Liquid injection in cross flows has applications in gas-turbine engines, afterburners and some rocket combustion chambers. Integral form of the conservation equations has been used to find a cubic formula for the drop size in liquid sprays in cross flows. Similar to the work on axial liquid sprays, the energy balance dictates that the initial kinetic energy of the gas and injected liquid be distributed into the final surface tension energy, kinetic energy of the gas and droplets, and viscous dissipation incurred. Kinetic energy of the cross flow is added to the energy balance. Then, only the viscous dissipation term needs to be phenomenologically modelled. The mass and energy balance for the spray flows renders to an expression that relates the drop size to all of the relevant parameters, including the gas- and liquid-phase velocities. The results agree well with experimental data and correlations for the drop size. The solution also provides for drop size-velocity cross-correlation, leading to drop size distributions based on the gas-phase velocity distribution. These aspects can be used in estimating the drop size for practical applications, and also in computational simulations of liquid injection in cross flows, and in other spray geometries in general.

Essential to the field of petroleum engineering, well testing is done to determine the important physical characteristics of a reservoir. In the case of a constant production rate (as opposed to a constant pressure), the well pressure drop is a function of both time and the formation's boundary conditions. This pressure drop goes through several distinct stages before reaching steady state or semi-steady state production. This paper focuses on the analysis of a circular well with a closed outer boundary and details the derivation of a new approximation, intended for the transient stage, from an existing steady state solution. This new approximation is then compared to the numerical solution as well as an existing approximate solution. The new approximation is accurate with a maximum 10% margin of error well into the semi-steady state phase with that error decreasing significantly as the distance to the closed external boundary increases. More accurate over a longer period of time than the existing line source approximation, the relevance and applications of this new approximate solution deserve further exploration.

Pseudo-steady state (PSS) flow is a dominant time-dependent flow regime during constant rate production from a closed reservoir. Recently Chen (2016) has obtained an exact analytical solution for the PSS flow of a fully-penetrated fractured vertical well with finite conductivity in an elliptical drainage area. The availability of this analytical solution shortens the computational time required for such a solution by several orders of magnitude. This paper correlates the PSS flow of a fully-penetrated fractured vertical well in square drainage areas to Chen’s solution for an elliptical drainage area using shape factors. Specifically such a shape factor is established by equating the dimensionless productivity index of the PSS flow in a square domain to that in an elliptical domain of identical area. The shape factor was dependent on the proppant number and fracture penetration ratio. Productivity index data for fractured wells with finite conductivity in square drainage area and no skin from Romero et al. (2003) was compared to Chen’s solution assuming equivalent drainage areas and identical proppant numbers, with the penetration ratio as a parameter. A non-linear multi-variable regression analysis results in a unified shape factor function with a correlation coefficient of 0.80 and a minimized sum of squared error of 36.1. The achieved shape factor allows the analytical solution for PSS flow of fractured well in an elliptical drainage area to be applied to square drainage areas. This generalization of the PSS flow solution is of practical significance in fracture design optimization and production rate decline analysis. Future recommendations including testing the accuracy of the shape factor in predictions of proppant numbers not used in analysis using COMSOL™, and increasing the dataset pool to increase the model accuracy.

Pseudo-steady state (PSS) flow is a dominant time-dependent flow regime during constant rate production from a closed reservoir. Using Chen's (2016) exact analytical solution for the PSS flow of a fully-penetrated fractured vertical well with finite conductivity in an elliptical drainage area, the computational time required to solve for the PSS constant b_D,PSS is greatly reduced. This constant is the inverse of the productivity index, J_D,PSS, which is often used in modern fracture design optimization. This paper correlates the PSS flow of a fully-penetrated fractured vertical well in triangular drainage areas to Chen's solution for an elliptical drainage area using shape factors. Numerical solutions for the PSS constant are created using COMSOL, which uses a 2D model of the fractured reservoir to output time and pressure data. For equivalent reservoir properties, the numerical data for the triangular reservoir yields a PSS constant that can be directly compared to the PSS constant obtained using Chen's solution. Lack of access to the Subsurface Flow Module of COMSOL greatly limited the number of simulations that could be run, thus more simulations would significantly improve the accuracy and applicability of the triangular shape factor by making it a function of the penetration ratio through nonlinear regression methods.

