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This dissertation presents a formulation of the Continuous Sensitivity Equation Method (CSEM) applied to the Computational Fluid Dynamics (CFD) simulation of thermoacoustic instability problems. The proposed sensitivity analysis approach only requires a single run of the CFD simulation. Moreover, the sensitivities of field variables, pressure, velocity and temperature to boundary-condition parameters are directly obtained from the solution to sensitivity equations. Thermoacoustic instability is predicted by the Rayleigh criterion. The sensitivity of the Rayleigh index is computed utilizing the sensitivities of field variables. The application of the CSEM to thermoacoustic instability problems is demonstrated by two classic examples. The first example explores the effects of the heated wall temperature on the one-dimensional thermoacoustic convection. The sensitivity of the Rayleigh index, which is the indicator of thermoacoustic instabilities, is computed by the sensitivity of field variables. As the heat wall temperature increases, the sensitivity of the Rayleigh index decreases. The evolution from positive to negative sensitivity values suggests the transition from a destabilizing trend to stabilizing trend of the thermoacoustic system. Thermoacoustic instabilities in a self-excited Rijke tube are investigated following the relatively simple thermoacoustic convection problem. The complexity of simulating the Rijke tube increases in both dimensions and mechanisms which incorporate the species transport process and chemical reactions. As a representative model of the large lean premixed combustor, Rijke tube has been extensively studied. Quantitative sensitivity analysis sets the present work apart from previous research on the prediction and control of thermoacoustic instabilities. The effects of two boundary-condition parameters, i.e. the inlet mass flow rate and the equivalence ratio, are tested respectively. Small variations in both parameters predict a rapid change in sensitivities of field variables in the early stage of the total time length of 1.2s. The sensitivity of the Rayleigh index "blows up" at a specific time point of the early stage. In addition, variations in the inlet mass flow rate and the equivalence ratio lead to opposite effects on the sensitivity of the Rayleigh index. There exist some common findings on the application of the CSEM. For both thermoacoustic problems, the sensitivities of field variables and the Rayleigh index exhibit oscillatory nature, confirming that thermoacoustic instability is an overall effect of the coupling process between fluctuations of pressure and heat release rate. All the sensitivities of the Rayleigh index show rapid changes and "blow up" in the early stage. Although the numerical errors could influence the fidelity of computational results, it is believed that the rapid changes reflect the susceptibility to thermoacoustic instabilities in the studied systems. It should also be noted that the sensitivities are obtained for small variations in influential parameters. Therefore, the resulting sensitivities do not predict the occurrence of thermoacoustic instabilities under a condition that is far from the reference state determined by either CFD simulation results (employed in this dissertation) or experimental data. The sensitivity solver developed for the present research has the feature of flexibility. Additional mechanisms and more complicated instability criteria could be easily incorporated into the solver. Moreover, the sensitivity equations formulated in this dissertation are derived from the full set of nonlinear governing equations. Therefore, it is possible to extend the use of the sensitivity solver to other CFD problems. The developed sensitivity solver needs to be optimized to gain better performance, which is considered to be the primary future work of this research. / Ph. D.

In the first part of this work, instability is correctly predicted for a Rijke tube with a new two-term acoustic forcing term derived from a one-dimensional flame dynamics model. The new two-term acoustic forcing term, which is comprised of the summation of chemical heat release rate and heat transfer due to convection, correctly predicts instability where older models of acoustic forcing based solely on chemical heat release rate incorrectly predicted stability. This stability analysis correctly predicts the inlet conditions of the instability in addition to the frequency of instability. In the second part of this work, networks of dynamic well-stirred reactors are used to model qualitative behavior observed in turbulent combustion. First a model of dynamic well-stirred reactor is derived, and then several reactors are coupled together by recirculation. The dynamics of the various models are computed and assessed. The models exhibit interesting behavior that has been viewed experimentally including hysteresis and peaking in the dynamic response. / Master of Science

