Publications

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A method is developed for modeling fluid transport in domains that do not conform to the finite element mesh. One or more level set functions are used to describe the fluid domain. A background, non-conformal mesh is decomposed into elements that conform to the level set interfaces. Enrichment takes place by adding nodes that lie on the interfaces. Unlike other enriched finite element methods, the proposed technique requires no changes to the underlying element assembly, element interpolation, or element quadrature. The complexity is entirely contained within the element decomposition routines. It is argued that the accuracy of the method is no less than that for eXtended Finite Element Methods (XFEM) with Heaviside enrichment. The accuracy is demonstrated using multiple numerical tests. In all cases, optimal rates of convergence are obtained for both volume and surface quantities. Jacobi preconditioning is shown to remove the ill-conditioning that may result from the nearly degenerate conformal elements.

In this report, we summarize our work on developing a production level foam processing computational model suitable for predicting the self-expansion of foam in complex geometries. The model is based on a finite element representation of the equations of motion, with the movement of the free surface represented using the level set method, and has been implemented in SIERRA/ARIA. An empirically based time- and temperature-dependent density model is used to encapsulate the complex physics of foam nucleation and growth in a numerically tractable model. The change in density with time is at the heart of the foam self-expansion as it creates the motion of the foam. This continuum-level model uses an homogenized description of foam, which does not include the gas explicitly. Results from the model are compared to temperature-instrumented flow visualization experiments giving the location of the foam front as a function of time for our EFAR model system.

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Many weapons components (e.g. firing sets) are encapsulated with blown foams. Foam is a strong lightweight material--good compromise between conflicting needs of structural stability and electronic function. Current foaming processes can lead to unacceptable voids, property variations, cracking, and slipped schedules which is a long-standing issue. Predicting the process is not currently possible because the material is polymerizing and multiphase with changing microstructure. The goals of this project is: (1) Produce uniform encapsulant consistently and improve processability; (2) Eliminate metering issues/voids; (3) Lower residual stresses, exotherm to protect electronics; and (4) Maintain desired properties--lightweight, strong, no delamination/cracking, and ease of removal. The summary of achievements in the first year are: (1) Developed patentable chemical foaming chemistry - TA; (2) Developed persistent non-curing foam for systematic evaluation of fundamental physics of foams--Initial testing of non-curing foam shows that surfactants very important; (3) Identified foam stability strategy using a stacked reaction scheme; (4) Developed foam rheology methodologies and shear apparatuses--Began testing candidates for shear stability; (5) Began development of computational model; and (6) Development of methodology and collection of property measurements/boundary conditions for input to computational model.

This report documents the results for the FY07 ASC Integrated Codes Level 2 Milestone number 2354. The description for this milestone is, 'Demonstrate level set free surface tracking capabilities in ARIA to simulate the dynamics of the formation and time evolution of a weld pool in laser welding applications for neutron generator production'. The specialized boundary conditions and material properties for the laser welding application were implemented and verified by comparison with existing, two-dimensional applications. Analyses of stationary spot welds and traveling line welds were performed and the accuracy of the three-dimensional (3D) level set algorithm is assessed by comparison with 3D moving mesh calculations.

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As part of an effort to reduce costs and improve quality control in encapsulation and potting processes the Technology Initiative Project ''Defect Free Manufacturing and Assembly'' has completed a computational modeling study of flows representative of those seen in these processes. Flow solutions are obtained using a coupled, finite-element-based, numerical method based on the GOMA/ARIA suite of Sandia flow solvers. The evolution of the free surface is solved with an advanced level set algorithm. This approach incorporates novel methods for representing surface tension and wetting forces that affect the evolution of the free surface. In addition, two commercially available codes, ProCAST and MOLDFLOW, are also used on geometries representing encapsulation processes at the Kansas City Plant. Visual observations of the flow in several geometries are recorded in the laboratory and compared to the models. Wetting properties for the materials in these experiments are measured using a unique flowthrough goniometer.

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Aria is a Galerkin finite element based program for solving coupled-physics problems described by systems of PDEs and is capable of solving nonlinear, implicit, transient and direct-to-steady state problems in two and three dimensions on parallel architectures. The suite of physics currently supported by Aria includes the incompressible Navier-Stokes equations, energy transport equation, species transport equations, nonlinear elastic solid mechanics, and electrostatics as well as generalized scalar, vector and tensor transport equations. Additionally, Aria includes support for arbitrary Lagrangian-Eulerian (ALE) and level set based free and moving boundary tracking. Coupled physics problems are solved in several ways including fully-coupled Newton's method with analytic or numerical sensitivities, fully-coupled Newton-Krylov methods, fully-coupled Picard's method, and a loosely-coupled nonlinear iteration about subsets of the system that are solved using combinations of the aforementioned methods. Error estimation, uniform and dynamic h-adaptivity and dynamic load balancing are some of Aria's more advanced capabilities. Aria is based on the Sierra Framework.

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