Theses and Dissertations from UMD
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Item Impact of Polymeric Drops on Drops and Films of a Different but Miscible Polymer(2024) Bera, Arka; Das, Siddhartha; Mechanical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)The fluid mechanics of a liquid drop impacting on another stationery (or spreading) liquid drop or on a liquid film (of thickness comparable, or smaller, or larger than the impacting drop) has attracted significant attention over the past several years. Such problems represent interesting deviations from the more widely studied problems of liquid drops impacting on solid surfaces having different wettabilities with respect to the impacting drops. These deviations stem from the fact that the resting liquid (in the form of the drop or the film) itself undergoes deformation on account of the drop impact and can significantly affect the overall combined drop-drop or drop-film dynamics. The problem becomes even more intriguing depending on the rheology of the drop(s) and the film as well as the (im)miscibility of the impacting drop with the underlying drop or the film. Interestingly, the majority of such drop-impact-on-drop or drop-impact-on-film studies have considered Newtonian drop(s) and films, with little attention to polymeric drop(s) and films. This thesis aims to bridge that void by studying, using Direct Numerical Simulation (DNS) based computational methods, the impact-driven dynamics of one polymeric drop on another (different but miscible) polymeric drop or film. As specific examples, we consider two separate problems. In the first problem, we consider the impact of a PMMA (poly-methyl methacrylate) drop on a resting PVAc (polyvinyl acetate) drop as well as the impact of a PVAc drop on a resting PMMA drop. In the second problem, we consider the impact of a PMMA drop on a PVAc film as well as the impact of a PVAc drop on a PMMA film. For the first problem, the wettability of the resting drop (on the resting surface), the Weber number of the impacting drop, the relative surface tension values of the two polymeric liquids (PVAc and PMMA), and the miscibility (or how fast the two liquids mix) dictate the overall dynamics. PVAc has a large wettability on silicon (considered as the underlying solid substrate); as a result, during the problem of the PMMA drop impacting on the PVAc drop, the PVAc drop spreads significantly and the slow mixing of the two liquids ensures that the PMMA drop spreads as a thin film on top of the PVAc film (formed as the PVAc drop spreads quickly on silicon). Depending on the Weber number, such a scenario leads to the formation of transient liquid films (of multitudes of shapes) with stratified layers of PMMA (on top) and PVAc (on bottom) liquids. On the other hand, for the case of the PVAc drop impacting on the PMMA drop, a combination of the weaker spreading of the PMMA drop on silicon and the “engulfing” of the PMMA drop by the PVAc drop (stemming from the PVAc having a smaller surface tension than PMMA) ensures that the impacting PVAc drop covers the entire PMMA drop and itself interacts with the substrate giving rise to highly intriguing transient and stratified multi-polymeric liquid-liquid structures (such as core-shell structure with PMMA core and PVAc shell). For both these cases, we thoroughly discuss the dynamics by studying the velocity field, the concentration profiles (characterizing the mixing), the progression of the mixing front, and the capillary waves (resulting from the impact-driven imposition of the disturbance). In the second problem, we consider a drop of the PMMA (PVAc) impacting on a film of the PVAc (PMMA). In addition to the factors dictating the previous problem, the film thickness (considered to be either identical or smaller than the drop diameter) also governs the overall droplet-impact-driven dynamics. Here, the impact, being on the film, the dynamics is governed by the formation of crown (signifying the pre-splashing stage) and a deep cavity (the depth of which is dictated by the film thickness) on the resting film. In addition to quantifying these facets, we further quantify the problem by studying the velocity and the concentration fields, the capillary waves, and the progression of the mixing front. For the PMMA drop impacting on the thin film, a noticeable effect is the quick thinning of the PMMA drop on the PVAc film (or the impact-driven cavity formed on the PVAc film), which gives rise to a situation similar to the previous study (development of transient multi-polymeric-liquid structures with stratified polymeric liquid layers). For the case of the PVAc drop impacting on the PMMA film, the PVAc liquid “engulfs” the deforming PMMA film, and this in turn, reduces the depth of the cavity formed, the extent of