A hazardous and not fully understood aeroelastic phenomenon is the transonic dip,the decrease in flutter dynamic pressure that occurs for most aircraft configurationsin transonic flows. The difficulty of predicting this phenomenon forces aircraft manufacturersto run long and costly flight test campaigns to demonstrate flutter-free behaviourof their aircraft at transonic Mach numbers.In this project, subsonic and transonic flutter calculations for the KTH-NASA genericfighter research model have been performed and compared to existing experimentalflutter data from wind tunnel tests performed at NASA Langley in 2016. For the fluttercalculations, industry-standard linear panel methods have been used together with afinite element model from NASTRAN.Further, an alternative approach for more accurate transonic flutter predictions usingthe full-potential solver Phi has been investigated. To predict flutter using this newmethodology a simplified structural model has been used together with aerodynamicmeshes of the main wing. The purpose of the approach was to see if it was possibleto find a method that was more accurate than panel methods in the transonic regimewhilst still being suitable for use during iterative design processes.The results of this project demonstrated that industry-standard linear panel methodssignificantly over-predict the flutter boundary in the transonic regime. It was alsoseen that the flutter predictions using Phi showed potential, being close to the linearresults for the same configuration as tested in Phi. For improved transonic accuracy inPhi, an improved transonic flow finite element formulation could possibly help .Another challenge with Phi is the requirement of an explicit wake from all liftingsurfaces in the aerodynamic mesh. Therefore, a method for meshing external storeswith blunt trailing edges needs to be developed. One concept suggested in this projectis to model external stores in "2.5D", representing external stores using airfoils withsharp trailing edges. / Ett farligt och inte helt utrett aeroelastiskt fenomen är den transoniska dippen, minskningeni dynamiska trycket vid fladder som inträffar för de flesta flygplan i transoniskaflöden. Svårigheten i att prediktera detta fenomen tvingar flygplanstillverkare attbedriva tidskrävande och kostsam flygprovsverksamhet för att demonstrera att derasflygplan ej uppvisar fladderbeteende i transonik inom det tilltänkta användningsområdet.I detta projekt har fladderberäkningar genomförts i både underljud och transonikför en generisk stridsflygplansmodell i skala 1:4 ämnad för forskning, byggd som ettsamarbete mellan KTH och NASA. Beräkningarna har också jämförts med fladderresultatfrån vindtunnelprov genomförda vid NASA Langley under sommaren 2016. Förfladderberäkningarna har industri-standarden linjära panelmetoder används tillsammansmed en befintlig finit element modell för användning i NASTRAN.Vidare har ett alternativt tillvägagångssätt för att förbättra precisionen i transoniskafladderresultat genom att använda potentiallösaren Phi undersökts. En förenkladstrukturmodell har använts tillsammans med aerodynamiska nät av huvudvingen föratt prediktera fladder. Syftet med denna metodik var att undersöka om det var möjligtatt hitta en metod som i transoniska flöden var mer exakt än panelmetoder men somfortfarande kunde användas i iterativa design processer.Resultaten från detta projekt visade att linjära panelmetoder, som de som används iindustrin, är signifikant icke-konservativa gällande fladdergränsen i transonik. Resultatenfrån Phi visade potential genom att vara nära de linjära resultaten som räknadesfram med hjälp av panelmetoder för samma konfiguration som i Phi. För ökad transonisknoggrannhet i Phi kan möjligen en förbättrad transonisk element-formuleringhjälpa.En annan utmaning med Phi är kravet på en explicit vak från alla bärande ytor idet aerodynamiska nätet. Därför behöver det utvecklas en metodik för nätgenereringav yttre laster med trubbiga bakkanter. Ett koncept som föreslås i denna rapport är attmodellera yttre laster i "2.5D", där alla yttre laster beskrivs genom att använda vingprofilermed skarpa bakkanter.

