Browsing by Subject "Flutter"

This dissertation explores the aeroelastic stability of a folding wing using both theoretical and experimental methods. The theoretical model is based on the existing clamped-wing aeroelastic model that uses beam theory structural dynamics and strip theory aerodynamics. A higher-fidelity theoretical model was created by adding several improvements to the existing model, namely a structural model that uses ANSYS for individual wing segment modes and an unsteady vortex lattice aerodynamic model. The comparison with the lower-fidelity model shows that the higher-fidelity model typical provides better agreement between theory and experiment, but the predicted system behavior in general does not change, reinforcing the effectiveness of the low-fidelity model for preliminary design of folding wings. The present work also conducted more detailed aeroelastic analyses of three-segment folding wings, and in particular considers the Lockheed-type configurations to understand the existence of sudden changes in predicted aeroelastic behavior with varying fold angle for certain configurations. These phenomena were observed in carefully conducted experiments, and nonlinearities - structural and geometry - were shown to suppress the phenomena. Next, new experimental models with better manufacturing tolerances are designed to be tested in the Duke University Wind Tunnel. The testing focused on various configurations of three-segment folding wings in order to obtain higher quality data. Next, the theoretical model was further improved by adding aircraft longitudinal degrees of freedom such that the aeroelastic model may predict the instabilities for the entire aircraft and not just a clamped wing. The theoretical results show that the flutter instabilities typically occur at a higher air speed due to greater frequency separation between modes for the aircraft system than a clamped wing system, but the divergence instabilities occur at a lower air speed. Lastly, additional experimental models were designed such that the wing segments may be rotated while the system is in the wind tunnel. The fold angles were changed during wind tunnel testing, and new test data on wing response during those transients were collected during these experiments.

This thesis explores the aeroelastic stability of a folding wing with an arbitrary number of wing segments. Simplifying assumptions are made such that it is possible to derive the equations of motion analytically. First, a general structural dynamics model based on beam theory is derived from a modal analysis using Lagrange's equations, and is used to predict the natural frequencies of different folding wing configurations. Next, the structural model is extended to an aeroelastic model by incorporating the effects of unsteady aerodynamic forces. The aeroelastic model is used to predict the flutter speed and flutter frequencies of folding wings. Experiments were conducted for three folding wing configurations - a two-segment wing, a three-segment wing, and a four-segment wing - and the outboard fold angle was varied over a wide range for each configuration. Very good agreement in both magnitude and overall trend was obtained between the theoretical and experimental structural natural frequencies, as well as the flutter frequency. For the flutter speed, very good agreement was obtained for the two-segment model, but the agreement worsens as the number of wing segments increases. Possible sources of error and attempts to improve correlation are described. Overall, the aeroelastic model predicts the general trends to good accuracy, offers some additional physical insight, and can be used to efficiently compute flutter boundaries and frequency characteristics for preliminary design or sensitivity studies.

In the vast majority of measured turbomachinery blade flutter occurrences, the response occurs predominately in a single mode. The primary reason for this single-mode flutter is that for turbomachinery applications the combination of high mass ratio, high solidity, and large natural frequency separation results in only slight mode coupling.

The increased importance of fuel efficiency is driving the development of improved turbofans and open-rotor fans. These new designs use fewer blades and will incorporate composite materials or hollowed airfoils in their fan blade designs. Both of these design changes result in lower mass ratio, lower solidity fan blades that may cause multi-mode flutter, rather than single-mode flutter as seen on traditional fan blades. Thus, a single mode flutter design analysis technique may not be adequate. The purpose of this study is to determine initial guidelines for deciding when a coupled-mode analysis is necessary.

The results of this research indicate that mass ratio, frequency separation, and solidity have an effect on critical rotor speed. Further, guidelines were developed for when a multi-mode flutter analysis is required. These guidelines define a critical mass ratio that is a function of frequency separation and solidity. For blade mass ratios lower than this critical value, a multi-mode flutter analysis is required. Finally, the limitations of aerodynamic strip-theory have been revealed in a three-dimensional coupled-mode flutter analysis.

This research presents the detailed investigation of coupled-mode flutter and non-synchronous vibration in turbomachinery. Coupled-mode flutter and non-synchronous vibration are two aeromechanical challenges in designing turbomachinery that, when present, can cause engine blade failure. Regarding flutter, current industry design practices calculate the aerodynamic loads on a blade due to a single mode. In response to these design standards, a quasi three-dimensional, reduced-order modeling tool was developed for identifying the aeroelastic conditions that cause multi-mode flutter. This tool predicts the onset of coupled-mode flutter reasonable well for four different configurations, though certain parameters were tuned to agree with experimentation. Additionally, the results of this research indicate that mass ratio, frequency separation, and solidity have an effect on critical rotor speed for flutter. Higher mass-ratio blades require larger rotational velocities before they experience coupled-mode flutter. Similarly, increasing the frequency separation between modes and raising the solidity increases the critical rotor speed. Finally, and most importantly, design guidelines were generated for defining when a multi-mode flutter analysis is required in practical turbomachinery design.

