# Browsing by Subject "Aerospace engineering"

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Item Open Access A General-Purpose Simulator for Evaluating Astronaut Radiation Exposure(2021) Houri, Jordan MeirPurpose: Current Monte Carlo simulations modeling space radiation exposure typically use simplistic human phantoms with low anatomical detail and minimal variability in physical characteristics. This thesis describes the development of a GEANT4-based simulation framework (EVEREST – Evaluation of Variable-Environment Radiation Exposure during Space Travel) that incorporates highly realistic and diverse 4D extended cardiac-torso (XCAT) digital phantoms, combined with advanced NASA models of planetary atmospheres, spaceflight trajectories, and space radiation spectra, to evaluate radiation exposure in interplanetary missions and on planetary habitats.

Methods: Galactic cosmic radiation spectra as a function of time and radial distance from the Sun were modeled using the Badhwar-O’Neill 2020 model, while the Van Allen belt spectra were modeled using the AE-8/AP-8 models, and solar particle event spectra could be selected from historical data. The magnetic field input to the AE-8/AP-8 model was generated using the 13th generation International Geomagnetic Reference Field. Planetary atmospheres were modeled using NASA Global Reference Atmospheric Models, which provide mean atmospheric data for any altitude, latitude, longitude, and time, and the effect of Earth’s magnetic field was accounted for using a geomagnetic cutoff rigidity algorithm. Planetary orbits, trajectories, and relative positions of objects in the Solar System were determined using the NAIF SPICE observation geometry information system. Finally, highly detailed extended cardiac-torso (XCAT) digital phantoms were integrated into EVEREST in order to accurately model radiation exposure to individual organs. XCAT phantoms model over 100 segmented structures, range in age from neonate to 78 years, and cover various combinations of height, weight, and BMI. The EVEREST framework itself was designed using a novel lookup table method, in which different stages of particle propagation were divided into separate simulations, which are then convolved in post-processing.

Results: EVEREST was validated against personal radiation dosimeter data collected by the lunar module pilot on the Apollo 15 mission and also flux data from the Mars Science Laboratory Radiation Assessment Detector (RAD). Simulation results were found to agree very well with dosimeter readings by the Apollo 15 command module pilot. Comparison of Martian surface particle fluxes simulated by EVEREST to RAD data demonstrated an agreement to within an order of magnitude, with the best agreement seen for protons, He4, Z=6-8, Z=14-24, and Z>24. Finally, as a proof of concept, EVEREST was used to evaluate radiation exposure to a population of eight XCAT phantoms (3 adult and 1 pediatric, male and female) under three different nominal shielding configurations on the surface of Mars (unshielded, 50 cm thick ice, and 50 cm thick Martian regolith) at four different timepoints during the day (12 am, 6 am, 12 pm, and 6 pm). Using the federal yearly occupational dose limit of 50 mSv (effective dose) as a metric, it was found that the phantoms evaluated would reach this limit within 70.9 – 83.8 days unshielded, 139.2 – 161.2 days with 50 cm ice shielding, and 188.1 – 235.7 days with 50 cm Martian regolith shielding, if terrestrial radiation protection standards were to be applied. The results revealed that the brain receives one of the highest organ doses in the body and that unshielded radiation exposure is lowest at midnight when analyzed across all phantoms. Based on these findings, it is recommended that extra care be taken to provide additional radiation shielding in astronauts’ helmets and that extended forays outside of the habitat be planned for late evening to reduce the biological impact of radiation exposure.

Conclusion: EVEREST is a tested and validated framework for accurate estimation of total body and organ dose in space. EVEREST’s geometric versatility makes it ideal for evaluating doses to diverse populations of XCAT phantoms within different types of planetary habitats and spacecraft, enabling optimization of mission planning with respect to radiation exposure in the near future. The model has currently been validated for Lunar and Martian missions, and the framework can be applied to any space travel mission or planetary mission where the atmospheric models for that planet are available.

