Research Collection
Doctoral Thesis
Reduced-order aeroelastic modeling of morphing wings for optimization and control
Author(s):
Fasel, Urban Publication Date:
2020
Permanent Link:
https://doi.org/10.3929/ethz-b-000428849
Rights / License:
In Copyright - Non-Commercial Use Permitted
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R E D U C E D - O R D E R A E R O E L A S T I C M O D E L I N G O F M O R P H I N G W I N G S F O R O P T I M I Z AT I O N
A N D C O N T R O L
A thesis submitted to attain the degree of D o c t o r o f S c i e n c e s o f ETH Z u r i c h
(Dr. sc. ETH Zurich)
presented by U r b a n F a s e l
Master of Science ETH in Mechanical Engineering born August 6, 1989
citizen of Switzerland
accepted on the recommendation of Prof. Dr. Paolo Ermanni, examiner Prof. Dr. Steven L. Brunton, co-examiner
Dr. Paolo Tiso, co-examiner
2020
d o i: 10.3929/ethz-b-000428849
Morphing wings are characterized by the ability to smoothly adjust their aerodynamic properties to a wide range of operating conditions. This can lead to significant performance improvements and may have transformative impact on future transportation and energy systems. The key challenge of introducing morphing wings is the conflicting requirement of realizing stiff and load-bearing structures, while maintaining the required flexibility to accomplish shape adaptability at limited actuation effort. Morphing wings thus feature highly coupled and nonlinear interactions between the aerodynamic and structural dynamics, which represents a considerable modeling, optimization, and control challenge. Additionally, modeling tech- niques are required to provide accurate and efficient analysis of complete flight missions. This is of utmost importance to comprehensively quantify system-level benefits associated with morphing.
This work addresses these challenges by developing reduced-order aeroe- lastic models that enable complete mission analysis, optimization, and control of morphing wings. The developed methods are demonstrated on airborne wind energy (AWE) systems, although the methods are gener- ally applicable to coupled aeroelastic systems. Airborne wind energy is a technology that extracts power from winds using tethered drones. The application of morphing to airborne wind energy is compelling, owing to the large operating regime these systems operate in and thus great potential for performance improvement through morphing.
The main contribution of this work is the development of two reduced- order modeling methods. The first reduced-order model enables concurrent aero-structural design optimizations considering complete flight missions.
In particular, a reduced-order aeroelastic model is coupled with an AWE morphing wing flight simulator. The coupled model is embedded in a multi- disciplinary design optimization framework, enabling concurrent complete flight mission and system design optimization. The power production capa- bility of the AWE system can be improved by enabling wing shape changes and thus adaptation of the aerodynamic properties through morphing at different flight conditions and operating modes. The results highlight the potential of the proposed modeling and system-level optimization approach:
the power production capability of the investigated system is improved by 46% compared to a sequentially optimized design, and by exploiting iii
increased by 8%.
The second reduced-order model developed in this work is based on data- driven modeling techniques. These techniques are leveraged to develop a highly accurate and tractable unsteady aeroelastic model for morphing wings. The model is valid over a wide range of operating conditions and is suitable for control. In particular, two extensions to the recent dynamic mode decomposition with control algorithm are developed. A formulation to handle algebraic equations is introduced, and an interpolation scheme to smoothly connect several linear models developed in different operating regimes is presented. The innovation lies in accurately modeling the non- linearities of the coupled aerostructural dynamics over multiple operating regimes, not restricting the validity of the model to a narrow region around a linearization point. This results in accurate and highly efficient prediction of nonlinear unsteady aeroelastic responses of morphing wings and enables using the reduced-order model for model predictive control applications.
The reduced-order modeling methods developed in this work allow to design, optimize, and control better performing morphing wings and may help enable the widespread adoption of morphing wings. Applied to airborne wind energy, the models contribute to developing systems with enhanced power production capabilities and may help the deployment of the emerging airborne wind energy technology.
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Formvariable Flügel zeichnen sich durch die Fähigkeit aus, ihre aerody- namischen Eigenschaften an ein breites Spektrum von Betriebsbedingungen anzupassen. Dies kann zu erheblichen Leistungsverbesserungen führen und sich auf zukünftige Transport- und Energiesysteme transformativ auswirken. Die grösste Herausforderung bei der Einführung von formvari- ablen Flügeln ist die widersprüchliche Anforderung, steife und tragende Strukturen zu realisieren und gleichzeitig die erforderliche Flexibilität zu bewahren, um die Formanpassung bei begrenztem Aktuationsaufwand zu erreichen. Formvariable Flügel weisen daher hochgradig gekoppelte und nichtlineare Wechselwirkungen zwischen der Aerodynamik und der Strukturdynamik auf, was eine beträchtliche Herausforderung bei der Mod- ellierung, Optimierung und Regelung darstellt. Darüber hinaus sind Mod- ellierungstechniken erforderlich, welche genaue und effiziente Analysen kompletter Flugmissionen ermöglichen. Dies ist von grösster Bedeutung, um die mit der Formvariabilität verbundenen Vorteile auf Systemebene umfassend zu quantifizieren.
Die vorliegende Arbeit befasst sich mit diesen Herausforderungen durch die Entwicklung von Aeroelastikmodellen reduzierter Ordnung, welche eine vollständige Missionsanalyse, Optimierung und Regelung von form- variablen Flügeln ermöglichen. Die entwickelten Methoden werden an Flug- windkraftwerken demonstriert, obwohl die Methoden allgemein auf gekop- pelte aeroelastische Systeme anwendbar sind. Bei Flugwindkraftwerken handelt es sich um eine Technologie, die mit Hilfe von Drohnen, welche mit Seilen am Boden verankerten sind, Energie aus dem Wind gewinnt.
Die Anwendung von formvariablen Flügeln auf Flugwindkraftwerke hat aufgrund des grossen Betriebsbereichs in dem diese Systeme arbeiten, und der damit verbundenen Möglichkeit zur Leistungsverbesserungen durch Formvariabilität, grosses Potential.
Der Hauptbeitrag dieser Arbeit ist die Entwicklung von zwei Model- lierungsmethoden reduzierter Ordnung. Das erste Modell reduzierter Ord- nung ermöglicht Aerodynamik- und Struktur-Design-Optimierung unter Berücksichtigung kompletter Flugmissionen. Insbesondere wird ein Aeroe- lastikmodell reduzierter Ordnung mit einem Flugwindkraftwerksimulator gekoppelt. Das gekoppelte Modell ist in einer multidisziplinären Design- Optimierung eingebettet, das eine gleichzeitige Optimierung der komplet- v
der Flügelform und damit die Anpassung der aerodynamischen Eigen- schaften bei verschiedenen Flugbedingungen und Betriebsarten ermöglicht werden. Die Ergebnisse verdeutlichen das Potenzial des vorgeschlagenen Ansatzes zur Modellierung und Optimierung auf Systemebene: Die Leis- tungserzeugung des untersuchten Systems wird im Vergleich zu einem sequentiell optimierten Design um 46% verbessert, und durch Ausnutzung der Formvariabilität zur kontinuierlichen Anpassung der aerodynamischen Eigenschaften des Flügels bei verschiedenen Betriebsbedingungen kann die Leistungserzeugung um weitere 8% gesteigert werden.
