DIRECT NUMERICAL SIMULATION OF INCOMPRESSIBLE MULTIPHASE FLOW WITH PHASE CHANGE

Phase change problems arise in many practical applications such as air-conditioning and refrigeration, thermal energy storage systems and thermal management of electronic devices. The physical phenomenon in such applications are complex and are often difficult to be studied in detail with the help of only experimental techniques. The efforts to improve computational techniques for analyzing two-phase flow problems with phase change are therefore gaining momentum. The development of numerical methods for multiphase flow has been motivated generally by the need to account more accurately for (a) large topological changes such as phase breakup and merging, (b) sharp representation of the interface and its discontinuous properties and (c) accurate and mass conserving motion of the interface. In addition to these considerations, numerical simulation of multiphase flow with phase change introduces additional challenges related to discontinuities in the velocity and the temperature fields. Moreover, the velocity field is no longer divergence free. For phase change problems, the focus of developmental efforts has thus been on numerically attaining a proper conservation of energy across the interface in addition to the accurate treatment of fluxes of mass and momentum conservation as well as the associated interface advection. Among the initial efforts related to the simulation of bubble growth in film boiling applications the work in \cite{Welch1995} was based on the interface tracking method using a moving unstructured mesh. That study considered moderate interfacial deformations. A similar problem was subsequently studied using moving, boundary fitted grids \cite{Son1997}, again for regimes of relatively small topological changes. A hybrid interface tracking method with a moving interface grid overlapping a static Eulerian grid was developed \cite{Juric1998} for the computation of a range of phase change problems including, three-dimensional film boiling \cite{esmaeeli2004computations}, multimode two-dimensional pool boiling \cite{Esmaeeli2004} and film boiling on horizontal cylinders \cite{Esmaeeli2004a}. The handling of interface merging and pinch off however remains a challenge with methods that explicitly track the interface. As large topological changes are crucial for phase change problems, attention has turned in recent years to front capturing methods utilizing implicit interfaces that are more effective in treating complex interface deformations. The VOF (Volume of Fluid) method was adopted in \cite{Welch2000} to simulate the one-dimensional Stefan problem and the two-dimensional film boiling problem. The approach employed a specific model for mass transfer across the interface involving a mass source term within cells containing the interface. This VOF based approach was further coupled with the level set method in \cite{Son1998}, employing a smeared-out Heaviside function to avoid the numerical instability related to the source term. The coupled level set, volume of fluid method and the diffused interface approach was used for film boiling with water and R134a at the near critical pressure condition \cite{Tomar2005}. The effect of superheat and saturation pressure on the frequency of bubble formation were analyzed with this approach. The work in \cite{Gibou2007} used the ghost fluid and the level set methods for phase change simulations. A similar approach was adopted in \cite{Son2008} to study various boiling problems including three-dimensional film boiling on a horizontal cylinder, nucleate boiling in microcavity \cite{lee2010numerical} and flow boiling in a finned microchannel \cite{lee2012direct}. The work in \cite{tanguy2007level} also used the ghost fluid method and proposed an improved algorithm based on enforcing continuity and divergence-free condition for the extended velocity field. The work in \cite{sato2013sharp} employed a multiphase model based on volume fraction with interface sharpening scheme and derived a phase change model based on local interface area and mass flux. Among the front capturing methods, sharp interface methods have been found to be particularly effective both for implementing sharp jumps and for resolving the interfacial velocity field. However, sharp velocity jumps render the solution susceptible to erroneous oscillations in pressure and also lead to spurious interface velocities. To implement phase change, the work in \cite{Hardt2008} employed point mass source terms derived from a physical basis for the evaporating mass flux. To avoid numerical instability, the authors smeared the mass source by solving a pseudo time-step diffusion equation. This measure however led to mass conservation issues due to non-symmetric integration over the distributed mass source region. The problem of spurious pressure oscillations related to point mass sources was also investigated by \cite{Schlottke2008}. Although their method is based on the VOF, the large pressure peaks associated with sharp mass source was observed to be similar to that for the interface tracking method. Such spurious fluctuation in pressure are essentially undesirable because the effect is globally transmitted in incompressible flow. Hence, the pressure field formation due to phase change need to be implemented with greater accuracy than is reported in current literature. The accuracy of interface advection in the presence of interfacial mass flux (mass flux conservation) has been discussed in \cite{tanguy2007level,tanguy2014benchmarks}. The authors found that the method of extending one phase velocity to entire domain suggested by Nguyen et al. in \cite{nguyen2001boundary} suffers from a lack of mass flux conservation when the density difference is high. To improve the solution, the authors impose a divergence-free condition for the extended velocity field by solving a constant coefficient Poisson equation. The approach has shown good results with enclosed bubble or droplet but is not general for more complex flow and requires additional solution of the linear system of equations. In current thesis, an improved approach that addresses both the numerical oscillation of pressure and the spurious interface velocity field is presented by featuring (i) continuous velocity and density fields within a thin interfacial region and (ii) temporal velocity correction steps to avoid unphysical pressure source term. Also I propose a general (iii) mass flux projection correction for improved mass flux conservation. The pressure and the temperature gradient jump condition are treated sharply. A series of one-dimensional and two-dimensional problems are solved to verify the performance of the new algorithm. Two-dimensional and cylindrical film boiling problems are also demonstrated and show good qualitative agreement with the experimental observations and heat transfer correlations. Finally, a study on Taylor bubble flow with heat transfer and phase change in a small vertical tube in axisymmetric coordinates is carried out using the new multiphase, phase change method.