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 New Hybrid Free-Wake Model for Wind Turbine Aerodynamics with Application to Wake Steering(2017) Su, KeyeWind energy has emerged as one of the most promising and rapidly growing renewable energy technologies in the United States and over the world. The offshore wind energy is of special interest because it has more consistent and faster wind speed, and is usually close to large population areas that are along the coast. However, wake shielding on offshore wind farms substantially reduces the efficiency of downstream wind turbines due to the interaction with the energy-depleted wakes from upwind turbines. This research considers a method to mitigate the wake shielding effect by tilting the turbine axes upward, which causes streamwise vorticity in the near wake so that the energy depleted wakes transport upward alleviating shielding, and pumping more energetic fluid into downstream turbines.

The wake simulations in this research employ a specially developed hybrid free-wake method for wind turbine wakes, that utilizes Vortex Lattice Method (VLM) for near wake representation with appropriate stall and unsteady models, and Constant Circulation Contours Method (CCCM) for turbine far wake representation with a large degree of downwind vorticity diffusion. This approach has been implemented to capture the natural behavior of multi-filament multi-blade complex turbine wakes in relatively short computation time, with the capability to simulate wake interaction with downstream turbines. It is validated through comparison to two wind tunnel tests, NREL/NASA-Ames Wind Tunnel Test and MEXICO, and two turbine wake numerical models, BEM and QBlade.

The wake steering effect for tilted turbines is verified and the degree of effectiveness is assessed. Detailed turbine wake structure is studied to obtain insights into how to strengthen the steering effect and decrease wake velocity deficit. Inline two turbine simulations where one turbine operates in the wake of the other have been performed to assess the advantage of wake steering in power generation of a system of turbines. Beyond the single rotor tilted turbine, an intermeshed rotor wind turbine configuration, consisting of two partially overlapping counter-rotating rotors, has been studied to assess its potential to strength wake steering effect and to intensify wake deficit recovery. These two turbine configurations are compared along with a discussion of potential advantages and challenges. Several model refinements for more robust turbine wake simulation are under development or considered as future research goals.

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 Aerodynamic Optimization of Helicopter Rotors using a Harmonic Balance Lifting Surface Technique(2018) Tedesco, Matthew BraxtonThis thesis concerns the optimization of the aerodynamic performance of conventional helicopter rotors, given a set of design variables to control the rotor's pitching angle, twist and chord distributions. Two models are presented for use. The lifting line model is a vortex lattice model that uses assumptions on the size and shape of the blade to simplify the model, but is unable to account for unsteady and small aspect ratio effects. The lifting surface model removes these assumptions and allows for a wider variety of accurate solutions, at the cost of overall computational complexity. The lifting surface model is chosen for analysis, and then condensed using static condensation and harmonic balance. The final system is discretized and pertinent values of power, force, and moment calculated using Kelvin's theorem and the unsteady Bernoulli equation. This system is then optimized in one of two ways: using a direct linear solve if possible, or the open source package IPOPT where necessary. The results of single-point and multi-point optimization demonstrate for low speed forward flight, the lifting line model is sufficient for modeling purposes. As the speed of the rotor increases, more unsteady effects become prominent in the system, and therefore the lifting surface model becomes more necessary. When conducting a chord optimization on the rotor, hysteresis effects and local minima are calculated for the non-linear optimization. The global minima within the set of captured local minima can be found through simple data visualization, and the global minima is confirmed to have similar behavior to the results of lifting line; a large spike in induced power at a critical advance ratio, with a sharp decline in induced power as the rotor flies faster. Within the realm of practical forward flight speeds of a conventional rotor, smooth, continuous results are demonstrated.

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 Aeroelastic Modeling of Blade Vibration and its Effect on the Trim and Optimal Performance of Helicopter Rotors using a Harmonic Balance Approach(2020) Tedesco, MatthewThis dissertation concerns the optimization of the aeroelastic performance of conventional

helicopter rotors, considering various design variables such cyclic and higher

harmonic controls. A nite element model is introduced to model the structural

eects of the blade, and a coupled induced velocity/projected force model is used

to couple this structural model to the aerodynamic model constructed in previous

works. The system is then optimized using two separate objective functions: minimum

power and minimum vibrational loading at the hub. The model is validated

against several theoretical and experimental models, and good agreement is demonstrated

in each case. Results of the rotor in forward

ight demonstrate for realistic

advance ratios the original lifting surface model is sucient for modeling normalized

induced power. Through use of the dynamics model the vibrational loading minimization

is shown to be extremely signicant, especially when using more higher

harmonic control. However, this decrease comes at an extreme cost to performance

in the form of the normalized induced power nearly doubling. More realistic scenarios

can be created using multi-objective optimization, where it is shown that vibrational

loading can be decreased around 60% for a 5% increase in power.