Thermoacoustic instabilities in gas turbine operation arise due to unsteady fluctuations in heat release coupled with acoustic oscillations, often caused by varying equivalence ratio perturbations within the flame field. These instabilities can cause irreparable damage to critical turbine components, requiring an understanding of the spatial/temporal variations in equivalence ratio values to predict flame response. The technique of computed tomography for flame chemiluminescence emissions allows for 3D spatially resolved flame measurements to be acquired using a series of integral projections (camera images). High resolution tomography reconstructions require a selection of projection angles around the flame, while captured chemiluminescence of radical species intensity fields can be used to determine local fuel-air ratios. In this work, a tomographic reconstruction algorithm program was developed and utilized to reconstruct the intensity fields of CH* and OH*, and these reconstructions were used to quantify local equivalence ratios in an acoustically forced flame. A known phantom function was used to verify and validate the tomography algorithm, while convergence was determined by subsequent monitoring of selected iterative criteria. A documented method of camera calibration was also reproduced and presented here, with suggestions provided for future calibration improvement. Results are shown to highlight fluctuating equivalence ratio trends while illustrating the effectiveness of the developed tomography technique, providing a firm foundation for future study regarding heat release phenomena. / Master of Science / Acoustic sound amplification occurs in the combustion chamber of a gas turbine due to the machine ramping up in operation. These loud sound oscillations continue to grow larger and can damage the turbine machinery and even threaten the safety of the operator. Because of this, many researchers have attempted to understand and predict this behavior in hopes of ending them altogether. One method of studying these sound amplifications is looking at behaviors in the turbine combustion flame so as to potentially shed light on how these large disturbances form and accumulate. Both heat release rate (the steady release of energy in the form of heat from a combustion flame) and equivalence ratio (the mass ratio of fuel to air burned in a combustion process) have proven viable in illustrating oscillatory flame behavior, and can be visualized using chemiluminescence imaging paired with computed tomography. Chemiluminescence imaging is used to obtain intensity fields of species from high resolution camera imaging, while computed tomography techniques are capable of reconstructing these images into a three-dimensional volume to represent and visualize the combustion flame. These techniques have been shown to function effectively in previous literature and were further implemented in this work. A known calibration technique from previous work was carried out along with reconstructing a defined phantom function to show the functionality of the developed tomography algorithm. Results illustrate the effectiveness of the tomographic reconstruction technique and highlight the amplified acoustic behavior of a combustion flame in a high noise environment.

This thesis describes the coincident prediction and observation of thermo-acoustic instabilities in a turbulent, swirl-stabilized research combustor using a stability model constructed from validated reduced-order component models. The component models included the acoustic response to flame heat release rate at various locations in the combustor, the turbulent diffusion of uneven fuel-air mixing, and the flame's response to perturbations in both inlet velocity and equivalence ratio. These elements are closed in a system-level model to reflect their natural dynamic coupling and assessed with linear stability criteria. The results include the empirical validation of each of the component models and limited validation of the total closed-loop model with a lean premixed gaseous fuel combustor not dissimilar to an industrial burner. The degree of agreement between the predictions and the measurements encourages the conclusion that the reduced-order technique described herein not only includes the relevant physics, but has characterized them with sufficient acuracy to be the basis for design techniques for the passive avoidance of thermo-acoustic instabilities. / Master of Science

The Morton Effect in the rotor - bearing systems may lead to an unstable operation. Up to the present, most of the established research efforts have been focused on the overhung rotor systems. In this dissertation, a systematic study on the Morton Effect induced instability in mid-span rotor systems is presented. First, the mechanism study is conducted. The simplified rotor models with isotropic linear bearing supports are adopted for the derivation of analytical expressions. The threshold speeds of instability in simple forms are obtained for the systems with the thermal imbalance acting concurrent with or perpendicular to the direction of the response displacement. For a perspective view of the system stability, a stability map for the damped rigid mid-span rotors with the thermal imbalance having arbitrary phase difference has been generated. It shows that the stable operating regions of the system are bounded by two curves of threshold of instability. The results show that the Morton Effect induced instability thresholds are actually affected by both the magnitude and relative phase of the thermal imbalance. The mechanism of the Morton Effect induced thermal instability of mid-span rotors supported by linear isotropic bearings can be explained through the fact that the Morton Effect introduces either negative stiffness or negative cross-coupled stiffness. Next, the steady-state response performance under the influence of the Morton Effect is discussed. The results show that the Morton Effect has a comprehensive impact on both the amplitude and phase lag of the steady-state unbalance response. It may shift both curves in a manner dependent on the relative magnitude and direction of the thermal imbalance. Then, the mid-span rotors supported by the hydrodynamic journal bearings are analyzed. The models to calculate the thermal bending of the shaft and the temperature distribution across the journal surface are established. The calculations of the temperature difference and its equivalent thermal imbalance are conducted and discussed with the comparison to the analytical results. It shows that the thermal imbalance may increase to the level of the mechanical imbalance and its influence on the system stability should be then included. The suggested thermal bending model also explains that the mid-span rotors are less liable to be influenced by the Morton Effect than are the overhung configurations, because of the restraining effect between the two supports. The simulation results of a symmetric mid-span rotor - hydrodynamic journal bearing system show that the inclusion of the Morton Effect may lead to an unstable operation of the system. Considering the existence of the oil film self-induced vibration due to the dynamic characteristics of fluid film bearings, the Morton Effect may make a further negative impact on the instabilities of the rotor system under some working conditions. Finally, the predictive solution method for the general mid-span rotors is discussed. The computer code, VT-MAP, is developed for the predictions of the Morton Effect induced instability of rotor systems in either mid-span and overhung configurations. / Ph. D.

