<p> The present investigation deals with Gas Turbine Blade Vibrations. Literature on the techniques employed for experimental investigation of gas turbine blade vibration characteristics has been summarised. Various steps have been explained by reviewing the different techniques. Several causes for possible excitation of blades as well as damping methods to suppress the resulting vibrations are also included. Attempts were made to determine experimentally the natural frequencies of cantilever plates of thin uniform rectangular cross section, with and without pretwist. First natural frequency_ -of the plate without twist was in good agreement with the one calculated from the plate formula. Free vibration analysis of cantilever plates of thin uniform rectangular cross section is made. Finite Element Technique is used to determine the elastic and inertial properties of a fully compatible triangular element. Computed values of natural freqencies and mode shapes are compared with other analytical results. </p> / Thesis / Master of Engineering (ME)

The United Nations have declared the effects of climate change as the “defining issue of our time” (United Nations, 2019). As a result of increased industrialization in the last century to keep up with the demands of a growing global population, the global output of greenhouse emissions has rocketed, which is linked to the shifting and abnormal weather patterns of the planet. Electricity and heat production alone are attributed to generating 25% of greenhouse gas emissions (Edenhofer, et al.). To alleviate the increasing levels of carbon emission there is an effort to transition in green energy power generation sources like wind energy that is abundantly available in the midwestern United States. This study aims to implement the Blade Element Method derived modeling methods for predicting the performance of a wind turbine. The experimental results obtained from the MEXICO project is employed as the validation source for the research.

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The advent of advanced vehicle concepts involving Urban Air Mobility (UAM) and small Unmanned Aerial Systems (sUAS) has brought about a new class of rotorcraft technology which operate predominantly in low-Reynolds ($Re$) number regimes. In such regimes, the flow experiences complex boundary layer phenomena like laminar separation, flow transition and reattachment. These effects are known to greatly alter the flow at and near the rotor wall, influencing its aerodynamic performance as well as the noise generated. Capturing these effects in our computational models is necessary to further our understanding of rotor aerodynamics and acoustics. The current study has introduced a novel RANS transition turbulence model, SSG/LRR-$\omega$-$\gamma$, that is capable of modeling different modes of transition involving natural, bypass, separation-induced and crossflow transition. The model framework uses a Reynolds stress transport model, SSG/LRR-$\omega$, as the base turbulence formulation and is coupled with Menter's $\gamma$ transition model. It was validated using a number of canonical cases that exhibited different transition mechanisms and the model performed equivalently or better than existing state-of-the-art transition models. It is worthy to note that the proposed model was able to perform well in three-dimensional flows, demonstrated using the case of a prolate spheroid. This underscores the capability of Reynolds stress models to accurately capture complex flow curvatures, improving upon the capabilities of linear eddy viscosity models. The transition model, integrated into OpenFOAM, was then employed to analyze two different UAV propellers. The rotor flow was examined using a URANS simulation with an overset grid. The objective was twofold: firstly, to validate the predictions generated by the proposed model for low-Reynolds number (low-$Re$) rotors, and secondly, to evaluate its effectiveness across a range of operating conditions. Comparisons were drawn against established fully turbulent and transition models. The analysis showed that transition models in general tended to be consistent in their predictions and less sensitive to changing operating conditions when compared to fully turbulent models. They also demonstrated the ability to accurately predict the mechanisms leading to separation and transition. Further, the proposed transition model demonstrated superior capability in capturing detailed flow features, particularly in the wake, compared to other fully turbulent and transition models, which is attributed to its Galilean invariant framework. To leverage the boundary layer information obtained from the proposed model, a semi-empirical broadband noise prediction method was implemented. This method utilized boundary layer data predicted by URANS simulations to estimate blade self-noise. An evaluation of the fully turbulent $k$-$\omega$ SST model and the proposed transition model revealed that both exhibited reasonable accuracy at lower rotor advance ratios. However, the transition model performed better at higher advance ratios. It was also observed that CFD-based approaches provided superior prediction accuracy compared to lower-fidelity aerodynamic models in the context of blade self-noise prediction Finally, the proposed aerodynamic and acoustic computational framework was applied to a design case study of swept propellers to understand the advantages of blade sweep on rotor aerodynamics and noise. A qualitative analysis of the flow suggested that the swept rotor exhibited lower levels of blade wake interaction compared to the unswept geometry, in line with the experimental observations. / Doctor of Philosophy / Advanced vehicle concepts such as air taxis for Urban Air Mobility (UAM) and other multi-copter applications like drone delivery, reconnaissance, etc. are emerging sectors in aviation that have garnered great industrial as well as academic interest. However, since these vehicles are expected to fly at low altitudes within urban settings, noise mitigation is of particular interest to improve their public acceptance. The vehicle configurations in these applications predominantly comprise of rotorcraft which operate at low Reynolds ($Re$) numbers and tip speeds. These operating conditions introduce complex phenomena like flow transition and separation within the boundary layer that significantly alter their aerodynamic as well as aeroacoustic performance. The current work proposes a novel transition turbulence model that improves prediction of these complex boundary layer mechanisms in low-$Re$ propellers compared to the state-of-the-art. Furthermore, this work establishes a fast broadband noise prediction method by leveraging the detailed flow data from the transition model. The focus of this method is on modeling those propeller noise sources that are directly influenced by the aforementioned boundary layer phenomena (blade self-noise). The noise prediction study revealed that transition models yield consistent predictions across different operating conditions. Finally, a brief design study is conducted using the proposed aerodynamic and acoustic framework to assess the flow dynamics and possible noise mitigation capabilities of a swept propeller.