thinning, and the amplitude of the generated capillary waves. All these fascinating phenomena get captured through the detailed DNS results that are provided. The specific problems considered in this thesis have been motivated by the situations often experienced during the droplet-based 3D printing processes (e.g., Aerosol jet printing or inkjet printing). In such printing applications, it is commonplace to find one polymeric drop interacting with an already deposited polymeric drop or a polymeric film (e.g., through the co-deposition of multiple materials during multi-material printing). The scientific background for explaining these specific scenarios routinely encountered in 3D printing problems, unfortunately, has been very limited. Our study aims to fill this gap. Also, the prospect of rapidly solidifying these polymeric systems (via methods such as in-situ curing) can enable us to visualize the formation of solidified multi-polymeric structures of different shapes (by rapidly solidifying the different transient multi-polymeric-liquid structures described above). Specifically, both PMMA and PVAc are polymers well-known to be curable using in-situ ultraviolet curing, thereby establishing the case where the present thesis also raises the potential of developing PMMA-PVAc multi-polymeric solid structures of various shapes and morphologies.Item EXPERIMENTAL INVESTIGATION OF BOUNDARY LAYER TRANSITION ON CONE-FLARE GEOMETRIES AT MACH 4(2024) Norris, Gavin; Laurence, Stuart J; Aerospace Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)This study investigates supersonic boundary layer transition on a cone-flarewith a 5° half-angle straight cone and flared bases of +5°, +10°, and +15°. The experiments used the University of Maryland's Multiphase Flow Investigations Tunnel (MIST), a Mach 4 Ludweig tube. Experiments were performed “dry”, without aerosols or droplets, and focus on the first-mode (Tollmien-Schlichting) boundary layer instability waves and their interaction with the compression corner. Using high-speed Schlieren imaging, the boundary layer dynamics on the cone-flare's top surface were analyzed. The data were processed through Power Spectral Density (PSD) and Spectral Proper Orthogonal Decomposition (SPOD) techniques to study the behavior of the first-mode waves and the transition location changes. The findings reveal coherent wave packets within the boundary layer at frequencies characteristic of the first-mode. The wave packets power increased along the cone and peaked near the compression corner before dissipation on the flare. These findings contribute to the understanding of first-mode boundary layer transition mechanisms in hypersonic flows for the cone-flare geometry.Item QUANTIFICATION OF MELT DISTRIBUTION, MELT CONNECTIVITY, AND ANISOTROPIC PERMEABILITY OF DEFORMED PARTIALLY MOLTEN ROCKS USING X-RAY MICROTOMOGRAPHY(2024) Bader, James Alexander; Zhu, Wenlu; Montesi, Laurent G.J.; Geology; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Volcanic activity plays a dominant role in shaping the surface of Earth and other planets. For example, Earth’s ocean floor is created by volcanic activity at mid-ocean ridges. There, magma is sourced from a ~60 km deep, ~100 km wide region of the mantle, from which partial rock ascends and erupts along narrow ridges that run along the middle of Earth’s oceans. Volcanic activity at mid-ocean ridges, the strength of Earth’s mantle, and the geochemical composition of volcanic rocks and ocean water are all influenced by how the melt is distributed in partially molten rocks, and how easily it can flow through the partially molten mantle beneath these ridges. In particular, it is often assumed that most of the melt ascends through isolated channels that direct it towards the mid-ocean ridges, making melt transport localized and anisotropic. A possible origin of these channels is the differential stress induced by upwelling mantle material beneath the ridge, which has been shown in laboratory experiments to localize melt into planar regions named “melt-rich bands.” To date, the development and characteristics of melt-rich bands have been studied principally using theoretical models and two-dimensional (2D) images of sheared partially molten rocks. There has been little experimental research using 3D techniques until now. This thesis uses 3D images of sheared partially molten rocks created in the laboratory, obtained using high-resolution x-ray microtomography (X-ray µCT), to investigate how the distribution of melt, its orientation, its connectivity, and its ability to flow through the rocks changes when stress is applied. This study shows how melt connectivity and, therefore, rock permeability changes as melt changes from being dispersed through a partially molten rock to being localized on well-developed