ADAPTIVE WING STRUCTURES FOR AEROELASTIC DRAG REDUCTION AND LOADS ALLEVIATION A thesis submitted to the University of Manchester for the degree of Doctor of Philosophy in the Faculty of Engineering and Physical Sciences September 2010 By Simon J. Miller School of Mechanical, Aerospace and Civil Engineering Contents Abstract 25 Declaration 26 Copyright 27 Acknowledgements 29 1 Introduction 30 1.1 Background and motivation . 30 1.2 Aircraftmorphing-pastandpresent . 33 1.2.1 Planformmorphing. 33 1.2.2 Performancemorphing . 46 1.3 Evolution of aircraft wing structures . 54 1.3.1 Unstressed wing construction . 54 1.3.2 Semi-monocoque wing construction . 55 1.4 Adaptiveinternalstructures . 56 1.5 Aeroelasticity ............................. 57 1.6 Aimsandobjectives ......................... 59 1.7 Contribution.............................. 59 1.8 Summarybychapter ......................... 61 1.9 Relatedpublications . 62 2 2 Overview of the rotating spars concept 64 2.1 Introduction.............................. 64 2.2 Wingwithasinglerotatingspar. 65 2.3 Wingwithmultiplerotatingspars . 66 2.4 Range of applicability . 66 2.5 Researchtodateontheconcept . 68 2.6 Areas identified for development . 69 3 Development of an aeroelastic model for a rotating spars wing 71 3.1 Introduction.............................. 71 3.1.1 Motivation........................... 71 3.1.2 Chapter overview . 72 3.1.3 Modeldescription. 72 3.2 Structuralmodel ........................... 74 3.2.1 Principle of Virtual Displacements . 74 3.2.2 Rayleigh-Ritz method . 90 3.2.3 Note on spar efficiency and lateral buckling . 95 3.3 Aerodynamicmodel.......................... 96 3.3.1 Fluiddynamics ........................ 96 3.3.2 Obtaining the aerodynamic forces . 99 3.3.3 Thehorseshoevortex. 103 3.3.4 Vortex-lattice aerodynamics . 112 3.4 Aeroelasticcoupling . 116 3.4.1 Discretising the virtual work for use with the aerodynamic model ............................. 117 3.4.2 Angle of incidence for a swept elastic wing as a function of theunknownamplitudes . 121 3.4.3 The complete equilibrium equations . 124 3.4.4 Solving the equilibrium equations . 125 3.5 Validation and verification . 127 3 3.5.1 Structuralcomparison . 127 3.5.2 Aerodynamic comparison . 130 3.5.3 Aeroelastic comparison . 134 3.6 Conclusions .............................. 139 4 An analytical study using the rotating spars aeroelastic model 140 4.1 Introduction.............................. 140 4.2 Parameterstudy ........................... 142 4.2.1 Structuralbehaviour . 142 4.2.2 Aeroelastic behaviour . 149 4.3 Establishing design guidelines . 160 4.3.1 Procedure ........................... 160 4.3.2 Suitability for planform . 163 4.3.3 Rotating spar placement and sizing . 167 4.4 Design of a rotating spars wing using a genetic algorithm . 172 4.4.1 Introduction. 172 4.4.2 Optimisation overview . 172 4.4.3 Geneticalgorithms . 176 4.4.4 Optimisation of the rotating spars wing to maximise effec- tivenessparameters. 185 4.5 Trimstudy .............................. 192 4.5.1 Introduction. 192 4.5.2 Trimmingthewing . 193 4.5.3 Effect of rotating spars on the trim state . 194 4.5.4 Minimisation of induced drag at the trim state via a steep- est descent optimisation algorithm . 198 4.6 Conclusions .............................. 204 5 Wind tunnel tests of a rotating spars wing 207 5.1 Introduction.............................. 207 4 5.2 Design of the model using an analytical approach . 209 5.2.1 Basic structural layout . 209 5.2.2 Establishing a baseline wing . 210 5.2.3 Effect of rotating spars on flutter behaviour . 217 5.2.4 Analytical refinement of the model . 218 5.2.5 Buckling check . 224 5.3 Constructionphase . 227 5.3.1 Overviewofthemodel . 227 5.3.2 Description of the wing . 228 5.3.3 Description of the actuator housing . 229 5.3.4 Description of the wing mount . 230 5.3.5 The complete assembly . 231 5.4 Equipment............................... 231 5.4.1 Windtunnel.......................... 232 5.4.2 Load-balance ......................... 232 5.4.3 Laser displacement system . 234 5.4.4 Servos ............................. 234 5.4.5 Data acquisition hardware . 236 5.4.6 Data acquisition software . 237 5.4.7 Otherequipment . 237 5.5 Tests.................................. 238 5.5.1 Determination of airspeed range and integrity of measure- ments ............................. 238 5.5.2 Effect of non-aerodynamic surfaces on the loads . 242 5.5.3 Structuralparametertests . 243 5.5.4 Aeroelastic parameter tests . 247 5.5.5 Control of the loads via a regression model . 250 5.5.6 Control of the deflections via a regression model . 255 5.5.7 Control of the loads via an optimisation approach . 256 5 5.5.8 Control of the deflections via an optimisation approach . 261 5.6 Conclusions .............................. 