High-lift System with Aeroelastic Loads
Proefschrift
ter verkrijging van de graad van doctor aan de Technische Universiteit Delft,
op gezag van de Rector Magnificus prof. ir. K.C.A.M. Luyben, voorzitter van het College voor Promoties,
in het openbaar te verdedigen op 4 juni 2012 om 12.30 uur door
Glenn Alfons Anita THUWIS
ingenieur Luchtvaart en Ruimtevaart geboren te Hasselt, België.
Dit proefschrift is goedgekeurd door de promotor: Prof. dr. Z. Gürdal
Copromotor: Dr. M.M. Abdalla
Samenstelling promotiecommissie:
Rector Magnificus, voorzitter
Prof. dr. Z. Gürdal, Technische Universiteit Delft, promotor Dr. M.M. Abdalla, Technische Universiteit Delft, copromotor Prof. dr. ir. drs. H. Bijl, Technische Universiteit Delft
Prof. dr. ir. M. van Tooren, Technische Universiteit Delft
Prof. dr. P. Ermanni, Eidgenössische Technische Hochschule Zürich Dr.-Ing. H.-P. Monner, Deutsches Zentrum für Luft- und Raumfahrt Dipl.-Ing. J.C. Simpson, Fraunhofer-Institut für Bauphysik
Prof. dr. A. Rothwell Technische Universiteit Delft, reservelid
Parts of this research were supported by the European Union’s Framework 7 Programme project Smart High Lift Devices for Next Generation Wings (grant no. ACP7-GA-2008-213442), and the European Union’s Green Regional Aircraft Integrated Technology Demonstrator project Leading Edge Actuation Topology Design and Demonstration (grant no. CSJU-GA-GRA-2010-271861).
Keywords: morphing, high-lift, aeroelasticity, composites, topology optimisation
ISBN 978-94-6191-326-5
Copyright c 2012 by Glenn A.A. Thuwis
All rights reserved. No part of the material protected by this copyright notice may be reproduced or utilised in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without the prior permission of the author.
Printed by Ipskamp Drukkers B.V., Enschede, The Netherlands. Typeset by the author with the LATEX Documentation System.
The thesis you are about to read is the result of an amazing journey with ups and downs that have made me a better aerospace engineer. You are about to set off and read a fascinating story about a possible design methodology of a morphing leading edge high-lift system on a future airplane. This research is but a small part of the large amount of research that is currently being performed in the area of green air-craft solutions. Every second we are using more and more of the fossil fuels that are available to us, and every second that supply is shrinking. Novel solutions are thus required if we want to keep travelling the world as we are doing today. Thus we need to use lower amounts of fossil fuels as our energy sources, and eventually maybe no fossil fuels at all? I can only hope that in ten or twenty years time you will be flying to a nice holiday destination and, when you look through the windows, you will see a fully morphing wing continuously changing its shape to optimise the airplane’s flight performance and reducing its energy requirements. In the meantime, enjoy reading this thesis as much as I have enjoyed working on it!
Glenn Thuwis June 4, 2012 Delft, The Netherlands
The past years have been an incredible experience in which I got to work on an exciting European project with partners from all across Europe and beyond. I have had the privilege to present my work on numerous occasions all over the world. I couldn’t have made this journey without the continuing support of my colleagues, friends and family.
First of all I would like to thank my promotor, Prof. dr. Gürdal and co-promotor, Dr. Abdalla for the opportunity they created to perform this research under their supervision. I have had the pleasure to work with a fine group of colleagues at the Aerospace Structures and Computational Mechanics department. I would like to thank them all for making the work feel less like work and more like play. A special word of thanks goes to my (former) roommates Mathieu, Terry, Mohammed, David, Johannes, Stanislav, Meysam, Tanvir, Ramzi and Ali, for the fun we had the past years. I am definitely going to miss working in such a pleasant office! I would like to thank Sam for providing a Matlab code to determine the element stiffness of the triangular membrane elements that were used in this work. My former Master’s thesis supervisor deserves a separate mention here; Roeland, you did a great job in convincing me to work on aeroelasticity. I am glad that we have had the chance to become good friends. We got to take part in some extremely interesting projects, to travel to conferences, and share long conversations about Formula One, airplanes, Belgian beers and of course Belgian politics.
No organisation would still be standing if it wasn’t because of their main pillar, a superb secretarial team. Annemarie, Collete, Angela, Lisette and Laura are all prime examples of strong pillars that keep the group going without any hiccups. I would especially like to thank Laura for the extra effort she has spent in supporting me with the paperworks to get this work approved and published. For some reason, Laura, Roeland and Mathieu, we were always on the same level when it came to jokes and humour, which led to some hilarious situations that made work just that little bit more special!
A special thanks goes to Miranda for taking the time to read and reread the text you are about to read, and are reading at the moment. Her help and comments have made my English so much better!
Part of being a PhD candidate involves supervising Master students. I have had the luck to work with a fine group of students, so thank you guys for the nice cooperation we had. I would like to thank Jaap and Alex because of their support for the research which is presented in this thesis. It has also been a pleasure to work with Jeremy and Luca, who built and tested the Formula One rear wing which I designed as part of my MSc thesis project. I was glad that I got to be part of those tests!
time as I started with my PhD. I would like to thank all the people who were involved in the project for their devotion to taking the development of morphing high-lift sys-tems to the next level. I would especially like to thank Durk who was my fellow PhD candidate from Delft working on the SADE project.
I would like to thank all my good friends with whom I got to share laughter and joy the past years. My best man, David, once told me that "friends are the family that you get to choose for yourself", and I can’t agree more with him. Throughout my study I have shared many joyful moments with Elie, Wim, Sven, Stef, Stanley, Michael, Ward, Mathieu, Gijs, Bert, Dirk and Jasper. Thanks for making my time in Delft unforgettable! My many trips back and forth between Belgium and The Nether-lands were, amongst other reasons, to keep in touch with my long time friends David, Anke, Eveline and Elisabeth, to who I am thankful for their continued friendship, even when I wasn’t always in the country.
The trips back and fort between The Netherlands and Belgium were also to visit my family. I am blessed with two brothers, Stevie and Kenneth, with whom I got to share so many wonderful experiences, and with whom I hope to share so much more in the future. Growing up with two brothers meant that I never got have a sister until my sisters-in-law Lotte and Daisy came into the family. I must admit it is a bit harder to talk about race cars, but other than that I cannot imagine a life without them anymore. Lotte’s effort to review the Dutch texts in this thesis was greatly ap-preciated. You usually hear people complaining about their parents-in-law, so I must be one lucky guy to have such nice and supporting parents-in-law and family-in-law! Every man should have a loving and caring wife at his side. Tine, you are (and were) always there when I need(ed) you most, even in times when work wasn’t going that well, and my mood was somehow going down as well. But you always managed to cheer me up, so I say thanks for your unconditional love and care!
Last, but definitely not least, I would like to say thanks to my parents. You have always loved and supported me, even when I made choices that at the time seemed odd. My move to Delft was one big adventure without knowing where it would end. Now, nine years later I am glad that you supported me in this adventure since it has given me the opportunity to become the person that I am today.
Stiffness and Layout Tailoring of a Morphing
High-lift System with Aeroelastic Loads
The design of a smooth seamless morphing leading edge high-lift system is presented in this thesis. Such smooth seamless morphing high-lift devices are primarily developed for application on a laminar cruise wing. Laminar cruise wings are being investig-ated to reduce wing drag during the cruise phase of an airplane and should lead to a reduction in fuel consumption. Laminar cruise wings require the gaps and surface irregularities on a wing due to slotted high-lift devices, such as slats, to be completely removed if the laminar flow region is to be extended to a larger part of the airfoil. A smooth seamless morphing high-lift system is expected to reduce airplane noise during take-off and landing since the gaps of slotted high-lift devices generate a fair amount of noise.