The general trend of efficiency increase, weight and noise reduction has derived in the design of more slender, loaded, and 3D shaped blades. This has a significant impact on the stability of fan, and low pressure turbine blades, which are more prone to aeroelastic phenomena such as flutter. The flutter phenomenon is a self-excited, self-sustained unstable vibration produced by the interaction of flow and structure. These working conditions will induce either blade overload, or High Cycle Fatigue (HCF) produced by Limited Cycle Oscillation (LCO). The main objectives of the present work are on the investigation of the aeroelastic properties of a high-lift low-pressure in the light of the local flow features present in such profiles, in nominal and extreme off-design conditions both in high and low subsonic Mach number, for three dif-ferent rigid body modes. In addition, the validity of the linearity assump-tion of the influence coefficient technique has also been investigated, in order to expand the understanding of the physical limits of this assumption. This work has been designed as experimental investigation in the influence coefficient domain focused on a high-lift low-pressure turbine designed by ITP within the framework of the European FP7 project FU-TURE. These experiments have been carried out in the Aeroelastic test rig (AETR), at KTH Stockholm, which consist of an instrumented annular sector cascade with a single oscillating blade. The results acquired have been supported by numerical results provided by a non-propietary commercial software package (ANSYS CFX). The results suggest that the typical three-dimensional effects associated secondary flow features and tip leakage flows have a significant influence on the aeroelastic performance and the cascade stability. However the major influence appears as a consequence of the separation surface on the pressure side which appears at extreme off-design operating conditions. The contribution to stability of this local feature depend on the oscillation mode showing for the axial and torsion mode a neutral stability contribution, which is directly associated with the geometrical properties of the cascade. However, on the circumferential mode this separation surface has a stabilizing effect much more independent of the blade geometry. The study of the linearity assumption of the influence coefficient domain has revealed, that an apparent linear relation between the integrated unsteady response and the vibrational amplitude, does not necessary imply that the local unsteady response is linear with respect to the oscillation amplitude. The results also suggest that the validity of the linearity as-sumption is more sensitive to high oscillation amplitudes at high Mach conditions. / <p>QC 20140609</p>

An analytical model of cracked composite beams vibrating in coupled bending-torsion is developed. The beam is made of fiber-reinforced composite with fiber angles in each ply aligned in the same direction. The crack is assumed open. The local flexibility concept is implemented to model the open crack and the associated compliance matrix is derived. The crack introduces additional boundary conditions at the crack location and these effects in conjunction with those of material properties are investigated. Free vibration analysis of the cracked composite beam is presented. The results indicate that variation of natural frequencies in the presence of a crack is affected by the crack ratio and location, as well as the fiber orientation. In particular, the variation pattern is different as the magnitude of bending-torsion coupling changes due to different fiber angles. When bending and torsional modes are essentially decoupled at a certain fiber angle if there is no crack, the crack introduces coupling to the initially uncoupled bending and torsion. Based on the crack model, aeroelastic characteristics of an unswept composite wing with an edge crack are investigated. The cracked composite wing is modeled by a cracked composite cantilever and the inertia coupling terms are included in the model. An approximate solution on critical flutter and divergence speeds is obtained by Galerkin's method in which the fundamental mode shapes of the cracked wing model in free vibration are used. It is shown that the critical divergence/flutter speed is affected by the elastic axis location, the inertia axis location, fiber angles, and the crack ratio and location. Moreover, model-based crack detection (size and location) by changes in natural frequencies is addressed. The Cawley-Adams criterion is implemented and a new strategy in grouping frequencies is proposed to reduce the probability of measurement errors. Finally, sensitivity of natural frequencies to model parameter uncertainties is investigated. Uncertainties are modeled by information-gap theory and represented with a collection of nested sets. Five model parameters that may have larger uncertainties are selected in the analysis, and the frequency sensitivities to uncertainties in the five model parameters are compared in terms of two immunity functions. / Ph. D.

