<div>Global warming is considered to result from excessive emission of CO₂ caused by human activity. The security of long term CO₂ capture and sequestration on the subsurface depends on the integrity of caprocks. Natural and engineered subsurface activities can generate fractures in caprocks that can lead to CO₂ leakage. Reactive fluids that flow through a fracture may seal a fracture through mineral precipitation or open a fracture through dissolution. It is extremely useful to CO₂ storage to understand the behavior of reactive fluids that generates mineral precipitation that can seal a fracture. Experiments on non-reactive and reactive fluid mixing were performed to explore gravity-driven chemical dynamics that control the mixing and spatial distribution of mineral precipitates. Fracture inclination, fracture apertures, fluid pumping rates, and density contrasts between fluids were studied for their effects on fluid mixing. From non-reactive fluid mixing experiments, a less dense fluid was found to be confined to a narrow path (runlet) by the denser fluid under the influence of gravity. Fracture inclination angle affected the shape of the less dense fluid runlet. As the angle of inclination decreased, the area of the less dense runlet increased. Improved mixing and a potentially larger area of precipitation formation will occur during reactive fluid mixing when the fracture plane is perpendicular to gravity. Fracture aperture affected the time evolution of the mixing of the fluids, while pumping rate affected fluid mixing by controlling the relative velocities between the two fluids. The fact that the spatial distribution of the two fluids, instead of the fracture roughness, dominated the fluid mixing sheds light on the potential behaviors of reactive fluids mixing in fractures. The location for the majority of precipitation formation and the transport of precipitates can be accordingly predicted from knowledge of the properties of the two reactive fluids and the orientation of the fracture.</div><div>From a small study on wave propagation across fractures with precipitates, simulation results showed that the impedance difference between the matrix material and the precipitate affects the transmitted signal amplitude. Both the aperture and fraction of aperture filled with precipitates affect signal amplitude.</div><div><br></div>

<div>Particle Image Velocimetry (PIV) is a non-invasive measurement technique which resolves the flow velocity by taking instantaneous snapshots of tracer particle motion in the flow and uses digital image cross-correlation to estimate the particle shift up to subpixel accuracy. The measurement chain incorporates numerous sets of parameters, such as the particle displacements, the particle image size, the flow shear rate, the out-of-plane motion for planar PIV and image noise to name a few, and these parameters are interrelated and influence the final velocity estimate in a complicated way. In the last few decades, PIV has become widely popular by virtue of developments in both the hardware capabilities and correlation algorithms, especially with the scope of 3-component (3C) and 3-dimensional (3D) velocity measurements using stereo-PIV and tomographic-PIV techniques, respectively. The velocity field measurement not only leads to other quantities of interest such as Pressure, Reynold stresses, vorticity or even diffusion coefficient, but also provides a reference field for validating numerical simulations of complex flows. However, such a comparison with CFD or applicability of the measurement to industrial design requires one to quantify the uncertainty in the PIV estimated velocity field. Even though the PIV community had a strong impetus in minimizing the measurement error over the years, the problem of uncertainty estimation in local instantaneous PIV velocity vectors have been rather unnoticed. A typical norm had been to assign an uncertainty of 0.1 pixels for the whole field irrespective of local flow features and any variation in measurement noise. The first article on this subject was published in 2012 and since then there has been a concentrated effort to address this gap. The current dissertation is motivated by such a requirement and aims to compare the existing 2D PIV uncertainty methods, propose a new method to directly estimate the planar PIV uncertainty from the correlation plane and subsequently propose the first comprehensive methods to quantify the measurement uncertainty in stereo-PIV and 3D Particle Tracking Velocimetry (PTV) measurements.</div><div>The uncertainty quantification in a PIV measurement is, however, non-trivial due to the presence of multitude of error sources and their non-linear coupling through the measurement chain transfer function. In addition, the advanced algorithms apply iterative correction process to minimize the residual which increases the complexity of the process and hence, a simple data-reduction equation for uncertainty propagation does not exist. Furthermore, the calibration or a reconstruction process in a stereo or volumetric measurement makes the uncertainty estimation more challenging. Thus, current uncertainty quantification methods develop a-posterior models utilizing the evaluated displacement information and combine it with either image information, correlation plane information or even calibration “disparity map” information to find the desired uncertainties in the velocity estimates.</div><div><br></div>

Despite the central importance of porous electrodes to any advanced electrochemical system, there is no clear answer to “<i>How to make the best electrode</i>?”. The source of ambiguity lies in the incomplete understanding of convoluted material interactions at smaller – difficult to observe length and timescales. Such mesoscopic interactions, however, abide by the fundamental physical principles such as mass conservation. The porous electrodes are investigated in such a physics-based setting to comprehend the interplay among structural arrangement and off-equilibrium processes. As a result, a synergistic approach exploiting the complementary characteristics of controlled experiments and theoretical analysis emerges to allow mechanistic insights into the associated mesoscopic phenomena. The potential of this philosophy is presented by investigating three distinct electrochemical systems with their unique peculiarities.

