Ph. D.

Flutter is an aeroelastic instability phenomenon that can result either in serious damage or complete destruction of a gas turbine blade structure due to high cycle fatigue. Although 90% of potential high cycle fatigue occurrences are uncovered during engine development, the remaining 10% stand for one third of the total engine development costs. Field experience has shown that during the last decades as much as 46% of fighter aircrafts were not mission-capable in certain periods due to high cycle fatigue related mishaps. To assure a reliable and safe operation, potential for blade flutter must be eliminated from the turbomachinery stages. However, even the most computationally intensive higher order models of today are not able to predict flutter accurately. Moreover, there are uncertainties in the operational environment, and gas turbine parts degrade over time due to fouling, erosion and corrosion resulting in parametric uncertainties. Therefore, it is essential to design engines that are robust with respect to the possible uncertainties. In this thesis, the robustness of an axial compressor blade design is studied with respect to parametric uncertainties through the Mu analysis. The nominal flutter model is adopted from [9]. This model was derived by matching a two dimensional incompressible flow field across the flexible rotor and the rigid stator. The aerodynamic load on the blade is derived via the control volume analysis. For use in the Mu analysis, first the model originally described by a set of partial differential equations is reduced to ordinary differential equations by the Fourier series based collocation method. After that, the nominal model is obtained by linearizing the achieved non-linear ordinary differential equations. The uncertainties coming from the modeling assumptions and imperfectly known parameters and coefficients are all modeled as parametric uncertainties through the Monte Carlo simulation. As iv compared with other robustness analysis tools, such as Hinf, the Mu analysis is less conservative and can handle both structured and unstructured perturbations. Finally, Genetic Algorithm is used as an optimization tool to find ideal parameters that will ensure best performance in terms of damping out flutter. Simulation results show that the procedure described in this thesis can be effective in studying the flutter stability margin and can be used to guide the gas turbine blade design.

The nonlinear dynamical behavior of a laterally compressed, flat, composite panel subjected to a high supersonic flow is analyzed. The structural model considers a higher-order shear deformation theory which also includes the effect of the transverse normal stress and satisfies the traction-free condition on both faces of the panel. The possibility of small initial imperfections and in-plane edge restraints are also considered. Aerodynamic loads based on the third-order piston theory are used and the panel flutter equations are derived via Galerkin’s method. Periodic solutions and their bifurcations are obtained by using a predictor-corrector type of numerical integration method, i.e., the Shooting Method, in conjunction with the Arclength Continuation Method for the static solution. For the perfect panel, the amplitudes and frequency of flutter obtained by the Shooting Method are shown to compare well with results from the Method of Multiple Scales when linear aerodynamics is considered and compressive loads are absent. It is seen that the presence of aerodynamic nonlinearities could result in the hard flutter phenomenon, i.e., a violent transition from the undisturbed equilibrium state to that of finite motions which may occur for pre-critical speeds also. Results show that linear aerodynamics correctly predicts the immediate post-flutter behavior of thin panels only. When compressive edge loads or edge restraints are applied, in certain cases multiple periodic solutions are found to coexist with the stable static solution, or multiple buckled states are possible. Thus it is seen that the panel may remain buckled beyond the flutter boundary, or it may flutter within the region where buck-led states exist. Furthermore, the presence of edge restraints normal to the flow tends to stabilize the panel by decreasing the flutter amplitudes and the possibility of hard flutter. Nonperiodic motions (i.e., quasiperiodic and chaotic) of the buckled panel are found to exist, and their associated Lyapunov exponents are calculated. The effects of transverse shear flexibility, aerodynamic nonlinearities, initial imperfections, and in-plane edge restraints on the stability boundaries are also studied. It is observed that the classical plate theory over-predicts the instability loads, and only the shear deformation theory correctly models the panel which is flexible in transverse shear. When aerodynamic nonlinearities are considered, multiple flutter speeds may exist. / Ph. D.

Ph. D.

The panel flutter analysis presented herein has been restricted to the problem of an isolated simply supported plate of uniform thickness. The same type of analysis can be applied, however, to other panel configurations. Clamped panels, integrally stiffened panels, arrays of panels, end others should be amenable to treatment by the model approach based on the static aerodynamic approximation. / Master of Science

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 1981. / Microfiche copy available in Archives and Barker. / Includes bibliographical references. / by Steven James Hollowell. / M.S.