Geochemistry of crustal formation and evolution

Terrestrial planets produce crusts as they differentiate. The Earth’s bi-modal crust, with a high-standing granitic continental crust and a low-standing basaltic oceanic crust, is unique in our solar system and links the evolution of the interior and exterior of this planet. Here I present geochemical observations to constrain processes accompanying crustal formation and evolution. My approach includes geochemical analyses, quantitative modeling, and experimental studies. The Archean crustal evolution project represents my perspective on when Earth’s continental crust began forming. In this project, I utilized critical element ratios in sedimentary records to track the evolution of the MgO content in the upper continental crust as a function time. The early Archean subaerial crust had >11 wt. % MgO, whereas by the end of Archean its composition had evolved to about 4 wt. % MgO, suggesting a transition of the upper crust from a basalt-like to a more granite-like bulk composition. Driving this fundamental change of the upper crustal composition is the widespread operation of subduction processes, suggesting the onset of global plate tectonics at ~ 3 Ga (Abstract figure). Three of the chapters in this dissertation leverage the use of Eu anomalies to track the recycling of crustal materials back into the mantle, where Eu anomaly is a sensitive measure of the element’s behavior relative to neighboring lanthanoids (Sm and Gd) during crustal differentiation. My compilation of Sm-Eu-Gd data for the continental crust shows that the average crust has a net negative Eu anomaly. This result requires recycling of Eu-enriched lower continental crust to the mantle. Mass balance calculations require that about three times the mass of the modern continental crust was returned into the mantle over Earth history, possibly via density-driven recycling. High precision measurements of Eu/Eu* in selected primitive glasses of mid-ocean ridge basalt (MORB) from global MORs, combined with numerical modeling, suggests that the recycled lower crustal materials are not found within the MORB source and may have at least partially sank into the lower mantle where they can be sampled by hot spot volcanoes. The Lesser Antilles Li isotope project provides insights into the Li systematics of this young island arc, a representative section of proto-continental crust. Martinique Island lavas, to my knowledge, represent the only clear case in which crustal Li is recycled back into their mantle source, as documented by the isotopically light Li isotopes in Lesser Antilles sediments that feed into the fore arc subduction trench. By corollary, the mantle-like Li signal in global arc lavas is likely the result of broadly similar Li isotopic compositions between the upper mantle and bulk subducting sediments in most arcs. My PhD project on Li diffusion mechanism in zircon is being carried out in extensive collaboration with multiple institutes and employs analytical, experimental and modeling studies. This ongoing project, finds that REE and Y play an important role in controlling Li diffusion in natural zircons, with Li partially coupling to REE and Y to maintain charge balance. Access to state-of-art instrumentation presented critical opportunities to identify the mechanisms that cause elemental fractionation during laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS) analysis. My work here elucidates the elemental fractionation associated with plasma plume condensation during laser ablation and particle-ion conversion in the ICP.