The design of a morphing leading edge high-lift system in the present work is split into the design of an airfoil skin and an internal actuation system which deforms the leading edge skin. Design of a morphing airfoil skin leads to a dilemma, choosing between a high or a low skin stiffness. A high skin stiffness is required to withstand the external aerodynamic loads and to transmit these loads to the supporting structure. A low skin stiffness is favourable since it allows for an easier deformation of the skin when morphing is required. The present work is aimed at finding the balance between high and low skin stiffness at specific places along the leading edge of an airfoil using a variable stiffness skin. Such a variable stiffness skin has a spatial stiffness variation, and in the present work, variable stiffness composites were considered to achieve a skin stiffness variation. A variable stiffness composite can be created using a spatial fibre angle variation in a single ply where thickness changes are or are not allowed, or using a spatial thickness variation with a constant fibre angle.
The close interaction between the structure and the varying aerodynamic loads were considered in a two-dimensional aeroelastic framework that coupled a non-linear Euler-Bernoulli beam element to model the airfoil skin and the internal actuation system, to a two-dimensional inviscid panel method that defined the varying aerodynamic forces acting on the wing. A corotational method was employed to model the geometrical non-linearity in the structural analysis module of the aeroelastic framework. A closely coupled aeroelastic analysis was created by including the derivatives of the aerody-namic loads with respect to the airfoil skin displacement, known as the aerodyaerody-namic stiffness matrix, in the aeroelastic routine. The nonlinear equilibrium path was found using the normal flow algorithm which was embedded in a Newton-Raphson iterative scheme. A radial basis function interpolation using Wendland’s C2-function was ap-plied to provide the interpolation of loads and displacements between the structural and aerodynamic models of the airfoil.
The skin stiffness was defined using two non-dimensional parameters to represent the lay-up of the composite skin and the skin thickness. A design space for the non-dimensional stiffness parameters was defined for a specific composite material using the classical lamination theory. A gradient based optimisation method could be used since the three skin stiffness design variables were continuous in nature. The sensitiv-ity information required by a gradient based optimiser was provided in the aeroelastic framework using the adjoint method, where partial derivatives were programmed ana-lytically into the aeroelastic framework. The skin stiffness optimisation objective was defined in terms of the skin curvature of the morphing leading edge. A target shape deformation of this morphing leading edge was defined based on extensive aerodynamic analysis which was beyond the scope of the present work. The difference in geomet-rical curvature of the target shape and the undeformed leading edge was defined to be the target curvature. A least squares difference between the actual skin curvature and the target curvature was used to define the morphing leading edge skin stiffness optimisation objective function. Skin strain constraints were included in the skin stiff-ness optimisation to avoid unrealistic skin stretching to occur for a deflected morphing leading edge.
A triangular membrane element with drilling degrees-of-freedom was included in the design framework to design an internal actuation system for the morphing leading edge high-lift system using topology optimisation. It needs to be noted that the topo-logy optimisation routine was limited to a linear deformation analysis of the morphing leading edge high-lift system. The simple isotropic material with penalisation (SIMP) method was used as the topology optimisation routine. Nodal density parameters were used to avoid checkerboard patterns occurring, and were converted into element dens-ities using compliance averaging. The actuation topology optimisation was performed using an objective function that was composed of the curvature based objective func-tion described above and a least squares difference between the achieved deformafunc-tion and the target deformation of the morphing leading edge. The addition of the last part was necessary to avoid the design of an internal actuation system that would simply deform the front part of the morphing leading edge system to match the target curvature while the leading edge deformation was far from target.
The actuation topology optimisation provided a blueprint of a possible actuation sys-tem layout, where the interpretation of the topology optimisation result by an engineer was required. The interpreted actuation system layout was optimised further in a post-processing step that took the effects of a nonlinear deformation into account. This actuation layout optimisation used the actuation node locations as design variables and is denoted in this work an actuation node location optimisation. This node loca-tion optimisaloca-tion could be performed using a predefined skin stiffness that remained constant throughout the node location optimisation, but it could also be performed in conjunction with a skin stiffness optimisation. For both cases, the skin strain con-straints were taken into account while performing the optimisation.
Results of an actuation topology optimisation are presented where the target shape and airfoil data from the European Union project Smart High Lift Devices for Next Generation Wings (SADE) were used. Two design spaces were considered with either a single actuation force or an actuation moment, while additionally two composite ma-terials, glass fibre and carbon fibre, were considered for the airfoil skin. The topology optimisation resulted in a set of four possible designs for an actuation system layout.
An interpretation of these actuation systems was made and a set of four actuation systems were generated. These actuation system layouts were used in an additional actuation layout optimisation. Two approaches were considered; one, a two step ap-proach where first the actuation layout was optimised, followed by a skin stiffness optimisation using the optimised actuation layout; and two, a single step approach where the actuation layout was optimised simultaneously with the skin stiffness. Both approaches led to a series of actuation system layouts combined with an optimised leading wing edge skin stiffness with a wide variation in performance with respect to the target shape and target curvature objective functions. The single step approach used in the present work for the simultaneous optimisation of the actuation system layout and spatial skin stiffness was superiour when the target shape objective func-tion was considered, and in 9 of the 12 morphing high-lift system designs resulted in a lower required actuation force compared to the counterpart high-lift designs that were obtained using the two step optimisation approach.
Choosing the best overall design was, however, not a trivial task based on the tar-get shape and tartar-get curvature objective function values, or based on the actuation force required to operate the high-lift system. The conclusion was made that such a decision would best be made based on an aerodynamic performance parameter such as lift-to-drag ratio. The current implementation of the aerodynamic routine in the aeroelastic design framework, however, does not allow such a comparison to be made. The present work did show that the aeroelastic design framework can be applied for the design of an actuation system for a morphing leading edge high-lift system, and the spatial skin stiffness optimisation of a morphing leading edge skin, can be either performed separately or simultaneously.
The following conclusions could be defined based on the results that were created us-ing the aeroelastic design framework described in the present work. The results of the actuation topology optimisation indicated that the choice of the best actuation system topology should not be made based on an assessment of the objective function value, but rather should be made from a qualitative point-of-view. The beam model inter-pretation of an actuation system for a morphing leading edge based on the topology optimisation results required a post-processing step in the form of an actuation layout optimisation that resulted in significant improvements of the final deformed shape for the cases studied in the present work. Including the geometrical non-linearity of the deformed leading edge high-lift system was found to be important to achieve a better match of the deformed leading edge with respect to the target leading edge deforma-tion. The ability to optimise the spatial skin stiffness variation resulted in a further improvement of the morphing leading edge to achieve the target shape since local skin stiffness tailoring was additionally possible compared to a constant stiffness skin. A maximum skin strain constraint was defined for all morphing leading edge high-lift system optimisations shown in the present work, and helped to ensure the feasibility of the final morphing system design. The spatial skin stiffness variation allowed for local skin stiffness and thickness variation to match better a target deformed shape without exceeding the maximum skin strain. Tests performed with a variable stiffness composite laminate showed the validity of designing a spatial skin stiffness distribution to facilitate a predefined deformed shape using the curvature difference between this deformed shape and the undeformed shape when a predefined external loading was applied.
The aeroelastic framework presented in this work can be used for the fast design of a morphing leading edge high-lift concept. Future work should initially focus on the addition of a higher fidelity aerodynamic routine which would enable the use of an aerodynamic performance characteristic such as lift-to-drag ratio as objective func-tion for a morphing high-lift optimisafunc-tion. The challenge for this necessary upgrade will be to include the required sensitivity information in the new aerodynamic module such that the aerodynamic stiffness matrix can be defined while keeping the computa-tional cost for a single aeroelastic analysis minimal. The variable stiffness composite skin which was considered in the present work requires additional work when produ-cibility of curved variable stiffness composite panels is considered. The challenge for this development will be to define and build the variable stiffness curved composite panel such that no thickness variation is present at the outer airfoil skin since such a thickness variation might deteriorate the laminar flow envisioned to be present on a laminar cruise aircraft wing.
