC MODELING
Colin Rhys Theodore, Doctor of Philosophy, 2000
Dissertation directed by: Dr. Roberto Celi, Associate Professor
Department of Aerospace Engineering
This dissertation describes the development of a coupled rotor-fuselage flight
dynamic simulation that includes a maneuvering free wake model and a coupled
flap-lag-torsion flexible blade representation. This mathematical model is used to
investigateeffectsofmainrotorinflowandblademodelingonvariousflightdynamics
characteristics for both articulated and hingeless rotor helicopters. The inclusion of
the free wake model requires the development of new numerical procedures for the
calculation of trim equilibrium positions, for the extraction of high-order, constant
coefficient linearized models, and for the calculation of the free flight responses to
arbitrary pilot inputs.
The free wake model, previously developed by other investigators at the Uni-
versity of Maryland, is capable of modeling the changes in rotor wake geometry
resulting from maneuvers, and the effects of such changes on the main rotor inflow.
The overall flight dynamic model is capable of simulating the helicopter behavior
during maneuvers that can be arbitrarily large. The combination of sophisticated
models of rotor wake and blade flexibility enables the flight dynamics model to cap-
ture the effects of maneuvers with unprecedented accuracy for simulations based
on first principles: this is the main contribution of the research presented in this
dissertation.
The increased accuracy brought about by the free wake model significantly im-
proves the predictions of the helicopter trim state for both helicopter configurations
considered in this study. This is especially true in low speed flight and hover. The
mostsignificantimprovementsareseeninthepredictionsofthemainrotorcollective
and power required by the rotor, which can be significantly underpredicted using
traditional linear inflow models.
Resultsshowthatthefree-flighton-axisresponsestopilotinputscanbepredicted
with good accuracy with a relatively unsophisticated models that do not include
either a free wake nor a refined flexible blade model. It is also possible to predict the
off-axis response from first principles, that is, without empirically derived correction
factors and without assumptions on the wake geometry. To do so, however, requires
much more sophisticated modeling. Both a free wake model that includes the wake
distortions caused by the maneuver and a refined flexible blade model must be used.
Most features of the off-axis response can be captured by using a simpler dynamic
inflow theory extended to account for maneuver-induced wake distortions, and for a
fraction of the cost of using a free wake model. The most cost-effective strategy, for
typical flight dynamic analyses, and if vibratory loads are not required, is probably
to calibrate such a theory using the more accurate free wake-based model, and then
use it in all further calculations.
(cid:1)c Copyright by
Colin Rhys Theodore
2000
Acknowledgements
ThisresearchwassupportedbytheNationalRotorcraftTechnologyCenterunder
the Rotorcraft Center of Excellence program. Detailed configuration parameters for
the BO-105 were provided by Dr. A. Desopper of ONERA, France. Flight test data
for the BO-105 were provided by Dr. C. Ockier of DLR, Germany . Flight test data
for the UH-60A were provided by Dr. M. Tischler of NASA Ames. I would like
to thank Drs. Ashish Bagai and J. Gordon Leishman for providing a copy of the
maneuvering free wake code and for many useful discussions.
I would also like to thank the members of my dissertation committee for their
valuable feedback: Drs. Balakumar Balachandran, Inderjit Chopra, Sung W. Lee
and J. Gordon Leishman. I especially would like to thank Dr. Roberto Celi, my
dissertation director, for his guidance and support during my graduate studies and
his invaluable assistance while I was writing this dissertation.
I would like to thank current and past colleagues at the Rotorcraft Center, who
helped me gain a better understanding of helicopter anaysis and made my time at
the University of Maryland more enjoyable, particularly fellow flight dynamicists
Chris Jones, Vineet Sahasrabudhe, Anne Spence, Steve Turnour and Rendy Cheng.
I would especially like to thank Ashish Bagai for his time and help with the free
wake code.
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I appreciate the love, support and encouragement my family provided me. Their
emails, faxes, phone calls and packages have meant a lot to me. Finally, I thank
my wife, Alisse, for all of her love and support in keeping me focused on a goal and
helping me to get this dissertation written.
