Combustion instability is a process which involves unsteady chemical kinetic, fluid mechanic, and acoustic processes. It can lead to unstable behavior and be detrimental in ways ranging from faster part fatigue to catastrophic system failure. In terms of combustion methodology, combustion instability has been a key issue for lean premixed combustion. The primary objective of this work is to improve understanding of combustion dynamics through an experimental study of lean premixed combustion using a low swirl combustor. This special burner was developed at the Lawrence Berkeley National Laboratory and has recently received significant interest from the gas turbine industry. In these experiments, acoustic perturbations (chamber modes) are imposed on a low swirl stabilized methane-air flame using loudspeakers. The flame response is examined and quantified with OH planar laser induced fluorescence. Rayleigh index maps of the flame are computed for each frequency and operating condition. Examining the structures in the Rayleigh maps, it is evident that, while the flame shows no significant response in some cases, acoustic forcing in the 70-150 Hz frequency range induces vortex shedding in the flame shear layer. These vortices distort the flame front and generate locally compact and sparse flame areas. This information about the flow field shows that, besides illuminating the combustion dynamics, the Rayleigh index is a useful way to reveal interesting aspects of the underlying flow. The experiments also revealed other interesting aspects of this flame system. It was found that the flame becomes unstable when the perturbation amplitude reaches 0.7% of the mean pressure. Decreasing the swirl number makes the flame shape more jet-like, but does little to alter the shear-layer coupling. In a similar fashion, increasing the pressure was found to alter the flame shape and flame extent, but the thermo-acoustic coupling and induced large scale structure persisted to 0.34MPa, the highest pressure tested.

Rotor-dynamic stability is a very important subject impacting the design, control, maintenance, and operating safety and reliability of rotary mechanical systems. As rotor-dynamic nonlinearities are significantly more prominent at higher rotary speeds, the demand for better and improved performance achievable through higher speeds has rendered the use of a linear approach for rotor-dynamic analysis both inadequate and ineffective. To establish the fundamental knowledge base necessary for addressing the need, it is essential that nonlinear rotor-dynamic responses indicative of the causes of nonlinearity, along with the bifurcated dynamic states of instability, be fully characterized. The objectives of the research are to study the various rotor-dynamic instabilities induced by crack breathing and bearing fluid film forces using a model rotor-bearing system and to investigate the applicability of the fundamental concept of instantaneous frequency for characterizing rotor-dynamic nonlinear responses. A comprehensive finite element model incorporating translational and rotational inertia, bending stiffness and gyroscopic moment is developed. The intrinsic modes extracted using the Empirical Mode Decomposition along with their instantaneous frequencies resolved using the Hilbert transform are applied to characterize the inception and progression of bifurcations suggestive of the changing rotor-dynamic state and impending instability. The dissertation presents and demonstrates an effective approach that integrates nonlinear rotor-dynamics, instantaneous time-frequency analysis, advanced notions of dynamic system diagnostics and numerical modeling applied to the detection and identification of sensitive variations indicative of a bifurcated dynamic state. All presented studies on rotor response subjected to various system configurations and ranges of parameters show good agreements with published results. Under the influence of crack opening, the rotor-bearing model system displays transitional behaviors typical of a nonlinear dynamic system, going from periodic to period-doubling, chaotic to eventual failure. When film forces are also considered, the model system demonstrates very different behaviors and failures from different settings and ranges of control parameters. As a result, a dynamic failure curve differentiating zones of stability and bifurcated instability from zones of dynamic failure is constructed and proposed as an alternative to the traditional stability chart. Observations and results such as these have important practical implications on the design and safe operation of high performance rotary machinery.

Internal friction has been known to be a cause of whirl instability in built-up rotors since the early 1900's. This internal damping tends to make the rotor whirl at shaft speeds greater than a critical speed, the whirl speed usually being equal to the critical speed. Over the years of research, though models have been developed to explain instabilities due to internal friction, its complex and unpredictable nature has made it extremely difficult to come up with a set of equations or rules that can be used to predict instabilities accurate enough for design. This thesis deals with suggesting improved methods for predicting the effects of shrink fits on threshold speeds of instability. A supporting objective is to quantify the internal friction in the system by measurements. Experimental methods of determining the internal damping with non-rotating tests are investigated, and the results are correlated with appropriate mathematical models for the system. Rotating experiments were carried out and suggest that subsynchronous vibration in rotating machinery can have numerous sources or causes. Also, subsynchronous whirl due to internal friction is not a highly repeatable phenomenon.

