Browsing by Subject "Aeroelasticity"

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.

One of the grand challenges faced by industry is the accurate prediction of unsteady aerodynamics events, including frequency lock-in and forced response. These aeromechanical incidents occurring in airplane engines and gas turbines can cause high-amplitude blade vibration and potential failure of the engine or turbine. During the last decades, the development of computational fluid dynamics has allowed the design and optimization of complex components while reducing the need for expensive engine testing. However, the validation of frequency lock-in and forced response numerical results with experimental data is very incomplete. Despite tremendous advances in computational capabilities, industry is still looking to validate design tools and guidelines to avoid these potentially costly aeroelastic events early in the design process.

The research efforts presented in this dissertation investigate the aeroelastic phenomena of frequency lock-in and forced response in turbomachinery. First, frequency lock-in is predicted for two structures, namely a two-dimensional cylinder and a single three-dimensional airfoil, and the results are compared to experimental data so that the methods can be extended to more complex structures. For these two simpler structures, a frequency domain harmonic balance code is used to estimate the natural shedding frequency and the corresponding lock-in region. Both the shedding frequencies and the lock-in regions obtained by an enforced motion method agree with experimental data from previous literature and wind tunnel tests. Moreover, the aerodynamic model of the vibrating cylinder is coupled with the structural equations of motion to form a fluid-structure interaction model and to compute the limit-cycle oscillation amplitude of the cylinder. The extent of the lock-in region matches the experimental data very well, yet the peak amplitude is underestimated in the numerical model. We demonstrate that the inclusion of the cylinder second degree of freedom has a significant impact on the cylinder first degree of freedom amplitude. Moreover, it is observed that two harmonics need to be kept in the equations of motion for accurate prediction of the unsteady forces on the cylinder.

The second important topic covered is a comprehensive forced response analysis conducted on a multi-stage axial compressor and compared with the initial data of the largest forced response experimental data set ever obtained in the field. Both a frequency domain and a time domain codes are used. The steady-state and time-averaged aerodynamic performance results compare well with experimental data, although losses are underestimated due to the lack of secondary flow paths and fillets in the model. The use of mixing planes in the steady simulations underpredicts the wakes by neglecting the important interactions between rows. Therefore, for similar cases with significant flow separation, the use of a decoupled method for forced response predictions cannot yield accurate results. A full multi-row transient analysis must be conducted for accurate prediction of the wakes and surface unsteady pressures. Finally, for the first time, predicted mistuned blade amplitudes are compared to mistuned experimental data. The downstream stator is found to be necessary for the accurate prediction of the modal forces and vibration amplitudes. The mistuned rotor is shown to be extremely sensitive to perturbations in blade frequency mistuning, aerodynamic asymmetry, and excitation traveling wave content. Since this dissertation presents the initial results of a five-year research program, more research will be conducted on this compressor to draw guidelines that can be used by aeromechanical engineers to safely avoid forced response events in the design of jet engines and gas turbines.

