A computational fluid dynamics (CFD) model is developed for pulsatile flows and particle transport to evaluate the possible thrombus trajectory in the feline aorta for Hypertrophic Cardiomyopathy (HCM) heart conditions. An iterative target mass flow rate boundary condition is developed, and turbulent simulations with Lagrangian particle transport model are performed using up to 11M grids. The model is validated for human abdominal aorta flow, for which the results agree within 11.6% of the experimental data. The model is applied for flow predictions in a generalized feline aorta for healthy and HCM heart conditions. Results show that in the HCM case, the flow through the iliac arteries decreases by 50%, due to the large recirculation regions in the abdominal aorta compared to the healthy heart case. The flow recirculation also result in stronger vortices with slower decay, causing entrapment of particles in the thoracic aorta and trifurcation regions.

Laser Doppler velocimetry (LDV) measurements and hydrogen-bubble flow-visualization techniques were used to examine the near-wall flow structure of 2-D and 3-D turbulent boundary layers (TBLs) over a range of low Reynolds numbers. The goals of this research were (1) an increased understanding of the flow physics in the near wall region of turbulent boundary layers, (2) to observe and quantify differences between 2-D and 3-D TBL flow structures, and (3) to document Reynolds number effects for 3-D TBLs. An ultimate application of this work would be to improve turbulence modeling for 3-D flows. The LDV data have provided results detailing the turbulence structure of the 2-D and 3-D TBLs, as well as low uncertainty skin friction estimates. These results include mean Reynolds stress distributions, flow skewing results, and U and V spectra. Effects of Reynolds number for the 3-D flow were examined when possible. Comparison to results with the same 3-D flow geometry but at a significantly higher Reynolds number provided unique insight into the structure of 3-D TBLs. While the 3-D mean and fluctuating velocities were found to be highly dependent on Reynolds number, a previously defined shear stress parameter was discovered to be invariant with Reynolds number. The hydrogen-bubble technique was used as a flow-visualization tool to examine the near-wall flow structure of 2-D and 3-D TBLs. Both the quantitative and qualitative results displayed larger turbulent fluctuations with more highly concentrated vorticity regions for the 2-D flow. The 2-D low-speed streaky structures experienced greater interaction with the outer region high-momentum fluid than observed for the 3-D flow. The near-wall 3-D flow structures were generally more quiescent. Numerical parameters quantified the observed differences, and characterized the low-speed streak and high-speed sweep events. All observations indicated a more stable near-wall flow structure with less turbulent interactions occurring between the inner and log regions for a 3-D TBL. / Ph. D.

High-amplitude freestream turbulence and surface roughness elements can excite a laminar boundary-layer flow sufficiently enough to cause streamwise-oriented vortices to develop. These vortices resemble elongated streaks having alternate spanwise variations of the streamwise velocity. Following the transient growth phase, the fully developed vortex structures downstream undergo an inviscid secondary instability mechanism and, ultimately, transition to turbulence. This mechanism becomes much more complicated in high-speed boundary layer flows due to compressibility and thermal effects, which become more significant for higher Mach numbers. In this research, we formulate and test an optimal control algorithm to suppress the growth rate of the aforementioned streamwise vortex system. The derivation of the optimal control algorithm follows two stages. In the first stage, to optimize the computational cost of the analysis, the study develops an efficient numerical algorithm based on the nonlinear boundary region equations (NBREs), a reduced form of the compressible Navier-Stokes equations in a high-Reynolds-number asymptotic framework. The NBREs algorithm results agree well with direct numerical simulation (DNS) results. The numerical simulations are substantially less computationally costly than a full DNS and have a more rigorous theoretical foundation than parabolized stability equation (PSE) based models. The substantial reduction in computational time required to predict the full development of a G\"{o}rtler vortex system in high-speed flows allows investigation into feedback control in reasonable total computational time, which is the focus of the second part of the study. In the second stage, the method of Lagrange multipliers is utilized -- via an appropriate transformation of the original constrained optimization problem into an unconstrained form -- to obtain the adjoint compressible boundary-region equations (ACBREs) and corresponding optimality conditions, which constitute the basis of the optimal control approach. Numerical solutions for high-supersonic and hypersonic flows reveal a significant decrease in the kinetic energy and wall shear stress for all configurations considered. Streamwise velocity contour plots illustrate the qualitative effect of the optimal control iterations, demonstrating a significant decrease in the amplitude of the primary vortex instabilities.

