Publications

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Melting and flowing of aluminum alloys is a challenging problem for computational codes. Unlike most common substances, the surface of an aluminum melt exhibits rapid oxidation and elemental migration, and like a bag filled with water can remain 2-dimensionally unruptured while the metal inside is flowing. Much of the historical work in this area focuses on friction welding and neglects the surface behavior due to the high stress of the application. We are concerned with low-stress melting applications, in which the bag behavior is more relevant. Adapting models and measurements from the literature, we have developed a formulation for the viscous behavior of the melt based on an abstraction of historical measurement, and a construct for the bag behavior. These models are implemented and demonstrated in a 3D level-set multi-phase solver package, SIERRA/Aria. A series of increasingly complex simulation scenarios are illustrated that help verify implementation of the models in conjunction with other required model components like convection, radiation, gravity, and surface interactions.

Macrohomogeneous battery models are widely used to predict battery performance, necessarily relying on effective electrode properties, such as specific surface area, tortuosity, and electrical conductivity. While these properties are typically estimated using ideal effective medium theories, in practice they exhibit highly non-ideal behaviors arising from their complex mesostructures. In this paper, we computationally reconstruct electrodes from X-ray computed tomography of 16 nickel-manganese-cobalt-oxide electrodes, manufactured using various material recipes and calendering pressures. Due to imaging limitations, a synthetic conductive binder domain (CBD) consisting of binder and conductive carbon is added to the reconstructions using a binder bridge algorithm. Reconstructed particle surface areas are significantly smaller than standard approximations predicted, as the majority of the particle surface area is covered by CBD, affecting electrochemical reaction availability. Finite element effective property simulations are performed on 320 large electrode subdomains to analyze trends and heterogeneity across the electrodes. Significant anisotropy of up to 27% in tortuosity and 47% in effective conductivity is observed. Electrical conductivity increases up to 7.5× with particle lithiation. We compare the results to traditional Bruggeman approximations and offer improved alternatives for use in cellscale modeling, with Bruggeman exponents ranging from 1.62 to 1.72 rather than the theoretical value of 1.5. We also conclude that the CBD phase alone, rather than the entire solid phase, should be used to estimate effective electronic conductivity. This study provides insight into mesoscale transport phenomena and results in improved effective property approximations founded on realistic, image-based morphologies.

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Battery electrodes are composed of polydisperse particles and a porous, composite binder domain. These materials are arranged into a complex mesostructure whose morphology impacts both electrochemical performance and mechanical response. We present image-based, particle-resolved, mesoscale finite element model simulations of coupled electrochemical-mechanical performance on a representative NMC electrode domain. Beyond predicting macroscale quantities such as half-cell voltage and evolving electrical conductivity, studying behaviors on a per-particle and per-surface basis enables performance and material design insights previously unachievable. Voltage losses are primarily attributable to a complex interplay between interfacial charge transfer kinetics, lithium diffusion, and, locally, electrical conductivity. Mesoscale heterogeneities arise from particle polydispersity and lead to material underutilization at high current densities. Particle-particle contacts, however, reduce heterogeneities by enabling lithium diffusion between connected particle groups. While the porous composite binder domain (CBD) may have slower ionic transport and less available area for electrochemical reactions, its high electrical conductivity makes it the preferred reaction site late in electrode discharge. Mesoscale results are favorably compared to both experimental data and macrohomogeneous models. This work enables improvements in materials design by providing a tool for optimization of particle sizes, CBD morphology, and manufacturing conditions.

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This document is a summary of the mathematical models that are used in the DARPA TRADES project for the solid rocket motor design challenge. It is hoped that this brief description of these models will be of use to those that are working on the project.

When the core is breached during a severe nuclear accident, a molten mixture of nuclear fuel, cladding, and structural supports is discharged from the reactor vessel. This molten mixture of ceramic and metal is often referred to as “corium”. Predicting the flow and solidification of corium poses challenges for numerical models due to the presence of large Peclet numbers when convective transport dominates the physics. Here, we utilize a control volume finite-element method (CVEM) discretization to stabilize the advection dominated flow and heat transport. This CVFEM approach is coupled with the conformal decomposition finite-element method (CDFEM), which tracks the corium/air interface on an existing background mesh. CDFEM is a sharp-interface method, allowing the direct discretization of the corium front. This CVFEM-CDFEM approach is used to model the spreading of molten corium in both two- and three-dimensions. The CVFEM approach is briefly motivated in a comparison with a streamwise upwind/Petrov-Galerkin (SUPG) stabilized finite-element method, which was not able to suppress spurious temperature oscillations in the simulations. Our model is compared directly with the FARO L26 corium spreading experiments and with previous numerical simulations, showing both quantitative and qualitative agreement with those studies.