The turbulent flow through a marine propulsor was experimentally modeled using a large cascade configuration with six 33 cm chord flat plates spanning the entire height of the test section in the Virginia Tech Stability Wind Tunnel. Three-component hot-wire velocity measurements were obtained ahead, throughout and behind both an unstaggered and a 35º staggered cascade configuration with blade spacing and onset turbulence integral scales on the order of the chord. This provided a much needed data-set of much larger Taylor Reynolds number than previous related studies and allowed a thorough investigation of the blade-blocking effects of the cascade on the incident turbulent field. In order to generate the large scale turbulence needed for this study, a mechanically rotating "active" grid design was adopted and placed in the contraction of the wind tunnel at a streamwise location sufficient to cancel out the relatively large inherent low frequency anisotropy associated with this type of grid. The resulting turbulent flow is one of the largest Reynolds number (Reλ &#61627; 1000) homogeneous near-isotropic turbulent flows ever created in a wind tunnel, and provided the opportunity to investigate Reynolds number effects on turbulence parameters, especially relating to inertial range dynamics. Key findings include 1) that the extent of local isotropy is solely determined by the turbulence generator and the size of the wind-tunnel that houses it; and 2) that the turbulence generator operating conditions affect the shape of the equilibrium range at fixed Taylor Reynolds number. The latter finding suggests that grid turbulence is not necessarily self-similar at a given Reynolds number independent of how it was generated. The experimental blade-blocking data was compared to linear cascade theory and showed good qualitative agreement, especially for wavenumbers above the region of influence of the wind tunnel and turbulence generator effects. As predicted, the turbulence is permanently modified by the presence of the cascade after which it remains invariant for a significant downstream distance outside the thin viscous regions. The obtained results support the claim that Rapid Distortion Theory (RDT) is capable of providing reasonable estimates of the flow behind the cascade even though the experimental conditions lie far outside the predicted region of validity. / Ph. D.