Das zweite in dieser Arbeit entwickelte Modell reduzierter Ordnung basiert auf einer datengestützten Modellierungstechnik. Diese Technik wird genutzt, um ein genaues und effizientes Aeroelastikmodell eines formvariablen Flügels zu entwickeln. Das Modell ist über einen weiten Bereich von Betriebsbedingungen gültig und eignet sich im speziellen zur Regelung des Flügels. Insbesondere werden zwei Erweiterungen des dy- namic mode decomposition with control Algorithmus entwickelt. Eine Formulierung zur Behandlung algebraischer Gleichungen wird eingeführt, und ein Interpolationsschema zur Verbindung mehrerer linearer Modelle, die in verschiedenen Betriebsregimen entwickelt wurden, wird vorgestellt.
Die Innovation liegt in der genauen Modellierung der Nichtlinearitäten der gekoppelten Struktur- und Aerodynamik über mehrere Betriebsregime hinweg, wobei die Gültigkeit des Modells nicht auf einen engen Bereich um einen Linearisierungspunkt beschränkt wird. Dies führt zu einer genauen und effizienten Vorhersage der nichtlinearen instationären Aeroelastik von formvariablen Flügeln und ermöglicht die Verwendung des Modells re- duzierter Ordnung für prädikative Regelung.
Die in dieser Arbeit entwickelten Modellierungsmethoden ermöglichen es, formvariable Flügel mit besserer Leistung zu entwerfen, zu optimieren und zu regeln, und können dazu beitragen, die Anwendung von form- variablen Flügeln auf breiter Basis zu ermöglichen. Angewandt auf Flug- windkraftwerke tragen die Modelle zur Entwicklung von Systemen mit verbesserter Energieerzeugung bei und können zur Einführung der neuen Flugwindkraftwerkstechnologie beitragen.
vi
The work presented in this thesis was carried out at the Composite Materials and Adaptive Structures Lab (CMASLab) at ETH Zurich. Many people supported me throughout this work and substantially contributed to the results presented in this thesis.
My first and most sincere thanks are to my supervisor Paolo Ermanni who gave me the opportunity to conduct my doctoral studies at CMASLab.
Paolo’s guidance and support was crucial in successfully completing my doctoral studies. I am very grateful not only for his introduction, support, and advice on morphing wings research, but also his encouragement and support to pursue ideas independently and to explore topics that are usually not investigated by the morphing wings research community.
Huge thanks are to Paolo Tiso and Steve Brunton for the exciting collabo- rations and their support throughout my work. Paolo’s advice and guidance on structural dynamics and reduced-order modeling was essential in devel- oping the airborne wind energy system model and optimization framework.
Steve’s support was crucial in developing the data-driven reduced-order models and the model predictive control strategy for morphing wings in unsteady flight conditions. I also want to thank Paolo and Steve for their willingness to act as co-examiners of my thesis.
I am extremely thankful to Giulio Molinari who introduced me to morph- ing wing conceptual design and optimization and helped me to smoothly start my doctoral studies. The modeling and optimization framework pre- sented in this thesis is based on Giulio’s work, and without his kind and patient introduction it would have been much more difficult to achieve the results presented in this thesis. Very special thanks go to Dominic Keidel who was the best collaborator and friend one can imagine. I am really thank- ful for his help and introduction at the beginning of my work at CMASLab, for the work and non-work related discussions, for the exciting conferences we visited together, and of course for occasionally having beers and great ski trips together. Big thanks go to Martina Rizzoli. Martina’s presence helped creating a great atmosphere at CMASLab, with many happy coffee breaks, and it is due to her that the group is running as smoothly as we know it. Furthermore, I would like to thank all my colleagues and lab mates for the great time spent at CMASLab. Special thanks to Falk, Arthur, and Dominic for the exciting collaborations on wing twisting by elastic vii
I would also like to thank all the students that either directly contributed to this thesis with their projects or that contributed to one of the ftero airborne wind energy projects. I especially thank Nicola Fonzi and Leo Baumann for their creative and devoted work throughout their projects that contributed to my research. Leo’s project led to the successful flight of an additively manufactured composite morphing wing, and Nicola’s project initiated and substantially contributed to the development of the data-driven reduced-order models presented in this thesis.
Finally, I want to express my deepest gratitude to my friends and to my family for their encouragement and patience, and especially to Miwa for her unconditional support.
viii
i i n t r o d u c t i o n
1 m o t i vat i o n 3
2 s tat e-o f-t h e-a r t 5
2.1 Morphing wings . . . 5
2.1.1 Morphing concepts . . . 5
2.1.2 Aeroelastic modeling of morphing wings . . . 8
2.1.3 Optimization of morphing wings . . . 10
2.2 Reduced-order aeroelastic modeling . . . 12
2.3 Airborne wind energy . . . 14
2.3.1 AWE systems . . . 16
2.3.2 Analysis of AWE systems . . . 19
3 r e s e a r c h n e e d s a n d o b j e c t i v e s 21 4 s t r u c t u r e o f t h e t h e s i s 25 ii a e r o-s t r u c t u r a l o p t i m i z at i o n 5 a e r o-s t r u c t u r a l o p t i m i z at i o n o f m o r p h i n g aw e w i n g s 29 5.1 Wing concept and analysis framework . . . 29
5.1.1 Morphing wing concept . . . 30
5.1.2 Aeroelastic analysis method . . . 31
5.1.3 AWE performance modeling . . . 32
5.1.4 Wind distribution . . . 34
5.2 Wing optimization . . . 35
5.2.1 Parametrization . . . 35
5.2.2 Optimization . . . 38
5.2.3 Initial condition identification . . . 40
5.3 Wing optimization results . . . 41
5.3.1 General design variables optimization . . . 41
5.3.2 Aerodynamic shape optimization . . . 43
5.3.3 Complete wing design optimization . . . 44
5.4 Conclusions of this study . . . 45
iii r e d u c e d-o r d e r m o d e l i n g 6 r e d u c e d-o r d e r a e r o s e r v o e l a s t i c m o d e l 49 6.1 Drone and morphing concept . . . 50
6.2 Modeling approach . . . 53 ix
6.2.1 Fluid-structure interaction . . . 53
6.2.2 Wake modeling . . . 60
6.2.3 Dynamic system model . . . 66
6.2.4 Flight control . . . 71
6.3 Results and discussion . . . 74
6.3.1 Comparison of full vs. reduced-order model . . . 74
6.3.2 Circular flight . . . 76
6.4 Conclusions of this study . . . 80
7 d ata-d r i v e n r e d u c e d-o r d e r d y na m i c m o d e l 81 7.1 Unsteady panel method . . . 84
7.1.1 Model implementation . . . 84
7.1.2 Model verification . . . 86
7.2 Dynamic mode decomposition with control . . . 90
7.3 Algebraic dynamic mode decomposition with control . . . . 92
7.4 Hybrid aDMDc for morphing wings . . . 93
7.5 Parametric aDMDc . . . 95
7.6 Application of aDMDc to different dynamic systems . . . 96
7.6.1 Generic differential-algebraic system of equations . . . 96
7.6.2 NACA0012 rigid wing . . . 96
7.6.3 Morphing AWE wing . . . 99
7.6.4 Parametric reduced-order aeroelastic model . . . .101
7.7 Unsteady aerodynamics AWE flight simulator . . . .103
7.8 aDMDc AWE flight simulator . . . .105
7.9 Conclusions of this study . . . .107
iv m o r p h i n g w i n g c o n t r o l a n d o p t i m i z at i o n 8 m o d e l-b a s e d m o r p h i n g w i n g c o n t r o l 113 8.1 Model predictive control . . . .114
