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Numerical Investigations of Transport and Chemistry Modeling for Lean Premixed Hydrogen Combustion
Get PDFThe use of hydrogen as a fuel for power generation applications has been suggested as an additive to, or replacement of, hydrocarbon fuels. The safety of hydrogen combustion has also received recent attention due to nuclear power plant disasters and the rise of hydrogen refuelling stations. In these uses and scenarios, lean hydrogen--air flames are prone to thermo-diffusive instabilities which can be dangerous to equipment and personnel. These instabilities are heavily influenced by two mechanisms: transport properties (e.g., diffusion) and chemical species production rates. This thesis investigates lean premixed hydrogen combustion using direct numerical simulations. A wide range of flame configurations are considered, spanning one-dimensional steady configurations to three-dimensional unsteady laminar and turbulent flames with high curvature. In particular, the two controlling mechanisms of thermo-diffusive instabilities are carefully investigated.
The effects of transport properties, in particular the importance of thermal diffusion in these mixtures, are quantified through global and local evaluations. Thermal diffusion is found to change flame speeds in one-dimensional flat flames, and also modify species profiles due to the increased diffusivity of light reactants. The impact of thermal diffusion is greatly enhanced in the presence of flame curvature, resulting in higher flame speeds (20% to 30% for two- and three-dimensional laminar and turbulent flames), fuel consumption, and flame surface area relative to simulations neglecting thermal diffusion. The mixture-averaged thermal diffusion model proposed by Chapman and Cowling (1970) is found to accurately reproduce global and local flame statistics (including enhanced burning and local extinction) computed using multicomponent transport at significantly reduced costs. Further cost reductions of the mixture-averaged thermal diffusion method are undertaken, and a new model is developed with constant computational requirements for large (~100 species) chemical models. The resulting reduced thermal diffusion model additionally improves upon the accuracy of the mixture-averaged thermal diffusion technique.
The effects of fluctuating chemical source terms on flame instabilities are then investigated using tabulated chemistry. One-dimensional unstretched flames including non-equal diffusion and thermal diffusion are incorporated into a chemistry table. This table successfully captures the interaction of differential diffusion and flame curvature. The chemistry tabulation approach is applied to a similar set of flame configurations, and accurate predictions of global and local statistics are found. The tabulated chemistry method reproduces flame curvature, local enhanced burning, and local extinction of unstable flames using one-dimensional, flat, burning flames in its construction. The proposed reduced-order thermal diffusion and chemistry tabulation models significantly reduce computational costs while simultaneously including physical properties necessary to predict lean premixed hydrogen--air flame instabilities.</p
Computational Investigation of Ionic Diffusion in Polymer Electrolytes for Lithium-Ion Batteries
Get PDFEnergy storage is a critical problem in the 21st century and improvements in battery technology are required for the next generation of electric cars and electronic devices. Solid polymer electrolytes show promise as a material for use in long-lifetime, high energy density lithium-ion batteries. Improvements in ionic conductivity, however, for the development of commercially viable materials, and, to this end, a series of computational studies of ionic diffusion were performed. First, pulsed charging is examined as a technique for inhibiting the growth of potentially dangerous lithium dendrites. The effective timescale for pulse lengths is determined as a function of cell geometry. Next, the atomistic diffusion mechanism in the leading polymer electrolyte, PEO-LiTFSI, is characterized as a function of temperature, molecular weight, and ionic concentration using molecular dynamics simulations. A novel model for describing coordination of lithium to the polymer structure is developed which describes two types of interchain motion "hops" and "shifts," the former of which is shown to contribute significantly to ionic diffusion. The methodology developed in this study is then applied to a new problem – the adsorption of CO2 at the surface of semi-permeable polymer membranes. Finally, a new method, PQEq, is developed, which provides an improved description of electrostatic interactions with the inclusion of explicit polarization, Gaussian shielding, and charge equilibration. The dipole interaction energies obtained from PQEq are shown to be in excellent agreement with QM and a preliminary application of PQEq to a polymer electrolyte suggest that it can provide an improved description of ionic diffusion. Taken as a whole, these techniques show promise as tools to explore and characterize novel materials for lithium-ion batteries
Thermal Transport in Three-Dimensional Nanoarchitected Materials
Get PDFMaterials that simultaneously possess ultralow thermal conductivity, high stiffness, and damage tolerance are highly desirable for engineering applications. However, this combination of properties has never been demonstrated in a single material because thermal and mechanical properties are coupled in most fully dense and porous solids. A new class of lattice materials with nanoscale features, called nanolattices, can fill this void in the material property space by virtue of their architecture and nanoscale dimensions. Extensive work on nanolattice mechanical properties report their excellent stiffness-to-density ratio and recoverability from large compressive strains. In contrast, the framework for studying their thermal properties has not been established. Our work develops the computational and experimental tools necessary to study heat conduction in nanoarchitected materials and applies those tools to prove the viability of octet-truss nanolattices as multifunctional thermal insulators.