melt-rich bands. This work shows that melt forms melt volumes that are preferentially elongated within the plane of melt-rich bands even before these bands form. This discovery emphasizes the importance of permeability anisotropy at all stages of melt-rich band development. We also measured permeability and melt connectivity at all scales, both inside and outside melt-rich bands. Our results show that melt can hardly flow perpendicular to melt-rich bands over distances larger than a few grains. Additionally, the permeability along the melt-rich bands is also reduced by half compared to that in a partially molten rock that is not subjected to differential stress. This research quantifies the uneven distribution of permeability in a sheared, partially molten rock. It also proposes a scheme to average local permeability estimates, helping us understand and quantify how melt travels along melt-rich bands at various scales. These findings provide valuable insights into how magma flows in the Earth’s mantle, especially at active plate boundaries like mid-ocean ridges. Overall, this research provides the first experimental constraints, based on 3D microtomography images, on the melt network and how melt flows in the presence of stress in partially molten rocks.Item AEROSOL EFFECTS IN HIGH SUPERSONIC FLOWS(2024) Schoneich, Antonio Giovanni; Laurence, Stuart J; Aerospace Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)The understanding of high-speed aerodynamics is becoming evermore pertinent with thegrowth of space tourism, continued interest in space exploration, and pursuit of advanced highspeed aircraft for both military and commercial use. For initial investigations, ground test facilities are preferred to flight tests as they are far cheaper and carry significantly less risk, although wind tunnels can only replicate a subset of the conditions experienced in actual flight. One of these conditions that has not been adequately captured in wind tunnels is the effect of particulates in the atmosphere. Typical wind tunnels use a pure, clean gas (air, nitrogen, etc.) for testing, but this does notcapture the aerosolized nature of the atmosphere, where humidity and condensation can produce a distribution of liquid droplet sizes ranging from the average rain drop of 2mm to sub-micron diameter particles. Similarly, volcanic eruptions and ever-present wildfires result in solid particles exhibiting a variety of species and sizes that are transported to every layer of the atmosphere. At supersonic speeds, encounters with particulates have been shown to lead to detrimental effects, such as material erosion and boundary layer transition. Previous attempts to study this problem in wind tunnels have focused mainly on sub-micronsized solid particles, since aerosol settling time is a major limiting factor. On the other hand, most high-speed experiments involving large liquid droplet impacts have been carried out in gas guns or ballistic ranges due to the difficulty of trying to accelerate a droplet to high speeds without causing it to break up. While these facilities can be used to study impacts, the moving model means that detailed aerodynamic studies are nearly impossible, leading to a large gap in knowledge. To perform high-speed wind tunnel testing with liquid aerosols representative of cloud-likeenvironments (5-20 μm), a Mach-4 facility, referred to as the Multi-phase Investigations Supersonic Tunnel (MIST) has been designed and developed at the University of Maryland (capable of producing supersonic, particle-laden flows). This range of aerosol sizes makes MIST a unique facility with significant potential for expanding the state of the art in high-speed multi-phase flows. The present work discusses the design and characterization of MIST as well as two major experimental investigations carried out using this new facility. The first investigation examines the force augmentation on a free-flying sphere exposed to supersonic, particle-laden flows. Freeflight measurements are performed with five different particle size and concentration combinations. When comparing the results for particle-free flow in the same facility, the drag coefficient of the sphere was shown to be 1.75-4.5% greater for all multi-phase cases; this is significantly higher than simple estimates based on the increased momentum flux in the freestream would indicate. In addition to force measurements, an experimental investigation into the effect of particle-ladenflows on boundary-layer transition was conducted. It is important to characterize the disturbance environment in wind tunnels since they typically do not represent the levels in atmospheric flight and can lead to earlier onset of boundary-layer transition. In performing such measurements using a single-point Focused Laser Differential