The skin panels used in high-speed flights are exposed to various types of loads, such as inertial, elastic, and aerodynamic loads. In addition, oblique shock impingement can cause flow separation and unsteady aerodynamic loading, which can reduce vehicle performance and result in acoustic noise and viscous heating. These loads, when combined, can result in a complex dynamic response, such as flutter. Flutter is characterized by sustained unsteadiness or structural vibrations. Although flutter might not be immediately harmful, it can lead to fatigue failure of the structural components. A vast amount of literature already exists on the panel flutter induced by two and three-dimensional supersonic flows with oblique shock impingement. The majority of the studies are focused on predicting the onset of flutter and understanding the influence of non-dimensional parameters on the amplitude and frequency of the oscillations. Recently, numerous experimental campaigns were conducted to understand the influence of thermal loading on panel flutter and provide validation datasets to develop fluid-structure-thermal interaction solvers. The focus of this dissertation is divided into three tasks. The first task focuses on how shock impingement can affect the coupling between fluid and structural interactions and the onset of chaotic flutter. The second task focuses on controlling chaotic flutter using a passive micro vortex generator. The third task focuses on the development and validation of the fluid-structure-thermal interaction solver for 3D FSI problems. The results indicate that sufficiently strong shocks can induce flow separation and boundary layer instabilities that interact nonlinearly with the structural instabilities, resulting in chaotic oscillations. Micro vortex generators can delay the onset of the chaotic flutter by lowering the fluid frequency, thereby synchronizing fluid and structural unsteadiness. A thermoelastic solver has been developed, and the role of thermal stresses on panel flutter characteristics is considered a future task.

<p>The continuous trend in gas turbine design towards lighter, more powerful and more reliable engines on one side and use of alternative fuels on the other side renders flutter problems as one of the paramount challenges in engine design. Flutter denotes a self-excited and self-sustained aeroelastic instability phenomenon that can lead to material fatigue and eventually damage of structure in a short period of time unless properly damped. The design for flutter safety involves the prediction of unsteady aerodynamics as well as structural dynamics that is mostly based on in-house developed numerical tools. While high confidence has been gained on the structural side unanticipated flutter occurrences during engine design, testing and operation evidence a need for enhanced validation of aerodynamic models despite the degree of sophistication attained. The continuous development of these models can only be based on the deepened understanding of underlying physical mechanisms from test data.</p><p>As a matter of fact most flutter test cases treat the turbomachine flow in two-dimensional manner indicating that the problem is solved as plane representation at a certain radius rather than representing the complex annular geometry of a real engine. Such considerations do consequently not capture effects that are due to variations in the third dimension, i.e. in radial direction. In this light the present thesis has been formulated to study three-dimensional effects during flutter in the annular environment of a low-pressure turbine blade row and to describe the importance on prediction of flutter stability. The work has been conceived as compound experimental and computational work employing a new annular sector cascade test facility. The aeroelastic response phenomenon is studied in the influence coefficient domain having one blade oscillating in various three-dimensional rigid-body modes and measuring the unsteady response on several blades and at various radial positions. On the computational side a state-of-the-art industrial numerical prediction tool has been used that allowed for two-dimensional and three-dimensional linearized unsteady Euler analyses.</p><p>The results suggest that considerable three-dimensional effects are present, which are harming prediction accuracy for flutter stability when employing a two-dimensional plane model. These effects are mainly apparent as radial gradient in unsteady response magnitude from tip to hub indicating that the sections closer to the hub experience higher aeroelastic response than their equivalent plane representatives. Other effects are due to turbomachinery-typical three-dimensional flow features such as hub endwall and tip leakage vortices, which considerably affect aeroelastic prediction accuracy. Both effects are of the same order of magnitude as effects of design parameters such as reduced frequency, flow velocity level and incidence. Although the overall behavior is captured fairly well when using two-dimensional simulations notable improvement has been demonstrated when modeling fully three-dimensional and including tip clearance.</p>

