# Browsing by Author "Dowell, Earl H"

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Item Open Access A New Approach to Model Order Reduction of the Navier-Stokes Equations(2012) Balajewicz, MaciejA new method of stabilizing low-order, proper orthogonal decomposition based reduced-order models of the Navier Stokes equations is proposed. Unlike traditional approaches, this method does not rely on empirical turbulence modeling or modification of the Navier-Stokes equations. It provides spatial basis functions different from the usual proper orthogonal decomposition basis function in that, in addition to optimally representing the solution, the new proposed basis functions also provide stable reduced-order models. The proposed approach is illustrated with two test cases: two-dimensional flow inside a square lid-driven cavity and a two-dimensional mixing layer.

Item Open Access A Nonlinear Harmonic Balance Solver for an Implicit CFD Code: OVERFLOW 2(2009) Custer, Chad H.A National Aeronautics and Space Administration computational fluid dynamics code, OVERFLOW 2, was modified to utilize a harmonic balance solution method. This modification allows for the direct calculation of the nonlinear frequency-domain solution of a periodic, unsteady flow while avoiding the time consuming calculation of long physical transients that arise in aeroelastic applications.

With the usual implementation of this harmonic balance method, converting an implicit flow solver from a time marching solution method to a harmonic balance solution method results in an unstable numerical scheme. However, a relatively simple and computationally inexpensive stabilization technique has been developed and is utilized. With this stabilization technique, it is possible to convert an existing implicit time-domain solver to a nonlinear frequency-domain method with minimal modifications to the existing code.

This new frequency-domain version of OVERFLOW 2 utilizes the many features of the original code, such as various discretization methods and several turbulence models. The use of Chimera overset grids in OVERFLOW 2 requires care when implemented in the frequency-domain. This research presents a harmonic balance version of OVERFLOW 2 that is capable of solving on overset grids for sufficiently small unsteady amplitudes.

Item Open Access A study of the aeroelastic behavior of flat plates and membranes with mixed boundary conditions in axial subsonic flow(2011) Bloomhardt, Elizabeth M.In support of the noise reduction targets for future generations of transport aircraft, as set forth by NASA, the fundamental aeroelastic behavior of trailing edge flap technology was explored. Using a plate structural model to approximate the structural configuration and linear potential flow theory to represent the aerodynamics, aeroelastic behavior was characterized for two structural configurations using two different sets of boundary conditions for each. The two structural configurations considered were a) all edges fixed and b) leading and side edges fixed, trailing edge free. In each configuration both simply supported and clamped boundary conditions were considered. Results are compared to calculations presented in the literature for the all edges simply supported configuration.Item Open Access A Theoretical and Computational Study of Limit Cycle Oscillations in High Performance Aircraft(2015) Padmanabhan, Madhusudan A.High performance fighter aircraft such as the F-16 experience aeroelastic Limit Cycle Oscillations (LCO) when they carry certain combinations of under-wing stores. This `store-induced LCO' causes serious problems including airframe fatigue, pilot discomfort and loss of operational effectiveness. The usual response has been to restrict the stores carriage envelope based on flight test experience, and accept the accompanying reduction in mission performance.

Although several nonlinear mechanisms - structural as well as aerodynamic, have been proposed to explain the LCO phenomenon, their roles are not well understood. Consequently, existing models are unable to predict accurately AND reliably the most critical LCO properties, namely onset speed and response level. On the other hand, the more accurate Computational Fluid Dynamics (CFD) based time marching methodology yields results at much greater expense and time. Clearly, there is a critical need to establish methods that are more rapid while providing accurate predictions more in line with flight test results than at present. Such a capability will also aid in future aircraft design and usage.

This work was undertaken to develop a better understanding of nonlinear aeroelastic phenomena, and their relation to classical flutter and divergence, with a particular focus on store-induced LCO in high performance fighter aircraft. The following systems were studied: (1) a `simple' wing with a flexible and nonlinear root attachment, (2) a `generic' wing with a flexible and nonlinear wing-store attachment and (3) the F-16 aircraft, again with nonlinear wing-store attachments.

While structural nonlinearity was present in all cases, steady flow aerodynamic nonlinearity was also included in the F-16 case by the use of a Computational Fluid Dynamics model based on the Reynolds Averaged Navier Stokes (RANS) equations. However, dynamic linearization of the CFD model was done for the present computations. The computationally efficient Harmonic Balance (HB) nonlinear solution technique was a key component of this work, with time marching simulations and closed form solutions being used selectively to confirm the findings of the HB solutions. The simple wing and the generic wing were both modeled as linear beam-rods whose displacements were represented using the primitive modes method. The wing aerodynamic model was linear (quasi-steady for the simple wing and based on the Vortex Lattice Method for the generic wing), and the store aerodynamics were omitted.

The presence of a cubic restoring force (of hardening or softening type, in stiffness or in damping) at the root of the simple wing led to several interesting results and insights. Next, various nonlinear mechanisms including cubic restoring force, freeplay and friction were introduced at the wing-store attachment of the generic wing and these led to a still greater variety in behavior. General relationships were established between the type of nonlinearity and the nature of the resulting response, and they proved very useful for tailoring the F-16 study and interpreting its results.

