Multiphase flows abound in nature and enterprises. Our daily interactions with fluids - washing, drinking, and cooking, for example - occur at a free surface and within the realm of multiphase flows. The applications of multiphase flows within the context of emulsions, which are caused by mixing two immiscible fluids, have been of interest since the nineteenth century: compartmentalizing one fluid in another is particularly of interest in applications in pharmaceutical, materials, microfluidics, chemical, and biological engineering. Even more control in compartmentalization and delivery can be obtained through the usage of double emulsions, which are emulsions of smaller drops (i.e., inner drop) within larger drops (i.e., outer drop). The goal of this work is to understand the dynamic behavior of compound drops in confined flow at low Reynolds numbers. These behaviors include the migration patterns, limit cycles, and equilibrium locations in confined flows such as channel flows.<br> <br>Firstly, we look at non-concentric compound drops that are subject to simple shear flows. The eccentricity in the inner drop is either within the place of shear, normal to the plane of shear, or mixed. We show unreported motions that persist throughout time regardless of the initial eccentricity, given that the deformations of the inner and outer drops are small. Understanding the temporal dynamics of compound drops within the simple shear flow, one of the simplest background flows that may be imposed, allows us to probe at the dynamics of more complicated background flows.<br> <br>Secondly, we look at the lateral migration of compound drops in a Poiseuille flow. Depending on the initial condition, we show that there are multiple equilibria. We also show that the majority of initial configurations results in the compound drop with symmetry about the short wall direction. We then show the time it takes for the interfaces to merge if a given initial configuration does not reach the aforementioned symmetry.<br> <br>Thirdly, while the different equilibria of compound drops offer some positional differences at different radii ratio, we show that the lift force profiles at non-equilibrium locations offer distinctly different results for compound drops with different radii ratio. We then look at how this effect is greater than changes that arise due to viscosity ratio changes, and offer insights on what may create such a change in the lift force profile.

A key component of research in the aerospace industry constitutes hypersonic flights (M>5) which includes the design of commercial high-speed aircrafts and development of rockets. Computational analysis becomes more important due to the difficulty in performing experiments and reliability of its results at these harsh operating conditions. There is an increasing demand from the industry for the accurate prediction of wall-shear and heat transfer with a low computational cost. Direct Numerical Simulations (DNS) create the standard for accuracy, but its practical usage is difficult and limited because of its high cost of computation. The usage of Reynold's Averaged Navier Stokes (RANS) simulations provide an affordable gateway for industry to capitalize its lower computational time for practical applications. However, the presence of existing RANS turbulence closure models and associated wall functions result in poor prediction of wall fluxes and inaccurate solutions in comparison with high fidelity DNS data. In recent years, machine learning emerged as a new approach for physical modeling. This thesis explores the potential of employing Machine Learning (ML) to improve the predictions of wall fluxes for hypersonic turbulent boundary layers. Fine-grid RANS simulations are used as training data to construct a suitable machine learning model to improve the solutions and predictions of wall quantities for coarser meshes. This strategy eliminates the usage of wall models and extends the range of applicability of grid sizes without a significant drop in accuracy of solutions. Random forest methodology coupled with a bagged aggregation algorithm helps in modeling a correction factor for the velocity gradient at the first grid points. The training data set for the ML model extracted from fine-grid RANS, includes neighbor cell information to address the memory effect of turbulence, and an optimal set of parameters to model the gradient correction factor. The successful demonstration of accurate predictions of wall-shear for coarse grids using this methodology, provides the confidence to build machine learning models to use DNS or high-fidelity modeling results as training data for reduced-order turbulence model development. This paves the way to integrate machine learning with RANS to produce accurate solutions with significantly lesser computational costs for hypersonic boundary layer problems.