Item Open Access Aeroelasticity and Enforced Motion Frequency Lock-in Associated with Non-Synchronous Vibrations in Turbomachinery(2022) Hollenbach III, Richard LeeOne 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.

Item Open Access An Aeroelastic Evaluation of the Flexible Thermal Protection System for an Inflatable Aerodynamic Decelerator(2015) Goldman, Benjamin DouglasThe 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.

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 Design for Coupled-Mode Flutter and Non-Synchronous Vibration in Turbomachinery(2013) Clark, Stephen ThomasThis 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.

Item Open Access Further Reduction of the Fundamental Mistuning Model Using Mistuned Aeroelastic Modes(2018) Quan, AaronDespite 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.

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 Minimum Power Requirements and Optimal Rotor Design for Conventional, Compound, and Coaxial Helicopters Using Higher Harmonic Control(2013) Giovanetti, Eli BattistaThis thesis presents a method for computing the optimal aerodynamic performance of conventional, compound, and coaxial helicopters in trimmed forward flight with a limited set of design variables, including the blade's radial twist and chord distributions and conventional and higher harmonic blade pitch control. The optimal design problem, which is cast as a variational statement, minimizes the sum of the induced and viscous power required to develop a prescribed lift and/or thrust. The variational statement is discretized and solved efficiently using a vortex-lattice technique. We present two variants of the analysis. In the first, the sectional blade aerodynamics are modeled using a linear lift curve and a quadratic drag polar, and flow angles are assumed to be small. The result is a quadratic programming problem that yields a linear set of equations to solve for the unknown optimal design variables. In the second approach, the problem is cast as a constrained nonlinear optimization problem, which is solved using Newton iteration. This approach, which accounts for realistic lift and drag coefficients including the effects of stall and the attendant increase in drag at high angles of attack, is capable of optimizing the blade planform in addition to the radial twist distribution and conventional and higher harmonic blade pitch control. We show that for conventional rotors, coaxial counterrotating rotors, and a wing-rotor compound, using radially varying twist and chord distributions and higher harmonic blade pitch control can produce significant reductions in required power, especially at high advance ratios.

Item Open Access Modeling the Aeroelastic Response of a Cantilevered Plate Using the Vortex Lattice Method and Modal Analysis(2024) Jin, CeceThe creation of an aeroelastic model for a cantilevered plate under a uniform flow is discussed. Starting with solving the aerodynamic load distribution over the plate using the vortex lattice method, this paper continues with discussing a structural model for the nonlinear behavior of an inextensible plate which utilizes the Euler-Lagrange equation and the Rayleigh-Ritz method to derive the equations of motion. The computation model discussed in this thesis couples the vortex lattice method with structural analysis to simulate the aeroelastic response of a thin plate. Computational results are shown which capture the time history of plate deflection at different flow velocities. The development of flutter dynamic’s instability is also observed by mapping limit cycle oscillation amplitudes at varying flow velocities and compared with experimental values from past studies.

Item Open Access Multi-Row Aerodynamic Interactions and Mistuned Forced Response of an Embedded Compressor Rotor(2016) Li, JingThis research investigates the forced response of mistuned rotor blades that can lead to excessive vibration, noise, and high cycle fatigue failure in a turbomachine. In particular, an embedded rotor in the Purdue Three-Stage Axial Compressor Research Facility is considered. The prediction of the rotor forced response contains three key elements: the prediction of forcing function, damping, and the effect of frequency mistuning. These computational results are compared with experimental aerodynamic and vibratory response measurements to understand the accuracy of each prediction.