<div>The current study is aimed at developing a well-posed and objective, i.e., frame invariant, Eulerian one-dimensional (1D) Two-Fluid Model (TFM) to predict flow regime transition from dispersed to clustered bubbly and slug flow for vertical adiabatic two-phase flows. Two-phase flows in general are characterized by local material wave or void fraction wave instabilities and flow regime transitions are one of the important consequences of these instabilities. The physical mechanism of wake entrainment for clustering of dispersed bubbles is proposed, leading to formation of bubble clusters and Taylor bubbles. The focus of the work is on simulation of the local interfacial structures for bubble clusters and Taylor bubbles, using a well-posed, unstable and non-linearly bounded 1D Shallow Water TFM.</div><div><br></div><div>The first part of the current study investigates the dynamic behavior of the well posed 1D mechanistic TFM obtained from the averaging approach of Ishii [1], due to wake entrainment instability. For this, a 1D Shallow Water TFM derived from the 1D mechanistic TFM is used, which retains the same dynamic behavior as that of the latter at short wavelengths and the required wake entrainment force is derived mechanistically. Three stability approaches are followed to study the dynamic behavior of the 1D Shallow Water TFM: characteristics, dispersion analysis, and nonlinear numerical simulations. An in-house code is used for the 1D numerical simulations of the growth of void fraction waves due to wake entrainment. The simulation results are validated with the experimental data of Cheng and Azzopardi [2] and Song et al. [3] To conclude the first part, the 1D results of the two-equation Shallow Water TFM are carried over to the complete four-equation TFM for quasi 1D simulations using the commercial CFD code of ANSYS Fluent.</div><div><br></div>As an alternative to the mechanistic approach, which is based on Newtonian mathematics, a variational approach based on Lagrangian and Hamiltonian mathematics is used in the second part of the thesis. While the mechanistic approach operates in terms of forces acting on the two-phase mixture, the variational approach operates in terms of energies of the two-phase system. To derive the equations of motion using the variational approach, the extended Hamilton principle of least action is applied to the Lagrangian density of the two-phase mixture. One of the appealing features<br>17<br>of this procedure is that the derived equations of motion are objective (Geurst [4]), in particular the added mass terms.<br>Thus, the second part of the current study focuses on deriving an objective, well-posed and unstable 1D TFM as well as developing a constitutive model for the wake entrainment effect using the variational method. Additional momentum transfer terms present in both the liquid phase and gas phase momentum equations, which render the variational TFM objective, are discussed. The variational method is then used to derive the 1D Shallow Water TFM using the fixed flux assumption. The conservative interfacial momentum transfer terms require formulation of the inertial coupling between the phases. Potential flow theory is first used to derive the inertial coupling coefficient for a single bubble and then for a pair of bubbles to consider interaction between the two bubbles. Then, a lumped parameter model is used to derive the inertial coupling coefficient for the wake entrainment effect. A local drag coefficient is obtained for the non-conservative interfacial drag force from the experimental data using kinematic approximation, i.e., force balance between drag and gravity. The linear and non-linear stability analyses are used to address the stability of the 1D variational Shallow Water TFM. The presence of appropriate short-wave physics makes the 1D Shallow Water TFM hyperbolic well-posed and kinematically unstable. Finally, numerical simulations are performed to demonstrate the development of void fraction waves due wake entrainment. The growth of void fraction waves is non-linearly bounded, i.e., Lyapunov stable. The simulation results are compared with the experimental data to validate the propagation properties of void fraction waves for bubble clusters and Taylor bubbles. This work illustrates the short-wave two-phase flow simulation capability of the TFM for the bubbly to slug flow regime transition.

<div>A growing global population and improved standard of living in developing countries have resulted in an unprecedented increase in energy demand over the past several decades. While renewable energy sources are increasing, a huge portion of energy is still converted into useful work using heat engines. The combustion process in diesel and petrol engines releases carbon dioxide and other greenhouse gases as an unwanted side-effect of the energy conversion process. By improving the efficiency of internal combustion engines, more chemical energy stored in petroleum resources can be realized as useful work and, therefore, reduce global emissions of greenhouse gases. This research focused on improving the thermal efficiency of opposed-piston engines, which, unlike traditional reciprocating engines, do not use a cylinder head. The cylinder head is a major source of heat loss in reciprocating engines. Therefore, the opposed-piston engine has the potential to improve overall engine efficiency relative to inline or V-configuration engines.</div><div><br></div>The objective of this research project was to further improve the design of opposed-piston engines by using computational fluid dynamics (CFD) modeling to optimize the engine geometry. The CFD method investigated the effect of intake port geometry and exhaust piston lead angle on the scavenging process and in-cylinder turbulence. After the CFD data was analyzed, scavenging efficiency was found insensitive to transfer port geometry and exhaust piston lead angle with a maximum change of 0.61%. Trapping efficiency was altered exclusively by exhaust piston lead angle and changed from 18% to 26% as the lead angle was increased. The in-cylinder turbulence parameters of the engine (normalized swirl circulation, normalized tumble circulation, and normalized TKE) experienced more complex relationships. All turbulence parameters were sensitive to changing transfer port geometry and exhaust piston lead angle. Some examples of trends seen during the analysis include: an increase in normalized swirl circulation from 0.01 to 4.45 due to changes in swirl angle, a change in normalized tumble circulation from -28.52 to 21.11 as swirl angle increased, and an increase in normalized tumble circulation from 14.20 to 33.68 as exhaust piston lead angle was increased. Based on the present work, an optimum configuration was identified for a swirl angle of 15°, a tilt angle of 10°, and an exhaust piston lead angle of 20°. Future work includes expanding the numerical model’s domain to support a complete cylinder-port configuration, adding combustion products to the diffusivity equation in the UDF, and running additional test cases to describe the entire input space for the sensitivity analysis.<br>