Previous work has shown that industry computational fluid dynamics can approximately predict non-synchronous vibration (NSV), but no real understanding of frequency lock-in and blade limit-cycle amplitude exists. Therefore, to understand the causes of NSV, two different reduced-order modeling approaches were used. The first approach uses a van der Pol oscillator to model a non-linear fluid instability. The van der Pol model is then coupled to a structural degree of freedom. This coupled system exhibits the two chief properties seen in experimental and computational non-synchronous vibration. Under various conditions, the fluid instability and the natural structural frequency will lock-in, causing structural limit-cycle oscillations. This research shows that with proper model-coefficient choices, the frequency range of lock-in can be predicted and the conditions for the worst-case, limit-cycle-oscillation amplitude can be determined. This high-amplitude limit-cycle oscillation is found at an off-resonant condition, i.e., the ratio of the fluid-shedding frequency and the natural-structural frequency is not unity. In practice, low amplitude limit-cycle oscillations are acceptable; this research gives insight into when high-amplitude oscillations may occur and suggests that altering a blade's natural frequency to avoid this resonance can potentially make the response worse.

The second reduced-order model uses proper orthogonal decomposition (POD) methods to first reconstruct, and ultimately predict, computational fluid dynamics (CFD) simulations of non-synchronous vibration. Overall, this method was successfully developed and implemented, requiring between two and six POD modes to accurately predict CFD solutions that are experiencing non-synchronous vibration. This POD method was first developed and demonstrated for a transversely-moving, two-dimensional cylinder in cross-flow. Later, the method was used for the prediction of CFD solutions for a two-dimensional compressor blade, and the reconstruction of solutions for a three-dimensional first-stage compressor blade.

This research is the first to offer a van der Pol or proper orthogonal decomposition approach to the reduced-order modeling of non-synchronous vibration in turbomachinery. Modeling non-synchronous vibration is especially challenging because NSV is caused by complicated, unsteady flow dynamics; this initial study helps researchers understand the causes of NSV, and aids in the future development of predictive tools for aeromechanical design engineers.

Despite decades of research and attention to the problem of mistuning in bladed disks, both industry and academic efforts have yet to yield a comprehensive design solution for the phenomenon. Regardless, reduced order models based on finite element models have equipped designers and researchers with valuable tools to understand and combat the behaviors of mistuned bladed disks. These models, when employed in probabilistic modeling, can yield accurate predictive distributions for the forced response and flutter characteristics of mistuned bladed disks. This effort focuses on the improvement of one such model by novel application of classical modal decomposition methods. In order to elucidate the status of mistuning research, a brief literature survey is conducted to preface the implementation of an additional reduction to the already simple fundamental mistuning model. Mistuned aeroelastic modes are computed after summing the effects of mistuning, structural coupling, and aerodynamic coupling. This new modal basis is then employed to diagonalize fully the forced response problem, allowing for greater computational efficiency and additional insights to be gained. The exactness of this approach is confirmed with a number of academic bladed disk examples and timing of the new methods yields operational cost reductions of more than 75% for most usage conditions. The new method is then employed in a probabilistic forced response analysis of a mistuned rotor. These results are compared to experimental data to further validate the effectiveness of the fundamental mistuning model.

The aeroelastic stability of beams and plates in three-dimensional flows is explored as the elastic and aerodynamic parameters are varied. First principal energy methods are used to derive the structural equations of motion. The structural models are coupled with a three-dimensional linear vortex lattice model of the aerodynamics. An aeroelastic model with the beam structural model is used to explore the transition between different fixed boundary conditions and the effect of varying two non-dimensional parameters, the mass ratio $\mu$ and aspect ratio $H^*$, for a beam with a fixed edge normal to the flow. The trends matched previously published theoretical and experimental data, validating the current aeroelastic model. The transition in flutter velocity between the clamped free and pinned free configuration is a non-monotomic transition, with the lowest flutter velocity coming with a finite size spring stiffness. Next a plate-membrane model is used to explore the instability dynamics for different combinations of boundary conditions. For the specific configuration of the trailing edge free and all other edges clamped, the sensitivity to the physical parameters shows that decreasing the streamwise length and increasing the tension in the direction normal to the flow can increase the onset instability velocity. Finally the transition in aeroelastic instabilities for non-axially aligned flows is explored for the cantilevered beam and three sides clamped plate. The cantilevered beam configuration transitions from an entirely bending motion when the clamped edge is normal to the flow to a typical bending/torsional wing flutter when the clamped edge is aligned with the flow. As the flow is rotated the transition to the wing flutter occurs when the flow angle is only 10 deg from the perfectly normal configuration. With three edges clamped, the motion goes from a divergence instability when the free edge is aligned with the flow to a flutter instability when the free edge is normal to the flow. The transition occurs at an intermediate angle. Experiments are carried out to validate the beam and plate elastic models. The beam aeroelastic results are also confirmed experimentally. Experimental values consistently match well with the theoretical predictions for both the aeroelastic and structural models.

