Publications

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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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