Interferometer, it was discovered that the presence of particles in the flow could significantly attenuate the acoustic disturbances generated by the wind tunnel. This finding was further reinforced when investigating the boundary-layer transition on a 5◦ half-angle, sharp cone using high-speed schlieren visualization. For each case presented in this work, the boundary-layer disturbance amplitudes were reduced and transition Reynolds numbers increased in the particle-laden flow cases. This was contrary to expectations, given that prior numerical studies have indicated that particles can induce early transition. These findings potentially open a path to substantially reduce freestream disturbance levels in conventional hypersonic wind tunnels.Item PARTICLE INDUCED TRANSITION IN HIGH-SPEED BOUNDARY-LAYER FLOWS(2024) Abdullah Al Hasnine, Sayed Mohammad; Brehm, Christoph; Aerospace Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Boundary-layer transition to turbulence presents a critical challenge in aerospace engineering due to its impact on thermal load, especially for hypersonic vehicles. This transition, influenced by various disturbances such as acoustic waves, entropy waves, and particle impingement, follows complex and non-unique pathways to turbulence. It significantly affects the surface heat flux and thus will impact the design of thermal protection systems. This dissertation focuses on the transition process initiated by particle impingement, which introduces small-scale disturbances through a complex receptivity process that typically initiates a natural transition path. Using direct numerical simulations, this study explores the particle-induced transition process. The disturbance spectrum, consisting of both stable and unstable modes along with continuous acoustic contributions, is meticulously reconstructed near the particle impingement site using biorthogonal decomposition to assess the contributions of different eigenmodes to the initial disturbance spectrum. A large number of discrete and continuous eigenmodes are seeded, but the dominant eigenmodes capture only a small fraction of the disturbance energy, with the majority reflected into the freestream through the continuous modes associated with the continuous acoustic branches. The modeling fidelity is also investigated, particularly the particle-source-in-cell (PSIC) approach, commonly used due to its efficiency in capturing particle-flow interactions. Comparisons with the Immersed-Boundary-Method (IBM), however, reveal that PSIC inadequately captures particle-wall interactions and needs correction for accurate disturbance modeling. Finally, a reduced-order model is developed for the prediction of particle-induced transition. This model integrates data from high-fidelity simulations, linear stability theory, and a saturation amplitude model while also considering particle characteristics like size, density and concentration. The model’s capability is demonstrated for a wide range of transition scenarios, including data from the HIFiRE-1 flight test, offering a robust tool for rapid transition prediction in hypersonicvehicle design.Item GLOBAL ANALYSIS OF TRANSITIONAL HYPERSONIC FLOW OVER CONE AND CONE-FLARE GEOMETRIES(2024) Sousa, Cole Edward; Laurence, Stuart; Aerospace Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Accurately predicting the laminar-to-turbulent boundary-layer transition on hypersonic vehiclesremains one of the principal challenges in characterizing the expected heat loads and skin friction the vehicle will experience in flight. Ground facilities, while incapable of replicating the complete set of flow conditions found at hypersonic flight, play a critical role in providing physical measurements of the transition process. The experimental characterization of hypersonic boundary-layer disturbances, however, has traditionally faced limitations in its ability to provide spatiotemporally dense data sets comparable to those of computational fluid dynamics (CFD) investigations. The present work aims to provide global off-body measurements of hypersonic boundary-layer disturbances at frequencies much greater than that of the fundamental instability, enabling the exploration of nonlinear phenomena and more extensive comparisons between experimental and computational studies. The current methodology utilizes the fact that hypersonic-boundary layer disturbances havebeen observed to propagate at measurable and statistically predictable velocities. Particularly for the second-mode instability, the density gradient fields acquired by a calibrated schlieren system provide an avenue for resolving dense high-frequency spatiotemporal data. Disturbance propagation velocities extracted from the schlieren images are used to conduct a time-interpolation of the