The tube hydroforming process has gained increasing attention in recent years. Coordination of the internal pressurization and axial feeding curves is critical in the tube hydroforming process to generate successful parts without fracture or wrinkling failure. The stress state at a given time and location varies with the process history and the design and control of the load paths. A new process parameter, counter-pressure, is introduced to achieve a favorable tri-axial stress state during the deformation process. The new process is referred to as dual hydroforming. The benefits offered by dual hydroforming will be characterized based upon the amount of wall thinning, plastic instability limit and final bulged configuration. An analytical model is developed to analyze the stress and strain state in the part (tube) during the dual hydroforming process. The stress-strain condition analyzed will be used to evaluate and compare thinning for tube hydroforming and dual hydroforming. The effect of applying counter-pressure on the plastic instability of thin-walled tubes with only internal pressure and combination of internal pressure and independent axial loading is considered. Finite element analysis is used to quantify the merits of dual hydroforming in terms of final bulged configuration. A parametric study has been conducted to investigate the effectiveness of dual hydroforming based on the various material properties and process conditions. Dual hydroforming results in different stress and strain states compared to tube hydroforming. The counter-pressure enabled favorable tri-axial stress state during deformation that resulted in different thickness and percentage thinning. Finite element analysis showed that for a particular amount of wall thinning there is an increase of around 8% in bulge height for dual hydroforming. Dual hydroforming delays the onset of plastic instability. This increase in the value of effective strain to failure results in an increase of around 12% in bulge height for dual hydroforming as shown by finite element simulations. Results of this study indicate that dual hydroforming can increase expansion i.e. more difficult parts can be designed and manufactured. Also, for a given part geometry, higher strength and less formable materials can be used.

Rotor-dynamic stability is a very important subject impacting the design, control, maintenance, and operating safety and reliability of rotary mechanical systems. As rotor-dynamic nonlinearities are significantly more prominent at higher rotary speeds, the demand for better and improved performance achievable through higher speeds has rendered the use of a linear approach for rotor-dynamic analysis both inadequate and ineffective. To establish the fundamental knowledge base necessary for addressing the need, it is essential that nonlinear rotor-dynamic responses indicative of the causes of nonlinearity, along with the bifurcated dynamic states of instability, be fully characterized. The objectives of the research are to study the various rotor-dynamic instabilities induced by crack breathing and bearing fluid film forces using a model rotor-bearing system and to investigate the applicability of the fundamental concept of instantaneous frequency for characterizing rotor-dynamic nonlinear responses. A comprehensive finite element model incorporating translational and rotational inertia, bending stiffness and gyroscopic moment is developed. The intrinsic modes extracted using the Empirical Mode Decomposition along with their instantaneous frequencies resolved using the Hilbert transform are applied to characterize the inception and progression of bifurcations suggestive of the changing rotor-dynamic state and impending instability. The dissertation presents and demonstrates an effective approach that integrates nonlinear rotor-dynamics, instantaneous time-frequency analysis, advanced notions of dynamic system diagnostics and numerical modeling applied to the detection and identification of sensitive variations indicative of a bifurcated dynamic state. All presented studies on rotor response subjected to various system configurations and ranges of parameters show good agreements with published results. Under the influence of crack opening, the rotor-bearing model system displays transitional behaviors typical of a nonlinear dynamic system, going from periodic to period-doubling, chaotic to eventual failure. When film forces are also considered, the model system demonstrates very different behaviors and failures from different settings and ranges of control parameters. As a result, a dynamic failure curve differentiating zones of stability and bifurcated instability from zones of dynamic failure is constructed and proposed as an alternative to the traditional stability chart. Observations and results such as these have important practical implications on the design and safe operation of high performance rotary machinery.

The objective of this dissertation is to analytically model a parallel plate electrostatic actuator operating in a liquid electrolyte and experimentally verify the analysis. The model assumes the system remains in thermodynamic equilibrium during actuation, which enables the ion mass balance equations and Guass’ Law to be combined into the Poisson-Boltzmann equation. The governing equations also include the linear momentum equation including the following forces: the electric force, the osmotic force, the spring force, the viscous damping force, and the van der Waals force. Equations are also derived for the energy stored in the actuator. The analytical results emphasize the stored energy at mechanical equilibrium and the voltage versus electrode separation behavior including the instability. The analytical results predict that the system may not be a good actuator because the displacement has a very limited stable range, although the actuator would be suitable for bistable applications. The experiment consisted of a fixed flat gold electrode and a movable gold electrode consisting of a gold sphere several micrometers in diameter mounted on the end of an Atomic Force Microscope (AFM) cantilever, which serves as the spring. The electrodes were separated by approximately 100nm of 1mM NaCl aqueous solution. The analytical results were not verified by the experiment. Relative to the analysis, the experiments did not show distinct critical points, and the experiments showed less electrode separation for a given applied electric potential. The experiments did show points at which the electrode separation versus electric potential rapidly changed slope, which may be instability points. It is suggested that this phenomenon may be due to coalesced gas bubbles on hydrophobic regions of the electrode surfaces, which are not included in the model. Although clean gold surfaces are hydrophilic, gold surfaces may become hydrophobic due to impurities.