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.

The successful, efficient, and safe turbine design requires a thorough understanding of the underlying physical phenomena. This research investigates the physical understanding and parameters highly correlated to flutter, an aeroelastic instability prevalent among low pressure turbine (LPT) blades in both aircraft engines and power turbines. The modern way of determining whether a certain cascade of LPT blades is susceptible to flutter is through time-expensive computational fluid dynamics (CFD) codes. These codes converge to solution satisfying the Eulerian conservation equations subject to the boundary conditions of a nodal domain consisting fluid and solid wall particles. Most detailed CFD codes are accompanied by cryptic turbulence models, meticulous grid constructions, and elegant boundary condition enforcements all with one goal in mind: determine the sign (and therefore stability) of the aerodynamic damping. The main question being asked by the aeroelastician, ``is it positive or negative?'' This type of thought-process eventually gives rise to a black-box effect, leaving physical understanding behind. Therefore, the first part of this research aims to understand and reveal the physics behind LPT flutter in addition to several related topics including acoustic resonance effects. A percentage of this initial numerical investigation is completed using an influence coefficient approach to study the variation the work-per-cycle contributions of neighboring cascade blades to a reference airfoil. The second part of this research introduces new discoveries regarding the relationship between steady aerodynamic loading and negative aerodynamic damping. Using validated CFD codes as computational wind tunnels, a multitude of low-pressure turbine flutter parameters, such as reduced frequency, mode shape, and interblade phase angle, will be scrutinized across various airfoil geometries and steady operating conditions to reach new design guidelines regarding the influence of steady aerodynamic loading and LPT flutter. Many pressing topics influencing LPT flutter including shocks, their nonlinearity, and three-dimensionality are also addressed along the way. The work is concluded by introducing a useful preliminary design tool that can estimate within seconds the entire aerodynamic damping versus nodal diameter curve for a given three-dimensional cascade.

This dissertation explores the stability of beams, plates and membranes due to subsonic aerodynamic flows or solar radiation forces. Beams, plates and membranes are simple structures that may act as building blocks for more complex systems. In this dissertation we explore the stability of these simple structures so that one can predict instabilities in more complex structures. The theoretical models include both linear and nonlinear energy based models for the structural dynamics of the featureless rectangular structures. The structural models are coupled to a vortex lattice model for subsonic fluid flows or an optical reflection model for solar radiation forces. Combinations of these theoretical models are used to analyze the dynamics and stability of aeroelastic and solarelastic systems. The dissertation contains aeroelastic analysis of a cantilevered beam and a plate / membrane system with multiple boundary conditions. The dissertation includes analysis of the transition from flag-like to wing-like flutter for a cantilevered beam and experiments to quantify the post flutter fluid and structure response of the flapping flag. For the plate / membrane analysis, we show that the boundary conditions in the flow direction determine the type of instability for the system while the complete set of boundary conditions is required to accurately predict the flutter velocity and frequency. The dissertation also contains analysis of solarelastic stability of membranes for solar sail applications. For a fully restrained membrane we show that a flutter instability is possible, however the post flutter response amplitude is small. The dissertation also includes analysis of a membrane hanging in gravity. This systems is an analog to a spinning solar sail and is used to validate the structural dynamics of thin membranes on earth. A linear beam structural model is able to accurately capture the natural frequencies and mode shapes. Finally, the dissertation explores the stability of a spinning membrane. The analysis shows that a nonlinear model is needed to produce a conservative estimate of the stability boundary.

Theoretical and experimental studies are conducted in the field of aeroelasticity. Specifically, two rectangular and one cropped delta wings with a hole are analyzed in this dissertation for their aeroelastic behavior.

The plate-like wings are modeled using the finite element method for the structural theory. Each wing is assumed to behave as a linearly elastic and isotropic, thin plate. These assumptions are those of small-deflection theory of bending which states that the plane sections initially normal to the midsurface remain plane and normal to that surface after bending. The wings are modeled in low speed flows according to potential flow theory. The potential flow is governed by the aerodynamic potential equation, a linear partial differential equation. The aerodynamic potential equation is solved using a distribution of doublets that relates pressure to downwash in the doublet lattice method. A hole in a wing-like structure is independently investigated theoretically and experimentally for its structural and aerodynamic behavior.

The aeroelastic model couples the structural and aerodynamic models using Lagrange's equations. The flutter boundary is predicted using the V-g method. Linear theoretical models are capable of predicting the critical flutter velocity and frequency as verified by wind tunnel tests. Along with flutter prediction, a brief survey on gust response and the addition of stores(missile or fuel tanks) are examined.