8.2 Morphing wing load control . . . .115
8.2.1 Gust load alleviation MPC . . . .116
8.2.2 Lift-force tracking MPC . . . .117
8.2.3 AWE trajectory and gust load alleviation MPC . . . . .118
8.3 AWE power cycle load control . . . .120
8.4 Conclusions of this study . . . .123
9 c o m p l e t e s y s t e m a n d m i s s i o n o p t i m i z at i o n 125 9.1 Drone and morphing concept . . . .126
9.2 Modeling approach . . . .127
9.2.1 Fluid-structure interaction . . . .127
9.2.2 Flight control . . . .128
9.3 Optimization framework . . . .130
9.3.1 AWE performance evaluation . . . .131
9.3.2 Parametrization . . . .132
9.3.3 Optimization problem formulation . . . .135
9.4 Optimization results . . . .139
9.4.1 Sequential vs. concurrent optimization . . . .140
9.4.2 Morphing optimization . . . .146
9.5 Conclusions of this study . . . .147
v c o n c l u s i o n a n d o u t l o o k 10 c o n c l u s i o n s 153 10.1 Summary of the main findings . . . .153
10.2 Aero-structural optimization of morphing wings . . . .153
10.3 Reduced-order aeroelastic modeling for optimization . . . . .154
10.4 Reduced-order aeroelastic modeling for control . . . .156
11 o u t l o o k 159
b i b l i o g r a p h y 163
p u b l i c at i o n s 187
Acronyms
aDMDc algebraic dynamic mode decomposition with control AIC aerodynamic influence coefficient matrix
AWE airborne wind energy
BP3434 Bezier-PARSEC 3434 parametrization CFRP carbon fiber reinforced plastic
CMA-ES covariance matrix adaptation evolution strategy CSM critical section method
DMDc dynamic mode decomposition with control FSI fluid-structure interaction
LPV linear parameter varying LTI linear time invariant MPC model predictive control
pMPC parametric MPC
ROM reduced-order model
TAP tether attachment point TED trailing edge displacement VTOL vertical take-off and landing
Symbols
αA euler angles
η structural modal amplitudes
µ doublet strengths
ω rotation rates
φ mode shapes
Ψ modal basis
Σˆt truncated singular values
σ source strengths
Ab,Bb,Aw body and wake source and doublet AIC A, ˜˜ B, ˜F aDMDc ROM
cp pressure coefficients
F external loads
FA forces acting on drone xii
FT forces acting on tether MDS generalized mass matrix M,C,K mass, damping, stiffness matrix ĂM,C,r Kr modal mass, damping, stiffness matrix
MA moments acting on drone
phf power harvesting factor
q mode amplitudes
T interpolation matrix
Uˆt truncated left singular vectors
u structural displacements, control inputs Vˆt truncated right singular vectors
x state vector
X,X1 states snapshot and time shifted snapshot matrix Y,Y1 inputs snapshot and time shifted snapshot matrix
α angle of attack
∆t dynamic system time step
Γ vortex strength
γ tether elevation angle
θ circumferential angle
as,cmd drone lateral acceleration
cD drag coefficient
cL lift coefficient cRoll roll coefficient
fW wind speed distribution probability
h FSI time step
J MPC cost function
k reduced frequency
L1 control reference point distance
lt tether length
ma morphing actuation level
P power
Ri mean relative error
S speed-up factor
VW wind speed
I N T R O D U C T I O N
1
M O T I VAT I O N
The development and deployment of innovative renewable energy and efficient air transportation technologies is essential to reduce greenhouse gas emissions and to mitigate climate change. Renewable energy technologies, in particular, play a major role in replacing current fossil fuel-based energy technologies, which contribute immensely to carbon dioxide emissions. In accordance with the Paris climate agreement, limiting global warming of 1.5°Cby 2100 requires approximately 8% cuts in greenhouse gas emissions on average per year on [1]. Despite these aims, man-made carbon dioxide emissions are currently still rising [2]. In contrast, conservative estimates of available power in the atmosphere considering physical and economic limits suggest wind being a vast energy source with the potential to cover around 20% of the global energy demand [3]. At the same time, technologies to harvest wind energy are ever improving [4]: wind turbines are growing in size, are more often deployed offshore where winds are stronger and steadier [5–7], and novel concepts like vertical axis wind turbines [8–10] and airborne wind energy (AWE) systems [11–13] are gaining traction. However, in order to reduce our dependence upon fossil fuel-based energy systems, it is necessary that efficient and cost-effective energy enabling technologies be further developed.
Another substantial contributor to global greenhouse gas emissions is aviation, accounting for 2.4% of global emissions in 2018 [14]. With rising passenger numbers [15] and the increasing demands on mobility of an ever growing human population [16], fuel consumption is projected to approximately triple by 2045 compared to 2015 [17]. To contribute to the reduction of greenhouse gas emissions in line with the objectives of the Paris climate agreement, disruptive technologies must be introduced in order to drastically improve the fuel efficiency of aircraft.
Aircraft and wind energy systems alike rely on aerodynamic surfaces that are required to adapt to a variety of operating conditions. Conventionally, aircraft wings and wind energy structures use discrete control surfaces to adapt their shape. A technology with the potential to have transformative impact in efficiency on future aircraft and wind energy systems are shape adaptive or so-called morphing structures [18–21]. Inspired by the incredi- ble performance of biological flight systems [22–25], these structures can
3
tailor their aerodynamic shape and properties to a wide range of operating conditions. Thereby, the compromise which otherwise results by the con- flicting design requirements given the large range of operating conditions can be reduced.
The key challenge of applying morphing structures to aircraft and wind energy systems is the contradicting requirement of realizing stiff and load- bearing structures, while maintaining the required flexibility to accomplish shape adaptability. This poses a considerable challenge in modeling and designing such structures, as they involve highly coupled interactions between the aerodynamic and structural dynamics. In addition to the tight coupling between the aerodynamic and structural dynamics, it is critical to assess the potential benefits achieved by morphing on system- level. Investigating maneuverability and optimizing aerodynamic drag by adopting morphing structures, for example, can lead to performance improvements regarding those specific objectives. However, this might not reflect the actual system-level performance. To comprehensively quantify the benefits of applying morphing to aircraft or wind energy systems, multidisciplinary design optimizations are required. These optimizations need to consider objectives representing the system performance, such as aircraft mission fuel consumption, wind energy power production or cost of energy.
Besides the analysis, design, and optimization challenge of morphing structures, the control of such high-dimensional dynamic systems consti- tutes a complex problem. The tight coupling of the multiple disciplines involved and the vast number of different shapes achievable by morphing demands highly efficient modeling methods for control. Establishing mod- els for control that enable to fully exploit the capabilities introduced by morphing is therefore critically important in the development of morphing structures.