Les écoulements transsoniques rencontrés dans le cadre de la propulsion aéronautique et spatiale sont associés à l'apparition d'ondes de choc. En impactant la couche limite se développant sur une paroi, un gradient de pression adverse est généré qui conduit à l'épaississement ou au décollement de la couche limite. Lors de la vibration de la structure, l'onde de choc oscille et interagit avec la couche limite, générant une fluctuation de la pression statique à la paroi. Il s'ensuit alors un échange d'énergie entre le fluide et la structure qui peut être stabilisant ou au contraire conduire à une instabilité aéroélastique (flottement). La modélisation de la réponse instationnaire de l'interaction onde de choc / couche limite pour l'étude des interactions fluide-structure est l'objet de ce travail de recherche. Il s'appuie sur la résolution des équations de Navier-Stokes moyennées (RANS) et la modélisation de la turbulence. Les méthodes et modèles utilisés ont été validés à partir de résultats expérimentaux issus d'une tuyère transsonique dédiée à l'étude des interactions fluide-structure. Ces travaux sont ensuite appliqués à l'amélioration de la prédiction du flottement en turbomachine. Une méthode linéarisée en temps permettant la résolution des équations RANS dans le domaine fréquentiel est utilisée. Nous confirmons l'importance de la dérivation du modèle de turbulence lors de la prédiction d'une interaction forte entre une onde de choc et une couche limite décollée. Une méthode de régularisation est présentée puis appliquée aux opérateurs non dérivables du modèle de turbulence k-! de Wilcox (2006). La prédiction de la réponse instationnaire de l'interaction onde de choc / couche limite dans une tuyère est évaluée à partir de simulations bidimensionnelles et présente un bon accord avec les données expérimentales. En évaluant l'influence de la fréquence réduite, une instabilité aéroélastique de type flottement transsonique est identifiée. Un dispositif de contrôle, reposant sur la génération d'ondes de pression rétrogrades à l'aval de la tuyère, est proposé puis validé numériquement. Enfin, une méthodologie est proposée pour comprendre les mécanismes aérodynamiques conduisant au flottement. Pour cela, il a été réalisé un dessin provisoire d'une soufflante transsonique à fort taux de dilution. Cette soufflante, l'ECL5, est destinée à l'étude expérimentale des instabilités aérodynamiques et aéroélastiques. La méthodologie proposée repose sur la simulation 2D d'une coupe de tête et met à profit la linéarisation pour analyser la contribution de sources locales en fonction de la fréquence réduite, du diamètre nodal et de la déformée modale / Transonic flows, which are common in aeronautical and spatial propulsion systems, produce shock-waves over solid boundaries. When a shock-wave impacts the boundary layer, an adverse pressure gradient is generated and a thickening or even a separation of the boundary layer is induced. If the solid boundary vibrates, the shock-wave oscillates, interacts with the boundary layer and produce a fluctuation of the static pressure at the wall. This induces an exchange of energy between the fluid and the structure which can be stabilising or lead to an aeroelastic instability (flutter).The main objective of this PhD thesis is the modelling of the unsteady behaviour the simulation of the shock-wave/boundary layer interaction for fluid-structure interaction studies. To this end, simulations have been carried out to solve Reynolds-Averaged Navier-Stokes equations using two equations turbulence model. The method is validated thanks to experimental data obtained on a transonic nozzle dedicated to aeroelastic studies. This method is then use to increase the predictability of flutter events in turbomachinery.A time linearised frequency-domain method is applied to RANS equations. It is shown that the unsteady behaviour of the turbulent boundary-layer contributes to the fluctuating static pressure when the shock-wave boundary layer interaction is strong. Hence, the frozen turbulence assumption is not valid and the turbulence model must be derivated. Thus, the regularisation of the non derivable operators is proposed and applied on k-? Wilcox (2006) turbulence model.The unsteady behaviour of the shock-wave/boundary-layer interaction in a transonic nozzle is evaluated thanks to 2D numerical simulations and shows good agreement with experimental data. When varying the reduced frequency an aeroelastic instability is found, known as transonic flutter. An active control device generating backward travelling pressure waves is then designed and numerically validated.Finally, a methodology is proposed to understand the aerodynamic onsets of transonic flutter. To this end, a preliminary design of a high bypass ratio transonic fan has been carried out. This fan, named ECL5, is dedicated to experimental aerodynamic and aeroelastic studies. The methodology relies on 2D simulations of a tip blade passage and uses linearisation to analyse the contribution of local sources as a function of reduced frequency, nodal diameter and mode shape