Stijfheid en Lay-out Aanpassing van een Morfend
Draagkrachtverhogend Systeem onder
Aero-elastische Belasting
Het ontwerp van een glad naadloos vervormbaar draagkrachtverhogend systeem aan de voorrand van een vliegtuigvleugel, kortweg een morfende neusklep, is gepresenteerd in dit proefschrift. Zulke morfende neuskleppen worden voornamelijk ontwikkeld om te worden toegepast op een vleugel met laminaire stroming in kruisvlucht. Dit soort vleu-gels wordt onderzocht om de weerstand van een vleugel in kruisvlucht te verminderen, wat op zijn beurt moet leiden tot een verminderd brandstofverbruik. Een vereiste voor vleugels met een laminaire stroming in kruisvlucht is dat alle openingen en onregel-matigheden op de huid van de vleugel als gevolg van draagkrachtverhogende kleppen, zoals spleetkleppen aan de neus van een vleugel, verwijderd worden. Op die manier kan het gebied met laminaire stroming op de vleugel verhoogd worden. Er wordt ook verwacht dat het gebruik van een morfende neusklep zal leiden tot een afname van het lawaai tijdens het opstijgen en landen omdat de openingen in spleetkleppen een redelijke hoeveelheid lawaai veroorzaken.
Het ontwerp van een morfende neusklep wordt in dit werk opgesplitst in het ont-werp van de vleugelhuid en het ontont-werp van het interne aandrijfmechanisme dat de vleugelvoorrand vervormt. De realisatie van een vervormbare vleugelhuid leidt tot een dilemma, namelijk kiezen tussen een hoge of een lage huidstijfheid. Een hoge huidstijfheid is nodig om de externe aerodynamische krachten op te vangen en over te dragen naar de onderliggende draagstructuur. Een lage huidstijfheid is dan weer gewenst omdat het een gemakkelijkere vervorming van de huid toelaat wanneer deze vervorming nodig is. Het huidige onderzoek is dan ook gericht op het vinden van de balans tussen een hoge en lage huidstijfheid op bepaalde plaatsen langs de voorrand van een vleugelprofiel door gebruik te maken van een huid met variabele stijfheid. Zo een huid heeft een ruimtelijke variatie in stijfheid wat in dit werk gerealiseerd wordt door toepassing van een composietmateriaal met een variabele stijfheid. Een com-posiet met variabele stijfheid kan gemaakt worden door een ruimtelijke variatie van de vezelhoek in een enkele composietlaag toe te passen waar een dikteverandering wel of niet wordt toegelaten, of door enkel een dikteverandering toe te passen waarbij de vezelhoeken constant blijven.
De nauwe interactie tussen de vleugelconstructie en externe aerodynamische krachten werden beschouwd in een twee-dimensionaal aero-elastisch kader dat een koppeling realiseerde tussen een niet-lineair Euler-Bernoulli balkelement om de vleugelhuid en de inwendige structuur te modelleren en een twee-dimensionaal wrijvingsloze panelen-code dat de variërende aerodynamische krachten definieerde. Een corotatie methode werd toegepast om de geometrische niet-lineariteit te modelleren in de structurele
ana-lysemodule in het aero-elastische kader. Een nauw gekoppeld aero-elastische analyse werd gerealiseerd door de afgeleiden van de aerodynamische krachten ten opzichte van de vleugelprofielverplaatsing, beter bekend als de aerodynamische stijfheidsmatrix, toe te voegen aan de aero-elastische routine. Het niet-lineaire evenwichtstraject werd gevonden door toepassing van het normale stroming algoritme dat gekoppeld was aan een Newton-Raphson iteratief stelsel. Een radiale basisfunctie interpolatie met be-hulp van Wendland’s C2-functie werd toegepast om de interpolatie van belastingen en verplaatsingen tussen het structurele en aerodynamische model van de vleugel te genereren.
De huidstijfheid werd gedefinieerd door middel van twee niet-gedimensioneerde para-meters die de lay-up van de composieten huid definieerde en een parameter die de dikte van de composieten huid bepaalde. Een ontwerpruimte voor de niet-gedimensioneerde stijfheidsparameters werd gecreëerd voor een bepaald composietmateriaal door middel van de klassieke laminaattheorie. Een optimalisatiemethode gebaseerd op gradiënten kon worden toegepast omdat de ontwerpvariabelen van het continue type waren. De afgeleiden die nodig waren voor de optimalisatie werden in het aero-elastische kader bepaald door middel van de adjoint methode, waar partiële afgeleiden analytisch gepro-grammeerd waren in het aero-elastische kader. De doelfunctie die gebruikt werd tijdens de optimalisatie van de huidstijfheid was gedefinieerd in functie van de huidkromming van de morfende neusklep. Een doelvervorming van deze neusklep werd gedefinieerd op basis van een uitgebreide aerodynamische analyse die buiten het kader van dit werk werd uitgevoerd. Het verschil in de geometrische kromming van de doelvorm en de onvervormde vleugelvoorrand werd als doelkromming gedefinieerd. Het klein-ste kwadraten verschil tussen de werkelijke huidkromming en de doelkromming van de huid werd gebruikt om de doelfunctie voor de optimalisatie van de vervormbare vleugelhuid te bepalen. Een limiet op de maximaal toelaatbare rek in de huid werd toegevoegd aan de optimalisatie van de huidstijfheid om een onrealistische rek in de huid als gevolg van een vervormde neusklep te vermijden.
Een driehoekig membraan element met rotatie vrijheidsgraden werd aan het ontwerp-kader toegevoegd om het ontwerp van een inwendig aandrijfmechanisme voor een morfende neusklep mogelijk te maken door middel van topologie-optimalisatie. Het moet hierbij opgemerkt worden dat de topologie-optimalisatieroutine gelimiteerd was tot de analyse van een lineaire vervorming van de morfende neusklep. De methode van het eenvoudig isotroop materiaal met benadeling werd toegepast als topologie-optimalisatiemethode. Nodale dichtheidsparameters werden gebruikt om schaakbord-patronen te vermijden en werden omgezet in een elementdichtheid door middel van middeling. De topologie-optimalisatie van het aandrijfmechanisme werd uitgevoerd met een doelfunctie die opgebouwd was uit de doelfunctie op basis van de krom-ming van de huid zoals eerder beschreven en een kleinste kwadraten verschil tussen de behaalde vervorming en de doelvervorming van de morfende neusklep. Deze laat-ste component werd toegevoegd aan de doelfunctie om het ontwerp van een intern aandrijfmechanisme te voorkomen dat enkel de huid van de morfende neusklep zou vervormen om de doelkromming van de huid te benaderen, terwijl er amper een ver-vorming van de gehele neusklep zou zijn in de richting van de doelverver-vorming. De topologie-optimalisatie van het aandrijfmechanisme resulteerde in een blauwdruk van een mogelijke lay-out van het aandrijfmechanisme, waarbij de interpretatie van de topologie-optimalisatieresultaten door een ingenieur nodig was. Deze
interpre-tatie van een aandrijfmechanisme werd verder geoptimaliseerd in een nabewerking stap waarbij de effecten van een niet-lineaire vervorming in rekening werden gebracht. Deze lay-out optimalisatie van het aandrijfmechanisme gebruikte de locaties van de knooppunten van het mechanisme als ontwerpvariabelen en zal doorheen dit werk als aandrijf-knooppunt optimalisatie worden aangeduid. De aandrijf-knooppunt opti-malisatie kon worden uitgevoerd samen met een voorgedefinieerde huidstijfheid welke constant bleef doorheen de knooppunt optimalisatie, maar kon eveneens worden uit-gevoerd in combinatie met een huidstijfheid optimalisatie. In beide gevallen werd een maximale rek van de vleugelhuid opgelegd tijdens de optimalisatie.