We implement significant improvements to a phonon Monte Carlo method to solve the Boltzmann transport equation (BTE) in highly complex geometries like the octet-truss. No prior works solve the BTE in a domain as intricate as a nanolattice, so we create a geometry representation scheme that can model any arbitrary 3-D body. Our enhanced variance-reduced Monte Carlo code incorporates this scheme, allowing us to predict the thermal conductivity of nanolattices and analyze the phonon transport behavior in them. Results suggest that hollow-beam silicon nanolattices indeed reach ultralow thermal conductivities. Based on Monte Carlo and finite element simulations, we develop a predictive thermal conductivity model that accounts for both diffusive and radiative phonon transport in nanolattices.
We also devise custom modifications to the 3ω method to experimentally measure the thermal conductivity of additively manufactured nanolattices. Since the serial fabrication process of nanolattices makes it costly to cover large areas, we design a specialized 3ω sample that minimizes the required structure size while maintaining good experimental sensitivity. We derive a new thermal model to account for conductive losses through the heater line in our novel sample geometry. 3ω measurements and compression tests of hollow-beam alumina nanolattices show that they combine ultralow thermal conductivity with excellent mechanical stiffness and resilience, which proves that nanolattices occupy a previously unreachable region in material property space. Our work provides motivation to further investigate and improve the thermal properties of architected materials.</p
Silicon Integrated Arrays: From Microwave to IR
Get PDFIntegrated chips have enabled realization and mass production of complex systems in a small form factor. Through process miniaturization many novel applications in silicon photonics and electronic systems have been enabled. In this thesis I have provided several examples of innovations that are only enabled by integration. I have also demonstrated how electronics and photonics circuits can complement each other to achieve a system with superior performance.</p
The Nested Periodic Subspaces: Extensions of Ramanujan Sums for Period Estimation
Get PDFIn the year 1918, the Indian mathematician Srinivasa Ramanujan proposed a set of sequences called Ramanujan Sums as bases to expand arithmetic functions in number theory. Today, exactly a 100 years later, we will show that these sequences re-emerge as exciting tools in a completely different context: For the extraction of periodic patterns in data. Combined with the state-of-the-art techniques of DSP, Ramanujan Sums can be used as the starting point for developing powerful algorithms for periodicity applications.
The primary inspiration for this thesis comes from a recent extension of Ramanujan sums to subspaces known as the Ramanujan subspaces. These subspaces were designed to span any sequence with integer periodicity, and have many interesting properties. Starting with Ramanujan subspaces, this thesis first develops an entire family of such subspace representations for periodic sequences. This family, called Nested Periodic Subspaces due to their unique structure, turns out to be the least redundant sets of subspaces that can span periodic sequences.
