Control of vortex-driven instabilities was demonstrated via a scaled-down, cold-flow simulation that modeled closed-end acoustics. When vortex shedding frequencies couple with the natural acoustic modes of a choked chamber, potentially damaging low-frequency instabilities may arise. Although passive solutions can be effective, an active control solution is preferable. An experiment was performed to demonstrate an active control scheme for the reduction of vortex-driven oscillations. A non-reacting experiment using a primary flow of air, where both the duct exit and inlet are choked, simulated the closed-end acoustics. Two plates, separated by 1.27 cm, produced the vortex shedding phenomenon at the chamber's first longitudinal mode. Two active control schemes, closed-loop and open-loop, were studied via a cold-flow simulation for validating the effects of reducing vortex shedding instabilities in the system. Actuation for both control schemes was produced by using a secondary injection method. The actuation system consisted of pulsing compressed air from a modifed, 2-stroke model airplane engine, controlled and powered by a DC motor. The use of open-loop only active control was not highly effective in reducing the amplitude of the first longitudinal acoustic mode, near 93 Hz, when the secondary injection was pulsed at the same modal frequency. This was due to the uncontrolled phasing of the secondary injection system. A Pulse Width Modulated (PWM) signal was added to the open-loop control scheme to correct for improper phasing of the secondary injection flow relative to the primary flow. This addition allowed the motor speed to be intermittently increased to a higher RPM before returning to the desired open-loop control state. This proved to be effective in reducing the pressure disturbance by approximately 46%. A closed-loop control scheme was then test for its effectiveness in controlling the phase of the secondary injection. Feedback of the system's state was determined by placing a dynamic pressure transducer near the chamber exit. Closed-loop active control, using the designed secondary injection system, was proven as an effective means of reducing the problematic instabilities. A 50% reduction in the FFT RMS amplitude was realized by utilizing a Proportional-Derivative controller to modify the phase of the secondary injection.

Modern gas turbine designs often include lean premixed combustion for its emissions benefits; however, this type of combustion process is susceptible to self-excited combustion instabilities that can lead to damaging heat loads and system vibrations. This study focuses on identifying a mechanism of combustion instability of a reacting jet in cross flow, a flow feature that is widely used in the design of gas turbine combustion systems. Experimental results from a related study are used to validate and complement three numerical tools that are applied in this study – self-excited Large Eddy Simulations, 3D thermoacoustic modeling, and 1D instability modeling. Based on the experimental and numerical results, a mechanism was identified that included a contribution from the jet in cross flow impedance as well as an overall jet flame time lag. The jet impedance is simply a function of the acoustic properties of the geometry while the flame time lag can be separated into jet velocity, equivalence ratio, and strain fluctuations, depending on the operating conditions and setup. For the specific application investigated in this study, it was found that the jet velocity and equivalence ratio fluctuations are important, however, the effect of the strain fluctuations on the heat release are minimal due to the high operating pressure. A mathematical heat release model was derived based on the proposed mechanism and implemented into a 3D thermoacoustic tool as well as a 1D instability tool. A three-point stability trend observed in the experimental data was correctly captured by the 3D thermoacoustic tool using the derived heat release model. Stability maps were generated with the 1D instability tool to demonstrate regions of stable operation that can be achieved as a function of the proposed mechanism parameters. The relative effect of the reacting jet in cross flow on the two dominant unstable modes was correctly captured in the stability maps. While additional mechanisms for a reacting jet in cross flow are possible at differing flow conditions, the mechanism proposed in this study was shown to correctly replicate the stability trends observed in the experimental tests and provides a fundamental understanding that can be applied for combustion system design.

