Browsing by Author "Kielb, Robert E"

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.

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

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

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

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

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

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

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

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

This 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.

This 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.

This dissertation presents an investigation of the complex aeromechanical phenomena in a multi-stage turbomachinery. As a major component of the inter-disciplinary design, aeromechanical study demonstrates the interaction of fluid and structure within turbomachines. The non-uniformity or the unsteadiness of the flow interacts with the bladed disks, causing vibrations of blades. As the integrity of the machine is at stake when vibrations are at presence, it is critical to understand the mechanism of aeromechanics behaviors of a turbomachine.

The research is conducted with computational methods on the Purdue 3.5-stage Compressor test facility. The prediction is compared against experimental aerodynamic data and vibratory response measurement data to uncover the interaction among different aeromechanics phenomena and the key drivers influencing the prediction of forced response. Both frequency-domain and time-domain computational methods are used in this study.

The first part of the study addresses the interaction of forced response and flutter. A quasi-3D stator-rotor configuration is selected for this study. The influence from flutter to forced response is observed: a one-way crosstalk at forced response frequency is observed, presented as the anomaly of unsteady velocity and unsteady pressure near the rear section of rotor blades and in the rotor wake region. The anomaly is speculated as the presence of increasing intensity of shedding vortices induced by the vibration of the blade. To further test the impact of this viscous effect, a numerical experiment is performed with inviscid rotor blades. In contrast to the crosstalk at forced response frequency, no obvious influence on the unsteady behavior is detected at the flutter frequency, and this observation is confirmed at multiple vibration amplitudes. Considering the relationship between unsteady pressure at flutter frequency and aerodynamic damping, we conclude the influence of forced response on the aerodynamic damping is negligible. In addition, a linearity of unsteady pressure at the flutter frequency vs. vibration amplitude is uncovered.

The second part of the study demonstrates the influence of the spurious of wave reflections when using reflecting boundary conditions and including the wake from the non-adjacent stator row. The aim is to provide an accurate prediction of forced response with the least computational effort. Previous research indicates that by reducing the computation domain from 7-row to a 3-row stator-rotor-stator (S1-R2-S2) configuration, the forcing function is over-predicted by 80%. To address this over-prediction, an investigation of boundary conditions and a study with additional rows are conducted. The influence of reflecting boundary conditions on the blade modal force is studied by preventing wave reflection. Additionally, a 5-row simulation is studied to take an extra source of excitation force, the IGV row with the same blade count as the other stators, into consideration. Three conclusions are drawn from this study: 1) boundary reflection has a significant influence on unsteady simulation and the modal force, thus should be avoided by using mesh treatment at both up- and down-stream; 2) the IGV wake mildly contributes to the forcing function but cannot be ignored; 3) the clocking feature of IGV, S1, and S2 renders the excitation energy transferred from 1st harmonic to other higher harmonics.

The third part of the study examines the physical wave reflections from blade rows in the compressor. When waves propagate through the compressor, the blade rows serve as “walls” with partial admission and will reflect waves. Those physical reflecting waves might interact with the original excitations and influence the results. The aim is to understand the significance of the physical wave reflections, and test the necessity of including the rows that are not directly contribute to the generation of excitations. By including the downstream R3 in the 4-row simulations (S1-R2-S2-R3), better prediction of the 1T-44EO forcing function is achieved. The rotor reflection contributes to about 30% of resulting modal force. By modifying the blade counts of S1, the forcing generated from up- and downstream of the imbedded rotor are separated and studied at the associated frequencies. Stator wave reflections are identified, which can contribute to to 30-50% of forcing function. Three conclusions are drawn from this study: 1) For a mistuned forced response, the averaged response should be used for as an indicator of the forcing function. 2) The reflecting waves from the downstream rotor create a destructive interference with the original excitations and increase the forcing, whereas the adjacent up- and downstream stators, both create constructive wave reflections. 3) When simulating a blade row sandwiched by two stators, even if the blade counts are not the same and gives excitations at different frequencies, it is still necessary to include both rows in the simulation, as the physical wave reflections are not simulated in 2-row cases.

This dissertation provides a guidance of forced response and flutter modeling, and the distilled computation principles can be employed for industrial analysis in practice.

Non-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.

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

In this work the interaction of flutter-a self-excited self-sustained aeroelastic vibration phenomenon-with wake excitation is investigated using a harmonic balance frequency domain CFD code to solve the 2D inviscid Euler equations for a rotor in choke flutter operation. The wake deficit and the blade-motion amplitude (torsion) are varied.