The Air Force Seek Eagle Office/Air Force Research Laboratory provided a modal structural model of an LCO-prone store configuration of the F-16 aircraft with stores included. In order to investigate a range of stores attachment configurations, the analysis required modification of the stiffness and damping of the wing-store attachment. Since the Finite Element model of the wing and store structure was not available, the modification was achieved by subtracting the store and adding it back with the necessary changes to the store or attachment using a dynamic decoupling/coupling technique. The modified models were subjected to flutter/LCO analysis using the Duke Harmonic Balance CFD RANS solver, and the resulting flutter boundaries were used in combination with the HB method to derive LCO responses due to the wing-store attachment nonlinearity.

Comparisons were made between the simulation results and the F-16 flight test LCO data. While multiple sources of nonlinearity are probably responsible for the wide range of observed LCO behavior, it was concluded that cubic softening stiffness and positive cubic damping were the more likely structural mechanisms causing LCO, in addition to nonlinear aerodynamics.

Item Open Access Aeroelastic and Flight Dynamics Analysis of Folding Wing Systems(2013) Wang, IvanThis 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.

Item Open Access Component Modal Analysis of a Folding Wing(2011) Wang, IvanThis 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.

Item Open Access Computational Studies of Buffet and Fluid-Structure Interaction in Various Flow Regimes(2020) Kruger Bastos, Kai MbaliThis dissertation explores a fluid instability known as buffet, which occurs in the subsonic, transonic, and supersonic regimes. Buffet has been observed in experiments and various computational studies, and its underlying physics are not well-established. The goal of this document is to provide insight into various configurations which produce buffet and attempt to understand the flow physics at play.

Item Open Access Convolution and Volterra Series Approach to Reduced Order Modelling of Unsteady Aerodynamic Loads and Improving Piezoelectric Energy Harvesting of an Aeroelastic System(2020) Levin, DaniA 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%.

Item Open Access Distributed Control of Heterogeneous Mobile Robotic Agents in the Presence of Uncertainties(2016) Fricke, Gregory KealohaSwarm robotics and distributed control offer the promise of enhanced performance and robustness relative to that of individual and centrally-controlled robots, with decreased cost or time-to-completion for certain tasks. Having many degrees of freedom, swarm-related control and estimation problems are challenging specifically when the solutions depend on a great amount of communication among the robots. Swarm controllers minimizing communication requirements are quite desirable.

Swarms are inherently more robust to uncertainties and failures, including complete loss of individual agents, due to the averaging inherent in convergence and agreement problems. Exploitation of this robustness to minimize processing and communication complexity is desirable.

This research focuses on simple but robust controllers for swarming problems, maximizing the likelihood of objective success while minimizing controller complexity and specialized communication or sensing requirements.

In addition, it develops distributed solutions for swarm control by examining and exploiting graph theoretic constructs. Details of specific implementations, such as nonholonomic motion and and numerosity constraints, were explored with some unexpectedly positive results.

In summary, this research focused on the development of control strategies for the distributed control of a swarm of robots, and graph-theoretic analysis of these controllers. These control strategies specifically consider probabilistic connectivity functions, based on requirements for sensing or communication. The developed control strategies are validated in both simulation and experiment.

Item Open Access Large Deflection Inextensible Beams and Plates and their Responses to Nonconservative Forces: Theory and Computations(2020) McHugh, Kevin AndrewThere 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.

Item Open Access Linear Aeroelastic Stability of Beams and Plates in Three-Dimensional Flow(2012) Gibbs IV, Samuel ChadThe 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.

Item Open Access Nonlinear Aeroelastic Analysis of Flexible High Aspect Ratio Wings Including Correlation with Experiment(2009) Jaworski, JustinA 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.

Item Open Access On Improving the Predictable Accuracy of Reduced-order Models for Fluid Flows(2020) Lee, Michael WilliamThe proper orthogonal decomposition (POD) is a classic method to construct empirical, linear modal bases which are optimal in a mean L2 sense. A subset of these modes can form the basis of a dynamical reduced-order model (ROM) of a physical system, including nonlinear, chaotic systems like fluid flows. While these POD-based ROMs can accurately simulate complex fluid dynamics, a priori model accuracy and stability estimates are unreliable. The work presented in this dissertation focuses on improving the predictability and accuracy of POD-based fluid ROMs. This is accomplished by ensuring several kinematically significant flow characteristics -- both at large scales and small -- are satisfied within the truncated bases. Several new methods of constructing and employing modal bases within this context are developed and tested. Reduced-order models of periodic flows are shown to be predictably accurate with high confidence; the predictable accuracy of quasi-periodic and chaotic fluid flow ROMs is increased significantly relative to existing approaches.

Item Open Access Stability of Beams, Plates and Membranes due to Subsonic Aerodynamic Flows and Solar Radiation Pressure(2014) Gibbs IV, Samuel ChadThis 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.

Item Open Access The Effect of Wing Damage on Aeroelastic Behavior(2009) Conyers, Howard J.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.