This work is thus dealing with the development of efficient and accurate numerical models that allow analysis, optimization, and control of mor- phing structures. Specifically, the models are applied to AWE, which is a technology that extracts power from winds using tethered drones. The application of morphing to AWE is particularly compelling, owing to the large operating regime these systems operate in and thus large potential for performance improvement through shape adaptation.
2
S TAT E - O F - T H E - A R T
2.1 m o r p h i n g w i n g s
Flying animals such as birds, bats, and insects are able to rapidly transition between changing flight conditions. Inspired by the incredible flight per- formance of these animals, aircraft pioneers early on tried to imitate and adopt these characteristics in their designs by introducing flexible structures into their flight machines. The first heavier than air aircraft designed by the Wright brothers already employed twist morphing wings: the wings were flexible and could be warped to change the wing twist enabling roll control. Although the aircraft used for the first successful manned flight incorporated flexible wings, they lost attraction following the demand for increased flight speeds. Aircraft with increased flight speeds required stiffer structures to avoid aeroelastic instabilities. Therefore, stiff wings incorporat- ing discrete wing control surfaces were employed and are conventionally used since.
Following the advancement in new lightweight materials [26], smart actuators [27], and additive manufacturing techniques enabling automated, cost-effective manufacturing of complex structures [28], research on morph- ing wings intensified again during the last two decades. Furthermore, the growth of satellite services, the maturing and miniaturization of avionics, and the resulting rapid advancement of drone technologies opened up a vast field of potential applications for morphing wings [18].
Hereafter, first, a brief overview covering the most recent morphing concepts relevant for this work is presented. Second, numerical methods related to system-level design and optimization of morphing wings are reviewed. This includes aeroelastic modeling, optimization methods, and reduced-order modeling of morphing wings.
2.1.1 Morphing concepts
Morphing wings can be roughly divided in airfoil-level morphing (cam- ber and thickness) and wing-level morphing (span, sweep, twist, and di- hedral) [18, 21]. A large volume of published studies focus on variable 5
Figure2.1: Flight test of the FlexSys Inc. adaptive compliant trailing edge on the NASA Air Force Gulfstream III test aircraft [45].
camber-morphing concepts. Camber-morphing wings attain variations of the local lift coefficient by changing the curvature of the airfoil. They offer the possibility to tailor the lift distribution for maneuvering and for adapt- ing to different operating conditions. The advantages of camber-morphing compared to wing-level morphing concepts are the higher potential in performance improvement, higher reliability, and lower manufacturing and assembly effort [21]. Camber-morphing wings can be further divided in wings achieving shape changes using compliant structures [29,30] and wings based on internal kinematic systems using hinged mechanisms [31–
37]. Most research is focusing on compliant structures, as they potentially result in more lightweight designs with lower complexity, reduced parts count, and have no wear, compared to hinged structures [38,39].
An important contribution to the development of compliant structure- based camber-morphing wings is presented by Kota and commercialized through FlexSys Inc. [30,40,41]. They obtained several patents covering the design of compliant structure-based leading and trailing edge morphing devices [42–44]. Furthermore, they performed flight tests of their morphing wing, shown in Figure2.1, and are planning to extend their experimental investigations with NASA and the U.S. Air Force Research Laboratory [41, 45].
Within the smart wing project of the Defense Advanced Research Projects Agency (DARPA), the development of adaptive wing structures based on
Figure2.2: Fish Bone Active Camber (FishBAC) morphing wing [51].
smart materials was addressed [33,46,47]. Aerodynamic and aeroelastic performance benefits were enabled by replacing conventional hinged control surfaces with flexible leading and trailing edge control surfaces, actuated by shape memory alloy actuators and piezoelectric motors. Deflection rates of up to 80°/s were achieved, and performance improvements in terms of pitching and rolling moment were investigated.
Woods et al. introduced the Fish Bone Active Camber (FishBAC) con- cept [48–51], a biologically inspired compliant structure-based morphing wing trailing edge device, shown in Figure2.2. The concept enables large, continuous shape changes and was tested in wind tunnel experiments. The experiments showed improvements in aerodynamic efficiency in the order of 20%´25%, comparing the morphing wing to a benchmark airfoil using a conventional trailing edge flap [49].
Further contributions in the field of compliant structure-based morphing concepts were presented by Molinari et al. [52–57]. They developed and flight tested a morphing concept based on selective compliance structures and distributed piezoelectric actuators, shown in Figure2.3. The concept is characterized by its lightweight design and was specifically developed to replace conventional ailerons. Flight tests confirmed sufficient controllability solely achieved by morphing. Similar approaches were followed by Previtali et al. [58–61] and Keidel et al. [62–64], using electromechanical actuators, owing to their high static load-carrying capability, their energy density, and their favorable force displacement characteristics. Previtali further
Figure2.3: Piezo-actuated selective compliance morphing wing [54].
introduced a double-corrugation based flexible skin and achieved morphing induced roll-controllability comparable to conventional ailerons [58]. Keidel applied the compliance based morphing structure to a tailless flying wing, achieving sufficient controllability around the roll-, pitch-, and yaw-axis of the flying wing solely by using morphing [64].
2.1.2 Aeroelastic modeling of morphing wings
In the design process of morphing structures, it is of paramount importance to consider the interaction between structural deformations and aerody- namic forces. The interaction between these two disciplines has long been recognized in the field of aeronautics. Therefore, this review considers modeling of flexible aerospace structures in general, which covers modeling of morphing structures.
The first wind tunnels at NACA/NASA were specifically dedicated to aeroelastic studies. Early flight suffered from aeroelastic issues, and as flight speed increased, it was not possible to neglect these effects [65]. Now, it is common practise to consider aeroelastic effects early in the design, to avoid expensive redesigns. Due to the different equations for the structure and for the aerodynamics, the two problems are typically modeled with separate techniques and coupled with an appropriate scheme [66]. Splines are usually used [67] to interpolate the structural displacements onto the aerodynamic grid, and the aerodynamic forces onto the structural nodes.
Nonlinear beam models are commonly used to describe the characteristic of flexible structures with a dominant spatial dimension [68–71]. The sec- tional properties of such structures are usually pre-calculated along their dominant direction. However, more refined models are required in the case of morphing and geometrically complex wings that exhibit flexibility in the chordwise direction and, therefore, strongly interact with the aero- dynamics. Detailed finite element models, based on both beam and shell elements, are therefore used to accurately represent the characteristics of such structures [53,62].
In terms of the aerodynamics, different models have been applied to aeroelastic problems, depending on the tradeoff between computational cost and accuracy of the simulation. Early studies considered simple 2-D geometries with analytical models for the aerodynamics, based on unsteady potential flow theory [72]. These methods rapidly evolved, and extensions to 3-D problems, based on strip theory, are still used today [73]. How- ever, for aeroelastic analysis, it is now common to use the doublet lattice method (DLM) [74] for the unsteady aerodynamic generalized forces, and its steady counterpart the vortex lattice method (VLM) [75,76]. Compared to computational fluid dynamics based on the Navier-Stokes equations, these methods are significantly more efficient, and they provide results that are accurate enough for the early design stages. These methods do not require discretizing the volume surrounding a body. Instead, the problem is reduced to an equivalent formulation on the boundaries of the domain and only the wing surface must be discretized. Therefore, these methods do not suffer from issues related to mesh deformations [77]. In turn, they do not represent viscous effects and are not suited for transonic applications.