In the last several years, there has been a significant growth in research in the field of power harvesting, the process of capturing the energy surrounding a system and converting it into usable electrical energy. This concept has received particular interest in recent years with the ever-increasing production of portable and wireless electronic devices. Many of these devices that are currently in production utilize electrochemical batteries as a power source, which while effective, maintain the drawback of having a finite energy supply, thus requiring periodic replacement. The concept of power harvesting, however, works to solve these issues through electronics that are designed to capture ambient energy surrounding them convert it into usable electronic energy. The use of power harvesting in energy scavenging devices allows for the possible development of devices that are self-powered and do not require their power sources to be replaced. Several models have been developed by Soldano et al [3] and Liao et al [2] that have been proven accurate at predicting the power output of a piezoelectric power harvester in a cantileaver beam configuration. The work in this paper will expand further on the model developed by Liao et al [2], and as its main goal will use a modified form of that model to predict the optimal dimensions for a beam power harvester to achieve the maximum power output possible. The model will be updated b replacing the mode shape function used to approximate the deflection of the beam with the true defletion, which is based on the complex wavenumber that incorporates the complex Young's modulus of the material used. Other changes to account for this replacement will also be presented, along with numerical results of the final model.

The formation and stability of a slowly evolving zonal jet in 2-D flow with beta effect is analyzed using the model developed by Manfroi and Young in which the final governing equation was derived by means of a perturbation analysis of a barotropic vorticity equation with sinusoidal meridional mean flow. However in the original study the term β0, that represents the effect of large-scale Rossby waves, was dropped and was proceeded on a path of finding solutions for a simplified 1-D flow. The idea of this study is to understand the effects of the dropped term on the overall dynamics of the zonal jet evolution. For this purpose the system that is entirely deterministic with no additional forcing is solved by means of a standard finite difference scheme. The Numerical solutions are found for varying β0 and μ values where μ represents the bottom drag. In addition to this the criteria for the formation of zonal jets developed originally for the 1-D system is verified for the 2-D system as well. The study reveals the similarity in some of the results of the 1-D and the 2-D system like the merging of jets in the absence of bottom drag, formation of steady jets in presence of a non-zero bottom drag and the adherence to the boundary criteria for the formation of zonal jets. But when it comes to the formation of steady jets, a finite β0 value is required above which the solution is similar to the 1-D system. Also the jets formed under the presence of non-zero bottom drag seem wavy in nature which is different from the steady horizontal jets produced in the 1-D system.

Environmental remote sensing has seen rapid growth in the recent years and Doppler wind lidars have gained popularity primarily due to their non-intrusive, high spatial and temporal measurement capabilities. While lidar applications early on, relied on the radial velocity measurements alone, most of the practical applications in wind farm control and short term wind prediction require knowledge of the vector wind field. Over the past couple of years, multiple works on lidars have explored three primary methods of retrieving wind vectors viz., using homogeneous windfield assumption, computationally extensive variational methods and the use of multiple Doppler lidars.

Building on prior research, the current three-part study, first demonstrates the capabilities of single and dual Doppler lidar retrievals in capturing downslope windstorm-type flows occurring at Arizona’s Barringer Meteor Crater as a part of the METCRAX II field experiment. Next, to address the need for a reliable and computationally efficient vector retrieval for adaptive wind farm control applications, a novel 2D vector retrieval based on a variational formulation was developed and applied on lidar scans from an offshore wind farm and validated with data from a cup and vane anemometer installed on a nearby research platform. Finally, a novel data visualization technique using Mixed Reality (MR)/ Augmented Reality (AR) technology is presented to visualize data from atmospheric sensors. MR is an environment in which the user's visual perception of the real world is enhanced with live, interactive, computer generated sensory input (in this case, data from atmospheric sensors like Doppler lidars). A methodology using modern game development platforms is presented and demonstrated with lidar retrieved wind fields. In the current study, the possibility of using this technology to visualize data from atmospheric sensors in mixed reality is explored and demonstrated with lidar retrieved wind fields as well as a few earth science datasets for education and outreach activities.

The objective of this research is to develop robust, accurate, and adaptive algorithms in the framework of the extended finite element method (XFEM) for fracture analysis of highly heterogeneous materials with complex internal geometries. A key contribution of this work is the creation of novel methods designed to automate the incorporation of high-resolution data, e.g. from X-ray tomography, that can be used to better interpret the enormous volume of data generated in modern in-situ experimental testing. Thus new algorithms were developed for automating analysis of complex microstructures characterized by segmented tomographic images.

A centrality-based geometry segmentation algorithm was developed to accurately identify discrete inclusions and particles in composite materials where limitations in imaging resolution leads to spurious connections between particles in close contact.To allow for this algorithm to successfully segment geometry independently of particle size and shape, a relative centrality metric was defined to allow for a threshold centrality criterion for removal of voxels that spuriously connect distinct geometries.

