# Browsing by Subject "Turbomachinery"

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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 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 Development of an Efficient Design Method for Non-synchronous Vibrations(2008-04-24) Spiker, Meredith AnneThis research presents a detailed study of non-synchronous vibration (NSV) and the development of an efficient design method for NSV. NSV occurs as a result of the complex interaction of an aerodynamic instability with blade vibrations. Two NSV design methods are considered and applied to three test cases: 2-D circular cylinder, 2-D airfoil cascade tip section of a modern compressor, and 3-D high pressure compressor cascade that encountered NSV in rig testing. The current industry analysis method is to search directly for the frequency of the instability using CFD analysis and then compare it with a fundamental blade mode frequency computed from a structural analysis code. The main disadvantage of this method is that the blades' motion is not considered and therefore, the maximum response is assumed to be when the blade natural frequency and fluid frequency are coincident. An alternate approach, the enforced motion method, is also presented. In this case, enforced blade motion is used to promote lock-in of the blade frequency to the fluid natural frequency at a specified critical amplitude for a range of interblade phase angles (IBPAs). For the IBPAs that are locked-on, the unsteady modal forces are determined. This mode is acceptable if the equivalent damping is greater than zero for all IBPAs. A method for blade re-design is also proposed to determine the maximum blade response by finding the limit cycle oscillation (LCO) amplitude. It is assumed that outside of the lock-in region is an off-resonant, low amplitude condition. A significant result of this research is that for all cases studied herein, the maximum blade response is not at the natural fluid frequency as is assumed by the direct frequency search approach. This has significant implications for NSV design analysis because it demonstrates the requirement to include blade motion. Hence, an enforced motion design method is recommended for industry and the current approach is of little value.Item Open Access Flutter and Forced Response of Turbomachinery with Frequency Mistuning and Aerodynamic Asymmetry(2008-04-25) Miyakozawa, TomokazuThis dissertation provides numerical studies to improve bladed disk assembly design for preventing blade high cycle fatigue failures. The analyses are divided into two major subjects. For the first subject presented in Chapter 2, the mechanisms of transonic fan flutter for tuned systems are studied to improve the shortcoming of traditional method for modern fans using a 3D time-linearized Navier-Stokes solver. Steady and unsteady flow parameters including local work on the blade surfaces are investigated. It was found that global local work monotonically became more unstable on the pressure side due to the flow rollback effect. The local work on the suction side significantly varied due to nodal diameter and flow rollback effect. Thus, the total local work for the least stable mode is dominant by the suction side. Local work on the pressure side appears to be affected by the shock on the suction side. For the second subject presented in Chapter 3, sensitivity studies are conducted on flutter and forced response due to frequency mistuning and aerodynamic asymmetry using the single family of modes approach by assuming manufacturing tolerance. The unsteady aerodynamic forces are computed using CFD methods assuming aerodynamic symmetry. The aerodynamic asymmetry is applied by perturbing the influence coefficient matrix. These aerodynamic perturbations influence both stiffness and damping while traditional frequency mistuning analysis only perturbs the stiffness. Flutter results from random aerodynamic perturbations of all blades showed that manufacturing variations that effect blade unsteady aerodynamics may cause a stable, perfectly symmetric engine to flutter. For forced response, maximum blade amplitudes are significantly influenced by the aerodynamic perturbation of the imaginary part (damping) of unsteady aerodynamic modal forces. This is contrary to blade frequency mistuning where the stiffness perturbation dominates.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 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 Physical Insights, Steady Aerodynamic Effects, and a Design Tool for Low-Pressure Turbine Flutter(2016) Waite, Joshua JosephThe 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.