Three classes of new algorithms are proposed using the Nested Periodic Subspaces: dictionaries, filter banks, and eigen-space methods based on the auto-correlation matrix of the signal. It will be shown that these methods are especially advantageous to use when the data-length is short, or when the signal is a mixture of multiple hidden periods. The dictionary techniques were inspired by recent advances in sparsity based compressed sensing. Apart from the l1 norm based convex programs currently used in other applications, our dictionaries can admit l2 norm formulations that have linear and closed form solutions, even when the systems is under-determined. A new filter bank is also proposed using the Ramanujan sums. This, named the Ramanujan Filter Bank, can accurately track the instantaneous period for signals that exhibit time varying periodic nature. The filters in the Ramanujan Filter Bank have simple integer valued coefficients, and directly tile the period vs time plane, unlike classical STFT (Short Time Fourier Transform) and wavelets, which tile the time-frequency plane. The third family of techniques developed here are a generalization of the classic MUSIC (MUltiple SIgnal Classification) algorithm for periodic signals. MUSIC is one of the most popular techniques today for line spectral estimation. However, periodic signals are not just any unstructured line spectral signals. There is a nice harmonic spacing between the lines which is not exploited by plain MUSIC. We will show that one can design much more accurate adaptations of MUSIC using Nested Periodic Subspaces. Compared to prior variants of MUSIC for the periodicity problem, our approach is much faster and yields much more accurate results for signals with integer periods. This work is also the first extension of MUSIC that uses simple integer valued basis vectors instead of using traditional complex-exponentials to span the signal subspace. The advantages of the new methods are demonstrated both on simulations, as well as real world applications such as DNA micro-satellites, protein repeats and absence seizures.
Apart from practical contributions, the theory of Nested Periodic Subspaces offers answers to a number of fundamental questions that were previously unanswered. For example, what is the minimum contiguous data-length needed to be able to identify the period of a signal unambiguously? Notice that the answer we seek is a fundamental identifiability bound independent of any particular period estimation technique. Surprisingly, this basic question has never been answered before. In this thesis, we will derive precise expressions for the minimum necessary and sufficient datalengths for this question. We also extend these bounds to the context of mixtures of periodic signals. Once again, even though mixtures of periodic signals often occur in many applications, aspects such as the unique identifiability of the component periods were never rigorously analyzed before. We will present such an analysis as well.
While the above question deals with the minimum contiguous datalength required for period estimation, one may ask a slightly different question: If we are allowed to pick the samples of a signal in a non-contiguous fashion, how should we pick them so that we can estimate the period using the least number of samples? This question will be shown to be quite difficult to answer in general. In this thesis, we analyze a smaller case in this regard, namely, that of resolving between two periods. It will be shown that the analysis is quite involved even in this case, and the optimal sampling pattern takes an interesting form of sparsely located bunches. This result can also be extended to the case of multi-dimensional periodic signals.
We very briefly address multi-dimensional periodicity in this thesis. Most prior DSP literature on multi-dimensional discrete time periodic signals assumes the period to be parallelepipeds. But as shown by the artist M. C. Escher, one can tile the space using a much more diverse variety of shapes. Is it always possible to account for such other periodic shapes using the traditional notion of parallelepiped periods? An interesting analysis in this regard is presented towards the end of the thesis.</p
The Avatar Paradigm in Granular Materials
Get PDFGranular materials are ubiquitous in both everyday life and various engineering and industrial applications, ranging from breakfast cereal to sand to rice to medical pills. However, despite the familiarity of granular materials, their behavior is complex and efforts to characterize them are currently broad research areas in physics and engineering. Research of granular materials, as is the case with the research of other engineering materials such as rocks and metals, is beset with two gaps: the gap between reconciling macroscopic behavior with microscale (particle-scale, in the case of granular materials) behavior, and the gap between reconciling experimental and computational results. In this dissertation, we bridge these gaps through the "avatar paradigm." The avatar paradigm is a two-step process that numerically characterizes (from experimental images) and simulates the shapes and behavior of individual particles, which we call avatars. First, we validate that our avatars