In this thesis we apply linear feedback control to spatially evolving flows in order to minimize disturbance growth. The dynamics is assumed to be described by the linearized Navier--Stokes equations. Actuators and sensor are designed and a Kalman filtering technique is used to reconstruct the unknown flow state from noisy measurements. This reconstructed flow state is used to determine the control feedback which is applied to the Navier--Stokes equations through properly designed actuators. Since the control and estimation gains are obtained through an optimization process, and the Navier--Stokes equations typically forms a very high-dimensional system when discretized there is an interest in reducing the complexity of the equations. One possible approach is to perform Fourier decomposition along (almost) homogeneous spatial directions and another is by constructing a reduced order model by Galerkin projection on a suitable set of vectors. The first strategy is used to control the evolution of a range of instabilities in the classical family of Falkner--Skan--Cooke flows whereas the second is applied to a more complex cavity type of geometry. / QC 20101122

The applications of inflatable membrane structures are increasing rapidly in the various fields of engineering and science. The geometric, material, force and contact non-linearities complicate this subject further, which in turn increases the demand for computationally efficient methods and interpretations of counter-intuitive behaviors noted by the  scientific community. To understand the complex behavior of membranes in biological and medical engineering contexts, it is necessary to understand the mechanical behavior of a membrane from a physics point of view.  The first part of the  present work studies the pre-stretched circular membrane in contact with a soft linear substrate. Adhesive and frictionless contact conditions are considered during inflation, while only adhesive contact conditions are considered during deflation. The peeling of membrane during deflation is studied, and a numerical formulation of the energy release rate is proposed. It is observed that the pre-stretch is having a considerable effect on the variation of the energy release rate. In the second part, free and constrained inflation of a cylindrical membrane is investigated. Adhesive and frictionless contact conditions are considered between the membrane and substrate. It is observed that the continuity of principal stretches and stresses depend on contact conditions and the inflation/deflation phase. The adhesive traction developed during inflation and deflation arrests the axial movement of material points, while an adhesive line force created at the contact boundary is responsible for a jump in stretches and stresses at the contact boundary. The pre-stretch produces a softening effect in free and constrained inflation of cylindrical membranes. The third part of the thesis discusses the instabilities observed for fluid containing cylindrical membranes. Both limit points and bifurcation points are observed on equilibrium branches. The secondary branches emerge from bifurcation points, with their directions determined by an eigen-mode injection method. The occurrence of critical points and the stability of equilibrium branches are determined by perturbation techniques. The relationship between eigenvalue analysis and symmetry is highlighted in this part of the thesis. / <p>QC 20150227</p>

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<p>Different techniques have been employed through the years to predict hydrodynamic instabilities on high speed liquid jets. In this work, a local linear stability analysis (LSA) has been chosen to estimate streamwise wavelengths on the jet surface near the jet exit.  Data for 0.24 to 0.5 diameters downstream in a high speed water jet issuing into air, given by Reynolds number based momentum thickness between 240 and 600, for validation of the method.  </p> <p>The hypothesis is: near the exit of the jet nozzle, for high speed liquid jets, the local velocity profile evolves based on the momentum thickness and, because of large inertia effects, the flow may be considered as inviscid for instability purposes. Therefore, the approach in this work is based on the Rayleigh equation and with the momentum thickness scaling, both non-dimensional and dimensional values of the most unstable wavelengths are obtained.</p> <p>The key aspect of the  approach is the relevance of the momentum thickness as the scaling factor for calculation purposes on dimensional values of wavelengths.</p> <p>Also, a hyperbolic tangent velocity profile is assumed for the Linear Stability Analysis based on the Rayleigh equation. Numerical restrictions and comparisons, using the Riccati transformation, are specified and described in detail to generalize this approach.</p> <p>Results show that analytical estimates of the most unstable streamwise wavelengths are close to the experimental measurements published by Portillo et al. in 2011.  The agreement using this new approach is often within the experimental uncertainty.</p> <p><br></p>

Fingering instabilities can be observed when studying many different phenomena and display elegant pattern formation. Adhesion-induced fingering instabilities, discovered in the early 2000s, are instability patterns that arise when elastic films are sandwiched between two rigid surfaces. In this thesis we investigate this adhesion-induced fingering instability in thin elastic films. This work builds upon previous research into this instability. Experiments based on studies in the literature were performed to further examine past results; general scaling rules were confirmed, but discrepancies between current and past data show that there is still much to understand theoretically. We also perform novel experiments to elucidate the effects of strain on the instability pattern. It is found that the pattern aligns with the direction of strain in a thin film. We provide a theoretical model to explain this result. / Thesis / Master of Science (MSc)