Covariant density functional theory (CDFT) is one of the modern theoretical tools for describing the nuclear structure physics of finite nuclei. Its performance is defined by underlying covariant energy density functionals (CEDFs). In this dissertation and within the framework of the CDFT, different physical properties of the ground and the excited states of rotating and non-rotating nuclei have been investigated. A systematic global investigation of pairing properties based on all available experimental data on pairing indicators has been performed for the first time in the framework of covariant density functional theory. It is based on separable pairing interaction of Ref.\ \cite{TMR.09}. The optimization of the scaling factors of this interaction to experimental data clearly reveals its isospin dependence in the neutron subsystem. However, the situation is less certain in the proton subsystem since similar accuracy of the description of pairing indicators can be achieved both with isospin-dependent and mass-dependent scaling factors. The differences in the functional dependencies of scaling factors lead to the uncertainties in the prediction of proton and neutron pairing properties which are especially pronounced at high isospin and could have a significant impact on some physical observables. Although the present investigation is based on the NL5(E) covariant energy density functional (CEDF), its general conclusions are expected to be valid also for other CEDFs built at the Hartree level. It is shown for the first time that rotational bands which are proton unbound at zero or low spins can be transformed into proton bound ones at high spin by collective rotation of nuclear systems. This is due to strong Coriolis interaction, which acts on high-$N$ or strongly mixed M orbitals and drives the highest in energy occupied single-particle states of nucleonic configurations into the negative energy domain. Proton emission from such proton bound rotational states is suppressed by the disappearance of static pairing correlations at high spins of interest. These physical mechanisms lead to a substantial extension of the nuclear landscape beyond the spin zero proton drip line. In addition, a new phenomenon of the formation of giant proton halos in rotating nuclei emerges: it is triggered by the occupation of strongly mixed M intruder orbitals. Possible experimental fingerprints of the transition from particle bound to particle unbound part of rotational bands are discussed and compared for proton and neutron rich nuclei near and beyond respective drip lines.

In axial compressors with a relatively large blade tip clearance, an unsteady phenomenon denoted as rotating instability (RI) can be detected when the compressor is throttled to the operating points near the stability limit. In the frequency domain, RIs are shown as a hump lower than the blade passing frequency. This indicates an increase in noise level and might cause blade vibration and other undesirable structural issues. In this thesis, a comprehensive study on RIs is performed based on an axial compressor rotor row of the Low Speed Research Compressor at Technische Universität Dresden. Three blade tip clearances are investigated, and a groove casing treatment is mounted over the shroud for flow control. Methods of numerical modeling are evaluated, and zonal large eddy simulation is selected as the numerical model. By analyzing the flow properties and applying the dynamic mode decomposition, the coherent flow structure corresponding to the dominant frequency of RIs is extracted and visualized as the waves located in the blade tip region. The criteria for the appearance of RIs in the investigated research object are concluded.

Earlier research has demonstrated that downstream of combustion in a rotating detonation engine, exhaust flow periodically reverses circumferential direction. For small periods, the circumferential flow reaches velocity magnitudes rivaling the bulk flow of exhaust, manifesting as a swirl. The minimization of this swirl is critical to maximizing thrust and engine performance for rocket propulsion. During this study, numerous nozzle contours were iteratively designed and analyzed for losses analytically. Once a nozzle was chosen, further losses were validated through computational fluid dynamics simulations and then tested experimentally. Three different configurations were run with the RDRE: no nozzle, a nozzle without a spike, and a nozzle with a spike. Images of the exhaust quality were recorded using OH* chemiluminescence in high-speed cameras. One camera was used to confirm the existence of a detonation and the frequency of detonation. The second camera is pointed perpendicular to the exhaust flow to capture the quality of exhaust. Quantitative results of the turbulent velocity fluctuations were obtained through particle image velocimetry of the side-imaging frames. All frames in each case were exported and converted to several time-averaged frames whereupon the time-averaged turbulent velocity fluctuation profiles could be compared between cases for swirl attenuation.