One of the most complex challenges in our world today is the interaction between fluids and structures. This complicated meeting is one of the focal points in the design and manufacturing of turbomachinery, whether in jet engines, steam turbines, or rocket pumps. When an unsteady aerodynamic instability interacts with the natural modes of vibration of a rigid body, a phenomenon known as Non-Synchronous Vibrations (NSV) occurs, also referred to in other parts of the world as Vortex-Induced Vibrations (VIV). These vibrations cause blade fracture and ultimately failure in jet engines; however, the underlying flow physics are much less understood than other aeroelastic phenomenon such as flutter or forced response. When the buffeting frequency of the flow around a bluff body nears one of its natural frequencies, the former frequency “locks in” to the latter. Within this “lock in” region there is only one main frequency, while outside of it there are two. Although this phenomenon has been documented both experimentally and computationally, the unsteady pressures associated with this phenomenon have not been accurately measured. In a comprehensive three-fold approach, the spectra of unsteady pressure amplitudes are collected around a few different, increasingly complex, configurations. 1. a circular cylinder 2. a symmetric NACA 0012 airfoil 3. a three-stage turbine All three exhibit NSV in wind tunnel experiments as well as computationally using fluid dynamics simulations. For all cases, the time domain unsteady lift and pressure data is Fast Fourier Transformed to provide frequency domain data. Then, the data is analyzed to understand the underlying flow physics; to do so, the unsteady pressures are separated into contributions due to the enforced motion of the body and those due to vortex shedding. Finally, the unlocked pressure spectrum is linearly combined to reconstruct the lock-in responses. These additional insights into NSV will pave the way towards a design tool for engine manufacturers. In addition, many attempts have been made to model this lock-in behavior, comparing it against experimental and computational fluid dynamics data. A reduced-order model (ROM) utilizes a Van der Pol oscillator model to capture the wake of vortices. This model has been expanded and improved to model NSV in cylinders, airfoils, and turbomachinery blades; the model proved to match experimental data better than its predecessors. This notional model will provide further insight into the phenomenon of NSV and will assist in creating a tool to design safe and efficient jet engines and steam turbines in the future. While this work focuses on Non-Synchronous Vibrations, some time was devoted to the design and manufacturing of another experimental test rig. The seven bladed linear cascade (aptly named “LASCADE”) will be used for flutter tests. The center blade oscillates about its mid-chord at an enforced frequency and amplitude, while the center three titanium printed blades contain pressure taps located at the midspan. Over the course of four years, the author has served as a design consultant, research mentor, manufacturing instructor, and project manager for this cascade. Ultimately, this work furthers the understanding of the underlying flow physics of enforced motion frequency lock-in associated with Non-Synchronous Vibrations and Flutter. The solitary experiments and simulations set the groundwork for additional studies on turbomachinery specific geometry. The three-stage turbine study is just the beginning of a full NSV study to be done in conjunction with experiments. Finally, the ROMs open the door for a full design tool to be constructed for use by turbomachinery designers and manufacturers, saving time, energy, and money in the end.

The purpose of this dissertation is to study the aeroelastic stability of a proposed flexible thermal protection system (FTPS) for the NASA Hypersonic Inflatable Aerodynamic Decelerator (HIAD). A flat, square FTPS coupon exhibits violent oscillations during experimental aerothermal testing in NASA's 8 Foot High Temperature Tunnel, leading to catastrophic failure. The behavior of the structural response suggested that aeroelastic flutter may be the primary instability mechanism, prompting further experimental investigation and theoretical model development. Using Von Karman's plate theory for the panel-like structure and piston theory aerodynamics, a set of aeroelastic models were developed and limit cycle oscillations (LCOs) were calculated at the tunnel flow conditions. Similarities in frequency content of the theoretical and experimental responses indicated that the observed FTPS oscillations were likely aeroelastic in nature, specifically LCO/flutter.

While the coupon models can be used for comparison with tunnel tests, they cannot predict accurately the aeroelastic behavior of the FTPS in atmospheric flight. This is because the geometry of the flight vehicle is no longer a flat plate, but rather (approximately) a conical shell. In the second phase of this work, linearized Donnell conical shell theory and piston theory aerodynamics are used to calculate natural modes of vibration and flutter dynamic pressures for various structural models composed of one or more conical shells resting on several circumferential elastic supports. When the flight vehicle is approximated as a single conical shell without elastic supports, asymmetric flutter in many circumferential waves is observed. When the elastic supports are included, the shell flutters symmetrically in zero circumferential waves. Structural damping is found to be important in this case, as "hump-mode" flutter is possible. Aeroelastic models that consider the individual FTPS layers as separate shells exhibit asymmetric flutter at high dynamic pressures relative to the single shell models. Parameter studies also examine the effects of tension, shear modulus reduction, and elastic support stiffness.

Limitations of a linear structural model and piston theory aerodynamics prompted a more elaborate evaluation of the flight configuration. Using nonlinear Donnell conical shell theory for the FTPS structure, the pressure buckling and aeroelastic limit cycle oscillations were studied for a single elastically-supported conical shell. While piston theory was used initially, a time-dependent correction factor was derived using transform methods and potential flow theory to calculate more accurately the low Mach number supersonic flow. Three conical shell geometries were considered: a 3-meter diameter 70 degree shell, a 3.7-meter 70 degree shell, and a 6-meter diameter 70 degree shell. The 6-meter configuration was loaded statically and the results were compared with an experimental load test of a 6-meter HIAD vehicle. Though agreement between theoretical and experimental strains was poor, circumferential wrinkling phenomena observed during the experiments was captured by the theory and axial deformations were qualitatively similar in shape. With piston theory aerodynamics, the nonlinear flutter dynamic pressures of the 3-meter configuration were in agreement with the values calculated using linear theory, and the limit cycle amplitudes were generally on the order of the shell thickness. Pre-buckling pressure loads and the aerodynamic pressure correction factor were studied for all geometries, and these effects resulted in significantly lower flutter boundaries compared with piston theory alone.