disturbances, which transforms spatially-available descriptions of the travelling waveforms into up-sampled temporal signals at specific pixel locations. When performed across the entire schlieren field of view, the resulting time-resolved signals have a new sampling frequency much greater than the original camera frame rate and a spatial density equal to the camera resolution. This enables the spectral analysis of high-frequency disturbances, including superharmonics of the fundamental instability, which are not originally resolvable from raw time series of the video data. The methodology is employed here in three different experimental data sets, comprising a7° half-angle sharp cone at zero incidence in Mach 6 flow, a 7° half-angle sharp cone at variable incidence in Mach 14 flow, and a cone-flare geometry composed of a 5° frustum with compression angles of +5°, +10°, and +15° at zero incidence in Mach 14 flow. A comprehensive global analysis is conducted on the linear and nonlinear development of the second-mode instability waves in each case. Pointwise measures of the autobicoherence are used to identify specific triadic interactions and the locations of their highest levels of quadratic phase coupling. Significant resonance interactions between the second-mode fundamental and harmonic instabilities are found along with interactions between these and the mean flow. Bispectral mode decomposition is employed to educe the flow structures associated with these interactions. A similar analysis is performed for the power spectrum, with power spectral densities computed for each pixel’s timeseries and spectral proper orthogonal decomposition employed to derive the modal structure and energy of the flow at specific frequencies. The instability measurements taken on the cone-flare geometry are the first of their kind atMach 14. The analysis reveals that incoming second-mode waves undergo extended interactions with the shock waves present at the corner, consistently leading to amplification of the waves and accelerating their nonlinear activity. The disturbance energy is also found to strongly radiate along the shock waves, a behavior that appears to be intensified at high Mach numbers. In the case of separated flow at the corner, additional low-frequency disturbances arise along the shear layer. Self-resonance of these disturbances leads to the radiation of elongated structures upstream of reattachment, which extend outward from the shear layer and terminate at the separation shock. This shear-layer disturbance is determined to be dominantly unstable between separation and reattachment but is significantly damped after reattachment.Item TURBULENCE AND SUPERFLUIDITY IN THE ATOMIC BOSE-EINSTEIN CONDENSATE(2024) Zhao, Mingshu; Spielman, Ian; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)In this dissertation I investigate turbulence in atomic Bose-Einstein condensates (BECs), focusing on the challenge of quantifying velocity field measurements in quantum fluids. Turbulence, a universal phenomenon observed across various scales and mediums – from classical systems like Earth's oceans and atmosphere to quantum fluids including neutron stars, superfluid helium, and atomic BECs – exhibits complex fluid motion patterns spanning a wide range of length scales. While classical turbulence has been extensively studied, quantum systems present many open questions, particularly regarding the existence of an inertial scale and the applicability of Kolmogorov scaling laws. I introduce a novel velocimetry technique, analogous to particle image velocimetry (PIV), using spinor impurities as tracer particles. This method enables the direct measurement of the velocity field and thereby the velocity structure functions (VSFs) in turbulent atomic BECs. The technique overcomes limitations of existing experimental approaches that rely on time of flight (TOF) measurements, offering a clearer connection to VSFs and enabling a more direct comparison of turbulence in atomic gases with other fluids. The cold-atom PIV technique enables directly measuring the velocity field, leading to a detailed analysis of both VSFs and the velocity increment probability density functions (VI-PDF). Key findings include the observation of superfluid turbulence conforming to Kolmogorov theory from VSFs, and intermittency from high order of VSFs and the non-Gaussian fat tail in the VI-PDF.Item Physics and Modelling of Compressible Turbulent Boundary Layer(2023) Lee, Hanju; Martin, Pino; Aerospace Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Key findings from a research study that focuses on understanding the effect of Mach number, Reynolds number and wall temperature on compressible turbulent boundary layers (CTBL) in the hypersonic regime are presented in this dissertation. The study utilizes a