Resultaten van een topologie-optimalisatie van een aandrijfmechanisme worden in dit werk gepresenteerd, waarbij het vleugelprofiel en de doelvorm van de morfende neusklep afkomstig zijn uit het Europese Unie project Smart High Lift Devices for Next Generation Wings (SADE). Twee ontwerpruimtes werden beschouwd waarbij ofwel een aandrijfkracht of een aandrijfmoment werden toegepast terwijl de huid van de vleugelvoorrand ofwel uit glasvezel of uit koolstofvezel was opgebouwd. Dit resul-teerde in een groep van vier mogelijke ontwerpen voor de lay-out van een aandrijfme-chanisme. Een interpretatie van deze topologieën werd uitgevoerd zodat vier mogelijke ontwerpen voor een aandrijfsysteem werden bekomen. Deze mogelijke ontwerpen wer-den gebruikt in de bijkomende lay-out optimalisatie die hierboven beschreven werd als de aandrijf-knooppunt optimalisatie. Twee verschillende naderingen werden hierbij beschouwd; een twee stappen aanpak waarbij eerst de lay-out van het aandrijfme-chanisme werd geoptimaliseerd, gevolgd door de optimalisatie van de huidstijfheid, of een enkele stap aanpak waarbij de lay-out van het aandrijfmechanisme tegelijk met de huidstijfheid van de morfende neusklep werd geoptimaliseerd. Beide aanpakken leidden tot een reeks van aandrijfmechanismes in combinatie met een geoptimaliseerde stijfheid van de vleugelhuid waarbij een sterke schommeling in prestatie zichtbaar was ten opzichte van de doelvorm van de morfende neusklep en de doelkromming van de huid. De enkele stap aanpak, waarbij de huidstijfheid samen met de lay-out van het aandrijfmechanisme werd ontworpen, was superieur wanneer de doelvorm doelfunctie werd beschouwd. Bovendien leidde deze methode in 9 van de 12 morfende neusklep ontwerpen in een lagere benodigde aandrijfkracht in vergelijking met de tegenhanger van de draagkrachtverhogende neusklep welke ontworpen werd met de twee stappen aanpak.
De keuze van het beste algemene ontwerp was echter niet eenvoudig, gebaseerd op de doelvorm of de doelkromming doelfuncties, of gebaseerd op de grootte van de kracht die nodig was om de morfende neusklep te gebruiken. Het werd geconcludeerd dat zo een beslissing het best gemaakt wordt op basis van een aerodynamische prestatie parameter zoals de verhouding draagkracht-tot-weerstand. De huidige implementatie van de aerodynamische analyse in het aero-elastische kader laat zo een vergelijking echter niet toe. Het huidige werk toont wel aan dat het aero-elastische ontwerp kader kan gebruikt worden om een aandrijfsysteem van een morfende neusklep en de stijf-heidsverdeling van de vleugelhuid te optimaliseren, hetzij samen of onafhankelijk van elkaar.
De volgende conclusies zijn gebaseerd op de resultaten die gecreëerd werden met het aero-elastische ontwerp en optimalisatie kader dat beschreven is in dit werk. De re-sultaten van de topologie-optimalisatie van een aandrijfmechanisme toonde aan dat het kiezen van het beste topologie-optimalisatieresultaat niet kon gebeuren vanuit een
kwantitatief standpunt, maar eerder moest gebeuren vanuit een kwalitatief standpunt. De interpretaties van een topologie-optimalisatie van een aandrijfmechanisme voor een morfende neusklep door middel van balkelementen eiste een extra nabewerking in de vorm van een lay-out optimalisatie, die resulteerde in significante verbeteringen van de uiteindelijke vervormde vorm van de neusklep. De toevoeging van de geometrische niet-lineariteit van de vervormde morfende neusklep bleek belangrijk en leidde tot een betere overeenkomst tussen de uiteindelijke vervorming van de neusklep ten opzichte van de doelvorm. De mogelijkheid om de huidstijfheid te variëren resulteerde in een extra verbetering van de morfende neusklep om de beoogde doelvorm te bereiken, aangezien het mogelijk was om de lokale huidstijfheid aan te passen. Dit is overigens onmogelijk bij een vleugelhuid met constante stijfheid. Een maximale toelaatbare rek van de vleugelhuid werd toegepast bij alle geoptimaliseerde ontwerpen van een morfende neusklep die gepresenteerd zijn in dit werk, wat er voor zorgde dat een realistisch en haalbaar ontwerp werd gerealiseerd. De ruimtelijke variatie van de huid-stijfheid maakte het mogelijk om lokaal de huidhuid-stijfheid en huiddikte aan te passen zodat de uiteindelijke vorm van de morfende neusklep dichter bij de doelvorm lag zon-der de maximale rek van de huid te overschrijden. Het werd door middel van proeven aangetoond dat het mogelijk is om een ruimtelijke stijfheidsverdeling van een lami-naat te ontwerpen waarbij een vooraf gedefinieerde vervorming moet worden bereikt als gevolg van een vooraf bepaalde externe belasting. Bij deze proeven werd enkel gebruik gemaakt van het verschil in de kromming van het onvervormde en vervormde proefstuk.
Het aero-elastische kader in dit werk kan worden gebruikt voor de snelle ontwikkeling van een morfende neusklep. Toekomstige werkzaamheden moeten zich in eerste in-stantie richten op de toevoeging van een meer gesofisticeerd aerodynamisch model waardoor het gebruik van een aerodynamische prestatie parameter, zoals de ver-houding draagkracht-tot-weerstand, als doelfunctie in een optimalisatie mogelijk zou worden. De toevoeging van de benodigde afgeleiden om de aerodynamische stijfheids-matrix te definiëren en tegelijkertijd de rekentijd beperken tot een minimum zal de grote uitdaging zijn bij de realisatie van deze update. Het composietmateriaal met een variabele stijfheid, dat werd beschouwd in dit werk, vraagt eveneens om extra aandacht wanneer de productie van gekromde composiet laminaten met een variabele stijfheid wordt overwogen. Het is hierbij de uitdaging om een gekromd composiet laminaat met variabele stijfheid te realiseren zodanig dat er geen verschil in dikte zichtbaar is aan de buitenzijde van het vleugelprofiel. Zo een variatie in dikte zou namelijk de laminaire stroming kunnen verstoren die gewenst is bij een laminair vleugelprofiel in kruisvlucht.