As computing power rapidly increases, quickly creating a representative and accurate discretization of complex geometries arises as a major hurdle towards achieving a next generation simulation capability. Component definitions may be in the form of solid (CAD) models or derived from 3D computed tomography (CT) data, and creating a surface-conformal discretization may be required to resolve complex interfacial physics. The Conformal Decomposition Finite Element Methods (CDFEM) has been shown to be an efficient algorithm for creating conformal tetrahedral discretizations of these implicit geometries without manual mesh generation. In this work we describe an extension to CDFEM to accurately resolve the intersections of many materials within a simulation domain. This capability is demonstrated on both an analytical geometry and an image-based CT mesostructure representation consisting of hundreds of individual particles. Effective geometric and transport properties are the calculated quantities of interest. Solution verification is performed, showing CDFEM to be optimally convergent in nearly all cases. Representative volume element (RVE) size is also explored and per-sample variability quantified. Relatively large domains and small elements are required to reduce uncertainty, with recommended meshes of nearly 10 million elements still containing upwards of 30% uncertainty in certain effective properties. This work instills confidence in the applicability of CDFEM to provide insight into the behaviors of complex composite materials and provides recommendations on domain and mesh requirements.

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Typical lithium-ion battery electrodes are porous composites comprised of active material, conductive additives, and polymeric binder, with liquid electrolyte filling the pores. The mesoscale morphology of these constituent phases has a significant impact on both electrochemical reactions and transport across the electrode, which can ultimately limit macroscale battery performance. We reconstruct published X-ray computed tomography (XCT) data from a NMC333 cathode to study mesoscale electrode behavior on an as-manufactured electrode geometry. We present and compare two distinct models that computationally generate a composite binder domain (CBD) phase that represents both the polymeric binder and conductive additives. We compare the effect of the resulting CBD morphologies on electrochemically active area, pore phase tortuosity, and effective electrical conductivity. Both dense and nanoporous CBD are considered, and we observe that acknowledging CBD nanoporosity significantly increases effective electrical conductivity by up to an order of magnitude. Properties are compared to published measurements as well as to approximate values often used in homogenized battery-scale models. All reconstructions exhibit less than 20% of the standard electrochemically active area approximation. Order of magnitude discrepancies are observed between two popular transport simulation numerical schemes (finite element method and finite volume method), highlighting the importance of careful numerical verification.

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Polyurethane foams are used widely for encapsulation and structural purposes because they are inexpensive, straightforward to process, amenable to a wide range of density variations (1 lb/ft3 - 50 lb/ft3), and able to fill complex molds quickly and effectively. Computational model of the filling and curing process are needed to reduce defects such as voids, out-of-specification density, density gradients, foam decomposition from high temperatures due to exotherms, and incomplete filling. This paper details the development of a computational fluid dynamics model of a moderate density PMDI structural foam, PMDI-10. PMDI is an isocyanate-based polyurethane foam, which is chemically blown with water. The polyol reacts with isocyanate to produces the polymer. PMDI- 10 is catalyzed giving it a short pot life: it foams and polymerizes to a solid within 5 minutes during normal processing. To achieve a higher density, the foam is over-packed to twice or more of its free rise density of 10 lb/ft3. The goal for modeling is to represent the expansion, filling of molds, and the polymerization of the foam. This will be used to reduce defects, optimize the mold design, troubleshoot the processed, and predict the final foam properties. A homogenized continuum model foaming and curing was developed based on reaction kinetics, documented in a recent paper; it uses a simplified mathematical formalism that decouples these two reactions. The chemo-rheology of PMDI is measured experimentally and fit to a generalized- Newtonian viscosity model that is dependent on the extent of cure, gas fraction, and temperature. The conservation equations, including the equations of motion, an energy balance, and three rate equations are solved via a stabilized finite element method. The equations are combined with a level set method to determine the location of the foam-gas interface as it evolves to fill the mold. Understanding the thermal history and loads on the foam due to exothermicity and oven curing is very important to the results, since the kinetics, viscosity, and other material properties are all sensitive to temperature. Results from the model are compared to experimental flow visualization data and post-test X-ray computed tomography (CT) data for the density. Several geometries are investigated including two configurations of a mock structural part and a bar geometry to specifically test the density model. We have found that the model predicts both average density and filling profiles well. However, it under predicts density gradients, especially in the gravity direction. Further model improvements are also discussed for future work.