A state-of-the-art time-marching computational fluid dynamic (CFD) code is used to predict the rotor forcing function. A highly-efficient nonlinear frequency-domain Harmonic Balance CFD code is employed for the prediction of aerodynamic damping. These allow the compressor aerodynamics to be depicted and the tuned rotor response amplitude to be predicted. Frequency mistuning is considered by using two reduced-order models of different levels of fidelity, namely the Fundamental Mistuning Model (FMM) and the Component Mode Mistuning (CMM) methods. This allows a cost-effective method to be identified for mistuning analysis, especially for probabilistic mistuning analysis.

The first topic of this work concerns the prediction of the forcing function of the embedded rotor due to the periodic passing of the neighboring stators that have the same vane counts. Superposition and decomposition methods are introduced under a linearity assumption, which states that the rotor forcing function comprises of two components that are induced by each neighboring stator, and that these components stay unchanged with only a phase shift with respect to a change in the stator-stator clocking position. It is found that this assumption captures the first-order linear relation, but neglects the secondary nonlinear effect which alters each stator-induced forcing functions with respect to a change in the clocking position.

The second part of this work presents a comprehensive mistuned forced response prediction of the embedded rotor at a high-frequency (higher-order) mode. Three steady loading conditions are considered. The predicted aerodynamics are in good agreement with experimental measurements in terms of the compressor performance, rotor tip leakage flow, and circumferential distributions of the stator wake and potential fields. Mistuning analyses using FMM and CMM models show that the extremely low-cost FMM model produces very similar predictions to those of CMM. The predicted response is in good agreement with the measured response, especially after taking the uncertainty in the experimentally-determined frequency mistuning into consideration. Experimentally, the characteristics of the mistuned response change considerably with respect to loading. This is not very well predicted, and is attributed to un-identified and un-modeled effects. A significant amplification factor over 1.5 is observed both experimentally and computationally for this higher-order mode.