An obvious reason for studying unsteady flows is the prediction of the effect of unsteady aerodynamic forces on a flight vehicle, since these effects tend to increase the likelihood of aeroelastic instabilities. This is a major concern in aerodynamic design of aircraft that operate in transonic regime, where the flows are characterised by the presence of adjacent regions of subsonic and supersonic flow, usually accompanied by weak shocks. It has been a common expectation that the numerical approach as an alternative to wind tunnel experiments would become more economical as computers became less expensive and more powerful. However even with all the expected future advances in computer technology, the cost of a numerical flutter analysis (computational aeroelasticity) for a transonic flight remains prohibitively high. Hence it is vitally important to develop an efficient, cheaper (in the sense of computational cost) and physically accurate flutter simulation tech nique which is capable of reproducing the data, which would otherwise be obtained from wind tunnel tests, at least to some acceptable engineering accuracy, and that it is essentially appropriate for industrial applications. This need motivated the present research work on exploring and developing efficient and physically accurate computational techniques for steady, unsteady and time-linearised calculations of transonic flows over an aircraft wing with moving shocks. This dissertation is subdivided into eight chapters, seven appendices and a bibliography listing all the reference materials used in the research work. The research work initially starts with a literature survey in unsteady transonic flow theory and calculations, in which emphasis is placed upon the developments in these areas in the last three decades. Chapter 3 presents the small disturbance theory for potential flows in the subsonic, transonic and supersonic regimes, including the required boundary conditions and shock jump conditions. The flow is assumed irrotational and inviscid, so that the equation of state, continuity equation and Bernoulli's equation formulated in Appendices A and B can be employed to formulate the governing fluid equation in terms of total velocity potential. Furthermore for transonic flow with free-stream Mach number close to unity, we show in Appendix C that the shocks that appear are weak enough to allow us to neglect the flow rotationality. The formulations are based on the main assumption that aerofoil slopes are everywhere small, and the flow quantities are small perturbations about their free-stream values. In Chapter 4, we developed an improved approximate factorisation algorithm that solves the two-dimensional steady subsonic small disturbance equation with nonreflecting far-field boundary conditions. The finite difference formulation for the improved algorithm is presented in Appendix D, with the description of the solver used for solving the system of difference equations described in Appendix E. The calculation of steady and unsteady nonlinear transonic flows over a realistic aerofoil are considered in Chapter 5. Numerical solution methods, based on the finite difference approach, for solving the two-dimensional steady and unsteady, general-frequency transonic small disturbance equations are presented, with the corresponding finite difference formulation described in Appendix F. The theories and solution methods for the time-linearised calculations, in the frequency and time domains, for the problem of unsteady transonic flow over a thin planar wing undergoing harmonic oscillation are presented in Chapters 6 and 7, respectively. The time-linearised calculations include the periodic shock motion via the shock jump correction procedure. This procedure corrects the solution values behind the shock, to accommodate the effect of shock motion, and consequently, the solution method will produce a more accurate time-linearised solution for supercritical flow. Appendix G presents the finite difference formulation of these time-linearised solution methods. The aim is to develop an efficient computational method for calculating oscillatory transonic aerodynamic quantities efficiently for use in flutter analyses of both two- and three-dimensional wings with lifting surfaces. Chapter 8 closes the dissertation with concluding remarks and future prospects on the current research work.