comprehensive CTBL database developed using an in-house direct numerical simulation (DNS) code at the CRoCCo laboratory. The database encompasses a range of semi-local Reynolds numbers (800 to 34,000) and Mach numbers up to 12, incorporating wall-cooling. The effects of density and viscosity fluctuations on the total stress balance are identified and used to create a new mean velocity transformation for compressible boundary layers. The role, significance and physical mechanisms connecting density and viscosity fluctuations to the momentum balance and to the viscous, turbulent and total stresses are presented, allowing the creation of generalized formulations. We identify the significant properties that thus-far have been neglected in the derivation of velocity transformations: (1) the Mach-invariance of the near-wall momentum balance for the generalized total stress, and (2) the Mach-invariance of the relative contributions from the generalized viscous and Reynolds stresses to the total stress. The proposed velocity transformation integrates both properties into a single transformation equation and successfully demonstrates a collapsing of all currently considered compressible cases onto the incompressible law of the wall, within the bounds of reported slope and intercept for incompressible data. Based on the physics embedded in the two scaling properties, the success of the newly proposed transformation is attributed to considering the effects of the viscous stress and turbulent stresses as well as mean and fluctuating density viscosity in a single transformation form. The Reynolds number trends of large turbulent structures in compressible turbulent boundary layers are investigated using the pre-multiplied energy spectra based on the density corrected fluctuating streamwise velocity signal. Results demonstrate the existence of friction as well as semi-local Reynolds number trend associated with large-scale structures, similar to trends observable in incompressible turbulent boundary layers (ITBL). In particular, the behavior of turbulence in the inner layer is seen to exhibit dependence based on both definitions of Reynolds numbers. On the contrary, the strength of large turbulent structures is seen to be only dependent on friction Reynolds number. This result directly contrasts with the observation of the near-wall turbulent intensity peak increasing with semi-local Reynolds number. The discrepancy is mended with a suggestion that the large turbulent scales in the log layer of which the strength increases with friction Reynolds number, are modified through the changes in local fluid properties such that the scale interaction near the wall increases as semi-local Reynolds number. In another words, closer to the wall, the CTBL flow behaves like a semi-local Reynolds number flow, while closer to the freestream, it behaves like a friction Reynolds number flow. Furthermore, the present study examines the Reynolds number dependence of the length scale between small and large turbulent scales. The analysis highlights the inadequacy of using a univariable wavelength based on viscous, semi-local or outer length scales to differentiate small and large scales. Based on this, the use of Reynolds number-dependent length scales is recommended. Overall, the study provides valuable insights into the Reynolds number trends of large turbulent structures in CTBL, emphasizing the influence of both semi-local Reynolds number and friction Reynolds number on turbulence characteristics.Item NONLINEAR INTERNAL WAVES AND SHORT-TERM VARIABILITY OF CARBON SYSTEM DRIVEN BY LATERAL CIRCULATION IN COASTAL PLAIN ESTUARY(2023) Li, Renjian; Li, Ming; Marine-Estuarine-Environmental Sciences; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Recent observations in Chesapeake Bay showed that the interaction between lateral circulation and channel-shoal bathymetry generated internal lee waves which subsequently propagated onto shallow shoals and evolved into internal solitary waves, leading to overturning and enhanced turbulent mixing. However, it is unknown under what hydrodynamic conditions the lee waves could be generated and how the nonlinear internal waves evolved. Using an idealized straight channel representative of a coastal plain estuary, we conducted numerical simulations to investigate internal wave generation over a range of river flows and tidal amplitudes. The model results are summarized using the estuarine classification diagram based on the freshwater Froude number Frf and the mixing parameter M. Δh decreases with increasing Frf as stronger stratification suppresses waves, and no internal waves are generated under large Frf. Δh initially increases with increasing M as the lateral flows become stronger with stronger tidal currents, but decreases or saturates to