Academic literature on the topic 'Flutter'

Flutter is a dynamic instability which can result in catastrophic failures of an air vehicle. Preventing flutter can be an important factor in the aircraft design, affecting the structural design. Thus, the weight and performance of the aircraft is also being affected. Understanding the role of each design factor of a wing on the onset of flutter can help designers on the flutter clearance of the aircraft. Analysis to predict flutter, ground vibration tests and flight flutter tests, which are performed to verify that the dedicated flight envelope is clear from flutter, are the most important certification processes in modern aviation. Flight flutter testing is a very expensive process. In flight flutter tests the air vehicle is instrumentated with exciters, accelerometers and transmitters to send the test data simultaneously to the ground station to be analyzed. Since flutter is a very severe instability, which develops suddenly, the data should be followed carefully by the engineers at the ground station and feedback should be provided to the pilot urgently when needed. Low test step numbers per flight, increases the cost of flutter testing. Increasing efforts in pre-flight test processes in flutter prediction may narrow the flight flutter test steps and decrease the costs. In this study, flutter prediction methods are investigated to aid the flutter test process. For incompressible flight conditions, some sample problems are solved using typical section model. Flutter solutions of a simple 3D wing are also performed via a coupled finite element linear aerodynamics approach using the commercial tool Nastran. 3D flutter solutions of the wing are compared with the typical section solutions to see how close can the typical section method predict flutter compared to the flutter analyis using the three dimensional wing model. A simulated flutter test method is introduced utilizing the two dimensional typical section method. It is shown that with a simple two dimensional typical section method, flutter test simulation can be performed successfully as long as the typical section model approximates the dynamic properties of the wing closely.

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2000.<br>"September 2000."<br>Includes bibliographical references (p. 223-228).<br>This thesis describes the effects of operational parameters upon aeroengine flutter stability. The study is composed of three parts: theoretical development of relevant parameters, exploration of a computational model, and analysis of fully scaled test data. Results from these studies are used to develop a rational flutter clearance methodology-a test procedure to ensure flutter-free operation. It is shown, under conditions relevant to aeroengines, that four nondimensional parameters are necessary and sufficient for flutter stability assessment of a given rotor geometry. We introduce a new parameter, termed the reduced damping, g/p *, which collapses the combined effects of mechanical damping and mass ratio (blade mass to fluid inertia). Furthermore, the introduction of the compressible reduced frequency, K*, makes it possible to uniquely separate the corrected performance map from the non-dimensional operating environment (including inlet temperature and pressure). Simultaneous plots of the performance map of corrected mass flow and corrected speed, (^.mc, Nc), with the (K*, g/p*) map provide a dimensionally complete and fully integrated view of flutter stability, as demonstrated in the context of a historic multimission engine. A parametric, computational study was conducted using a 2D, linearized unsteady, compressible, potential flow model of a vibrating cascade. This study showed the independent effects of Mach number, inlet flow angle, and reduced frequency upon flutter stability in terms of critical reduced damping, which corroborates the 4D view of flutter stability. Test data from a full-scale transonic fan, spanning the full 4D parameter space, were also analyzed. A novel boundary fitting tool was developed for data processing, which can handle the generic case of sparse, multidimensional, binary data. The results indicate that the inlet pressure does not alone determine the flight condition effects upon flutter, which necessitates the use of the complete 4D parameter set. Such a complete view of the flutter boundary is constructed, and sensitivities with respect to various parameters are estimated. A rational flutter clearance procedure is proposed. Trends in K* and g/p* allow one to rapidly determine the worst-cases for testing a given design. One may also use sensitivities to extend the results of sea level static (SLS) testing, if the worst case is relatively close to the SLS condition.<br>by Asif Khalak.<br>Ph.D.