<p>Nanosecond spark plasma actuators provide an opportunity to reduce pollutants by promoting efficient combustion in engines or provide targeted, tunable, flow control over vehicles, due to their ability to influence flow and combustion through multiple mechanisms. The plasma actuators can be physically unobtrusive, can be turned on and off and their low duty cycle, large bandwidth, and light weight make them more appealing than other control approaches. One method by which these plasma actuators interact with the environment is by inducing a complex local flow field and in order, to design scalable, high frequency actuators effectively, it is necessary to first understand the flow induced by a single spark discharge. Most experimental analysis on the flow induced by spark discharges has been restricted to qualitative descriptions of the flow field, primarily due to the difficulties associated with measuring such a transient and highly complex flow with sufficient spatiotemporal resolution. Quantitative, experimental characterization of the flow induced by a spark discharge remains lacking. </p><p> </p><p>A spark discharge produces a shock wave and a hot gas kernel with a complex flow field following the shock. In this work, combined experimental and theoretical characterization of the spark induced flow is performed through a series of high spatiotemporal resolution measurements of the density and velocity fields and reduced-order modeling. The work investigates the mechanisms driving the cooling and vorticity generation in spark induced flow and the 3D nature of the flow field. Planar (2D-3C) and volumetric (3D-3C) velocity measurements are taken using stereoscopic particle image velocimetry (SPIV) and tomographic PIV, respectively. Density measurements are taken using background oriented schlieren (BOS) and high speed schlieren imaging is used to capture the shock wave induced by the spark.</p><p> </p><p>The work shows that spark plasma discharges induce vortex rings whose vorticity is likely generated due to baroclinic torque arising from the non-uniform strength of the induced shock wave. The hot gas kernel cools in two stages: an initially fast cooling regime, followed by a slower cooling process. Reduced order analytical models are developed to describe the cooling observed in the fast regime and the role of the vortex rings in the entrainment of cold ambient gas and the cooling of the hot gas kernel. The results show that the vortex rings entrain ambient gas and drive cooling in the fast, convective regime, cooling approximately 50% of the hot gas within the first millisecond of the induced flow. An increase in the electrical energy deposited in the spark gap increases the shock strength and curvature and increases the vortex ring strength, thereby increasing the cooling rate and expansion of the hot gas kernel. The volumetric velocity measurements capture one of the two induced vortex rings and provide a framework for the improvements needed in future tomographic PIV experiments of the spark induced flow field, necessary in assessing the 3D nature of the induced vortex rings.</p><p> </p><p> The results of this work provide the first set of quantitative, experimental data on flow induced by nanosecond spark discharges that can be used for validation of computational fluid dynamics (CFD) simulations. The results demonstrate that spark plasmas induce vortex ring-driven mixing flows and the results on mixing and cooling of the hot gas kernel can be extended to any passive scalars present in the flow field as well as inform pulsation frequencies and actuator designs for flow and combustion control. The results from the reduced order modeling can inform future studies and applications of nanosecond spark discharges and can be extended to a variety of other types of plasma discharges like laser sparks, long duration sparks and surface discharges with similar induced flow fields.<br></p>

<div>This dissertation focuses on a consistent and conservative Phase-Field method for multiphase flow problems, and it includes both model and scheme development. The first general question addressed in the present study is the multiphase volume distribution problem. A consistent and conservative volume distribution algorithm is developed to solve the problem, which eliminates the production of local voids, overfilling, or fictitious phases, but follows the mass conservation of each phase. One of its applications is to determine the Lagrange multipliers that enforce the mass conservation in the Phase-Field equation, and a reduction consistent conservative Allen-Cahn Phase-Field equation is developed. Another application is to remedy the mass change due to implementing the contact angle boundary condition in the Phase-Field equations whose highest spatial derivatives are second-order. As a result, using a 2nd-order Phase-Field equation to study moving contact line problems becomes possible.</div><div><br></div><div>The second general question addressed in the present study is the coupling between a given physically admissible Phase-Field equation to the hydrodynamics. To answer this general question, the present study proposes the <i>consistency of mass conservation</i> and the <i>consistency of mass and momentum transport</i>, and they are first implemented to the Phase-Field equation written in a conservative form. The momentum equation resulting from these two consistency conditions is Galilean invariant and compatible with the kinetic energy conservation, regardless of the details of the Phase-Field equation. It is further illustrated that the 2nd law of thermodynamics and <i>consistency of reduction</i> of the entire multiphase system only rely on the properties of the Phase-Field equation. All the consistency conditions are physically supported by the control volume analysis and mixture theory. If the Phase-Field equation has terms that are not in a conservative form, those terms are treated by the proposed consistent formulation. As a result, the proposed consistency conditions can always be implemented. This is critical for large-density-ratio problems.</div><div><br></div><div>The consistent and conservative numerical framework is developed to preserve the physical properties of the multiphase model. Several new techniques are developed, including the gradient-based phase selection procedure, the momentum conservative method for the surface force, the boundedness mapping resulting from the volume distribution algorithm, the "DGT" operator for the viscous force, and the correspondences of numerical operators in the discrete Phase-Field and momentum equations. With these novel techniques, numerical analyses ensure that the mass of each phase and momentum of the multiphase mixture are conserved, the order parameters are bounded in their physical interval, the summation of the volume fractions of the phases is unity, and all the consistency conditions are satisfied, on the fully discrete level and for an arbitrary number of phases. Violation of the consistency conditions results in inconsistent errors proportional to the density contrasts of the phases. All the numerical analyses are carefully validated, and various challenging multiphase flows are simulated. The results are in good agreement with the exact/asymptotic solutions and with the existing numerical/experimental data.</div><div> </div><div><br></div><div>The multiphase flow problems are extended to including mass (or heat) transfer in moving phases and solidification/melting driven by inhomogeneous temperature. These are accomplished by implementing an additional consistency condition, i.e., <i>consistency of volume fraction conservation</i>, and the diffuse domain approach. Various problems are solved robustly and accurately despite the wide range of material properties in those problems.</div>