The need to design a controller that self-schedules itself during the flight of an aircraft has been an active area of research. New methods have been developed beyond the traditional gain-scheduling approach. One such design method leads to a linear parameter varying (LPV) controller that changes based on the real-time variation of system dynamics. Before such a controller can be designed, the system has to also be represented as an LPV system. The current effort proposes a LPV modeling technique that is inspired by an affine LPV modeling techniques found in recent research. The properties of the proposed modeling method are investigated and compared to the affine modeling technique. It is shown that the proposed modeling technique represents the actual system behavior more closely than the existing affine modeling technique. To study the effect of the two LPV modeling techniques on controller design, a linear quadratic regulator (LQR) controller using linear matrix inequality (LMI) formulation is designed. This control design method provides a measure of conservatism that is used to compare the controllers based on the different modeling techniques. An F-16 short-period model is used to implement the modeling techniques and design the controllers. It was found that the controller based on the proposed LPV modeling method is less conservative than the controller based on the existing LPV method. Interesting features of LMI formulation for multiple plant models were also discovered during the exercise. A stability robustness analysis was also conducted as an additional comparison of the performance of the controllers designed using the two modeling methods. A scalar measure, called the probability of instability, is used as a measure of robustness. It was found that the controller based on the proposed modeling technique has the necessary robustness properties even though it is less conservative than the controller designed based on the existing modeling approach. / Master of Science

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New insight into the temperature dependent evolution of internal strain in the austenite phase during the martensitic phase transformation in NiTi shape memory alloys is provided via classical molecular dynamics simulations that employ well-established interatomic potentials for NiTi. It is shown, for the first time, that the developed strain tensor in the austenite phase is tetragonal in nature, with exponential temperature-dependence. Equally importantly, it is found that the developed internal strain (parallel to the habit plane) in the austenite varies linearly with the evolving martensite phase fraction. Interestingly, the Richard’s equation is found to describe the temperature dependence of the martensite phase fraction as well as the internal strain components parallel to the habit plane in the austenite phase. An analysis of the temperature dependent phonon dispersion of strained austenite revealed the competition between phonon softening of the TA2 branch and internal strain that leads to stabilization of the austenite phase in the two phase regime.

In this thesis we cover the dynamics of the macro magnetic transformations (spin avalanches) in crystals of molecular nanomagnets, also known as magnetic deflagration and detonation. Taking a single-molecule Hamiltonian, we calculate the dependence of Zeeman energy and the activation energy as a function of an external magnetic field at different angles relative to the easy axis of the crystal. Using quantum mechanical calculations, we show that the energy levels of the molecule exhibit complex behavior in presence of a transverse component of the magnetic field. For an arbitrarily aligned magnetic field, the energy levels do not arrange in a simple "double-well" manner. We extend existing theoretical models by generalizing the Zeeman energy for a wide range of magnetic fields and its different orientations. We obtain a new type of front instability in magnetization-switching media. Due to the dipole-dipole interaction between the molecules magnetic instability results to the front banding and change in the front propagation velocity. The magnetic instability has a universal physical nature similar to the Darrieus-Landau instability. The instability growth rate and the cutoff length are calculated for the spin avalanches in the crystals of nanomagnets. Finally, we investigate the internal structure of the magnetic detonation front. We calculate the continuous shock profile using the transport processes of the crystal such as thermal conduction and volume viscosity. Such an approach can be applied to any weak shock wave in solids. Zero volume viscosity leads to an isothermal jump, i.e., the temperature changes continuously while the pressure and the density experience discontinuity. The analysis has shown that the volume viscosity plays a major role in the formation of the detonation front.