A Level-Set Immersed Boundary Method for Reactive Transport in Complex Topologies with Moving Interfaces

A simulation framework based on the level-set and the immersed boundary methods (LS-IBM) has been developed for reactive transport problems in porous media involving a moving solid-fluid interface. The interface movement due to surface reactions is tracked by the level-set method, while the immersed boundary method captures the momentum and mass transport at the interface. The proposed method is capable of accurately modeling transport near evolving boundaries in Cartesian grids. The framework formulation guarantees second order of accuracy. Since the interface velocity is only defined at the moving boundary, a physics-based interface velocity propagation method is also proposed. The method can be applied to other moving interface problems of the "Stefan" type. Here, we validate the proposed LS-IBM both for flow and transport close to an immersed object with reactive boundaries as well as for crystal growth. The proposed method provides a powerful tool to model more realistic problems involving moving reactive interfaces in complex domains

An Analysis Platform for Multiscale Hydrogeologic Modeling with Emphasis on Hybrid Multiscale Methods

One of the most significant challenges faced by hydrogeologic modelers is the disparity between the spatial and temporal scales at which fundamental flow, transport, and reaction processes can best be understood and quantified (e.g., microscopic to pore scales and seconds to days) and at which practical model predictions are needed (e.g., plume to aquifer scales and years to centuries). While the multiscale nature of hydrogeologic problems is widely recognized, technological limitations in computation and characterization restrict most practical modeling efforts to fairly coarse representations of heterogeneous properties and processes. For some modern problems, the necessary level of simplification is such that model parameters may lose physical meaning and model predictive ability is questionable for any conditions other than those to which the model was calibrated. Recently, there has been broad interest across a wide range of scientific and engineering disciplines in simulation approaches that more rigorously account for the multiscale nature of systems of interest. In this article, we review a number of such approaches and propose a classification scheme for defining different types of multiscale simulation methods and those classes of problems to which they are most applicable. Our classification scheme is presented in terms of a flowchart (Multiscale Analysis Platform), and defines several different motifs of multiscale simulation. Within each motif, the member methods are reviewed and example applications are discussed. We focus attention on hybrid multiscale methods, in which two or more models with different physics described at fundamentally different scales are directly coupled within a single simulation. Very recently these methods have begun to be applied to groundwater flow and transport simulations, and we discuss these applications in the context of our classification scheme. As computational and characterization capabilities continue to improve, we envision that hybrid multiscale modeling will become more common and also a viable alternative to conventional single-scale models in the near future

Hybrid models of transport in crowded environments

This dissertation deals with multi-scale, multi-physics descriptions of flow and transport in crowded environments forming porous media. Such phenomena can be described by employing either pore-scale or continuum-scale (Darcy- scale) models. Continuum-scale formulations are largely phenomenological, but often provide accurate and efficient representations of flow and transport. In the first part of the dissertation, we employ such a model to describe fluid flow through carbon nanotube (CNT) forests placed in a turbulent ambient environment of a microscopic wind tunnel. This analysis leads to closed-form analytical formulae that enable one to predict elastic response of CNT forests to aerodynamic loading and to estimate elastic properties of individual CNTs, both of which were found to be in a close agreement with experimental data. The second part of this work explores the applicability range of continuum-scale models of transport of chemically active solutes undergoing nonlinear homogeneous and heterogeneous reactions with the porous matrix. We use two upscaling techniques (the volume averaging method and multiple-scale expansions) to formulate sufficient conditions for the validity of continuum-scale models in terms of dimensionless numbers characterizing key pore-scale transport mechanisms (e.g. Péclet and Damköhler numbers). When these conditions are not satisfied, standard continuum-scale models have to be replaced with upscaled equations that are nonlocal in space and time, effective parameters (e.g. dispersion tensors, effective reaction rates) do not generally exist, and pore- and continuum- scales cannot be decoupled. Such transport regimes necessitate the development of hybrid numerical methods that couple the pore- and continuum-scale models solved in different regions of the computational domain. Hybrid methods aim to combine the physical rigor of pore-scale modeling with the computational efficiency of its continuum-scale counterpart. In the third and final part of this dissertation, we use the volume averaging method to construct two hybrid algorithms, one intrusive and the other non-intrusive, that facilitate the coupling of pore- and continuum-scale models in a computationally efficient manne

Module-Fluidics: Building Blocks for Spatio-Temporal Microenvironment Control

Generating the desired solute concentration signal in micro-environments is vital to many applications ranging from micromixing to analyzing cellular response to a dynamic microenvironment. We propose a new modular design to generate targeted temporally varying concentration signals in microfluidic systems while minimizing perturbations to the flow field. The modularized design, here referred to as module-fluidics, similar in principle to interlocking toy bricks, is constructed from a combination of two building blocks and allows one to achieve versatility and flexibility in dynamically controlling input concentration. The building blocks are an oscillator and an integrator, and their combination enables the creation of controlled and complex concentration signals, with different user-defined time-scales. We show two basic connection patterns, in-series and in-parallel, to test the generation, integration, sampling and superposition of temporally-varying signals. All such signals can be fully characterized by analytic functions, in analogy with electric circuits, and allow one to perform design and optimization before fabrication. Such modularization offers a versatile and promising platform that allows one to create highly customizable time-dependent concentration inputs which can be targeted to the specific application of interest

Module-Fluidics: Building Blocks for Spatio-Temporal Microenvironment Control

Generating the desired solute concentration signal in micro-environments is vital to many applications ranging from micromixing to analyzing cellular response to a dynamic microenvironment. We propose a new modular design to generate targeted temporally varying concentration signals in microfluidic systems while minimizing perturbations to the flow field. The modularized design, here referred to as module-fluidics, similar in principle to interlocking toy bricks, is constructed from a combination of two building blocks and allows one to achieve versatility and flexibility in dynamically controlling input concentration. The building blocks are an oscillator and an integrator, and their combination enables the creation of controlled and complex concentration signals, with different user-defined time-scales. We show two basic connection patterns, in-series and in-parallel, to test the generation, integration, sampling and superposition of temporally-varying signals. All such signals can be fully characterized by analytic functions, in analogy with electric circuits, and allow one to perform design and optimization before fabrication. Such modularization offers a versatile and promising platform that allows one to create highly customizable time-dependent concentration inputs which can be targeted to the specific application of interest

Optimization of Multi-Materials In-Flight Melting in Laser Engineered Net Shaping (LENS) Process

A heterogeneous object has potentially many advantages and in many cases can realize appearance and/or functionality that homogeneous objects cannot achieve. LENSTM, a Direct Metal Deposition process, is one technology with the potential to fabricate heterogeneous objects. In-flight melting provides an advantageous condition for better mixing of multiple materials with different properties, thus critical for fabricating heterogeneous objects. In this study, a multi-materials in-flight melting model of the LENS process is developed for the cases of single and multiple particles jets. The impact of in-flight particles melting as well as substrate melting on materials mixing is investigated. An optimization method is proposed for the LENS fabrication of heterogeneous objects based on the concurrent melting of particles and substrate. A cermet composite material fabrication test case is utilized to demonstrate the applicability of the method. Inconel 718 powders and alumina ceramic powders are used as building materials in the test case. A group of optimized process parameters are provided: using a 320 W, 600 μm spot diameter laser moving at 10 mm/s, the injection angles are 20°, the injection velocities are 1 m/s, the material feeding rates are 0.5 g/min, the particle diameters are 20 μm, and the nozzle diameters are 0.7 mm for both materials. Moreover, the material with a lower melting point should be injected in the front of the laser moving direction, while the material with a higher melting point should be injected from the rear.Mechanical Engineerin