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Table of Contents
List of Tables ix
List of Figures x
Nomenclature xxxi
1 Introduction and Literature Review 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.2.1 Flight dynamic simulation modeling . . . . . . . . . . . . . . . 8
1.2.2 Aeromechanical models and comprehensive analyses . . . . . . 14
1.2.3 Wake and inflow models suitable for flight dynamics work . . . 17
1.2.4 Helicopter analysis in coordinated turns . . . . . . . . . . . . 24
1.2.5 Helicopter cross-coupling . . . . . . . . . . . . . . . . . . . . . 26
1.3 Objectives of Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2 Mathematical Model 35
2.1 Overview. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.2 Coordinate Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.2.1 Body coordinate systems . . . . . . . . . . . . . . . . . . . . . 38
2.2.2 Wind coordinate system . . . . . . . . . . . . . . . . . . . . . 40
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2.2.3 Main rotor coordinate systems . . . . . . . . . . . . . . . . . . 41
2.2.4 Free wake coordinate systems . . . . . . . . . . . . . . . . . . 46
2.2.5 Coupling of the flight dynamic and the free wake coordinate
systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
2.3 Main assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
2.4 Main rotor equations of motion . . . . . . . . . . . . . . . . . . . . . 56
2.4.1 Main rotor aerodynamic loads . . . . . . . . . . . . . . . . . . 58
2.4.2 Main rotor inertial loads . . . . . . . . . . . . . . . . . . . . . 65
2.4.3 Main rotor structural loads . . . . . . . . . . . . . . . . . . . 67
2.4.4 Lag damper loads . . . . . . . . . . . . . . . . . . . . . . . . . 71
2.4.5 Tension-induced loads . . . . . . . . . . . . . . . . . . . . . . 71
2.4.6 Finite element analysis . . . . . . . . . . . . . . . . . . . . . . 72
2.4.7 Blade mode shapes . . . . . . . . . . . . . . . . . . . . . . . . 79
2.4.8 Modal coordinate transformation . . . . . . . . . . . . . . . . 82
2.5 Fuselage equations of motion . . . . . . . . . . . . . . . . . . . . . . . 84
2.5.1 Main rotor loads . . . . . . . . . . . . . . . . . . . . . . . . . 86
2.5.2 Fuselage aerodynamic loads . . . . . . . . . . . . . . . . . . . 88
2.5.3 Empennage aerodynamic loads . . . . . . . . . . . . . . . . . 92
2.5.4 Tail rotor loads . . . . . . . . . . . . . . . . . . . . . . . . . . 96
2.6 Tail rotor inflow dynamics . . . . . . . . . . . . . . . . . . . . . . . . 99
2.7 Dynamic inflow model . . . . . . . . . . . . . . . . . . . . . . . . . . 100
2.8 Assembly of equations of motion . . . . . . . . . . . . . . . . . . . . . 103
2.9 Free wake model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
3 Solution Methods: Trim 127
3.1 Baseline trim procedure . . . . . . . . . . . . . . . . . . . . . . . . . 127
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3.1.1 Definition of the flight condition . . . . . . . . . . . . . . . . . 128
3.1.2 Unknowns of the trim problem . . . . . . . . . . . . . . . . . 128
3.1.3 Formulation of the trim problem . . . . . . . . . . . . . . . . 131
3.1.4 Solution of baseline trim equations . . . . . . . . . . . . . . . 138
3.2 Trim Procedure with Free Wake Inflow Model . . . . . . . . . . . . . 138
3.2.1 Formulation of the trim problem with the free wake . . . . . . 139
3.2.2 Calculation of Main Rotor Inflow . . . . . . . . . . . . . . . . 140
3.2.3 Solution of Trim Equations with Free Wake Model. . . . . . . 145
3.3 State vector corresponding to the trim solution . . . . . . . . . . . . 149
4 Solution Methods: Linearization of the Equations of Motion 158
4.1 Linearization of baseline equations of motion . . . . . . . . . . . . . . 159
4.2 Linearization of equations of motion with free wake model . . . . . . 164
5 Solution Methods: Time Integration 172
5.1 Time integration of baseline equations of motion . . . . . . . . . . . . 172
5.1.1 Integration of non-linear equations of motion . . . . . . . . . . 172
5.2 Time integration of equations of motion with free wake . . . . . . . . 173
5.2.1 Numerical integration of the non-linear equations of motion . 174
6 Aircraft Modeling Configurations 179
6.1 BO-105 configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
6.2 UH-60A configuration . . . . . . . . . . . . . . . . . . . . . . . . . . 181
7 Trim Results 206
7.1 BO-105 Trim Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 206
7.1.1 Effect of inflow and blade modeling . . . . . . . . . . . . . . . 207
7.1.2 Effect of tip vortex strength . . . . . . . . . . . . . . . . . . . 213
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7.1.3 Effect of vortex wake resolution . . . . . . . . . . . . . . . . . 217
7.1.4 Effect of fuselage aerodynamic modeling . . . . . . . . . . . . 218
7.1.5 Effect of downwash on horizontal tail . . . . . . . . . . . . . . 221
7.1.6 Effect of the number of finite elements . . . . . . . . . . . . . 223
7.2 UH-60A trim results - straight and level flight . . . . . . . . . . . . . 224
7.3 UH-60A trim results - turning flight . . . . . . . . . . . . . . . . . . . 227
7.4 Discussion of trim results . . . . . . . . . . . . . . . . . . . . . . . . . 231
8 Linearized Model Results 294
8.1 UH-60A in hover . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295
8.1.1 Poles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296
8.1.2 On-axis frequency response . . . . . . . . . . . . . . . . . . . 298
8.1.3 Off-axis frequency response . . . . . . . . . . . . . . . . . . . 301
8.2 UH-60A in forward flight . . . . . . . . . . . . . . . . . . . . . . . . . 305
8.2.1 Poles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306
8.2.2 On-axis frequency response . . . . . . . . . . . . . . . . . . . 307
8.2.3 Off-axis frequency response . . . . . . . . . . . . . . . . . . . 309
8.3 BO-105 in hover . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311
8.3.1 Poles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311
8.3.2 On-axis frequency response . . . . . . . . . . . . . . . . . . . 313
8.3.3 Off-axis frequency response . . . . . . . . . . . . . . . . . . . 314
8.4 BO-105 in forward flight . . . . . . . . . . . . . . . . . . . . . . . . . 315
8.4.1 Poles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315
8.4.2 On-axis frequency response . . . . . . . . . . . . . . . . . . . 316
8.4.3 Off-axis frequency response . . . . . . . . . . . . . . . . . . . 318
8.5 Effect of free wake resolution . . . . . . . . . . . . . . . . . . . . . . . 319
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