Panel methods are mainly divided into frequency-domain and time- domain methods. Representing unsteady aerodynamics in the frequency domain is useful for flutter predictions. A linear state space model is usually preferred for response analysis and control design [78–80]. If DLM is used, this requires a specific fitting of the matrices, obtained at different reduced frequencies, using techniques such as Roger’s method [81]. It is possible to directly identify the system matrices using time domain methods. Murua et al. [82] proposed a promising approach based on the unsteady vortex lattice method (UVLM). The UVLM is the direct extension of VLM in the unsteady time domain. In this specific case, linearising the nonlinear equations for lifting surfaces and aerodynamics, the state-space form is easily obtained.
The limitations of UVLM are related to the approximation of the surface as an infinitely thin sheet. If the camber effect is important, as in the context
of morphing structures or flexible airfoils, this requires more detailed models, such as the unsteady 3-D panel method [66, 83, 84]. Analysis techniques widely used in the context of morphing wings are based on nonlinear extended lifting-line methods [53,85,86]. The sectionwise 2-D aerodynamic properties of the wing can be calculated using a 2-D panel method (XFOIL is commonly used, which is a panel method coupled with a boundary layer model that can represent viscous effects [87,88]). The resulting lift curves can then be used to efficiently calculate the 3-D lift distribution using a lifting line method. However, the limitations of the methods are the viscous boundary layer only modeled as two-dimensional and the unsteadiness of the flow not being considered.
2.1.3 Optimization of morphing wings
Current optimization methods used for designing morphing wings can be roughly divided in: 1) topology optimization, 2) high-fidelity gradient- based aero-structural optimization and 3) evolutionary algorithm-based multidisciplinary optimization.
Topology optimization was first introduced by Bendsøe and Kikuchi [89]
and deals with optimizing the material distribution of a structure within a predetermined design domain [90]. In particular, the compliance of a structure subject to a volume constraint is minimized. The method is widely used in aerospace applications [91–97], and two extensions and specific applications of topology optimization are relevant for morphing, namely compliant mechanism topology optimization [98–100] and topology opti- mization considering fluid-structure interaction [101–104]. Several studies on designing compliant structure-based morphing wings using topology optimization were presented [105–109]. These studies can provide valuable insights in the conceptual design phase of morphing wings, as the design space can be fully exploited by freely distributing material within the pre- scribed wing domain. However, they are mostly based on single discipline models, not considering aeroelastic effects.
The second branch of optimization methods dealing with morphing wings relies on high-fidelity aero-structural models [110]. Using high- fidelity models is especially important for accurately predicting aerody- namic drag. Burdette et al. [111–113] published several studies on the performance improvement potential of camber-morphing wings. In these studies, no specific morphing concept is considered. Thus, the aim is to assess the general potential of morphing wings. The results of these stud-
ies are very promising, with a reported wing structural weight reduction of 15.7% and a fuel burn reduction of 2.7%. The structural weight and fuel burn reduction are achieved considering the mission discipline in sequence to the aero-structural optimization. By considering a fully cou- pled mission-aero-structural optimization, the performance improvements through morphing could be further increased [113].
Venkatesan-Crome et al. [114] propose another promising approach towards optimizing morphing wings using high-fidelity aero-structural models. They use the open-source software SU2 [115,116], developed for aerodynamic optimization with its extension to consider fluid-structure in- teraction. The fluid is modeled using the Reynolds-averaged Navier–Stokes (RANS) equations and the structure solving a geometrically-nonlinear solid mechanics problem [117,118]. Both stiff and compliant structures are op- timized, with the optimized stiff structure resembling the results found in previous studies by pure aerodynamic optimizations. The compliant structure, however, resulted in a different optimized shape, highlighting the necessity of considering aero-structural optimization in compliant wing design. In a recent study [119,120], the high-fidelity compliant airfoil shape optimization described in [114] is combined with a density-based topology optimization. The method couples shape and topology optimization using high-fidelity aero-structural models and is demonstrated on a compliant airfoil load alleviation problem. An improved design is obtained using the concurrent shape and topology optimization compared to shape opti- mization, highlighting the importance of considering multiple disciplines concurrently.
The third branch of optimization methods dealing with morphing wings is using evolutionary algorithms. Evolutionary algorithms, such as genetic algorithms [121] and evolutionary strategies [122], are families of optimiza- tion methods inspired by evolutionary biology, using principles such as mutation, recombination, and selection. These algorithms formulate opti- mization problems that evolve a population of individuals toward better solutions by mutating and altering the properties of the individuals. Recent methods such as the covariance matrix adaptation evolution strategy (CMA- ES) [123,124] and the estimation of distribution algorithm [125,126] involve the identification of correlations between parameters of selected individuals and introduce learning strategies of probability distributions [127]. These methods are now commonly used due to their favorable performance in terms of convergence rate and since they require no extensive parameter tuning. In morphing wing design studies, evolutionary algorithm-based
multidisciplinary optimizations are mostly exploited where gradients are unavailable, their calculation is prohibitively expensive, or where objective functions are expected to be non-smooth. Due to the large number of func- tion evaluations needed, compared to gradient-based optimizations, most studies using evolutionary algorithms are assessing the wing performance using low fidelity aero-structural models [50, 53, 61, 63]. These model- ing and optimization frameworks allow fast integration of new compliant mechanism concepts. They mostly rely on two-way coupled fluid-structure interaction (FSI) methods, coupling detailed structural finite-element mod- els with panel method based aerodynamic models. The aerodynamic shape and the internal structure are parametrized and embedded in an optimiza- tion framework where a high-level objective (e.g. aerodynamic efficiency) is maximized. The tight parametrization might restrict the final design com- pared to using topology optimization where the material can be distributed freely in the whole design space. However, the parametrization can be chosen to only obtain manufacturable designs, avoiding manual redesigns that potentially impair performance. Another great benefit is the simple integration of models considering multiple disciplines, critically important in evaluating system-level morphing wing performance.
2.2 r e d u c e d-o r d e r a e r o e l a s t i c m o d e l i n g
The aeroelastic methods introduced in the previous section provide accurate models of aeroelastic effects. However, faster models are often necessary for optimization and control, even at the expense of some fidelity. This tradeoff between accuracy and efficiency has motivated reduced-order models, which model the behavior of the system with as few states as possible.
There is a wide variety of model reduction techniques in the literature [128].
A rough classification of reduced-order modeling methods is shown in Figure2.4. Both data-driven and model-based approaches are common.
The latter is exemplified by the modal reduction of structural dynamics: an eigenvalue problem is solved and a reduced set of orthogonal modes are used to describe the state of the system [129,130]. Different variants of the modal reduction are used and a range of extensions have been proposed to consider structural dynamics featuring geometric nonlinearities [131–136].