Summary
xiSamenvatting
xvList of Figures
xxiiiList of Tables
xxviiList of Symbols
xxix1 Introduction
11.1 Morphing and aircraft - an overview . . . 5
1.1.1 A brief history of morphing systems on aircraft . . . 6
1.1.2 Airfoil morphing . . . 8
1.1.3 Morphing skin . . . 12
1.2 Composite tailoring - the variable stiffness concept . . . 13
1.2.1 Introducing composites . . . 13
1.2.2 The variable stiffness concept . . . 14
1.3 Topology optimisation - finding the optimal shape . . . 16
1.3.1 Introducing topology optimisation . . . 16
1.3.2 Topology optimisation in an aeroelastic setting . . . 17
1.4 Thesis objectives . . . 18
1.5 Thesis outline . . . 19
2 A two-dimensional aeroelastic analysis framework
21 2.1 Structural model . . . 212.1.1 Linear Euler-Bernoulli beam element . . . 22
2.1.2 Geometric nonlinearity using a corotational framework . . . 24
2.1.3 Validation . . . 27
2.2 Aerodynamic model . . . 29
2.2.1 Inviscid panel code . . . 29
2.2.2 Validation . . . 32
2.3 Aeroelastic framework . . . 34
2.3.1 Fluid-structure coupling . . . 34
2.3.2 Fluid-structure interaction methodology . . . 37
3 Formulation of aeroelastic optimisation of morphing leading edge devices
433.1 Optimisation formulation . . . 43
3.2 Skin stiffness optimisation . . . 45
3.2.1 Skin stiffness parameterisation . . . 45
3.2.2 Optimisation formulation . . . 51
3.3 Actuation topology optimisation . . . 53
3.3.1 Topology optimisation implementation . . . 54
3.3.2 Optimisation characteristics . . . 55
3.3.3 Validation of the topology optimisation routine . . . 56
3.4 Actuation node location optimisation . . . 58
3.4.1 Implementing the actuation node location optimisation . . . . 58
3.4.2 Optimisation formulation . . . 60
3.5 Optimisation using the aeroelastic analysis framework - an overview . 62
4 Design of a morphing leading edge actuation system
65 4.1 Smart High Lift Devices for Next Generation Wings . . . 654.2 Actuation system design . . . 69
4.2.1 Actuation topology optimisation . . . 69
4.2.2 Beam representation of an actuation system . . . 76
4.3 Skin stiffness optimisation and actuation topology post-processing . . 82
4.3.1 Two step actuation node location and skin stiffness optimisation approach . . . 86
4.3.2 Single step actuation node location and skin stiffness optimisa-tion approach . . . 110
4.3.3 Comparing the two step and single step optimisation approach 130 4.3.4 Remarks on design consideration . . . 133
5 Design and testing of a variable stiffness composite laminate for target curvature
deformation
135 5.1 Experiment definition . . . 1375.2 Test specimen design and manufacturing . . . 140
5.2.1 Linear optimisation results . . . 140
5.2.2 Nonlinear optimisation results . . . 142
5.2.3 Ply drop location optimisation . . . 143
5.2.4 Test specimen manufacturing and quality control . . . 144
5.3 Experimental setup . . . 145
5.3.1 Load application . . . 145
5.3.2 Load introduction . . . 146
5.3.3 Measurement system . . . 148
5.4 Test results and comparison . . . 149
5.5 Concluding remarks on experimental results . . . 151
6 Design of a morphing leading edge actuation system demonstrator
153 6.1 Leading edge actuation topology design and demonstration . . . 1536.3 Leading edge actuation system test specimen design . . . 157
7 Conclusions and recommendations
161 7.1 Conclusions . . . 1617.1.1 Aeroelastic design and analysis framework . . . 162
7.1.2 Smooth morphing leading edge high-lift system . . . 163
7.2 Recommendations and future work . . . 164
7.2.1 Aeroelastic design and analysis framework . . . 164
7.2.2 Smooth morphing leading edge high-lift system . . . 165
Bibliography
167Curriculum Vitae
1771.1 Otto Lillienthal whilst performing a glider flight around 1895 . . . 2 1.2 First successful flight of the Wright Flyer on December 17, 1903 . . . . 3 1.3 Simplified classification of airplane morphing mechanisms . . . 6 1.4 Timeline indicating the historic development and use of morphing
sys-tems on airplanes . . . 7 1.5 Examples of morphing systems on historic airplanes . . . 8 1.6 Zero and positive camber on an airfoil cross-section . . . 9 1.7 US Patent 4252287, Dornier GmbH, 1979 [Zimmer, 1981] . . . 11 1.8 Components of a composite material: reinforcement and matrix . . . . 13 1.9 From reinforcement to laminate . . . 14 1.10 Comparing a lamina with constant and variable fibre angle . . . 14
2.1 Representation of a wing segment using a 2D beam model . . . 22 2.2 Example of a geometric nonlinear deformation . . . 22 2.3 Deformation of a beam loaded by a pure bending moment using the
Euler-Bernoulli assumptions . . . 23 2.4 Finite element representation of an Euler-Bernoulli beam element . . . 24 2.5 Deformation of a single element to indicate the corotational method . 25 2.6 2D beam models used to validate the structural model . . . 27 2.7 Chordwise airfoil cross-section divided into panels containing a source
and doublet . . . 30 2.8 Comparison ofCpbetween the present aerodynamic module and XFOIL
using the FNG reference airfoil . . . 33 2.9 Example of cosine spacing . . . 34 2.10 Global supported radial basis functions . . . 36 2.11 Compact supported radial basis functions . . . 37 2.12 Flow diagram of a close coupled staggered approach where the inner
iterations assure the close coupling . . . 39
3.1 Laminate cross-section definition in classical lamination theory . . . . 47 3.2 Contour ofα− β design space for balanced symmetric laminates . . . 50 3.3 Possible combinations of skin thickness and layup inxskin . . . . 52 3.4 Hinge representation in the output of a topology optimisation and its
interpretation . . . 53 3.5 Example of a triangular mesh applied to the design domain in a leading
edge . . . 54 3.6 Representation of the connection between a beam element and a
3.7 Design domain of the force inverter example . . . 56 3.8 Optimised topology for the force inverter with a volume constraint of
20% . . . 57 3.9 Example of an actuation system in a morphing leading edge, indicating
type 1 and type 2 nodes . . . 59 3.10 Example movement of a ’type 2’ actuation node along multiple airfoil
skin beam elements . . . 60 3.11 Flowchart representation of the iterative approach to actuation node
location optimisation, with i varying between 1 and the total number of actuation nodes . . . 61
4.1 Flowchart for the design of a morphing leading edge high-lift device as applied to the FNG wing . . . 66 4.2 Cross-section of the FNG airfoil used in the SADE project . . . 67 4.3 Zero skin strain target shape for landing and take-off on the FNG airfoil
[Kühn and Wild, 2010] . . . 68 4.4 Geometric curvature of the deformed and undeformed FNG leading
edge, used to define the target curvatureκt . . . 69 4.5 Design spaces for the actuation topology optimisation . . . 70 4.6 Best actuation system topologies based on the objective function value
Ishape . . . 73 4.7 Best undeformed actuation system topologies based on the proposed
actuation topology . . . 75 4.8 Layout of TopOpt 1ζ=0.7with interpretation guidelines . . . 78 4.9 Layout of TopOpt 2ζ=0.9with interpretation guidelines . . . 78 4.10 Layout of TopOpt 3ζ=0.5with interpretation guidelines . . . 79 4.11 Layout of TopOpt 4ζ=0.7with interpretation guidelines . . . 79 4.12 Interpretation of TopOpt 1ζ=0.7 . . . 80 4.13 Interpretation of TopOpt 2ζ=0.9 . . . 80 4.14 Interpretation of TopOpt 3ζ=0.5 . . . 81 4.15 Interpretation of TopOpt 4ζ=0.7 . . . 81 4.16 Comparing ActNode 1 to ActNode 1rev1 . . . 84 4.17 Comparing ActNode 2 to ActNode 2rev1 . . . 84 4.18 Comparing ActNode 3 to ActNode 3rev1 . . . 85 4.19 Comparing ActNode 4 to ActNode 4rev1 . . . 85 4.20 Comparing ActNode 1 to ActNode 1rev2 . . . 88 4.21 Comparing ActNode 2 to ActNode 2rev2 . . . 88 4.22 Comparing ActNode 3 to ActNode 3rev2 . . . 89 4.23 Comparing ActNode 4 to ActNode 4rev2 . . . 89 4.24 Deformation of different optimised skin types for ActNode 1rev2 . . . 91 4.25 Skin curvature of different optimised skin types for ActNode 1rev2 . . 91 4.26 Maximum skin strain of the different skin types for ActNode 1rev2 . . 92 4.27 Design parametersα, β and h for the skin types with ActNode 1rev2 . 93 4.28 Skin stiffnessesEI and EA for the skin types with ActNode 1rev2 . . 94 4.29 Deformation of different optimised skin types for ActNode 2rev2 . . . 96 4.30 Skin curvature of different optimised skin types for ActNode 2rev2 . . 96 4.31 Maximum skin strain for the different skin types with ActNode 2rev2 97