Item Open Access Multi-row Aeromechanical and Aeroelastic Aspects of Embedded Gas Turbine Compressor Rotors(2021) hegde, shreyasThis research helps address one of the grand challenges of turbomachinery i.e., the accurate prediction of the forced response in multi-row compressors subjected to various crossings and operating points. Specifically, this focuses on understanding the impact of multi-row interaction on the unsteady aerodynamics and mistuned forced response behavior of a subsonic axial compressor. The phenomena of forced response remain one of the most challenging areas of turbomachinery aeromechanics. This thesis helps address some of the shortcomings in current literature related to unsteady aerodynamics and mistuned forced response predictions. The flow is inherently unsteady due to the complex flow field, blade row interactions, and secondary flows. Predicting the forced response behavior is a challenging task. Blade failures due to aeromechanical problems have resulted in fatalities and severe engine/aircraft damage, with some of the recent incidents being on Air France Flight 66 and Southwest Airlines Flight 1380. The experimental compressor studied herein is the Purdue 3.5 stage compressor, representing the rear stages of a modern high-pressure compressor (HPC). The focus of this research is on the vibratory response of rotor 2 (R2). One interesting feature of this configuration is that three rows have the same vane count i.e., the inlet guide vanes (IGV), stator 1, and stator 2. All contribute to the forcing function simultaneously. Also, the difference in blade count between the embedded R2 and the other rotors is the same. Computational data obtained using a commercial computational fluid dynamics (CFD) code, CFX, and an in-house mistuning response code MISER are compared against experimental data to understand the physical phenomena, determine the predictions' accuracy, and develop methods to improve predictions further. The first part of this research presents results from the torsional mode (1T) and a higher-order mode (1CWB) for the case where the stator count (44) of both neighboring stators is the same. Since both contribute to the forcing simultaneously, wake and potential field effects cannot be easily distinguished. The impact of physical wave reflection from downstream (Rotor 3) and the upstream influence from the IGV is also determined. The influence of operating conditions on the forcing function is also investigated. This is further fed into an in-house mistuning code, which predicts the response of all blades. The computational results are compared with experimental data. Finally, the effect of sideband traveling wave excitations (both amplitude and phase) on the blade response prediction was determined. The second part of the thesis deals with the study extended to a more realistic case in which the stator count of the embedded stators is different. Since the upstream and downstream influences are at different frequencies, we can separate the effects. This creates two torsional mode crossings (1T/44 and 1T/38) at different rotational speeds. Once again, the impact of operating conditions on the forced response behavior and the individual blade responses are determined. Further, this research contributes to the future development of model reduction methods and quantifies the error induced by utilizing model reduction techniques under different circumstances. The third section of the thesis deals with a configuration in which the stator is asymmetric i.e., has a different stator count on either side of the “split line.” The idea of having an asymmetric configuration originated in a NASA report [45] but has received little attention in the literature. Although current literature provides an insight into the steady aerodynamic performance of such configurations, no work to date explains the complex unsteady blade row interactions occurring in such configurations. This research describes the forcing function reduction phenomena due to asymmetry, provides general guidance on modeling techniques for such cases, and investigates possible scenarios and outcomes. The thesis then dives into determining the impact of stator hub cavities on the forced response prediction. Currently, the research on stator hub cavities only involves determining their influence on steady aerodynamics. The current work helps fill up the gap in the literature by determining its influence on unsteady aerodynamics and mistuned blade predictions. The fourth section discusses the impact of hub cavities on the steady flow in multiple locations around the blade passage and the impact of hub cavity flow on the unsteady aerodynamics, which determines the magnitude of the forcing function. The last chapter of the thesis quantifies the individual blade responses for all multi-row cases described in the previous sections. This section also discusses the impact of veering region modes and mode localization on the mistuned response prediction. The idea of perturbing the system mode frequency in a probabilistic manner was introduced in this thesis for the first time. Physical responses and dependencies have never been seen in the literature. The concept of strain energy-based mistuning models was expanded. For the first time in two decades, two new mistuning models were introduced, which were developed under the framework of the FMM. Also, the idea of perturbing structural damping in a probabilistic manner was introduced for the first time in this thesis. This thesis contributes extensively to understanding the various steady and unsteady aerodynamic interactions of multi-row configurations and some of the key findings are: 1. The impact of a downstream rotor (R3) cannot be neglected in forced response computations. The modal force prediction was within 10% accuracy, which was achieved by adding the downstream row. 2. The work also highlights the significance of having a downstream row that does not contribute to the forcing function at the same frequency but acts as a wall to reflect waves, contributing to the forcing. 3. The impact of spurious wave reflections on the forcing function was also quantified. In the absence of non-reflecting boundary conditions, these spurious waves can have a tremendous influence on the forcing function 4. The fidelity of model reductions techniques, particularly the time transformation method, is highlighted. This can not only serve as a guiding tool for the development of methods in the future but also reduce computational time significantly (3-4X reduction) 5. The impact of having an asymmetric stator exciting an embedded rotor was determined at multiple operating conditions. The benefit of asymmetry was limited to how the asymmetric stator excited the embedded rotor and not when any other rows excited the rotor. The asymmetry also results in the creation of sideband excitation responses, the magnitude of which is comparable to the dominant response. Also, the influence of stator hub cavities on the unsteady aerodynamic flow field was quantified, and the modal force prediction was found to improve by 10% for a 3-row case 6. Finally, the mistuned blade response was predicted using the modal forces obtained earlier, system modes obtained computationally, and blade frequencies obtained experimentally. This work contains several new insights into mistuned predictions. The mistuning work described here provides guidance, including sideband traveling wave excitations in the mistuning model. The thesis also introduced the concept of system mode and structural damping perturbations in a probabilistic manner, and the result was found to be deterministic. Several new plotting methods were introduced to represent data in a novel manner. Two new high fidelity strain energy-based mistuning models helped improve the blade response prediction and provided the most accurate date under the FMM framework. This work guides mistuning computations, including the effect of sideband excitations on mistuning parameters.