are indeed capable of faithfully capturing particle kinematics and interparticle contact, then apply the characterization process, level set imaging (LS-imaging), to two experimental specimens to compute particle kinematics and contact statistics. We then detail a computational method, the level set discrete element method (LS-DEM), that is able to simulate the behavior of avatars, and apply it (and LS-imaging) to two other experimental specimens, calibrating the model to one specimen and using the results to predict the behavior of the other, thus providing some reconciliation between experimental and computational results. Finally, we use the avatar process to characterize and simulate yet another experimental specimen, this time analyzing the results at length scales ranging from particle behavior to local behavior to macroscopic behavior, further validating the ability of the avatar paradigm to bridge experiments and computations and showing its power to reconcile different length scales
Utilizing Machine Learning Techniques to Rapidly Identify MUC2 Expression in Colon Cancer Tissues
Get PDFColorectal cancer is the third-most common form of cancer among American men and women. Like most tumors, colon cancer is sustained by a subpopulation of “stem cells” that possess the ability to self-renew and differentiate into more specialized cell types. It would be useful to detect stem cells in images of colon cancer tissue, but the first step in being able to do so is to know what genes are expressed in the stem cells and how to detect their expression pattern from the tissue images. Machine learning (ML) is a powerful tool that is widely used in biological research as a novel and innovative technique to facilitate rapid diagnosis of cancer. The current study demonstrates the feasibility and effectiveness of using ML techniques to rapidly detect the expression of the gene MUC2 (mucin 2) in colon cancer tissue images. We analyzed histological images of colon cancer and segmented the nuclei to look for features (area, perimeter, eccentricity, compactness, etc.) that correlate with high or low levels of MUC2. Grid search was then run on this data set to tune the hyper-parameters, and the following models were tested as potential classifiers: random forest, gradient boosting, decision trees with AdaBoost, and support vector machines. Of all of the tested models, it was found that the random forest classifier (f1 score of 0.71) and the gradient boosting classifier (f1 score of 0.72) were able to predict the output label most accurately. Under certain conditions, we have identified four features that have predictive capabilities. Predicting individual gene expression with machine learning is the first step in detecting genes that are specific to cancer stem cells in the early stages of cancer, while there is still hope for a cure
Proliferation of Twinning in Metals: Application to Magnesium Alloys
Get PDFIn the search for new alloys with a great strength-to-weight ratio, magnesium has emerged at the forefront. With a strength rivaling that of steel and aluminum alloys --- materials which are deployed widely in real world applications today --- but only a fraction of the density, magnesium holds great promise in a variety of next-generation applications. Unfortunately, the widespread adoption of magnesium is hindered by the fact that it fails in a brittle fashion, which is undesirable when it comes to plastic deformation mechanisms. Consequently, one must design magnesium alloys to navigate around this shortcoming and fail in a more ductile fashion.
However, such designs are not possible without a thorough understanding of the underlying mechanisms of deformation in magnesium, which is somewhat contested at the moment. In addition to slip, which is one of the dominant mechanisms in metallic alloys, a mechanism known as twinning is also present, especially in hexagonal close-packed (HCP) materials such as magnesium. Twinning involves the reorientation of the material lattice about a planar discontinuity and has been shown as one of the preferred mechanisms by which magnesium accommodates out-of-plane deformation. Unfortunately, twinning is not particularly well-understood in magnesium, and needs to be addressed before progress can be made in materials design. In particular, though two specific modes of twinning have been acknowledged, various works in the literature have identified a host of additional modes, many of which have been cast aside as "anomalous" observations.
To this end, we introduce a new framework for predicting the modes by which a material can twin, for any given material. Focusing on magnesium, we begin our investigation by introducing a kinematic framework that predicts novel twin configurations, cataloging these twins modes by their planar normal and twinning shear. We then subject the predicted twin modes to a series of atomistic simulations, primarily in molecular statics but with supplementary calculations using density functional theory, giving us insight on both the energy of the twin interface and barriers to formation. We then perform a stress analysis and identify the twin modes which are most likely to be activated, thus finding the ones most likely to affect the yield surface of magnesium.