The Republic of Moldova: The very existence of this country is not widely known around the world, especially in the United States. When mentioning the country in an international context, journalists and political leaders refer to Moldova’s status as Europe’s poorest country, its two-year struggle to elect a president, or its breakaway region of Transnistria. In a reemerging Russia, however, the Republic of Moldova is of considerable strategic importance. Because of Moldova’s geographic location and ethnic make-up, Russia has a genuine interest in ensuring that Moldova maintains the status quo and continues to be a poor, divided, and weak state. Based on the lack of a national identity, an absent economy, and a struggling government; it is questionable whether or not Moldova should be an independent state in the first place. This report will argue that despite attractive prospects for Moldova to unite with Romania or integrate into the European Union, Russia will ensure that it remains an independent, yet divided country. / text

In this thesis we explore the relationship between aeroelastic flutter and multiparameter spectral theory. We first introduce the basic concept of the relationship between these two fields in abstract terms. Then we expand on this initial concept, using it to devise visualisation methods and a wide variety of solvers for flutter problems. We assess these solvers, applying them to real-life aeroelastic systems and measuring their performance. We then discuss and devise methods for improving these solvers. All our conclusions are supported by a variety of evidence from numerical experiments. Finally, we assess all of our methods, providing recommendations as to their use and future development. We do achieve several things in this thesis which have not been achieved before. Firstly, we solved a non-trivial flutter problem with a direct solver. The only direct solvers that have previously been presented are those that arise from classical flutter analysis, which applies only to very simple systems. Secondly, and as an extension of this first point, we solved a system with Theodorsen aerodynamics (approximated by a highly accurately) with a direct solver. This was achieved in an industrially competitive time (0.2s). This has never before been achieved. Thirdly, we solved an unstructured multiparameter eigenvalue problem. Unstructured problems have not been considered before, even in theoretical literature. This result is thus of significance both for multiparameter spectral theory and aeroelasticity. However, the single most important contribution of this thesis is the opening of a whole new field of study which stretches beyond aeroelasticity and into other industries: the treatment of instability problems using multiparameter methods. This field of research is wide and untrodden, and has the potential to change the way we analyse instability across many industries.

Explosions are a common phenomena in the Universe. Beginning with the Big Bang, one could say the history of the Universe is narrated by a series of explosions. Yet no matter how large, small, or complex, all explosions occur through a series of similar physical processes beginning with their initiation to their dynamical interaction with the environment. Of particular interest to this study is how these processes are modified in a magnetized medium. The role of the magnetic field is investigated in two scenarios. The first scenario addresses how a magnetic field alters the propagation of a gaseous detonation where the application of interest is the modification of a condensed-phase explosion. The second scenario is focused on the aftermath of the explosion event and addresses how fluid mixing changes in a magnetized medium. A primary focus of this thesis is the development of a numerical tool capable of simulating explosive phenomenon in a magnetized medium. While the magnetohydrodynamic (MHD) equations share many of the mathematical characteristics of the hydrodynamic equations, numerical methods developed for the conservation equations of a magnetized plasma are complicated by the requirement that the magnetic field must be divergent free. The advantages and disadvantages of the proposed method are discussed in relation to explosion applications.

The Richtmyer-Meshkov instability is studied in vertical shock tube experiment. The instability is initiated by the passage of an incident shock wave over an interface between two dissimilar gases. The interface is formed by opposed gas flows in which air and SF₆ enter the shock tube from the top and from the bottom of the shock tube driven section. The gases exit the test section through a series of small holes in the test section side walls, leaving behind a flat, diffuse membrane-free interface at that location. Random three-dimensional perturbations are imposed on the interface by oscillating the column of gases in the vertical direction, using two loud speakers mounted in the shock tube wall. The development of the turbulent mixing is observed as a result of the shock-interface interaction. The flow is visualized using planar Mie scattering in which the light from a laser sheet is scattered by smoke particles seeded in one of the experimental gases and image sequences are captured using high-speed CMOS cameras. The primary interest of the study is the determination of the growth rate of the turbulent mixing layer that develops after an impulsive acceleration of the perturbed interface between the two gases (air/SF₆) by a weak M=1.2 incident shock wave. Measurements of the mixing layer width following the initial shock interaction show a power law growth h ~ tᶿ similar to those observed in previous experiments and simulations with θ ~ 0.40. The experiments reveal that the growth rate of the mixing width significantly varies from one experiment to another. This is attributed to the influence of initial perturbations imposed on the interface. However, better consistency for the mixing layer growth rate is obtained from the mixing generated by the reflected shock wave. A novel approach that is based on mass and linear momentum conservation laws in the moving reference frame leads to a new definition of the spike and bubble mixing layer widths, which does not depend on the initial conditions.