The growth of data capacity in optical communications links, which form the critical backbone of the modern internet, is facing a slowdown due to fundamental nonlinear limitations, leading to an impending "capacity crunch" on the horizon. Current technology has already exhausted degrees of freedom such as wavelength, amplitude, phase and polarization, leaving spatial multiplexing as the last available dimension to be efficiently exploited. To minimize the significant energy requirements associated with digital signal processing, it is critical to explore the upper limit of unmixed spatial channels in an optical fiber, which necessitates ideally packing spatial channels either in real space or in momentum space. The former strategy is realized by uncoupled multi-core fibers whose channel count has already saturated due to reliability constraint limiting fiber sizes. The later strategy is realized by the unmixed multimode fiber whose high spatial efficiency suggest the possibility of high channel-count scalability but the right subset of mode ought to be selected in order to mitigate mode coupling that is ever-present due to the plethora of perturbations a fiber normally experiences. The azimuthal modes in ring-core fibers turn out to be one of the most spatially efficient in this regard, by exploiting light’s orbital angular momentum (OAM). Unmixed mode counts have reached 12 in a ~1km fiber and 24 in a ~10m fiber. However, there is a fundamental bottleneck for scalability of conventionally bound modes and their relatively high crosstalks restricts their utility to device length applications. In this thesis, we provide a fundamental solution to further fuel the unmixed-channel count in an MMF. We utilize the phenomenon of topological confinement, which is a regime of light guidance beyond conventional cutoff that has, to the best of our knowledge, never been demonstrated till publications based on the subject matter of this thesis. In this regime, light is guided by the centrifugal barrier created by light’s OAM itself rather than conventional total internal reflection arising from the index inhomogeneity of the fiber. The loss of these topologically confined modes (TCMs) decreases down to negligible levels by increasing the OAM of fiber modes, because the centrifugal barrier that keeps photons confined to a fiber core increases with the OAM value of the mode. This leads to low-loss transmission in a km-scale fiber of these cutoff modes. Crucially, the mode-dependent confinement loss of TCMs further lifts the degeneracy of wavevectors in the complex space, leading to frustration of phase-matched coupling. This thus allows further scaling the mode count that was previously hindered by degenerate mode coupling in conventionally bound fiber modes. The frustrated coupling of TCMs thus enables a record amount of unmixed OAM modes in any type of fiber that features a high index contrast, whether specially structured as a ring-core, or simply constructed as a step-index fiber. Using all these favorable attributes, we achieve up to 50 low-loss modes with record low crosstalk (approaching -45 dB/km) over a 130-nm bandwidth in a ~1km-long ring-core fiber. The TCM effect promises to be inherently scalable, suggesting that even higher modes counts can be obtained in the future using this design methodology. Hence, the use of TCMs promises breaking the record spectral efficiency, potentially making it the choice for transmission links in future Space-Division-Multiplexing systems. Apart from their chief attribute of significantly increasing the information content per photon for quantum or classical networks, we expect that this new light guidance may find other applications such as in nonlinear signal processing and light-matter interactions.

Simulations were performed to evaluate solution adaptive meshing strategies for flows with vortices whose axes of rotation are parallel to the bulk fluid motion. Two configurations were investigated: a wing in a wind tunnel and a missile spinning at 30Hz and 60Hz at 0◦ angle of attack with canards deflected 15◦. Feature-based descriptors were used to identify regions of the flow near vortices that are candidate regions for adaptive meshing. Several different adaptive meshing techniques were evaluated. These techniques include refinement around the vortex core, refinement near the vortex extent surface, refinement inside the extent surface, refinement inside and near the extent surface, and mesh regeneration using the vortex extent surface as an embedded surface. Results for the wing case, compared to experimental data, indicate that it is necessary to refine the region within and near the vortex extent surface to accurately recreate physical characteristics and achieve an acceptable solution.