The unsteady ow around an aerofoil placed in a uniform ow stream with an angle of attack is investigated, under the assumption of inviscid, incompressible, two-dimensional flow. In particular, a function of the velocity jump over the wake is achieved, where this function depends on the horizontal displacement and time. The aerofoil geometry is represented by two arbitrary functions, one for the upper and one for the lower side of the aerofoil. These functions are dependent on time, hence the aerofoil can perform oscillating movement, which is the case when subjected to utter. The governing equations for the ow are the Euler equations. By assuming thin aerofoil, small angle of attack and that the perturbation of the wake is small, the problem is linearised. It is shown that the linearised Euler equations can be rewritten as the Cauchy-Riemann equations, and an analytic function exists where its real part is the horizontal velocity component and its imaginary part is the vertical velocity component with opposite sign. The ow eld is then investigated in the complex plane by making an appropriate branch cut removing all discontinuities, and with restrictions on the analytic function such that the kinematic and boundary conditions are satis ed. By using Cauchy's integral formula an expression for the anti-symmetric part of the analytic function is achieved. A general expression for the velocity jump over the wake is obtained, which is applied to the speci c case of harmonic oscillations for a symmetric aerofoil. In the end three types of utter is investigated; twisting oscillations around the centre of stiness, vertical oscillation, and aileron flutter.

Modern gas turbine design continues to drive towards improved performance, reduced weight and reduced cost. This trend of aero-engine design results in thinned blade aerofoils which are more prone to aeroelastic problems such as flutter. Whilst extensive work has been conducted to study the flutter of isolated turbomachinery blades, the number of research concerning the unsteady interactions between the blade vibration, the resulting acoustic reflections and flutter is very limited. In this thesis, the flutter of such embedded blade rows is studied to gain understanding as for why and how such interactions can result in flutter. It is shown that this type of flutter instability can occur for single stage fan blades and multi-stage core compressors. Unsteady CFD computations are carried out to study the influence of acoustic reflections from the intake on flutter of a fan blade. It is shown that the accurate prediction of flutter boundary for a fan blade requires modelling of the intake. Different intakes can produce different flutter boundaries for the same fan blade and the resulting flutter boundary is a function of the intake geometry in front of it. The above finding, which has also been demonstrated experimentally, is a result of acoustic reflections from the intake. Through in-depth post-processing of the results obtained from wave-splitting of the unsteady CFD solutions, the relationship between the phase and amplitude of the reflected acoustic waves and flutter stability of the blade is established. By using an analytical approach to calculate the propagation and reflection of acoustic waves in the intake, a novel low- fidelity model capable of evaluating the susceptibility of a fan blade to flutter is proposed. The proposed model works in a similar fashion to the Campbell diagram, which allows one to identify the region (in compressor map) where flutter is likely to occur at early design stages of an engine. In the second part of this thesis, the influence of acoustic reflections from adjacent blade rows on flutter stability of an embedded rotor in a multi-stage compressor is studied using unsteady CFD computations. It is shown that reflections of acoustic waves, generated by the rotor blade vibration, from the adjacent blade rows have a significant impact on the flutter stability of the embedded rotor, and the computations using the isolated rotor can lead to significant over-optimistic predictions of the flutter boundary. Based on the understanding gained, an alternative strategy, aiming to reduce the computational cost, for the flutter analysis of such embedded blades is proposed. The method works by modelling the propagation and reflection of acoustic waves at the adjacent blade rows using an analytical method, whereby flutter computations of the embedded rotor can be performed in an isolated fashion by imposing the calculated reflected waves as unsteady plane sources. Computations using the proposed model can lead to two orders of magnitude reduction in computational cost compared with time domain full annulus multi-row computations. The computed results using the developed low-fidelity model show good correlation with the results obtained using full annulus multi-row models.