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The vibration of complex mechanical systems that include coupled rotating and stationary bodies motivates this work. A semi-analytical model is developed for high-speed, compliant, rotating bodies. Exploiting the axisymmetry of the rotating body, the developed semi-analytical model only discretizes the two-dimensional radial cross-section; Fourier series are used in the circumferential direction. The corresponding formulation for thin-walled, axisymmetric shells is given. Even though the body is axisymmetric, its deflection as well as external forces, constraints, and supports acting on the body are allowed to be asymmetric. These asymmetric elements can be stationary or rotating. The model includes Coriolis and centripetal effects. The prestress (or geometric) stiffness matrix that arises from external forces and constant centripetal acceleration has additional terms compared to the literature, and these terms can significantly change the natural frequencies. Discrete stiffness-damper elements, elastic foundations, and constraint equations are used to couple the rotating body to other rotating and stationary bodies. The model is developed in a stationary reference frame to avoid time-dependent coefficients in the equations of motion when coupled to stationary components. Surface constraints are developed using equivalent force relations between multiple points on the surface and a reference node. Discrete stiffness-dampers, asymmetric elastic foundation, and asymmetric constraints introduce non-axisymmetry in the system. The speed-dependent natural frequencies and complex-valued vibration modes, presence of multiple Fourier harmonics in each mode, changes to critical speeds, divergence and flutter instability phenomena, and eigenvalue veering are investigated for spinning systems with asymmetric features. The developed semi-analytical model is used for rotationally periodic systems, for example, planetary gears. Rotationally periodic systems consist of multiple vibrating, rotating central components and substructures. The model is developed in a reference frame rotating with the central component that supports the substructures. Structured modal properties of the cyclically symmetric systems and diametrically opposed systems are investigated. The modes of the spinning system are categorized into translational-tilting, rotational-axial, and substructure modes. Time-varying coupling elements act as parametric excitation in the system. Large strain energy in the coupling elements lead to large parametric instability regions. The analytical closed-form expression of the parametric instability bandwidth obtained using a perturbation method compares well with numerical results from Floquet theory. / Doctor of Philosophy / Complex mechanical systems, for example, mechanical transmission, consist of coupled rotating and stationary bodies. The vibrations of rotating bodies are transmitted to the other bodies through coupling elements. To reduce weight of the system, the rotating bodies are made thin-walled resulting in increased flexibility of the body. The existing lumped parameter/rigid body models do not account for the flexibility of these rotating bodies. Conventional three-dimensional finite element models lead to a large number of degrees of freedom in the system, increasing the computational cost. We aim to develop a computationally efficient model to analyze the dynamics and vibration of complex mechanical systems. Most rotating bodies can be approximated as axisymmetric. The axisymmetric property of the rotating body is harnessed to reduce the three-dimensional model of the body to a two-dimensional radial cross-section using Fourier series in the circumferential direction. This reduces the system degrees of freedom. Coriolis, centripetal, and prestress effects are included in the model. Discrete stiffness-dampers, elastic foundations, and constraint equations couple the rotating body to other rotating and stationary bodies. Non-axisymmetric coupling elements and forces introduce asymmetry in the system. The system model for these asymmetric systems are developed in a stationary reference frame to avoid time-dependent coefficient equations of motion. Flexible stationary bodies alter the natural frequencies and vibration modes of the system. Instabilities, critical speeds, effects of asymmetry on the natural frequencies and vibration modes of the system are investigated. The model is extended for rotationally periodic systems, for examples, planetary gears and bearings. This model is developed in the reference frame that rotates with the central component that supports substructures. Structured modal characteristics are observed for the rotationally periodic systems. Changing contact conditions act as a source of parametric excitation in systems. Parametric resonances occur when natural frequencies of vibration with large strain energy in the coupling elements sum to the excitation frequency. Parametric instability regions obtained using an analytical equation compare well with numerical results.

