Publications

GOMA is a two- and three-dimensional finite element program which excels in analyses of manufacturing processes, particularly those involving free or moving interfaces. Specifically, the full-Newton-coupled heat, mass, momentum, and pseudo-solid mesh motion algorithm makes GOMA ideally suited for simulating processes in which the bulk fluid transport is closely coupled to the interfacial physics. Examples include, but are not limited to, coating and polymer processing flows, soldering, crystal growth, and solid-network or solution film drying. The code is based on the premise that any boundary can be (1) moving or free, with an apriori unknown position dictated by the distinguishing physics, (2) fixed, according to a global analytical representation, or (3) moving in time and space under user-prescribed kinematics. The goal is to enable the user to predict boundary position or motion simultaneously with the physics of the problem being analyzed and to pursue geometrical design studies and fluid-structure interaction problems. The moving mesh algorithm treats the entire domain as a computational Lagrangian solid that deforms subject to the physical principles which dictate boundary position. As an added benefit, the same Lagrangian solid mechanics can be exploited to solve multi-field problems for which the solid motion and stresses interact with other transport phenomena, either within the same material phase (e.g. shrinking coating) or in neighboring material phases (e.g. flexible blade coating). Thus, analyses of many fluid-structure interaction problems and deformable porous media problems are accessible. This document serves as a user`s guide and reference for GOMA and provides a brief overview of GOMA`s capabilities, theoretical background, and classes of problems for which it is targeted.

Electron-Beam (EBeam) melting furnaces are routine used to minimize the occurrence of second-phase particles in the processing of segregation-sensitive alloys. As one part of the process, a circulating electron beam impinges the surface of a crucible melt pool to help control the shape of the solidification front below. By modeling melt pool hydrodynamics, heat transfer, and the shape of solidification boundaries, we plan to optimize the dwell pattern of the beam so that the material solidifies with a composition as spatially homogeneous as possible. Both two- and three-dimensional models are being pursued with FIDAP 5.02, the former serving as a test bed for various degrees of model sophistication. A heat flux distribution is specified on the top of the domain to simulate the EBeam dwell pattern. In two dimensions it is found that an inertially-driven recirculation in the melt pool interacts with a counter-rotating buoyancy-driven recirculation, and that both recirculations are influenced heavily by surface tension gradients on the melt-pool surface. In three dimensions the inertial cell decays quickly with distance from the position of the inlet stream, causing the fluid to precess the crucible. Ingot macrosegregation patterns for a U-6 wt. % Nb alloy are calculated with the Flemings-Mehrabian equation of solute redistribution; the sensitivity of these patterns to EBeam dwell pattern is explored.

Dip coating is the primary means of depositing sol-gel films for precision optical coatings. Sols are typically multicomponent systems consisting of an inorganic phase dispersed in a solvent mixture, with each component differing in volatility and surface tension. This, together with slow coating speeds (<1cm/s), makes analysis of the coating process complicated; unlike most high-speed coating methods, solvent evaporation, evolving rheology, and surface tension gradients alter significantly the fluid mechanics of the deposition stage. We set out to understand these phenomena with computer-aided predictions of the flow and species transport fields. The underlying theory involves mass, momentum, and species transport on a domain of unknown shape, with models and constitutive equations for vapor-liquid equilibria and surface tension. Due accounting is made for the unknown position of the free surface, which locates according to the capillary hydrodynamic forces and solvent loss by evaporation. Predictions of the effects of mass transfer, hydrodynamics, and surface tension gradients on final film thickness are compared with ellipsometry measurements of film thickness on a laboratory pilot coater. Although quantitative agreement is still lacking, both experiment and theory reveal that the film profile near the drying line takes on a parabolic shape. 2 refs., 2 figs.