The continuous trend in gas turbine design towards lighter, more powerful and more reliable engines on one side and use of alternative fuels on the other side renders flutter problems as one of the paramount challenges in engine design. Flutter denotes a self-excited and self-sustained aeroelastic instability phenomenon that can lead to material fatigue and eventually damage of structure in a short period of time unless properly damped. The design for flutter safety involves the prediction of unsteady aerodynamics as well as structural dynamics that is mostly based on in-house developed numerical tools. While high confidence has been gained on the structural side unanticipated flutter occurrences during engine design, testing and operation evidence a need for enhanced validation of aerodynamic models despite the degree of sophistication attained. The continuous development of these models can only be based on the deepened understanding of underlying physical mechanisms from test data. As a matter of fact most flutter test cases treat the turbomachine flow in two-dimensional manner indicating that the problem is solved as plane representation at a certain radius rather than representing the complex annular geometry of a real engine. Such considerations do consequently not capture effects that are due to variations in the third dimension, i.e. in radial direction. In this light the present thesis has been formulated to study three-dimensional effects during flutter in the annular environment of a low-pressure turbine blade row and to describe the importance on prediction of flutter stability. The work has been conceived as compound experimental and computational work employing a new annular sector cascade test facility. The aeroelastic response phenomenon is studied in the influence coefficient domain having one blade oscillating in various three-dimensional rigid-body modes and measuring the unsteady response on several blades and at various radial positions. On the computational side a state-of-the-art industrial numerical prediction tool has been used that allowed for two-dimensional and three-dimensional linearized unsteady Euler analyses. The results suggest that considerable three-dimensional effects are present, which are harming prediction accuracy for flutter stability when employing a two-dimensional plane model. These effects are mainly apparent as radial gradient in unsteady response magnitude from tip to hub indicating that the sections closer to the hub experience higher aeroelastic response than their equivalent plane representatives. Other effects are due to turbomachinery-typical three-dimensional flow features such as hub endwall and tip leakage vortices, which considerably affect aeroelastic prediction accuracy. Both effects are of the same order of magnitude as effects of design parameters such as reduced frequency, flow velocity level and incidence. Although the overall behavior is captured fairly well when using two-dimensional simulations notable improvement has been demonstrated when modeling fully three-dimensional and including tip clearance.

<p>A series of aeroelastic analyses is performed for a flexible high-aspect-ratio wing representative of a high altitude long endurance (HALE) aircraft. Such aircraft are susceptible to dynamic instabilities such as flutter, which can lead to large amplitude limit cycle oscillations. These structural motions are modeled by a representative linear typical section model and by Hodges-Dowell beam theory, which includes leading-order nonlinear elastic coupling. Aerodynamic forces are represented by the ONERA dynamic stall model with its coefficients calibrated to CFD data versus wind tunnel test data. Time marching computations of the coupled nonlinear beam and ONERA system highlight a number of features relevant to the aeroelastic response of HALE aircraft, including the influence of a tip store, the sensitivity of the flutter boundary and limit cycle oscillations to aerodynamic CFD or test data, and the roles of structural nonlinearity and nonlinear aerodynamic stall in the dynamic stability of high-aspect-ratio wings.</p> / Dissertation

In this thesis a fluid-structure coupling procedure which consists of a commercial flow solver, FLUENT, a finite element structural solver, MSC/NASTRAN, and the coupling interface between the two disciplines is developed in order to solve static and dynamic aeroelastic problems. The flow solver relies on inviscid Euler equations with finite volume discretization. In order to perform faster computations, multiple processors are parallelized. Closely coupled approach is used to solve the coupled field aeroelastic problems. For static aeroelastic analysis Euler equations and elastic linear structural equations are coupled to predict deformations under aerodynamic loads. Linear interpolation using Alternating Digital Tree data structure is performed in order to exchange the data between structural and aerodynamic grid. Likewise for dynamic aeroelastic analysis, a numerical method is developed to predict the aeroelastic response and flutter boundary. Modal approach is used for structural response and Newmark algorithm is used for time-marching. Infinite spline method is used to exchange displacement and pressure data between structural and aerodynamic grid. In order to adapt the new shape of the aerodynamic surface at each aeroelastic iteration, Computational Fluid Dynamic mesh is moved based on spring based smoothing and local remeshing method provided by FLUENT User Defined Function. AGARD Wing 445.6 and a generic slender missile are modeled and solved with the developed procedure and obtained results are compared with numerical and experimental data available in literature.