There are many limitations to the current methods used to measure vibration on rotating structures. These limitations include physical flow blockages, relating the measurement spot to the structure rotation, data processing issues, and having to physically alter the engine. This work further describes aspects of a self-tracking laser vibrometry system that can be used to measure the vibrations of rotating structures. This method, if setup correctly, has the capability to overcome many of the limitations listed above. A study of all misalignment effects is presented in this thesis. The study consists of a parametric sensitivity analysis of misalignment variables, a parametric Monte Carlo analysis of misalignment variables, and a full interaction Monte Carlo analysis of misalignment variables. In addition, the results of the misalignment variable analyses were used to develop a self-tracker test rig for obtaining fan vibration from a Pratt and Whitney JT15D turbofan engine. A prototype this test rig was designed, built, and tested on the turbofan. It was found that in order to achieve acceptable amounts of position and velocity error using the self-tracker LDV system, very strict alignment of the optical equipment is necessary. Additionally, the alignment criteria can likely be achieved with the use of digitally controlled high precision linear motion equipment. / Master of Science

The interaction of an unsteady wake with a solid body can induce sizable loading of the structure, which has many detrimental side effects in both the structural and acoustic senses. These interactions are ubiquitous in nature and engineering. A flow control technique is sought to mitigate this interaction, thereby decreasing the level of structural vibration. This thesis investigates the effectiveness of steady leading-edge blowing (LEB) flow control for modifying the vortex induced vibrations on an airfoil in the wake of a circular cylinder. The airfoil was allowed to oscillate perpendicular to the fluid flow direction in response to the impinging Von-Karman vortex street. The flow field and airfoil vibrations were simultaneously captured using Digital Particle Image Velocimetry (DPIV) and accelerometer measurements in a time-resolved sense. The results indicate that LEB can significantly reduce the degree of unsteady loading due to the blade vortex interaction (BVI). In some cases, the LEB jet appears to break the coherency of a vortex incident on the airfoil, and in other cases the jet increase the mean stand-off distance of the vortex as it convects over the airfoil surface. It was also found that, for large circular cylinders, if the airfoil is within the mean closure point of the circular cylinder wake, the LEB can increase the level of BVI. The Proper Orthogonal Decomposition (POD) was also used to analyze the DPIV data. POD is mathematically superior for reducing a data rich field into fundamental modes; a suitable basis function for the reduction is chosen mathematically and it is not left to the researcher to pick the basis function. A comparison of the energy in these modes is useful in ascertaining the dynamics of the BVI. For one of the two cases examined with POD, it was found for no LEB the fundamental (i.e. most energetic) mode is given by the vortex shedding of the circular cylinder upstream. The addition of LEB reduces the energy contained in this fundamental mode. Thus the LEB jet has the effect of reducing the flow field coherency; the structure of the large vortices is broken up into smaller vortices. For the other case, the LEB jet has the opposite effect: the jet has the ability to organize the circular cylinder wake into coherent structures. This acts to increase the coherency of the circular cylinder wake and increases the level of BVI. / Master of Science

Increased efficiency and durability of gas turbine components is driven by demands for reduced fuel consumption and increased reliability in aircraft and power generation applications. The complex flow near the endwall of an axial gas turbine has been identified as a significant contributing factor to aerodynamic loss and increased part temperatures. Three-dimensional (non-axisymmetric) contouring of the endwall surface has been shown to reduce aerodynamic losses, but the effect of the contouring on endwall heat transfer is not well understood. This research focused on understanding the general flow physics of contouring and the sensitivity of the contouring to perturbations arising from leakage features present in an engine. Two scaled low-speed cascades were designed for spatially-resolved measurements of endwall heat transfer and film cooling. One cascade was intended for flat and contoured endwall studies without considering typical engine leakage features. The other cascade modeled the gaps present between a stator and rotor and between adjacent blades on a wheel, in addition to the non-axisymmetric endwall contouring. Comparisons between a flat and contoured endwall showed that the contour increased endwall heat transfer and increased turbulence in the forward portion of the passage due to displacement of the horseshoe vortex. However, the contour decreased heat transfer further into the passage, particularly in regions of high heat transfer, due to delayed development of the passage vortex and reduced boundary layer skew. Realistic leakage features such as the stator-rotor rim seal had a significant effect on the endwall heat transfer, although leakage flow from the rim seal only affected the horseshoe vortex. The contours studied were not effective at reducing the impact of secondary flows on endwall heat transfer and loss when realistic leakage features were also considered. The most significant factor in loss generation and high levels of endwall heat transfer was the presence of a platform gap between adjacent airfoils. / Ph. D.