267 6 Adaptive wing tip devices for loads alleviation 269 6.1 Introduction.............................. 269 6.1.1 Next generation surveillance aircraft . 270 6.2 Loads alleviation systems . 272 6.2.1 Stateoftheart ........................ 272 6.2.2 Proposed loads alleviation concept . 273 6.3 Development of a dynamic aeroelastic model for a wing incorpo- ratingawingtipdevice . 275 6.3.1 Introduction. 275 6.3.2 Structuralmodel . 276 6.3.3 Aerodynamicmodel . 283 6.3.4 Solving the aeroelastic equations of motion . 289 6.4 Parameterstudyusingtheaeroelasticmodel . 293 6.4.1 Analyses of the baseline system . 293 6.4.2 Analyses of the modified system . 296 6.5 Casestudyforstressreduction. 301 6.5.1 Description of the baseline platform . 301 6.5.2 Aeroelastic analyses of the baseline system . 301 6.5.3 Aeroelastic analyses of the modified system . 304 6.6 Casestudyformassreduction . 311 6.6.1 Uniform mass reduction . 311 6.6.2 Mass reduction via optimisation . 312 6.7 Conclusions .............................. 317 7 Conclusions and future work 319 7.1 Conclusions .............................. 319 7.2 Suggestionsforfurtherwork . 323 6 References 326 Additional sources of information 342 Final word count: 63,310 7 List of Tables 3.1 Comparison of rigid lift coefficient between the VLM and DLM. 132 3.2 Comparison of rigid lift coefficient between the VLM and Tornado code................................... 133 3.3 Comparison of rigid induced drag coefficient between the VLM andTornadocode. .......................... 134 3.4 Comparison of aeroelastic lift coefficient between the RR VLM \ model and FE DLMmodel. ..................... 135 \ 3.5 Comparison of divergence dynamic pressure between the RR VLM \ model and FE DLMmodel. ..................... 136 \ 4.1 Variable range and increments. 178 4.2 Transformed variable range and increments. 179 4.3 Representation of possible solutions with binary strings and con- version back to transformed and actual variable decimal values. 180 4.4 Fitnessofeachgene. 180 4.5 Crossoverofgenes. .......................... 181 4.6 Inversionofgenes. .......................... 182 4.7 Translationofgenes. 183 4.8 Introductionofnewblood. 184 4.9 Carry-over of elite gene from previous generation. 184 4.10 Parameter ranges and number of increments. 186 4.11 Basic fixed parameter values. 187 4.12 Optimisation constraints for the design of the rotating spars wing. 188 8 4.13 GAoptimisationresults. 190 5.1 Performance of the baseline wing design. 222 5.2 Parameter ranges for the refinement of the wing design. 223 5.3 Parameter values for the refined wing design. 223 5.4 Performanceoftherefinedwingdesign. 223 5.5 Force requirement for lateral buckling of the spars. 226 5.6 Failuremodeofspars. 226 5.7 Data acquisition hardware connections. 237 5.8 Typical variation in signal voltage as a percentage of transducer range. ................................. 240 5.9 Results demonstrating the repeatability of the optimisation rou- tine to achieve a reference αetip by varying φr. ...........262 6.1 Undamped natural frequencies of the baseline system. 294 6.2 Undamped natural frequencies when the loads alleviation device isemployed............................... 296 6.3 Parameterranges.. 313 6.4 Ribparameters............................. 315 6.5 Sparparameters. ........................... 316 6.6 Othercomponentparameters. 316 9 List of Figures 1.1 Examples of variable sweep aircraft. 34 1.2 NextGen Aeronautics Morphing Aircraft Structures concept. 35 1.3 The small wing area and aspect ratio of the Lockheed F-104. 37 1.4 Diagram of the Fowler flap operation. 37 1.5 Telescoping wing sections of the LIG-7 by Bakshaev for chordwise areaincrease. ............................. 38 1.6 Telescoping wing sections of the MAK-123 by Makhonine for span- wiseareaincrease. .......................... 38 1.7 A recent spanwise telescoping wing concept. 39 1.8 Lockheed Martin folding wing concept. 40 1.9 Variable anhedral wing tips of the North American XB-70. 40 1.10 Biplane-to-monoplane morphing examples. 42 1.11 Inflatablewingexamples.. 43 1.12 Retractable undercarriage of a Boeing 787. 44 1.13 Variable droop nose on the A´erospatiale-BAC Concorde. 44 1.14 Examples of V/STOL aircraft. 45 1.15 Effect of camber on an arbitrary lift curve. 47 1.16 Commonflaptypes........................... 47 1.17 Patented designs for continuous variable camber wings. ..... 48 1.18 Geometry of a traditional jointed mechanism that maintains upper surfacecontinuity.. 48 10 1.19 The internal structure and actuators of the compliant Mission AdaptiveWing............................. 49 1.20 Smart Wing ultrasonic piezoelectric motors. 49 1.21 Mission Adaptive Compliant Wing trailing-edge demonstrating 10◦ deflections. ........................... 50 ± 1.22 A DLR-developed