Over the course of our investigation, we show that many different modes actually participate on the yield surface of magnesium; the two classical modes which are accepted by the community are confirmed, but many additional modes --- some of which are close to modes which have been previously regarded as anomalies --- are also observed. We also perform some extensional work, showing the flexibility of our framework in predicting twins in other materials and in other environments and highlighting the complicated nature of twinning, especially in HCP materials.</p
On the Effect of Large-Scale Patterned Wettability on Contact Line Hydrodynamics
Get PDFNumerous studies have investigated how liquid water behaves on solid surfaces with uniformly hydrophilic or uniformly hydrophobic wetting properties. In particular, uniformly hydrophobic surfaces have been widely studied for modifying flow behavior of rivulets and drops at smaller scales, as well as for drag reduction on ships or other free-surface-piercing bodies at larger scales. Despite the extensive body of work on surfaces with uniform wetting properties, minimal work has been done to investigate how combining hydrophilic and hydrophobic regions onto a single surface to create macroscopic non-uniform wetting properties affects flows. Research in this vein has predominantly focused on low Reynolds number flows, such as in microfluidic channels or droplet impacts.
This thesis expands on the current literature by investigating contact line dynamics and global flow behavior on surfaces with larger-scale non-uniform wetting properties. Experiments were first carried out to study thin sheet flow down an inclined plate at Re ~ 50 - 1200. The plate's wetting condition was changed by introducing alternating hydrophilic and hydrophobic bands 2-25 mm wide oriented at different angles with respect to the flow direction. Results show that the contact line of such flows is heavily modified compared to the uniform cases. At low Reynolds numbers, large-scale wettability heterogeneities are observed to tune the fingering instability wavelength if the bands are parallel to the flow direction and to dampen finger oscillations if the bands are perpendicular to the flow direction. At higher Reynolds numbers, roller structures are introduced at every hydrophilic-to-hydrophobic junction, modifying the global flow morphology. Entrained air bubbles are also captured and observed to coalesce if the bands are perpendicular to the flow direction.
These experiments were then extended to a surface-piercing hydrofoil coated with alternating hydrophilic and hydrophobic bands. Experiments were run in Caltech's Free Surface Laboratory water tunnel for Re on the order of 104 to 105. The experiments demonstrate that the contact line is modulated in this context, alternating from concave to convex over the different wettability regions. The modulation of the contact line propagates to the rest of the water free-surface via the generation of standing waves and further modifies the free-surface separation point's location and steadiness. In addition, changes in wettability are observed to generate side force, which is of interest for vessel maneuvers in naval applications.</p
On the Kinetics of Materials of Geophysical Interest
Get PDFKnowledge of the equation of state and phase diagram of magnesium silicates and light iron alloys is important for understanding the thermal evolution and interior structure of terrestrial planets. Dynamic compression techniques are the primary viable methods to create the temperature and pressure conditions that are relevant to Earth and super-Earth (1-10 Earth mass) sized planets. However, due to the kinetic constraints imposed by the timescale of dynamic compression experiments, the nature of the state within the dynamically compressed sample (whether equilibrium or metastable) is uncertain. Here, we present the results of a series of dynamic compression experiments performed on both laser driven compression and plate impact facilities to study the nanosecond to microsecond response of forsterite and iron silicide. In situ x-ray diffraction measurements are used to probe the crystal structure of solid phases and test for the presence of melt, from which we investigate the decomposition of forsterite and iron silicide into compositionally distinct phases at high pressure. For forsterite, we do not observe chemical segregation in the solid phase, however the presence of melt speeds up the kinetics and allows chemical segregation to occur on nanosecond timescales. For iron silicide, our results show a textured solid phase upon shock compression to pressures ranging from 166(14) to 282(24) GPa consistent with cubic and hcp structures in coexistence. Above 313(29) GPa, the intense and textured solid diffraction peaks give way to a diffuse scattering feature and loss of texture, consistent with melting along the Hugoniot