In recent years, data-driven approaches have become increasingly power- ful and widely adopted. Similar to modal reduction methods, data-driven projection methods, such as the proper orthogonal decomposition (POD), project the governing equations onto a set of modes [137,138]. The method
Reduced-order models
Model-based Data-driven
Projection System identification
Modal-reduction POD AIR + ERA DMD, SINDy
Input/Output Full state
Figure2.4: Categorization of reduced-order modeling methods.
is relying on data obtained using experiments or solution snapshots of a computational model to generate the modes. Other data-driven modeling techniques may be categorized as system identification, where a model for the input–output behavior is constructed based on data. Time domain tech- niques are especially common, such as the aerodynamic impulse response (AIR) [139–142], where the system is perturbed with an impulsive input, and the output response may be used to predict the response to future input maneuvers via convolution. Although these techniques are typically linearized, nonlinear kernels may also be employed in a Volterra series [140, 143]. State-space realizations are becoming increasingly common, especially for control applications [78, 80]. The eigensystem realization algorithm (ERA) [144] was developed specifically to model the structural response of aerospace structures, although the resulting model is formulated in terms of a nonphysical state that is difficult to interpret. However, when the entire physical state can be observed, it is possible to construct state-space models in terms of a reduced state that is related to the physical domain. The dynamic mode decomposition (DMD) [145–149] and the sparse identifi- cation of nonlinear dynamics (SINDy) [150–152] both result in physically interpretable models of the dynamics, and they have been extended to input–output systems for control [153,154].
DMD results in a linear time-invariant (LTI) system, which is valid in a particular operating regime. There are several approaches to interpolate LTI systems to obtain a linear parameter varying (LPV) system, as a function of the flight condition [155–162]. However, it is generally challenging and there is no universal solution to interpolate LTIs.
2.3 a i r b o r n e w i n d e n e r g y
This work is concerned with the development of efficient and accurate numerical models that enable optimization and control of morphing wings.
The morphing wing modeling and optimization methods are applied to AWE, although the methods are generally applicable to any coupled aeroser- voelastic system operating over multiple operating regimes. AWE is a par- ticularly compelling application for morphing, owing to the large operating regime these systems cover and thus great potential for performance im- provement. The AWE technology is therefore introduced in the following.
AWE is a technology that extracts power from winds using tethered drones [11,12]. In comparison to conventional wind turbines, these systems can reach higher altitudes, characterized by stronger and more consistent winds, and therefore potentially extract more power [163]. Additionally, lower manufacturing and material costs are expected, due to the lack of expensive infrastructure like wind turbine towers and foundations [11].
The long term vision is thus to replace tons of steel and concrete with soft- ware and advanced materials [164], exemplified in Figure2.5. A shipping container-sized AWE system developed by the Swiss start-up Twingtec [165]
is shown next to a conventional wind turbine of comparable power. How- ever, the wind turbine accounts for 20 times the mass of the AWE system.
In recent years, the research activities and commercial interest in the field of AWE increased drastically. Most studies focus on the crosswind power concept first introduced by Loyd [166] in 1980. In this approach, soft kites or rigid-wing drones fly crosswind trajectories, and either use the high lift forces to drive a ground-based generator via a tether (lift mode) or use the high flight velocities to drive on-board wind turbines (drag mode).
The two approaches are shown in Figure2.6. Both the lift and drag mode are investigated by various start-ups and academic research groups. Most academic groups work with soft kites, as they are generally less expensive, whereas most start-ups rely on rigid-wing drones (Makani Power [164], Ampyx Power [167]), as this technology is more promising in terms of performance due to the favorable aerodynamic efficiency [12].
Currently, modeling, control, and automation of the airborne system are regarded as the major challenges. Hence, this attracts the attention of most research groups investigating AWE systems. The majority of studies focus on developing different strategies for the control and optimization of the traction-phase flight trajectory, as well as automating both the take-off and landing of the airborne system and the transition between the differ-
Figure2.5: Conventional wind turbine next to Twingtec’s shipping container sized AWE system with comparable power [165].
ent flight phases. In addition to the control and automation aspects, the structure and aerodynamics of the airborne system are crucial to extract maximum power. In terms of optimal performance, the wide range of wind speeds in which the airborne system needs to operate represents a big challenge. Furthermore, the operational environment is particularly demanding due to the presence of gusts and turbulence. These have the potential of significantly increasing the load factor, hence, leading to the necessity of constraining the flight envelope and possibly reducing the power production. Additionally, in the case of lift-based power-generator systems, the system extracts power by periodically reeling-out (traction phase) and reeling-in (retraction phase) the tether. Thus, the drone con- stantly changes between two distinct operating modes. In the traction phase, maximum power is produced by operating the drone at high flight speeds, large incidence angle, and high-lift forces. In contrast, in the retraction phase, the load on the tether is minimized by decreasing the incidence angle to reduce the required reel-in power. The drone is therefore required to operate both at high and low wing loading over a wide range of wind
Lift mode Drag mode
Figure2.6: Different crosswind AWE modes. Left: drag mode, producing power on board, Right: lift mode, producing power on ground [168].
speeds, while simultaneously maneuvering to follow a desired trajectory.
This creates the need for highly adaptable drones. Taking this into account, conventional rigid wings would not represent an entirely optimal solution, as their design is always the result of a compromise between the require- ments of different flight conditions. The application of morphing wings to AWE is therefore particularly compelling, owing to the large potential for performance improvements through shape adaptation.
2.3.1 AWE systems
Several start-up companies are developing AWE systems and are working towards their commercialization. The largest potential for AWE is currently seen in floating offshore systems. In Europe, 80% of all offshore wind resources are located in water where conventional bottom fixed offshore wind energy systems are commercially unattractive [169]. Those resources can only be efficiently exploited by floating offshore wind energy systems.
Conventional wind turbine based floating offshore systems rely on large platforms anchored to the seabed by multiple lines, whereas floating AWE systems rely on simple, small platforms and existing supply chains and infrastructures [164]. Therefore, a large potential towards cost-efficient power production using floating offshore AWE systems exists.
Figure2.7: Top: Makani Power’s AWE system tested on a floating platform in the North Sea [164]. Center: Artistic view of Ampyx Power’s megawatt-scale AWE off-shore wind farm [167]. Bottom: Artistic view of Twingtec’s 100 kW off-grid AWE system [165].
Different strategic approaches are followed by AWE companies to un- lock these offshore wind energy resources. The company Makani Power is directly targeting the megawatt-scale offshore wind energy market [164].
They follow the drag-based power production approach, converting wind power on the tethered drone using on-board turbines. The drone is flying circular trajectories and the electric power is transmitted to the ground via a conductive tether. The power production is therefore continuous, compared to the discontinuous power production due to the alternating traction and retraction phase of the ground-based approach. The second large advantage of Makani’s concept is its vertical take-off and landing approach, using the on-board turbines as propellers and the generators as motors. This allows space-efficient take-off and landing from a floating offshore platform without the need for a runway. However, the disadvantages of the concept are the higher weight and complexity of the drone when placing the gener- ators on the wing compared to a ground-based approach. Furthermore, the larger diameter of the conductive tether increases the aerodynamic drag and thus reduces the performance of the system. Currently, the company is extensively testing their 28m wingspan and 600kW scale system both onshore and offshore on floating platforms, shown in Figure2.7.