In the final phase of this work, the existing linear and nonlinear FTPS shell models were coupled with NASA's FUN3D Reynolds Averaged Navier Stokes CFD code, allowing for the most physically realistic flight predictions. For the linear shell structural model, the elastically-supported shell natural modes were mapped to a CFD grid of a 6-meter HIAD vehicle, and a linear structural dynamics solver internal to the CFD code was used to compute the aeroelastic response. Aerodynamic parameters for a proposed HIAD re-entry trajectory were obtained, and aeroelastic solutions were calculated at three points in the trajectory: Mach 1, Mach 2, and Mach 11 (peak dynamic pressure). No flutter was found at any of these conditions using the linear method, though oscillations (of uncertain origin) on the order of the shell thickness may be possible in the transonic regime. For the nonlinear shell structural model, a set of assumed sinusoidal modes were mapped to the CFD grid, and the linear structural dynamics equations were replaced by a nonlinear ODE solver for the conical shell equations. Successful calculation and restart of the nonlinear dynamic aeroelastic solutions was demonstrated. Preliminary results indicated that dynamic instabilities may be possible at Mach 1 and 2, with a completely stable solution at Mach 11, though further study is needed. A major benefit of this implementation is that the coefficients and mode shapes for the nonlinear conical shell may be replaced with those of other types of structures, greatly expanding the aeroelastic capabilities of FUN3D.

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.

A combined approach of linear convolution and higher order Volterra series to reduced order modelling of unsteady transonic aerodynamic loads is presented. The new approach offers a simple method to determine the memory depth of the system, significantly reduces the effort required to generate a model for a wide range of reduced frequencies, and clearly separates the linear and the non-linear contributions. The generated models are completely separated from any specific input signal or a particular reduced frequency. The models were verified in an aeroelastic simulation of a 2D NACA 0012 airfoil. The results correlate well with wind tunnel tests and previously calculated LCO levels.

Our experimental study sought to answer the question: how to maximize the piezoelectric power extraction of an aeroelastic system? A simple rectangular cantilever plate, which experiences LCO, was used as a basic vibrating system. The plate was covered entirely with piezoelectric elements on both sides. By adding small discrete masses along the plate, we were able to increase the power generation efficiency by 260% while reducing the airspeed required to produce this power by 150%, and the level of vibrations by 320%.

There is a growing interest among aeroelasticity researchers for insight into large deflection oscillations of aerospace structures. Here, a new beam and plate model is derived using Hamilton's Principle to lay the structural framework for a nonlinear, large deflection aeroelastic model. Two boundary conditions of the beam are explored: cantilevered and free-free. For a plate, the cantilevered boundary condition is considered. In these conditions, the nonlinearity stems from the structure's large curvature rather than from stretching. Therefore, this model makes use of the simplifying assumption that the the structure has no strain along the midplane; thus the model is ``inextensible." Insight into the nonlinearity of this system is gained by applying harmonic loads to the structure, and stability conditions are also investigated by applying nonconservative follower loads.

Upon validating the structural model, the model is then coupled with aerodynamic models to form new, nonlinear aeroelastic models. Using classical aeroelasticity tools such as Piston Theory to model aerodynamic forces on the largely deflected cantilever, new insights are gained into the stability behavior of the system, the post-flutter behavior of the system, and the utility of these classic techniques with these novel configurations. With the large deflection cases, several novel nonlinearities are introduced, and it is shown that the systems are highly sensitive to the inclusion of these nonlinearities. Of course these classical aerodynamic theories are derived assuming small deflections, so attention is given to ensure that the Classical Piston Thoery is applicable in the current configurations. Also a new aerodynamic theory is proposed for pressures on structures undergoing large deflections. In total, this document proposes and explores new methodologies for modeling aeroelastic structures which tend to undergo large elastic deformations.

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.

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.