The main objective of this thesis is to study and investigate the dynamics and stability of cantilevered structures subjected to internal, external, or simultaneous internal and external axial flows. This was accomplished, in some cases, by deriving the linear equations of motion using a Newtonian approach and, in other cases, by making the necessary modifications to existing theoretical models. The continuous cantilevered systems were then discretized using the Galerkin method in order to determine their complex eigenfrequencies. Moreover, numerous experiments were performed to compare and validate, or otherwise, the theoretical models proposed. More specifically, the four cantilevered systems studied were the following: (i) a pipe conveying fluid that is fitted with a stabilizing end-piece, which suppresses flutter by blocking the straight-through exit of flow at the downstream end; (ii) a pipe aspirating fluid, which flutters at low flow velocities in its first mode; (iii) a free-clamped cylinder (i.e. with the upstream end free and the downstream end clamped) in confined axial flow, which also flutters at low flow velocities in its first mode and eventually develops a buckling instability; and (iv) a pipe subjected to internal flow, which after exiting the pipe is transformed to a confined counter-current annular flow, that becomes unstable by flutter too.

No description available.

A general aerodynamic model for two-dimensional inviscid flows is developed. This model is used to simulate wakes and blade-vortex interaction. This model is also coupled with dynamics and feedback controls to simulate flutter and flutter suppression. The flow is assumed to be attached and incompressible. The present aerodynamic model is based on a vorticity-panel method coupled with vortex dynamics. The present aerodynamic model is used to simulate some actual experiments: wakes generated by oscillating airfoils and blade-vortex interactions in which one airfoil is placed in or near the wake generated by another oscillating airfoil upstream. The present numerical model predicts wake structures, vorticity strength, and velocity profiles across the wake that compare very favorably with the experiments. The present numerical results of the blade-vortex interaction show good agreement with the experiments when separation does not occur. If separation is involved, the present model fails to accurately simulate blade-vortex interaction because separation is not considered in the present model. Flutter is studied by means of numerical simulations. In an incompressible flow, an airfoil is mounted on an elastic support. The airfoil can pitch (rotate) and plunge (translate vertically). The dynamic equations that describe this two-degree-of-freedom motion are general and nonlinear. To calculate the aerodynamic loads on the airfoil, the aerodynamic model is coupled with this dynamic model. The motions of the airfoil and flowing air are calculated interactively and simultaneously. The coupled aerodynamic/dynamic model accurately predicts the critical flutter speed of the freestream, the speed at which the motion of the airfoil grows spontaneously. The contributions of the phase difference and energy exchange to the flutter motion are discussed. The effect of the static angle of attack on the critical flutter speed is investigated. Also the effect of the nonlinearity of the elastic support (cubic term in the hardening spring) is studied. A feedback control is coupled with aerodynamics/dynamics to suppress the flutter motion of the airfoil. A flap is added at the trailing edge of the airfoil as a control surface, and its deflection (rotation) about the hinge point is commanded by a feedback-control law. The flow, airfoil, elastic support, and control device are considered as one system, and the flow, the motions of the airfoil, and the flap deflections are calculated simultaneously. With carefully designed control laws, oscillations that would be unstable (i.e., growing) without control are suppressed. The numerical results show different control variables can be used. The model of aerodynamics/dynamics/control is also used to successfully suppress the response to a wind gust with the same control laws as used for the suppression of flutter. / Ph. D.

A method is presented for calculating the shape sensitivity of a wing aeroelastic response with respect to changes in geometric shape. Yates’ modified strip method is used in conjunction with Giles' equivalent plate analysis to predict the flutter speed, frequency, and reduced frequency of the wing. Three methods are used to calculate the sensitivity of the eigenvalue. The first method is purely a finite difference calculation of the eigenvalue derivative directly from the solution of the flutter problem corresponding to the two different values of the shape parameters. The second method uses an analytic expression for the eigenvalue sensitivities of a general complex matrix, where the derivatives of the aerodynamic, mass, and stiffness matrices are computed using a finite difference approximation. The third method also uses an analytic expression for the eigenvalue sensitivities but the aerodynamic matrix is computed analytically. All three methods are found to be in good agreement with each other. The sensitivities of the eigenvalues were used to predict flutter speed, frequency , and reduced frequency. These approximations were found to be in good agreement with those obtained using a complete reanalysis. However, it is recommended that higher order terms be used in the calculations in order to assure greater accuracy. / Master of Science / incomplete_metadata