Ampyx Power follows a repowering strategy, where they plan to replace existing end of life offshore turbines by reusing their foundations and electrical infrastructure [167]. In a second phase, they plan to enter the floating offshore market with larger-scale systems. Their system is following the ground-based power production concept, with a short runway catapult start and landing approach, shown in Figure2.7. For their current 12 m wingspan and 150 kW scale system, the platform has a diameter of only 20 m. The start and landing concept is considered as critical. However, following this concept, the generator can be placed on the platform and the complexity and mass of the drone can be reduced.
Companies including Twingtec and other smaller start-ups initially tar- get smaller-scale off-grid markets, characterized by systems in the range of 10´100 kW, before potentially upscaling to megawatt-scale offshore systems [165]. The big advantage of this approach is the comparably high cost of energy in off-grid markets. Therefore, non-subsidized AWE systems can be employed, being independent of governmental policies. Twingtec’s system is following the ground-based power production concept, similar to Ampyx Power. However, they use a vertical take-off and landing strat- egy, using three motors and propellers. This provides the advantage of a compact take-off and landing, although introduces additional weight and
complexity to the drone. Their first commercial system has a wingspan of 15 m, a rated power of 100 kW, and can be packed into a standard size shipping container.
2.3.2 Analysis of AWE systems
The complexity of developing an AWE system is extremely high and so far no specific AWE concept has prevailed, as shown in the previous section.
It is therefore of paramount importance to develop numerical models allowing to analyze and optimize AWE systems. Several studies on AWE flight dynamics modeling have been conducted, mostly considering point mass or rigid-body flight dynamics of soft kites [170–172]. More recent studies considered multibody system dynamics [173], particle systems used to model detailed tether dynamics [174], and finite element models of soft kites [175]. First studies on the aeroelastic characteristics of rigid- wing AWE drones were presented recently. Wijnja et al. [176] extended an aeroelastic simulation framework [177] to consider a tensile support system and conducted wind tunnel tests to analyze the aeroelastic characteristics of an on-board power generation AWE drone. Candade et al. [178] presented an efficient aero-structural model of a tethered swept wing. The modeling framework allowed analysis of different bridle configurations and weight optimization of carbon composite wings at the initial design stage. In terms of optimization and control, a vast amount of studies have been published, covering control strategies and testing of the power production phase [179–181], strategies for the control of the take-off and landing [182], and studies focusing on model-based control strategies [183–188]. However, the modeling, optimization, and control of AWE systems remain challenging and solutions for comprehensive analysis need to be further investigated.
3
R E S E A R C H N E E D S A N D O B J E C T I V E S
Compliant structure-based morphing wings provide high tailorability of their aerodynamic properties and may have transformative impact on future aircraft and wind energy systems. However, the contradicting requirements on the morphing structure pose a great challenge: the structure needs to be sufficiently stiff and load-bearing while keeping the required flexibility to accomplish shape adaptability. This represents a considerable design and modeling challenge, as it involves highly coupled interactions between the aerodynamic and structural dynamics. Furthermore, current modeling and optimization techniques are not capable of providing accurate and efficient analysis of complete flight missions. However, this is of utmost importance to comprehensively understand and quantify the potential of morphing wings. Therefore, the vision of this work is to better understand and quantify the system-level performance gains achievable by morphing by providing fast and accurate modeling methods that allow analysis, opti- mization, and control of morphing wings. The motivation of this research, the research needs, and the research objectives are summarized in Figure3.1 and discussed in the following.
Aero-structural optimization of morphing wings At present, design and optimization methods for morphing wings are unable to concurrently consider the aerodynamic shape, the compliant structure, and the mate- rial topology of the wing. Existing optimization methods are restricted to concurrent aerodynamic shape and compliant structure optimization, detailed structural topology optimization, or high-fidelity aerostructural optimization not considering a specific morphing structure. Concurrently considering these parameters in the design of morphing wings allows exploiting interdisciplinary interactions and is expected to result in the identification of morphing wings with improved performance. To better understand the influence of these parameters and their mutual interac- tion on the performance of morphing wings, modeling and optimization frameworks need to be investigated that allow concurrent multidisciplinary optimization of the aerodynamic shape, compliant structure, and material topology of morphing wings.
21
Efficient modeling for optimization and control
Understanding and modeling aero- servoelastic effects
Framework for complete system optimization Morphing wingsenable smooth adaptation
of their aerodynamic shape during flight Great potential to optimize flight system characteristics
Accurate and efficient numerical models for system-level analysis, optimization, and control
𝒒𝑖𝑛+1= ෩𝑨𝒒𝑖𝑛+ ෩𝑩𝒖𝑛+ ෩𝑭𝒖𝑛+1 𝒙𝑖𝑛+1= 𝑼𝒒𝑖𝑛+1
MotivationNeedsObjectives allows requires
allows
Tailoring aerodynamic properties to a wide range of operating conditions for optimal performance
Figure3.1: Overview research motivation, needs, and objectives.
Reduced-order aeroelastic modeling for optimization Current model- ing frameworks for morphing wings mostly neglect flight dynamic effects and are restrictive in considering complete flight missions. However, this is of paramount importance in the design and optimization of morphing wings. By considering complete flight missions, system-level objectives can be formulated. This allows to comprehensively quantify the performance benefits of morphing wings. Therefore, it is crucial to investigate complete flight mission aeroservoelastic modeling techniques that enable to accu- rately evaluate and optimize morphing wings. Critically important are thereby efficient models that allow performing multidisciplinary design optimizations where the underlying model must be constantly updated.
Specifically, reduced-order modeling techniques need to be investigated that offer low computational costs for both building the model (offline cost) and for executing the model (online cost). Hence, to comprehensively quantify the performance benefits of morphing wings, aeroservoelastic modeling techniques need to be investigated that allow running mission performance analysis and complete system optimization.
Reduced-order aeroelastic modeling for control A critical limitation of current morphing wing modeling techniques is the reliance upon steady or quasi-steady aerodynamic methods. Accurate and highly efficient reduced- order models that include complete system dynamics considering the un- steadiness of the flow are therefore required to understand the morphing wing performance in realistic flight conditions. These models are especially important for control and analysis of morphing wings in gusty and turbu- lent wind fields. A considerable modeling challenge is posed by the large operating regime of morphing wings. When operating conditions change, reduced-order models may lose their validity. Therefore, unsteady aeroelas- tic reduced-order models need to be investigated, which are applicable to flight systems covering large operating regimes.
4
S T R U C T U R E O F T H E T H E S I S
The methods investigated and developed during this work contribute to the state of the art of modeling, optimization, and control of morphing wings.
Specifically, reduced-order modeling methods enabling optimization and control of morphing wings applied to AWE are developed.
In Part II of the thesis, an aeroelastic modeling and optimization frame- work for morphing AWE wings is introduced. The modeling framework allows assessing the camber-morphing performance of highly loaded AWE wings and highlights the importance of concurrently considering aerody- namic and structural interactions. The model is embedded into an evolu- tionary algorithm based optimization framework. Thereby, a large number of design parameters can be optimized while interdisciplinary interactions can be assessed and exploited.
Part III of the thesis is concerned with reduced-order aeroelastic modeling methods and with complete flight mission modeling of morphing wings.