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The thesis develops singly-periodic mathematical models for complex laminar wakes which are formed behind vortex-shedding bluff bodies. These wake structures exhibit a variety of patterns as the bodies oscillate or are in close proximity of one another. The most well-known formation comprises two counter-rotating vortices in each shedding cycle and is popularly known as the vk vortex street. Of the more complex configurations, as a specific example, this thesis investigates one of the most commonly occurring wake arrangements, which consists of two pairs of vortices in each shedding period. The paired vortices are, in general, counter-rotating and belong to a more general definition of the 2P mode, which involves periodic release of four vortices into the flow. The 2P arrangement can, primarily, be sub-classed into two types: one with a symmetric orientation of the two vortex pairs about the streamwise direction in a periodic domain and the other in which the two vortex pairs per period are placed in a staggered geometry about the wake centerline. The thesis explores the governing dynamics of such wakes and characterizes the corresponding relative vortex motion. In general, for both the symmetric as well as the staggered four vortex periodic arrangements, the thesis develops two-dimensional potential flow models (consisting of an integrable Hamiltonian system of point vortices) that consider spatially periodic arrays of four vortices with their strengths being +/-1 and +/-2. Vortex formations observed in the experiments inspire the assumed spatial symmetry. The models demonstrate a number of dynamic modes that are classified using a bifurcation analysis of the phase space topology, consisting of level curves of the Hamiltonian. Despite the vortex strengths in each pair being unequal in magnitude, some initial conditions lead to relative equilibrium when the vortex configuration moves with invariant size and shape. The scaled comparisons of the model results with experiments conducted in a flowing soap film with an airfoil, which was imparted with forced oscillations, are satisfactory and validate the reduced order modeling framework. The experiments have been performed by a collaborator group at the Department of Physics and Fluid Dynamics at the Technical University of Denmark (DTU), led by Dr. Anders Andersen. Similar experiments have also been run at Virginia Tech as part of this dissertation and the preliminary results are included in this treatise. The thesis also employs the same dynamical systems techniques, which have been applied to study the 2P regime dynamics, to develop a mathematical model for the P+S mode vortex wakes, with three vortices present in each shedding cycle. The model results have also been compared favorably with an experiment and the predictions regarding the vortex circulation data match well with the previous results from literature. Finally, the thesis introduces a novel concept of clean and renewable energy extraction from vortex-induced vibrations of bluff bodies. The slow-moving currents in the off-shore marine environments and riverine flows are beyond the operational capabilities of the more established hydrokinetic energy converters and the discussed technology promises to be a significant tool to generate useful power from these copiously available but previously untapped sources. / Ph. D.

Granular flows are ubiquitous both in natural and industrial processes such as pharmaceuticals production, mining and food–processing. Within a gas-solid fluidized bed, fundamental phenomena such as heat and mass transfer are impacted by particle convection, mixing and segregation due to rising gas bubbles. The free-bubbling regime is promising in enhancing the gas-solid contact but its mathematically chaotic bubble motion make system design challenging. Furthermore, a better understanding of rheological characteristics of these gas-solid flows is pertinent to developing accurate mathematical descriptions of granular flows. Despite their decades of usage and significance in all walks of technology, gas-solid fluidized beds remain poorly understood. In the first section of this dissertation, we investigate the combined effects of vibration and gas flow on a binary gas-solid fluidized bed. At resonant conditions, this external excitation generates a periodic, triangular, equisized, structured array of rising bubbles, reducing the chaos. Through a combination of experiments, Computational Fluid Dynamics-Discrete Element Method (CFD-DEM), and Multi Fluid Model (MFM) simulations, we demonstrate that the structured bubbling facilitates particle mixing whereas the gas flow alone (no vibration conditions) results in smaller, unstructured bubbles that promote segregation. The CFD-DEM simulations accurately capture the bubble structuring and somewhat, qualitatively and quantitively, match with the optically imaged experimental data. These investigations provide valuable insights into the dynamics of particle mixing and segregation under complex fluidization conditions. The MFM simulations failed to predict the mixing observed, indicating a need for further refinement of these models. In the second section of this dissertation, we explore the complex rheological behavior of the dry, dense particulate flows using the Discrete Element Method (DEM) simulations. In these simulations, we choose 3−D Couette cell geometry to visualize Granular Taylor–Vortex flow for various particle diameters and densities. The simulations examined the effects of varying particle volume fractions, from 0.45 to 0.60, under different shear rates, revealing a distinct rheological transition from shear-thickening to Newtonian and finally to shear-thinning behavior. The formation and nature of these vortices were compared with those observed in continuum simulations of Newtonian and shear-thinning fluids, to elucidate the unique aspects of granular flow dynamics. The third section of this thesis investigated the rheology of granular particles subjected to 1−D shear combined with sinusoidal vibration, aiming to understand the effects on pressure, shear stress, and coordination number across a range of shear rates and particle fractions. A novel vibrational regime was observed at low shear rates, below a critical threshold, characterized by a rate-independent pressure intermediate between the inertial and quasi-static regimes. These findings provide significant insights while advancing our understanding of granular material dynamics.