4.32 Design parametersα, β and h for the skin types with ActNode 2rev2 . 98 4.33 Skin stiffnessesEI and EA for the skin types with ActNode 2rev2 . . 99 4.34 Deformation of different optimised skin types for ActNode 3rev2 . . . 101 4.35 Skin curvature of different optimised skin types for ActNode 3rev2 . . 101 4.36 Maximum skin strain for the different skin types with ActNode 3rev2 102 4.37 Design parametersα, β and h for the skin types with ActNode 3rev2 . 103 4.38 Skin stiffnessesEI and EA for the skin types with ActNode 3rev2 . . 104 4.39 Deformation of different optimised skin types for ActNode 4rev2 . . . 106 4.40 Skin curvature of different optimised skin types for ActNode 4rev2 . . 106 4.41 Maximum skin strain for the different skin types with ActNode 4rev2 107 4.42 Design parametersα, β and h for the skin types with ActNode 4rev2 . 108 4.43 Skin stiffnessesEI and EA for the skin types with ActNode 4rev2 . . 109 4.44 Deformation of different optimised skin types for ActNode 1rev3-5 . . 111 4.45 Skin curvature of different optimised skin types for ActNode 1rev3-5 . 112 4.46 Maximum skin strain for different skin types with ActNode 1rev3-5 . . 112 4.47 Design parametersα, β and h for the skin types with ActNode 1rev3-5 113 4.48 Skin stiffnessesEI and EA for the skin types with ActNode 1rev3-5 . 114 4.49 Deformation of different optimised skin types for ActNode 2rev3-5 . . 116 4.50 Skin curvature of different optimised skin types for ActNode 2rev3-5 . 117 4.51 Maximum skin strain for different skin types with ActNode 2rev3-5 . . 117 4.52 Design parametersα, β and h for the skin types with ActNode 2rev3-5 118 4.53 Skin stiffnessesEI and EA for the skin types with ActNode 2rev3-5 . 119 4.54 Deformation of different optimised skin types for ActNode 3rev3-5 . . 121 4.55 Skin curvature of different optimised skin types for ActNode 3rev3-5 . 122 4.56 Maximum skin strain for different skin types with ActNode 3rev3-5 . . 122 4.57 Design parametersα, β and h for the skin types with ActNode 3rev3-5 123 4.58 Skin stiffnessesEI and EA for the skin types with ActNode 3rev3-5 . 124 4.59 Deformation of different optimised skin types for ActNode 4rev3-5 . . 126 4.60 Skin curvature of different optimised skin types for ActNode 4rev3-5 . 127 4.61 Maximum skin strain for the different skin types with ActNode 4rev3-5 127 4.62 Design parametersα, β and h for the skin types with ActNode 4rev3-5 128 4.63 Skin stiffnessesEI and EA for the skin types with ActNode 4rev3-5 . 129
5.1 Leading edge skin patch simplification into a cantilevered laminate . . 136 5.2 Cantilever beam loaded with distributed and concentrated loads . . . 137 5.3 Internal moment distribution of simulating the distributed load with a
different number of concentrated loads . . . 139 5.4 Internal moment distribution for different load cases . . . 140 5.5 Laminate optimisation results using linear analysis . . . 141 5.6 Objective function sensitivity with respect to initial laminate thickness 142 5.7 Laminate optimisation results using nonlinear analysis . . . 143 5.8 Laminate optimisation results for discrete thickness variation . . . 144 5.9 C-scan quality control results of variable stiffness composite laminate . 146 5.10 Experimental setup to test the variable stiffness composite laminate . 147 5.11 Strain gauge placement on variable stiffness composite laminate . . . . 149 5.12 Comparison of curvature measurements and simulation results . . . . 150
5.13 Comparison of curvature measurements and simulation results around ply drop . . . 151
6.1 Undeformed and deformed leading edge shape for the LeaTop reference airfoil . . . 154 6.2 Design space for the LeaTop project with 10 different actuated node
locations . . . 155 6.3 Best actuation topology design for the LeaTop design . . . 156 6.4 Beam model representation of the LeaTop actuation system . . . 156 6.5 Final optimised beam model representation of the LeaTop actuation
system . . . 156 6.6 Deformed leading edge comparison between present design tool and
Abaqus . . . 157 6.7 3D CAD model of the LeaTop morphing actuation system demonstrator
2.1 Validation results of the structural model . . . 28
3.1 Composite material properties . . . 48 3.2 Values for C1 through C12 to define the design space of a 12 layer
laminate using Equations (3.23)-(3.28) . . . 53 3.3 Overview of optimisation capabilities and the corresponding design
variables . . . 64
4.1 SADE project partners . . . 67 4.2 Definition of the actuation topology optimisation design cases . . . 70 4.3 Optimisation characteristics of design cases TopOpt 1-4 . . . 72 4.4 Optimal objective function values for design case TopOpt 1 . . . 72 4.5 Optimal objective function values for design case TopOpt 2 . . . 72 4.6 Optimal objective function values for design case TopOpt 3 . . . 72 4.7 Optimal objective function values for design case TopOpt 4 . . . 72 4.8 Comparison between initial and improved ActNode models for the two
step optimisation approach . . . 87 4.9 Objective function values for ActNode 1rev2 with optimised skin . . . 90 4.10 Objective function values for ActNode 2rev2 with optimised skin . . . 95 4.11 Objective function values for ActNode 3rev2 with optimised skin . . . 100 4.12 Objective function values for ActNode 4rev2 with optimised skin . . . 105 4.13 Objective function values for ActNode 1rev3-5 with optimised skin . . 112 4.14 Objective function values for ActNode 2rev3-5 with optimised skin . . 115 4.15 Objective function values for ActNode 3rev3-5 with optimised skin . . 120 4.16 Objective function values for ActNode 4rev3-5 with optimised skin . . 125 4.17 Objective function results for the two step and single step optimisation
of the skin stiffness and actuation layout of the morphing leading edge design example . . . 131 4.18 Total actuation load to deform the leading edge actuation system, with
a lock loadflock to lock the mechanism in the undeformed shape, and an actuation forcefactto create the final deformed shape of the leading edge . . . 132
Abbreviations
2D Two-dimensional
3D Three-dimensional
ACARE Advisory Council for Aeronautics Research in Europe ANDES Assumed natural deviatoric strain
AoA Angle-of-attack
AT Air Transport
BC Before Christ
CAD Computer-aided design
CL/VT Constant layup, variable thickness skin
DOC Direct operating cost
FEA Finite Element Analysis
FNG Flügel neuer generation
FP7 Framework Programme 7
FPS Finite plate spline
GCMMA Globally convergent method of moving asymptotes
GRA Green Regional Aircraft
HARLS High aspect ratio low sweep IIM Inverse isoparametric mapping IPS Infinite plate spline
ITD Integrated Technology Demonstrator
LeaTop Leading Edge Actuation Topology Design and Demonstration
MMA Method of moving asymptotes
MQ Multiquadric-biharmonics
NACA National Advisory Committee for Aeronautics NACRE New Aircraft Concepts Research
NASA National Aeronautics and Space Administration
NUBS Non-uniform B-spline
OPT Optimal ANDES Template
SADE Smart High Lift Devices for Next Generation Wings SDS Selectively deformable structures
SLE Smart leading edge
SMA Shape memory alloy
SME Small and medium enterprises
TELFONA Testing For Laminar Flow On New Aircraft
TPS Thin plate spline
TRL Technology readiness level
UD Unidirectional
VL/UT Variable layup, uniform thickness skin VL/VT Variable layup, variable thickness skin
Greek Symbols
α Non-dimensional bending stiffness layup parameter
-β Non-dimensional in-plane stiffness layup parameter
-γ Deformed beam element orientation rad
γ0 Initial beam element orientation rad
δ Virtual
-∆max
node Maximum displacement parameter for an actuation node m
δs Partial displacement of actuation-skin connection point m
∆θ Tip rotation, page 27 rad
∆l Distance between two adjacent collocation points, page 31 m
∆s Displacement of actuation-skin connection point m
∆x Horizontal tip displacement, page 27 m
∆z Vertical tip displacement, page 27 m
Small parameter, Figure 2.12
- Strain
-ζ Objective function ratio parameter
-η Nondimensional length parameter along a panel, page 44
-θ Local nodal rotation rad
θ Fibre angle of a single lamina rad
θ Rotation in the xz-plane about the y-axis, section 2.1 rad
θi Inclination angle of paneli, page 30 rad
θR Rigid body rotation of a beam element rad
κ Curvature m−1
λ Load control variable
-µ Doublet, page 30 m2/s
ν Poisson ratio
-ξ Actuation node location design variable
-ρ Air density kg/m3
σ Source, page 30 m/s
Φ Potential disturbance m2/s
φ Radial basis function
-χ Ply drop location parameter
-Φ∞ Freestream potential m2/s
Φ∗ Velocity potential m2/s
ω Volume constraint parameter
-Latin Symbols
A Cross-sectional area m2
Ai Area of triangular elementi m2
Aij Element of in-plane stiffness matrix N/m
a Radial basis shape control parameter, in Equation (2.49)
a Slope of a skin element, page 59
-B Composite test specimen width, in chapter 5 m
Bij Source influence coefficient, page 30 m
b Wing section span m
C Constraint constant to defineα− β design space, page 49
-Cij Doublet influence coefficient, page 30
-Cp Aerodynamic pressure coefficient
-c Wing section chord m
D Drag force N