<p> With new technologies taking advantages of the rapid miniaturization of devices to microscale across emerging industries, there is an unprecedented increase in the heat fluxes generated. The relatively low phase-change thermal resistance associated with boiling is beneficial for dissipating high heat flux densities in compact spaces. However, for boiling heat transfer, a high degree of geometrical confinement significantly alters two-phase interface dynamics which affects the flow pattern, wetting dynamics, and moreover, the heat transfer rate of the boiling processes. Hence, it is crucial to have a deeper understanding of the mechanistic effects of confinement on two-phase heat dissipation and carefully examine the applicability of boiling correlations developed for unconfined pool boiling to predict and optimize design of extremely compact two-phase thermal management solutions. This dissertation develops and demonstrate a fundamental understanding of the impact of confinement on pool boiling. To elucidate the mechanisms that impact confined boiling, this study experimentally evaluates boiling characteristics through the quantification of boiling curves and high-speed visualization across a range of gap spacing smaller than the capillary length of the working fluid. </p> <p><br></p> <p> This work reveals the existence of two distinct boiling regime uniquely observed in boiling in confined configurations (namely, intermittent boiling and partial dryout). In contrast to pool boiling where the maximum heat transfer coefficient occurs below the critical heat flux limit, the intermittent boiling regime demonstrates the highest heat transfer coefficient in confined boiling. Then, this study provides a mechanistic explanation for the enhanced heat transfer rate due to geometrical confinement. Mainly, small residual pockets of vapor, termed ‘stem bubbles’ herein, remain on the boiling surface through a pinch-off process. These stems bubbles act as seeds for vapor growth in the next phase of the boiling process without the need for active nucleation sites. Furthermore, this dissertation develops a more accurate, mechanistic-based model for the phenomena that occur at CHF in confined configurations. The newly developed mechanistic understanding and model provides guidance on new directions for designing extremely compact two-phase thermal solutions.</p>

Accuracy in turbulence modeling remains a hurdle in the widespread use of Computational Fluid Dynamics (CFD) as a tool for furthering fluids dynamics research. Meanwhile, computational power remains a significant concern for solving real-life wall-bounded flows, which portray a wide range of length and time scales. The tools for turbulence analysis at our disposal, in the decreasing order of their accuracy, include Direct Numerical Simulation (DNS), Large Eddy Simulation (LES), and Reynolds-Averaged Navier Stokes (RANS) based models. While DNS and LES would remain exorbitantly expensive options for simulating high Reynolds number flows for the foreseeable future, RANS is and continues to be a viable option utilized in commercial and academic endeavors. In the first part of the present work, flow over the back-step test case was solved, and parametric studies for various parameters such as re-circulation length (X_r), coefficient of pressure (C_p), and coefficient of skin friction (C_f) are presented and validated with experimental results. The back-step setup was chosen as the test case as turbulent modeling of flow past backward-facing step has been pivotal to understand separated flows better. Turbulence modeling is done on the test case using RANS (k-ε and k-ω models), and LES modeling, for different values of Reynolds number (Re ∈ {2, 2.5, 3, 3.5} × 10⁴) and expansion ratios (ER ∈ {1.5, 2, 2.5, 3}). The LES results show good agreement with experimental results, and the discrepancy between the RANS results and experimental data was highlighted. The results obtained in the first part reveal a pattern of under-prediction noticed with using RANS-based models to analyze canonical setups such as the backward-facing step. The LES results show close proximity to experimental data, as mentioned above, which makes it an excellent source of training data for the machine learning analysis outlined in the second part. The highlighted discrepancy and the inability of the RANS model to accurately predict significant flow properties create the need for a better model. The purpose of the second part of the present study is to make systematic efforts to minimize the error between flow properties from RANS modeling and experimental data, as seen in the first part. A machine learning model was constructed in the second part of the present study to predict the eddy viscosity parameter (μt) as a function of turbulent kinetic energy (TKE) and dissipation rate (ε) derived from LES data, effectively working as an ad hoc eddy-viscosity based turbulence model. The machine learning model does not work well with the flow domain as a whole, but a zonal analysis reveals a better prediction of eddy viscosity than the whole domain. Among the zones, the area in the vicinity of the re-circulation zone gives the best result. The obtained results point towards the need for a zonal analysis for the better performance of the machine learning model, which will enable us to improve RANS predictions by developing a reduced order turbulence model.

<p>Fractional calculus is the integration and differentiation to an arbitrary or fractional order. The techniques of fractional calculus are not commonly taught in engineering curricula since physical laws are expressed in integer order notation. Dr. Richard Magin (2006) notes how engineers occasionally encounter dynamic systems in which the integer order methods do not properly model the physical characteristics and lead to numerous mathematical operations. In the following study, the application of fractional order calculus to approximate the angular position of the disk oscillating in a Newtonian fluid was experimentally validated. The proposed experimental study was conducted to model the nonlinear response of an oscillating system using fractional order calculus. The integer and fractional order mathematical models solved the differential equation of motion specific to the experiment. The experimental results were compared to the integer order and the fractional order analytical solutions. The fractional order mathematical model in this study approximated the nonlinear response of the designed system by using the Bagley and Torvik fractional derivative. The analytical results of the experiment indicate that either the integer or fractional order methods can be used to approximate the angular position of the disk oscillating in the homogeneous solution. The following research was in collaboration with Dr. Richard Mark French, Dr. Garcia Bravo, and Rajarshi Choudhuri, and the experimental design was derived from the previous experiments conducted in 2018.</p>

<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>