a certain amplitude as M further increases. This regime diagram suggests that internal lee waves can be generated in a wide range of estuarine conditions. To examine the nonlinear evolution of internal waves, a three-dimensional nonhydrostatic model with nested model domains and increasing grid resolution was configured. The lee wave steepens into a shorter elevation wave due to shoaling and soon evolves into a depression with a train of undular waves at its tail as bottom boundary mixing elevates the halocline above the mid-depth. These nonlinear internal waves enhance the turbulent dissipation rate over the deep channel and shallow shoal, suggesting an important energy source for mixing in stratified coastal plain estuaries. In addition, a pH sensor deployed at the middle reach of Chesapeake Bay recorded high-frequency variability in bottom pH driven by along-channel winds. Though wind-driven lateral circulation can advect high pH water downward, the slow air-sea exchange of CO2 limits the lateral ventilation. With DIC and TA budget analysis and comparison with cross-sections at upper- and lower-Bay where strong lateral circulation was confined in the surface layer, we found vertical mixing and replenishment of oceanic water by longitudinal advection could be more important mechanisms to ventilate bottom pH.Item Model Order Reduction for Parameter-Dependent Partial Differential Equations with Constraints(2023) Davie, Kayla Diann; Elman, Howard C; Applied Mathematics and Scientific Computation; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Reduced-order methods have been used to reliably solve discrete parametrized mathematical models and to lessen the associated computational complexity of these models by projecting them onto spaces of reduced order. The reduced-order spaces are spanned by a finite number of full-order solutions, a reduced basis, that, if well-chosen, provide a good approximation of the entire solution manifold. Reduced-order methods have been used with various problem classes including different types of constrained parametrized problems such as constrained parametrized partial differential equations (PDEs) where the constraints are built into the PDEs, and parametrized PDE-constrained optimization problems, or PDE-control problems, where the constraints themselves are PDEs. In the deterministic setting, both of these problem classes involve discrete models that are of saddle-point form and can be computationally expensive to solve. It is well known that saddle-point problems must satisfy an inf-sup condition to ensure stability of the solution, thus, solving deterministic variations of these models requires the consideration and satisfaction of an inf-sup stability condition. When these models are subject to parametrization, the solution to a deterministic problem is sought for many parameter values. Reduced-order models for these problem classes are often constructed so that they mirror the full-order models and are also of saddle-point form. In the established RB methods we study for the problem classes explored in this thesis, the reduced basis is represented as a block-diagonal matrix that produces a saddle-point reduced system and is augmented to satisfy inf-sup stability. Two methods of building an augmented RB to ensure inf-sup stability that have been well studied are augmentation by aggregation and augmentation by the supremizer. We present a comparative study of these two common methods of stabilizing reduced order models, through use of the supremizer and through aggregation, and compare the accuracy, efficiency, and computational costs associated with them for solving the parametrized PDE-control problem. We propose a new approach to implementing the RB basis, the stacked reduced basis, that produces a reduced system that is not of saddle-point form. Implementing the stacked reduced basis avoids the necessity to satisfy the inf-sup condition to ensure stability and therefore, to augment the reduced bases spaces. This results in a reduced basis system of smaller order, which reduces the computational work in the online step. While inf-sup stability is avoided, there are still issues with the stability of the stacked reduced system during RB construction, particularly for the constrained PDE problem class. We show that this can be addressed by penalization and present results to show that penalization improves the stability of an established augmented RB method as well. We present numerical results to compare the new approach to two developed ways of implementing the RB method (with both commonly accepted choices of augmentation) and prove the efficiency of the proposed approach. We study the efficiency of the stacked reduced basis for both PDE-control problems and constrained PDEs subject to parametrization.