Two reduced-order models are introduced, the first based on a structural mode superposition method and a linearization of the quasi-steady aerody- namic model, and the second based on a data-driven approach considering the unsteadiness of the flow. Both models are coupled with an AWE flight simulator, allowing to perform complete flight mission analysis.
Part IV of the thesis addresses the application of the introduced reduced- order models from Part III to control and optimization problems. The data-driven reduced-order model considering unsteady aerodynamics is used for model predictive control, whereas the reduced-order model based on quasi-steady aerodynamics is applied to complete system and flight mission design optimization.
25
A E R O - S T R U C T U R A L O P T I M I Z AT I O N
5
A E R O - S T R U C T U R A L O P T I M I Z AT I O N O F M O R P H I N G AW E W I N G S
The results presented in this chapter are based on the following manuscript:
Urban Fasel, Dominic Keidel, Giulio Molinari, and Paolo Ermanni.
”Aerostructural optimization of a morphing wing for airborne wind energy applications”. In:Smart Materials and Structures, vol. 26, no. 9, 2017
The major challenge of applying morphing structures to highly loaded wings are the contradicting requirements on the structure to be stiff and load-carrying, but still being compliant enough to achieve the required shape changes to operate optimally across different flight conditions. There- fore, a morphing wing design method is required that considers aeroelastic effects from an early design stage. In this study, a procedure to concurrently optimize the aerodynamic shape, wing structure, and composite layup of morphing wings for AWE applications is presented. The optimization pro- cedure is applied to a reference AWE wing, with an area of approximately 5 m2, operating at typical offshore wind conditions. In the following section, the wing concept, the analysis framework, and the analytical models to assess the performance of the AWE system are presented. In Section 5.2 and5.3, the wing optimization procedure and the results are described. In Section5.4, the main findings of the study are summarized.
5.1 w i n g c o n c e p t a n d a na ly s i s f r a m e w o r k
The drone configuration considered within this study is based on a high aspect-ratio wing, fuselage and T-tail configuration, shown in Figure5.1.
The tether is split in three leads, attached not only at the fuselage but also at the wing. This increases the structural efficiency of the wing in comparison to conventional cantilever wings and has the benefit of significantly reduc- ing the root bending moment. In this investigation, the design of the other components of the AWE drone (e.g. fuselage and tail) is determined prior to the optimization and frozen throughout the study. This simplification does 29
Tail Main wing
Tether Fuselage
x z y
Figure5.1: Drone configuration with three tether attachment points based on an early concept of Makani Power [189].
not lead to a loss of generality, as the impact of wing parameter changes on the other components would be minor. Thus, the resulting performance of the system is exclusively linked to the wing design, facilitating the process of identifying the benefits permitted by different morphing designs.
5.1.1 Morphing wing concept
The morphing wing concept investigated in this study is developed from the compliant structure introduced by Molinari et al. [53–56]. The concept attains variations of the local lift coefficient by means of chordwise mor- phing and is shown in Figure5.2. Differently from the concept introduced by Molinari, in the proposed design the mechanical energy required to morph the structure is provided by electromechanical linear actuators in- stead of active piezoelectric elements. These actuators are chosen due to their higher static load-carrying capability (capacity of maintaining a fixed position without using energy), their energy density, and their favorable force-displacement characteristics [58,59]. The deformation introduced by the actuators is guided by a numerically optimized rib based on distributed compliance. The actuators and ribs are organized in rib-actuator sets, con- sisting of a rib-pair and a single actuator. To achieve the desired shape changes, the possibility to elongate part of the compliant skin is crucial.
Therefore, a corrugated skin with highly anisotropic stiffness is introduced on the lower side of the wing. This corrugated skin allows the desired in-plane elongation to occur, while contributing to withstand the large bending loads experienced by the structure [60,190,191].
Overall, the wing consists of nine evenly distributed rib-actuator sets per half span. A stiff D-nose wingbox carries the majority of the bending, shear, and torsional loads. The material used for the wing and for the internal compliant rib is carbon fiber reinforced plastic (CFRP), owing
Compliant ribs Spar
Skin Stringers
Corrugated flexible skin Electromechanical actuator
Figure5.2: Representation of the wing morphing concept.
to its anisotropy and favorable lightweight characteristics. The layup is concurrently optimized with the structure and aerodynamic shape, and is presented in Section5.2.1.
5.1.2 Aeroelastic analysis method
To accurately predict the aerodynamic and structural behavior of the wing and to assess the resulting performance, it is necessary to consider aeroelas- tic interactions. This is particularly important given the high wing loading and the compliance of the wing. The response of the wing on actuation inputs and aerodynamic loads is thus assessed by using a two-way weakly coupled 3-D static aeroelastic analysis tool [53]. The aerodynamic behavior of the wing is simulated with a 3-D panel method [66,192] and a nonlinear extended lifting-line technique [66,85], the latter using XFOIL [87,88] to calculate the sectionwise 2-D aerodynamic characteristics. The structural behavior is assessed by means of a 3-D finite element model. The wing skin and internal structure are modeled by plate elements, the stringers and actuators are modeled, respectively, as beam and rod elements. The corrugated skin is modeled using a substitute plate model [193,194]. The aeroelastic analysis tool, validated through high-fidelity numerical simula- tions and wind tunnel tests [53,56], iteratively assesses the aerodynamic characteristics (lift and drag) and the structural displacements caused by actuation inputs and aerodynamic loads.
5.1.3 AWE performance modeling
In this study, analytical models are used to assess the energy extraction capabilities of the AWE wing. The powerPproduced by an AWE system in the traction phase at optimal reel-out speed can be modeled as a function of the lift and effective drag coefficientcLandcD, the wing areaA, wind speedVW, and angle between tether and groundγ[11, Ch. 1]:
P= 2 27ρAc3L
c2DVW3 cos3(γ) (5.1) The reel-in phase is neglected in this investigation, as it is strongly depen- dent upon the followed trajectory. The effective drag coefficient consists of the drag of the wing and also of the drag of the tether. Houska et al. [195]
suggest the following approximation:
cD=cD,wing+1 4
ltether¨dtether Awing
cD,tether (5.2)
At a given wind speed, the flight speedVat optimal reel-out speed (Vro,opt
=1/3VW) can be calculated as [11, Ch. 1]:
V= 2 3
cL
cDVWcos(γ) (5.3)
The influence of the mass of the dronemA=mWing+mActuator+mFuselage on the power output of the AWE system can be considered in the analysis by increasing the tether elevation angle by∆γmass(cosine losses), and by rolling the drone into the circular trajectory (of radius r) to counteract centrifugal forces [11, Ch. 3]:
P= 2 27ρAc3L
c2DVW3 cos3(γ+∆γmass)¨ 1´
2mA AρcLr
2!32
(5.4) The mass of the wingmWingis obtained from the FE-model, and the mass of the fuselage is set tomFuselage = 10 kg, to account for the mass of the wing-to-tail connection, the tail empennage, and the electronics. The mass of the actuators is determined as a function of the required power using the relationmActuator=0.1317¨(PActuator)0.8251[58]. The required actuator power output can be calculated by the force acting on the actuator, assessed within the aeroelastic simulation, the maximum stroke of the actuator, and