The objective of this project is to improve the fidelity of battery-scale simulations of abuse scenarios through the creation and application of microscale (particle-scale) electrode simulations.

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The migration and trapping of supercritical CO2 (scCO2) in geologic carbon storage is strongly dependent on the geometry and wettability of the pore network in the reservoir rock. During displacement, resident fluids may become trapped in the pits of a rough pore surface forming an immiscible two-phase fluid interface with the invading fluid, allowing apparent slip flow at this interface. We present a two-phase fluid dynamics model, including interfacial tension, to characterize the impact of mineral surface roughness on this slip flow. We show that the slip flow can be cast in more familiar terms as a contact-angle (wettability)-dependent effective permeability to the invading fluid, a nondimensional measurement which relates the interfacial slip to the pore geometry. The analysis shows the surface roughness-induced slip flow can effectively increase or decrease this effective permeability, depending on the wettability and roughness of the mineral surfaces. Configurations of the pore geometry where interfacial slip has a tangible influence on permeability have been identified. The results suggest that for large roughness features, permeability to CO2 may be enhanced by approximately 30% during drainage, while the permeability to brine during reimbibition may be enhanced or diminished by 60%, depending on the contact angle with the mineral surfaces and degrees of roughness. For smaller roughness features, the changes in permeability through interfacial slip are small. A much larger range of effective permeabilities are suggested for general fluid pairs and contact angles, including occlusion of the pore by the trapped phase.

The migration and trapping of supercritical CO₂ (scCO₂) in geologic carbon storage is strongly dependent on the geometry and wettability of the pore network in the reservoir rock. During displacement, resident fluids may become trapped in the pits of a rough pore surface forming an immiscible two-phase fluid interface with the invading fluid, allowing apparent slip flow at this interface. We present a two-phase fluid dynamics model, including interfacial tension, to characterize the impact of mineral surface roughness on this slip flow. We show that the slip flow can be cast in more familiar terms as a contact-angle (wettability)-dependent effective permeability to the invading fluid, a nondimensional measurement which relates the interfacial slip to the pore geometry. The analysis shows the surface roughness-induced slip flow can effectively increase or decrease this effective permeability, depending on the wettability and roughness of the mineral surfaces. Configurations of the pore geometry where interfacial slip has a tangible influence on permeability have been identified. The results suggest that for large roughness features, permeability to CO₂ may be enhanced by approximately 30% during drainage, while the permeability to brine during reimbibition may be enhanced or diminished by 60%, depending on the contact angle with the mineral surfaces and degrees of roughness. For smaller roughness features, the changes in permeability through interfacial slip are small. As a result, a much larger range of effective permeabilities are suggested for general fluid pairs and contact angles, including occlusion of the pore by the trapped phase.

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Lithium-ion battery electrodes are composed of active material particles, binder, and conductive additives that form an electrolyte-filled porous particle composite. The mesoscale (particle-scale) interplay of electrochemistry, mechanical deformation, and transport through this tortuous multi-component network dictates the performance of a battery at the cell-level. Effective electrode properties connect mesoscale phenomena with computationally feasible battery-scale simulations. We utilize published tomography data to reconstruct a large subsection (1000+ particles) of an NMC333 cathode into a computational mesh and extract electrode-scale effective properties from finite element continuum-scale simulations. We present a novel method to preferentially place a composite binder phase throughout the mesostructure, a necessary approach due difficulty distinguishing between non-active phases in tomographic data. We compare stress generation and effective thermal, electrical, and ionic conductivities across several binder placement approaches. Isotropic lithiation-dependent mechanical swelling of the NMC particles and the consideration of strain-dependent composite binder conductivity significantly impact the resulting effective property trends and stresses generated. Our results suggest that composite binder location significantly affects mesoscale behavior, indicating that a binder coating on active particles is not sufficient and that more accurate approaches should be used when calculating effective properties that will inform battery-scale models in this inherently multi-scale battery simulation challenge.