Dij Element of bending stiffness matrix N/m
d0 Translational degree-of-freedom scaling parameter, page 41
-E Modulus of elasticity N/m2
F Discrete load N
FH Horizontal load in x-direction N
FN Normal force N
FV Vertical load in z-direction N
f Force N
G Shear modulus of elasticity N/m2
h Thickness m
h Non-dimensional thickness
-I Objective function
-I Second moment of inertia m4
L Deformed element length m
L Length m
L Lift force N
Li Length of paneli, page 44 m
M Moment load Nm
Na Number of panels on the aerodynamic model
-Nlayers Number of layers
-Nn Number of nodes on airfoil skin of structural model
-Np Number of panels on airfoil skin on structural model
-Npd Number of ply drops
-Ntri Number of triangular elements
-n Panel normal
-P Augmented objective function
-p Penalisation factor
-Q Reduced stiffness constant in material principle direction N/m2
Q Transformed reduced stiffness for single UD layer N/m2
q Distributed load N/m
r Distance from a singularity, page 30 m
r Support radius , page 36 m
r0 Rotational degree-of-freedom scaling parameter, page 41
-S Airfoil boundary
-s Arc length parameter m
t Element thickness, page 27 m
t Lamina layer thickness, page 47 m
t Membrane thickness m
u Displacement in x-direction m
u Local element extension m
V Virtual work Nm V∞ Freestream velocity m/s Vt Tangential velocity m/s W Work Nm w Displacement in z-direction m w Element width m
w Width of airfoil cross-section, page 31 m
x Position along x-axis m
z Position along z-axis m
zk Distance between lamina and center of laminate, in Figure 3.1 m
Subscripts
0 Reference
1 In principle direction, page 48
2 In transverse direction, page 48
2 Node type 2 parameter
∞ Freestream parameter
act Actuation
aero Aerodynamic
alu Aluminium
a On aerodynamic model
bot Bottom surface, in chapter 5
curv Target curvature
cv Constant layup, variable thickness
ext External
e Element parameter
g Global
in Input, section 3.3.3
in Internal
i Inside the body, page 29
i On paneli
j On panelj
k Of layerk, page 47
lock To lock the actuation system
l Local
max Maximum value
norm Normalised
n Nodal parameter
out Output, section 3.3.3
pd Ply drop
ply Of a single ply
ref Reference
sisj From node si to node sj
shape Target shape
skin Of the skin beam elements
s On structural model
top Of the triangular membrane elements top Top surface, in chapter 5
t Target
vu Variable layup, uniform thickness vv Variable layup, variable thickness
Superscripts
0 Initial
a Defined on the aerodynamic model
cp At collocation point, page 31 i/i+1 At iterationi/i + 1
ini Initial
l Local variable
new Updated location
opt Optimal value
R Rotational degree of freedom
skin Of the skin
T Translational degree of freedom
Matrices and Vectors
α Non-dimensional bending stiffness vector β Non-dimensional in-plane stiffness vector ∆λ Load control increment vector
∆u Displacement increment vector
λ Load control variable vector
ξ Actuation node location design variable vector
ρn Nodal density vector
χ Ply drop location design variable vector
ψ Adjoint vector
A Coupling matrix, page 35
A In-plane stiffness matrix
b Column ofTT
C Coupling matrix, page 35
c Scaling vector to define actuation load magnitude D Out-of-plane stiffness matrix
f Load vector
H Interpolation matrix, page 35
h Wing skin thickness vector
K Stiffness matrix
n Panel normal
R Residual vector
S Normalisation matrix
T Transformation matrix
V Velocity vector
v Initial displacement vector, page 41
x Design variable vector
one miles. Longest 57 seconds. Inform press. Home Christmas
Orville Wright, December 17, 1903
1
Introduction
Over the course of time, humankind has drastically changed and improved the meth-ods it uses to travel the world. Early homo sapiens, and their ancestors, had to travel the earth on foot, only small distances could be covered in a day, and humans lived mostly isolated and ignorant of the rest of the world. In due time, animals such as horses, camels and oxen were domesticated and became a source of food and trans-portation. Larger distances could then be covered in less time, heavier goods could be hauled, further and faster once the wheel was invented. Travel by water was achieved once rafts and boats were invented. Dugout canoes and rafts, assumed to be the first ’boats’, have a recorded use tracing back to the paleolithic. Water was no longer a boundary now it facilitated a super highway of early travellers. The seas and rivers became the territory of many vessels that were used to fish, to explore the world and to trade goods to far flung lands and back. Large quantities of goods could be trans-ported in an easy manner, and large cities started to arise at strategic points along the seashore and at river crossings and junctions.The invention of the wheel somewhere in the 4th millennium BC revolutionised travel by land in most lands. Carts and wagons were created that were often pulled by an-imals. Road transport was born. It took until the Industrial Revolution in the 19th century before transport by land saw another major revolution. The improved steam engine of Thomas Newcomen and James Watt in 1763, set on rails, became the first mechanical way to travel any real distance opening a new form of transport. The steam engine quickly found its way into boats and trains. Land transport without the need for animal or human power was possible, and the invention of the modern automobile by Karl Benz in 1886 brought us closer to present day land transportation systems.
So humankind had mastered travelling over land and water, but there were birds, and looking upwards men and women dreamt of having the means and freedom to
fly. Early attempts to mimic birds all resulted in failure, some attempts even leading to casualties. The Montgolfier brothers Joseph-Michel and Jacques-Étienne success-fully achieved the first recorded human lighter-than-air flight in a hot air balloon on November 21, 1783. These balloons were not practical since they were dependent on windspeed to cover a certain distance and more importantly on wind direction to travel in a certain direction. The dirigible, or steerable balloon, introduced by Jean-Pierre Blanchard in 1784 was therefore a necessary improvement.
Figure 1.1: Otto Lillienthal whilst performing one of his 2500+ glider flights around 1895, with thanks to the United States Library of Congress, Prints and Photographs Division.
Heavier-than-air travel took more time to mature into a feasible design. The first un-manned powered flight was achieved by John Stringfellow in 1848, and George Cayley, in 1853, documented his manned flights in a glider. George Cayley is often referred to as the Father of aviation due to his extensive scientific research into the design of winged flying machines, and his identification of the four main forces involved in flight - weight, lift, drag and thrust. Many other people devoted time and resources to the continuing development of gliders. Otto Lilienthal, shown in Figure 1.1, was the first person to make, repeatedly 2500 plus, controlled glides, and his passion for gliders eventually led to his death on August 10, 1896 from injuries sustained in a glider crash. Lilienthal’s book on aerodynamics, published posthumously in 1889, or Octave Chanute’s Progress in Flying Machines, published in 1894, were, amongst others, the reference books that were studied by the Wright Brothers, Orville and Wilbur, and it still took them several years before they achieved the legendary first controlled, powered heavier-than-air flight in their Wright Flyer on December 17, 1903 at Kitty Hawk [Wright, 1953]. The legendary picture taken by John T. Daniels, shown
in Figure 1.2, shows the Wright Flyer during its 12 second flight at 10:35 a.m. with Orville Wright at the controls and Wilbur Wright running alongside to balance the Flyer. This historic mile-point was the start of a burst of development in air transport that would change the world on a scale, and arguably to a scale, nobody could have foreseen. Just over 100 years later, the first commercial flight of the Airbus A380, the world’s largest commercial passenger airline, in October 2007 shows the immense leaps in the development of heavier-than-air flight that have taken place. The world now seems smaller than ever, with our ability to travel around the world in hours rather than days, weeks, months or even years as in the historic past.
Figure 1.2: First successful flight of the Wright Flyer at 10:35 a.m. on December 17, 1903 at Kitty Hawk. Orville Wright can be seen controlling the aircraft, with his brother Wilbur Wright running alongside the Flyer to balance the airplane. This image was created by John T. Daniels courtesy of the United States Library of Congress, Prints and Photographs Division.