<p>In order to eliminate or reduce vibration problems inturbomachines without a high increase in the complexity of thevibratory behavior, the adjacent airfoils around the wheel areoften mechanically connected together with lacing wires, tip orpart-span shrouds in a number of identical sectors. Although anaerodynamic stabilizing effect of tying airfoils together ingroups on the whole cascade is indicated by numerical andexperimental studies, for some operating conditions suchsectored vane cascade can still remain unstable.</p><p>The goal of the present work is to investigate thepossibilities of a sectored vane cascade to undergoself-excited vibrations or flutter. The presented method forpredicting the aerodynamic response of a sectored vane cascadeis based on the aerodynamic work influence coefficientrepresentation of freestanding blade cascade. The sectored vaneanalysis assumes that the vibration frequency is the same forall blades in the sectored vane, while the vibration amplitudesand mode shapes can be different for each individual blade inthe sector. Additionally, the vibration frequency as well asthe amplitudes and mode shapes are supposed to be known.</p><p>The aerodynamic analysis of freestanding blade cascade isperformed with twodimensional inviscid linearized flow model.As far as feasible the study is supported by non-linear flowmodel analysis as well as by performing comparisons againstavailable experimental data in order to minimize theuncertainties of the numerical modeling on the physicalconclusions of the study.</p><p>As has been shown for the freestanding low-pressure turbineblade, the blade mode shape gives an important contributioninto the aerodynamic stability of the cascade. During thepreliminary design, it has been recommended to take intoaccount the mode shape as well rather than only reducedfrequency. In the present work further investigation using foursignificantly different turbine geometries makes these findingsmore general, independent from the low-pressure turbine bladegeometry. The investigation also continues towards a sectoredvane cascade. A parametrical analysis summarizing the effect ofthe reduced frequency and real sector mode shape is carried outfor a low-pressure sectored vane cascade for differentvibration amplitude distributions between the airfoils in thesector as well as different numbers of the airfoils in thesector. Critical (towards flutter) reduced frequency maps areprovided for torsion- and bending-dominated sectored vane modeshapes. Utilizing such maps at the early design stages helps toimprove the aerodynamic stability of low-pressure sectoredvanes.</p><p>A special emphasis in the present work is put on theimportance for the chosen unsteady inviscid flow model to bewell-posed during numerical calculations. The necessity for thecorrect simulation of the far-field boundary conditions indefining the stability margin of the blade rows isdemonstrated. Existing and new-developed boundary conditionsare described. It is shown that the result of numerical flowcalculations is dependent more on the quality of boundaryconditions, and less on the physical extension of thecomputational domain. Keywords: Turbomachinery, Aerodynamics,Unsteady CFD, Design, Flutter, Low-Pressure Turbine, Blade ModeShape, Critical Reduced Frequency, Sectored Vane Mode Shape,Vibration Amplitude Distribution, Far-field 2D Non-ReflectingBoundary Conditions. omain.</p><p><b>Keywords:</b>Turbomachinery, Aerodynamics, Unsteady CFD,Design, Flutter, Low-Pressure Turbine, Blade Mode Shape,Critical Reduced Frequency, Sectored Vane Mode Shape, VibrationAmplitude Distribution, Far-field 2D Non-Reflecting BoundaryConditions.</p>

The problem of flutter is first introduced. The equations of motion of an airfoil with two degrees of freedom, in pitch and plunge, are obtained. Then, the unsteady aerodynamic theories for different flow regimes are presented. The traditional solutions to the flutter problem, namely, the p-k and U-g methods, are formulated, and the Laplace transformation method for flutter analysis is also introduced. Then, the effect of different design parameters of an airfoil on the flutter speed is analyzed, both in the incompressible and transonic regimes. Furthermore, the effect of the relative values of the design parameters on the occurrence of flutter is investigated. Finally, some general conclusions regarding the above-mentioned phenomena are derived. The goal of this work is the fact that, the unsteady aerodynamic data has been used, both in the incompressible and transonic regimes, and, therefore, the obtained results are fairly precise.

The flutter is a dangerous aeroelastic instability that can cause dramatic failures. It is important to evaluate in which conditions it can occur to ensure the safety of the pilots and the passengers. As flight tests are very expensive and hazardous, the need for efficient and trustworthy numerical tools becomes essential. This report focuses on two methods to predict the flutter conditions in the transonic domain. To evaluate the accuracy of these tools, their results are compared to experimental data gathered during a wind-tunnel test. The influence of the Mach number and the angle of attack on the flutter conditions is studied and physical explanations are put forward.