An enriched finite element method is described for capillary hydrodynamics including dynamic wetting. The method is enriched via the Conformal Decomposition Finite Element Method (CDFEM). Two formulations are described, one with first-order accuracy and one with second-order accuracy in time. Both formulations utilize a semi-implicit form for the surface tension that is shown to effectively circumvent the explicit capillary time step limit. Sharp interface boundary conditions are developed for capturing the dynamic contact angle as the fluid interface moves along the wall. By virtue of the CDFEM, the contact line is free to move without risk of mesh tangling, but is sharply captured. Multiple problems are used to demonstrate the effectiveness of the methods.

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Battery performance, while observed at the macroscale, is primarily governed by the bicontinuous mesoscale network of the active particles and a polymeric conductive binder in its electrodes. Manufacturing processes affect this mesostructure, and therefore battery performance, in ways that are not always clear outside of empirical relationships. Directly studying the role of the mesostructure is difficult due to the small particle sizes (a few microns) and large mesoscale structures. Mesoscale simulation, however, is an emerging technique that allows the investigation into how particle-scale phenomena affect electrode behavior. In this manuscript, we discuss our computational approach for modeling electrochemical, mechanical, and thermal phenomena of lithium-ion batteries at the mesoscale. We review our recent and ongoing simulation investigations and discuss a path forward for additional simulation insights.

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Interface-conforming elements generated by the conformal decomposition finite element method can have arbitrarily poor quality due to the arbitrary intersection of the base triangular or tetrahedral mesh with material interfaces. This can have severe consequences for both the solvability of linear systems and for the interpolation error of fields represented on these meshes. The present work demonstrates that snapping the base mesh nodes to the interface whenever the interface cuts close to a node results in conforming meshes of good quality. Theoretical limits on the snapping tolerance are derived, and even conservative tolerance choices result in limiting the stiffness matrix condition number to within a small multiple of that of the base mesh. Interpolation errors are also well controlled in the norms of interest. In 3D, use of node-to-interface snapping also permits a simpler and more robust vertex ID-based element decomposition algorithm to be used with no serious detriment to mesh quality.

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We are studying PMDI polyurethane with a fast catalyst, such that filling and polymerization occur simultaneously. The foam is over-packed to tw ice or more of its free rise density to reach the density of interest. Our approach is to co mbine model development closely with experiments to discover new physics, to parameterize models and to validate the models once they have been developed. The model must be able to repres ent the expansion, filling, curing, and final foam properties. PMDI is chemically blown foam, wh ere carbon dioxide is pr oduced via the reaction of water and isocyanate. The isocyanate also re acts with polyol in a competing reaction, which produces the polymer. A new kinetic model is developed and implemented, which follows a simplified mathematical formalism that decouple s these two reactions. The model predicts the polymerization reaction via condensation chemis try, where vitrification and glass transition temperature evolution must be included to correctly predict this quantity. The foam gas generation kinetics are determined by tracking the molar concentration of both water and carbon dioxide. Understanding the therma l history and loads on the foam due to exothermicity and oven heating is very important to the results, since the kinetics and ma terial properties are all very sensitive to temperature. The conservation eq uations, including the e quations of motion, an energy balance, and thr ee rate equations are solved via a stabilized finite element method. We assume generalized-Newtonian rheology that is dependent on the cure, gas fraction, and temperature. The conservation equations are comb ined with a level set method to determine the location of the free surface over time. Results from the model are compared to experimental flow visualization data and post-te st CT data for the density. Seve ral geometries are investigated including a mock encapsulation part, two configur ations of a mock stru ctural part, and a bar geometry to specifically test the density model. We have found that the model predicts both average density and filling profiles well. However, it under predicts density gradients, especially in the gravity direction. Thoughts on m odel improvements are also discussed.

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