Rotating blades, which are the most critical components of any turbo-machinery, need to be designed to withstand forced vibrations due to accidental tip rub impact against inner surface of casing. These vibrations are typically dependent on operating conditions and geometric parameters. In the current study, a rotor test rig with a maximum tip speed capability of 144 km/hr has been developed for studying the dynamic behavior of representative jet engine compressor blades actuated by the closure of clearance between the tip of a given rotating blade and a sector of the inner lining of the casing. Ten different blade profiles are chosen in the present research. The blades are obtained by lofting NACA GOE123 airfoil cross-section along different stacking axes. Rotor test rigs which simulate transient dynamic events require high frequency data acquisition systems like slip ring arrangement or telemetric transmission. While slip rings introduce noise into the signal, the telemetric transmission works out to be rather expensive. To circumvent the stated shortcomings of data acquisition systems, a novel rotor-mounted data acquisition system has been implemented here which captures dynamic strains in vibrating blades during operation. The current data acquisition system can store data for duration of five seconds with a sampling rate of 35 kHz. It has been calibrated with four standard tests, and provides a simple and efficient mode of data capturing. Three blades with airfoil sections (a flat beam-type blade of uniform rectangular cross-section, a blade with twisted cross-sections stacked along a straight line, and a blade similar to the latter but with a curved stacking axis) are tested under controlled rub conditions at four different speeds. The maximum test speed is restricted to 800 rpm for reasons of safety although the set-up is designed to operate up to a maximum speed of 2000 rpm. For each of the rotor speeds, a blade is tested for three to four different stagger angles in the range of 0o-30o. By plotting the RMS values of measured dynamic responses with respect to stagger angle for a given rotor speed, it has been observed, perhaps for the first time in published literature, that a stagger angle of around 20o yields the maximum RMS value of strain response. A major objective of the current study has been to utilize the data generated in the tip rub impact tests for validating a predictive numerical model of the test set-up using explicit finite element analysis. To this end, a finite element model of the rotor rig inclusive of a rotor with two blades and the static frame structure is developed and analyzed using an explicit LS-DYNA solver. This model is calibrated with the test results of the three blade designs described above. In particular, it has been shown that the frequency contents of the measured dynamic strain responses agree quite well with frequencies obtained from the numerically computed responses. It has been found in the experimental responses that a given blade vibrates with two main frequencies: one corresponding to the first natural frequency of the rotor-blade system during the tip-rubbing phase (which lasts until the blade tip is in contact with the rub element which is a sector of the circular casing), and another corresponding to the first natural frequency of the blade when it vibrates freely without its tip being in contact with the rub-liner of the casing. A shortcoming of the current modeling approach is its inability to realistically represent the damping behaviors observed in the tests. For reasons of computational efficiency and consistent with the fact that there was no perceptible damage in the tested blades, an elastic constitutive behavior is specified for the blades, while the sacrificial PVC rub-liner is assumed to behave elasto-plastically. A limited study has also been carried out by assigning an elasto-plastic constitutive model to one of the blades previously represented with elastic properties only, and although incipient yielding is observed in a highly localized region at the tip of a blade (which can also be a numerical artifact), the responses under the two material behavior considerations (i.e. elastic and elasto-plastic) are found to be nearly same. Finally, this validated modeling approach is applied to the study of blades of ten distinct geometric profiles (including the three configurations already considered) at a speed of 800 rpm and the resonant speed of a given blade. Comparisons are made between the relevant responses (such as time-histories of root strain, shaft torque, blade axial displacement, bearing load and rub force) of nine blades with airfoil cross-sections (leaving aside the results for the first blade of rectangular cross-section which is only of academic interest). Based on this study, of all the blade designs, it has been found that the curve-stacked airfoils exhibit better ‘Rub-tolerant’ behavior. Both experimental and simulation results have predominantly proven the fact that adding curvature to a straight stacked blade through curve-stacked or bow result in reducing the rub induced vibration. While sweep and bow provide some aerodynamic advantages, they are not much helpful in containing the vibrations to a sustainable extent.

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