The developments that have taken place the last 100 years in the aerospace industry would fill multiple books, see for example Anderson [2002]; Crouch [2004]; Wright et al. [2009]. It is the evolution of the materials that were, or are still, used to create our mighty flying machines that is of special interest in this work. The Wright Brother’s first flight was accomplished using an airplane constructed of wood for its structural parts and cotton cloth was used to define the aerodynamic shape of its wings. Plywood made its way into the juvenile aerospace industry relatively fast because it enabled stressed skin to be designed. A stressed skin design is a construction where the skin is also used to carry part of the load. Such a feat was not possible using fabric skins. The first application of such a plywood stressed skin design was created by Jack Northdrop when he built the 1920 S-1. His second design, the Lockheed Vega, was a bigger suc-cess. A famous example of a wooden plane is the de Havilland Mosquito, also known
as The Wooden Wonder. Ford’s 4-AT (Air Transport), also known as The Tin Goose, was the first metal airplane when it was introduced in 1925. It did not become a commercial success, but it did pave the way for future full metal airplanes such as the DC-3 in 1935. With the de Havilland Comet, making its maiden flight in 1949, the aerospace industry was presented with the phenomena of metal fatigue. Unfortunately, several airplanes were destroyed and lives lost in a series of crashes before the metal fatigue issue was discovered. The Boeing 747, entered into service in 1970, is without a doubt worlds most recognised airplane, and a fitting example of the full metal aircraft designs that helped shape air travel, but these aircraft are comparatively heavy and fuel costly.
The constant search for lighter airplanes has resulted in a search for different, better, safe materials to use to replace metals as the main materials used in the airplanes of today and tomorrow. Lighter composite materials have been part of the military airplane industry for several decades, with the B2 bomber (1989) being the first fully composite aircraft. Moving on from the military, composites began to be used mostly for secondary structures for parts of commercial aircraft in the 1980s. The recent first commercial flight of the Boeing 787, and the upcoming maiden flight of the Airbus A350-XWB, herald the advent of a new material era in aircraft design, the era of commercial composite airplanes.
The pace of evolution seen so far in heavier-than-air transport is not expected to slow down in the coming years and decades. The Advisor Council for Aeronautics Research in Europe (ACARE) is promoting the continuous development of novel sys-tems for future airplanes to meet the goals defined in their VISION2020 [ACARE, 2008], while taking into account the fact that air traffic is increasing, yet the resources available to build and required to run aircraft are decreasing and finite. Fuel costs account for 25% to 40% of the direct operating cost (DOC) of an airplane [Szodruch and Hilbig, 1988], depending on the aircraft type and flight distance. An improvement of the aerodynamic performance of an airplane will have a direct effect on the fuel con-sumption, and as such will have a considerable impact on the direct operating costs for an airplane. This influence on an airplane’s economics is an additional reason for aircraft manufacturers, and the aerospace research community, to search continuously for novel systems and structures that can be applied to their fleets of aircraft to reduce DOCs.
Aerospace engineers often find inspiration for novel systems in nature. Birds, and other flying creatures, seem to be able to soar the skies almost effortlessly. Nature’s fliers have, through evolution, optimised their shape and shape changing capabilities to provide the best shape to perform a specific task. A bird’s wing changes its shape to provide optimal performance for each specific part of its flight, thereby minimising the energy required. Humankind’s drive to mimic this behaviour of flying creatures that change their shape has led to the introduction of shape changing capabilities on aircraft. The systems that are introduced to the airplane to provide these shape chan-ging functions are often referred to as morphing structures.
The present research is a contribution to the continuous development of novel applic-ations and systems that can be fitted to the next generation of airplanes to reduce DOCs. An alternative of the commonly used slat, a leading edge high-lift system, is introduced, where the goal is to achieve an alternative design which allows for the
smooth gapless deformation of a leading edge of an airfoil. Such a smooth leading edge high-lift system, known as a morphing system, requires an internal actuation system and an external airfoil skin to be designed. A brief historic overview of morphing and morphing system in airplanes is presented in the next section. The composite material era we are in now is providing researchers with the chance to use composites in critical and non-critical airplane components. The use of a composite as a morphing skin is reported here. An introduction to composites is provided in the second section of this chapter. The design of an internal actuation system for a smooth morphing leading edge high-lift system uses topology optimisation, which is explained in more detail in the third section of this chapter. The objectives of the work presented in this thesis are discussed in the fourth section, followed by a thesis outline in the final section of the chapter.
1.1
Morphing and aircraft - an overview
A large part of the present work is focussed on the design of a morphing system. The question now is: What is morphing? Merriam-Webster’s Collegiate Dictionary [Mish, 2005] provides the following definition of the verb morph:
to undergo transformation, (...) to change the form or character of
A more appropriate definition of morphing, specific to the aerospace industry, is defined, based on earlier definitions given in Barbarino et al. [2011]; Weisshaar [2006], as:
to enable an increase in a vehicles performance by manipulating certain characteristics to match better the vehicle state to the environment and task at hand.
There is no common agreement on the definition of morphing aircraft systems. A simple and well-known system such as a retractable landing gear is a morphing sys-tem using the definition presented above. The deflected landing gear enables take-off and landing, while a retracted landing gear reduces aerodynamic drag and increases the airplane’s performance in flight. High-lift systems such as slats and flaps are also considered to be morphing mechanisms in the definition above. Other definitions of morphing in the literature such as that presented in Sofla et al. [2010]; Thill et al. [2008] go a step further, specifying additional restrictions on the morphing systems such that slats or flaps are no longer considered to be morphing systems. These al-ternative definitions consider morphing to be radical shape changes in the aircraft’s structural form or changes that require futuristic technologies to be applied. Such nar-row definitions of morphing are neglected here, and the broader definition presented above is used.
A simple classification scheme of airplane morphing mechanisms is presented in Fig-ure 1.3. The focus of the remainder of this section about morphing mechanisms will be on wing aircraft morphing mechanisms. Other types of aircraft morphing, such as the variable incidence nose of a Concorde or the thrust vector control on a Hawker Siddeley Harrier, are neglected in the present work.
1.1: Morphing and aircraft - an overview Aircraft morphing Wing Large change (wing/wing segment) Span Sweep Dihedral Twist Small change (airfoil) Camber Chord Other (Fuselage, engine, ...)
Figure 1.3: Simplified classification of airplane morphing mechanisms
A brief overview of morphing and it’s application in aircraft history is presented in the first subsection, followed by a more detailed presentation of airfoil morphing in the second subsection. It needs to be noted that only a brief overview of morphing is given in this section, so interested readers are referred to the extensive review papers on morphing by Sofla et al. [2010] or Friswell and Inman [Barbarino et al., 2011] if additional information is required.
1.1.1
A brief history of morphing systems on aircraft
The use of morphing mechanisms nowadays appears to be a novel idea, but the con-trary is true: morphing mechanisms have been applied to aircraft or gliders throughout the relatively brief history of heavier-than-air flight. An overview of the characterisa-tion of most of these historic applicacharacterisa-tions is presented in this seccharacterisa-tion.
A timeline is shown in Figure 1.4 where a number of aircraft and gliders are listed in chronological order. The type of morphing mechanism present on each particular aircraft is used to place them into one of five different categories.
The application of morphing mechanisms to alter the sweep of the wing is the most popular category among the historic attempts made to produce morphing wings. The F-14 Tomcat is probably one of the best known examples of an aircraft with morphing wings due to its appearance in Tony Scott’s blockbuster Top Gun. The F-14 Tomcat’s ability to alter the sweep of its wing allows the airplane to operate at optimal lift-to-drag ratio for a range of Mach numbers. Take-off and landing can thus be performed at a lower velocity when the wing is unswept, while a large wing sweep allows for su-personic flight. Swept back wings were introduced nearly 40 years before the maiden flight of the F-14 Tomcat when Geoffrey Hill introduced the Pterodactyl IV. This