Item Open Access Non-Synchronous Vibration: Lock-in Region and Unsteady Pressure Analysis on NACA0012 Airfoil(2022) WANG, KECHENGNon-synchronous vibration (NSV) in turbomachinery is a complex phenomenon of interest that has been studied but not yet fully understood. The interaction between fluid dynamic instabilities and natural vibration of the blades are the main reason NSV occurs. When the natural instability frequency/shedding frequency is close to the natural frequency of the body, the system is locked in, namely the shedding frequency “locks in” to the natural frequency of the body, catastrophic turbine or wing failure can potentially occur. The research done in this thesis report consists of both experimental studies performed on a symmetric NACA0012 airfoil in Duke University Subsonic Wind Tunnel and computational studies using Computational Fluid Dynamics software ANSYS Fluent, under various flow and airfoil motion conditions. Utilizing data acquisition system and LabVIEW control software, pressure data along the upper and lower surfaces of the airfoil were collected in time domain and transformed into frequency domain data with Fast Fourier Transform and analyzed in MATLAB. To understand the underlying flow physics and relationships between unsteady pressure contributed by shedding and natural vibration, the region where the two frequencies are locked in is more accurately identified. A preliminary model to predict the unsteady pressure distribution under lock-in condition from unlocked pressure data is defined. The solitary experiments and computational simulations done on NACA0012 airfoil, and the results found in this thesis provide a better understanding of lock-in condition and its relationship to flow conditions and serve as footstone for future studies on other geometries of interest under various flow conditions. The goal of steady/unsteady pressure analysis as part of the research is to visualize the pressure distribution on the surface of the airfoil in both locked-in and unlocked conditions. From the pressure distribution, the lock-in phenomenon can be better understood, as of when and why it occurs, and ultimately, how to avoid it in real-world operations.

Item Open Access Optimal Aerodynamic Design of Conventional and Coaxial Helicopter Rotors in Hover and Forward Flight(2015) Giovanetti, Eli BattistaThis dissertation investigates the optimal aerodynamic performance and design of conventional and coaxial helicopters in hover and forward flight using conventional and higher harmonic blade pitch control. First, we describe a method for determining the blade geometry, azimuthal blade pitch inputs, optimal shaft angle (rotor angle of attack), and division of propulsive and lifting forces among the components that minimize the total power for a given forward flight condition. The optimal design problem is cast as a variational statement that is discretized using a vortex lattice wake to model inviscid forces, combined with two-dimensional drag polars to model profile losses. The resulting nonlinear constrained optimization problem is solved via Newton iteration. We investigate the optimal design of a compound vehicle in forward flight comprised of a coaxial rotor system, a propeller, and optionally, a fixed wing. We show that higher harmonic control substantially reduces required power, and that both rotor and propeller efficiencies play an important role in determining the optimal shaft angle, which in turn affects the optimal design of each component. Second, we present a variational approach for determining the optimal (minimum power) torque-balanced coaxial hovering rotor using Blade Element Momentum Theory including swirl. We show that the optimal hovering coaxial rotor generates only a small percentage of its total thrust on the portion of the lower rotor operating in the upper rotor's contracted wake, resulting in an optimal design with very different upper and lower rotor twist and chord distributions. We also show that the swirl component of induced velocity has a relatively small effect on rotor performance at the disk loadings typical of helicopter rotors. Third, we describe a more refined model of the wake of a hovering conventional or coaxial rotor. We approximate the rotor or coaxial rotors as actuator disks (though not necessarily uniformly loaded) and the wake as contracting cylindrical vortex sheets that we represent as discrete vortex rings. We assume the system is axisymmetric and steady in time, and solve for the wake position that results in all vortex sheets being aligned with the streamlines of the flow field via Newton iteration. We show that the singularity that occurs where the vortex sheet terminates at the edge of the actuator disk is resolved through the formation of a 45 degree logarithmic spiral in hover, which results in a non-uniform inflow, particularly near the edge of the disk where the flow is entirely reversed, as originally hypothesized by previous authors. We also quantify the mutual interference of coaxial actuator disks of various axial spacing. Finally, we combine our forward flight optimization procedure and the Blade Element Momentum Theory hover optimization to form a variational approach to the multipoint aerodynamic design optimization of conventional and coaxial helicopter rotors. The resulting nonlinear constrained optimization problem may be used to map the Pareto frontier, i.e., the set of rotor designs for which it is not possible to improve upon the performance in one flight condition without degrading performance in the other. We show that for both conventional and coaxial rotors analyzed in hover and high speed flight, a substantial tradeoff in performance must be made between the two flight conditions. Finally, computational results demonstrate that higher harmonic control is able to improve the Pareto efficiency for both conventional and coaxial rotors.