To automate incorporation of microstructural information from high-resolution images, two methods were developed that initialize signed distance fields on adaptively-refined finite element meshes. The first method utilizes a level set evolution equation that is directly solved on the finite element mesh through Galerkins method. The evolution equation is formulated to produce a signed distance field that matches geometry defined by a set of voxels segmented from tomographic images. The method achieves optimal convergence for the order of elements used. In a second approach, the fast marching method is employed to initialize a distance field on a uniform grid which is then projected by least squares onto a finite element mesh. This latter approach is shown to be superior in speed and accuracy.

Lastly, extended finite element method simulations are performed for the analysis of particle fracture in metal matrix composites with realistic particle geometries initialized from X-ray tomographic data. In the simulations, particles fracture probabilistically through a Weibull strength distribution. The model is verified through comparisons with the experimentally-measured stress-strain response of the material as well as analysis of the fracture. Further, simulations are then performed to analyze the effect of mesh sensitivity, the effect of fracture of particles on their neighbors, and the role of a particles shape on its fracture probability.

Environmentally responsive microgels have drawn significant attention due to their intrinsic ability to change volume in response to various external stimuli such as pH, temperature, osmotic pressure, or electric and magnetic fields. The extent of particle swelling is controlled by the nature of the polymer-solvent interaction. This thesis focuses on design and synthesis of environmentally responsive microgels and their composites, and encompasses methods of utilizing microgel systems in applications as vehicles for the adsorption, retention, and targeted delivery of chemical species. Furthermore, self-assembled microgel particles at ionic liquid (IL)-water interfaces demonstrate responsive colloidal lattice morphology. The thesis first reports on the fundamental aspects of synthesis, functionalization, and characteristic properties of multifunctional environmentally responsive microgels derived from poly(N-isopropylacrylamide) (PNIPAm) and other functional co-monomers. In particular, the uptake and release of active chemical species such as rheology modifiers into and from these ionic microgels is demonstrated. Moreover, a facile tunable method for the formation of organic-inorganic composites with Fe3O4 nanoparticles adsorbed and embedded within ionic microgel particles is explored. Additionally, the development of zwitterionic microgels (ZI-MG) is presented. These aqueous ZI-MG dispersions exhibit reversible parabolic swelling as a function of pH and display a minimum hydrodynamic diameter at a tunable isoelectric point (IEP). This study also elucidates the controlled uptake and release of surfactants from these particle systems. The extent of surfactant loading and the ensuing relative swelling/deswelling behaviors within the polymer networks are explained in terms of their binding interactions. The latter part of this thesis highlights the versatility of fluorescently labeled microgel particles as stabilizers for IL-water droplets. When the prepared particles form monolayers and equilibrate at the liquid-liquid interface, the colloidal lattice organization may re-order itself depending on the surface charge of these particles. Finally, it is shown that the spontaneously formed and densely packed layers of microgel particles can be employed for extraction applications, as the interface remains permeable to small active species.

The study of deflagration to detonation transition (DDT) in explosives is of prime importance with regards to insensitive munitions (IM). Critical damage owing to thermal or shock stimuli could translate to significant loss of life and material. The present study models detonation and deflagration of a commonly used granular explosive: cyclotetramethylene-tetranitramine, HMX. A robust literature review is followed by computational modeling of gas gun and DDT tube test data using the Sandia National Lab three-dimensional multi-material Eulerian hydrocode CTH. This dissertation proposes new computational practices and models that aid in predicting shock stimulus IM response. CTH was first used to model experimental data sets of DDT tubes from both Naval Surface Weapons Center and Los Alamos National Laboratory which were initiated by pyrogenic material and a piston, respectively. Analytical verification was performed, where possible, for detonation via empirical based equations at the Chapman Jouguet state with errors below 2.1%, and deflagration via pressure dependent burn rate equations. CTH simulations include inert, history variable reactive burn and Arrhenius models. The results are in excellent agreement with published HMX detonation velocities. Novel additions include accurate simulation of the pyrogenic material BKNO3 and the inclusion of porosity in energetic materials. The treatment of compaction is especially important in modeling precursory hotspots, caused by hydrodynamic collapse of void regions or grain interactions, prior to DDT of granular explosives. The CTH compaction model of HMX was verified within 11% error via a five pronged validation approach using gas gun data and employed use of a newly generated set of P-α parameters for granular HMX in a Mie-Gruneisen Equation of State. Next, the additions of compaction were extended to a volumetric surface burning model of HMX and compare well to a set of empirical burn rates. Lastly, the compendium of detonation and deflagration models was applied to the aforementioned DDT tubes and demonstrate working functionalities of all models, albeit at the expense of significant computational resources. A robust hydrocode methodology is proposed to make use of the deflagration, compaction and detonation models as a means to predict IM response to shock stimulus of granular explosive materials.