To reduce costs and hazardous wastes associated with the production of lead-based active ceramic components, an injection molding process is being investigated to replace the current machining process. Here, lead zirconate titanate (PZT) ceramic particles are suspended in a thermoplastic resin and are injected into a mold and allowed to cool. The part is then bisque fired and sintered to complete the densification process. To help design this new process we use a finite element model to describe the injection molding of the ceramic paste. Flow solutions are obtained using a coupled, finite-element based, Newton-Raphson 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. Thermal, rheological, and wetting properties of the PZT paste are measured for use as input to the model. The viscosity of the PZT is highly dependent both on temperature and shear rate. One challenge in modeling the injection process is coming up with appropriate constitutive equations that capture relevant phenomenology without being too computationally complex. For this reason we model the material as a Carreau fluid and a WLF temperature dependence. Two-dimensional (2D) modeling is performed to explore the effects of the shear in isothermal conditions. Results indicate that very low viscosity regions exist near walls and that these results look similar in terms of meniscus shape and fill times to a simple Newtonian constitutive equation at the shear-thinned viscosity for the paste. These results allow us to pick a representative viscosity to use in fully three-dimensional (3D) simulation, which because of numerical complexities are restricted to using a Newtonian constitutive equation. Further 2D modeling at nonisothermal conditions shows that the choice of representative Newtonian viscosity is dependent on the amount of heating of the initially room temperature mold. An early 3D transient model shows that the initial design of the distributor is sub-optimal. However, these simulations take several months to run on 4 processors of an HP workstation using a preconditioner/solver combination of ILUT/GMRES with fill factors of 3 and PSPG stabilization. Therefore, several modifications to the distributor geometry and orientations of the vents and molds have been investigated using much faster 3D steady-state simulations. The pressure distribution for these steady-state calculations is examined for three different distributor designs to see if this can indicate which geometry has the superior design. The second modification, with a longer distributor, is shown to have flatter, more monotonic isobars perpendicular to the flow direction indicating a better filling process. The effects of the distributor modifications, as well as effects of the mold orientation, have also been examined with laboratory experiments in which the flow of a viscous Newtonian oil entering transparent molds is recorded visually. Here, the flow front is flatter and voids are reduced for the second geometry compared to the original geometry. A horizontal orientation, as opposed to the planned vertical orientation, results in fewer voids. Recently, the Navier-Stokes equations have been stabilized with the Dohrman-Bochev PSPP stabilization method, allowing us to calculate transient 3D simulations with computational times on the order of days instead of months. Validation simulations are performed and compared to the experiments. Many of the trends of the experiments are captured by the level set modeling, though quantitative agreement is lacking mainly due to the high value of the gas phase viscosity necessary for numerical stability, though physically unrealistic. More correct trends are predicted for the vertical model than the horizontal model, which is serendipitous as the actual mold is held in a vertical geometry. The full, transient mold filling calculations indicate that the flow front is flatter and voids may be reduced for the second geometry compared to the original geometry. The validated model is used to predict mold filling for the actual process with the material properties for the PZT paste, the original distributor geometry, and the mold in a vertical orientation. This calculation shows that voids may be trapped at the four corners of the mold opposite the distributor.
In this report, we document the accomplishments in our Laboratory Directed Research and Development project in which we employed a technical approach of combining experiments with computational modeling and analyses to elucidate the performance of hydrogen-fed proton exchange membrane fuel cells (PEMFCs). In the first part of this report, we document our focused efforts on understanding water transport in and removal from a hydrogen-fed PEMFC. Using a transparent cell, we directly visualized the evolution and growth of liquid-water droplets at the gas diffusion layer (GDL)/gas flow channel (GFC) interface. We further carried out a detailed experimental study to observe, via direct visualization, the formation, growth, and instability of water droplets at the GDL/GFC interface using a specially-designed apparatus, which simulates the cathode operation of a PEMFC. We developed a simplified model, based on our experimental observation and data, for predicting the onset of water-droplet instability at the GDL/GFC interface. Using a state-of-the-art neutron imaging instrument available at NIST (National Institute of Standard and Technology), we probed liquid-water distribution inside an operating PEMFC under a variety of operating conditions and investigated effects of evaporation due to local heating by waste heat on water removal. Moreover, we developed computational models for analyzing the effects of micro-porous layer on net water transport across the membrane and GDL anisotropy on the temperature and water distributions in the cathode of a PEMFC. We further developed a two-phase model based on the multiphase mixture formulation for predicting the liquid saturation, pressure drop, and flow maldistribution across the PEMFC cathode channels. In the second part of this report, we document our efforts on modeling the electrochemical performance of PEMFCs. We developed a constitutive model for predicting proton conductivity in polymer electrolyte membranes and compared model prediction with experimental data obtained in our laboratory and from literature. Moreover, we developed a one-dimensional analytical model for predicting electrochemical performance of an idealized PEMFC with small surface over-potentials. Furthermore, we developed a multi-dimensional computer model, which is based on the finite-element method and a fully-coupled implicit solution scheme via Newton's technique, for simulating the performance of PEMFCs. We demonstrated utility of our finite-element model by comparing the computed current density distribution and overall polarization with those measured using a segmented cell. In the last part of this report, we document an exploratory experimental study on MEA (membrane electrode assembly) degradation.
Simplified models that are based on macroscopic force balances and droplet-geometry approximations are presented for predicting the onset of instability leading to removal of water droplets at the gas diffusion layer (GDL)/gas flow channel (GFC) interface. Visualization experiments are carried out to observe the formation, growth, and removal or instability of the water droplets at the GDL/GFC interface of a simulated polymer electrolyte fuel cell cathode. Droplet-instability diagrams or windows computed by the simplified models are compared with those measured experimentally, and good agreement is obtained. Two-dimensional flow simulations employing the finite element method coupled with an arbitrary Lagrangian-Eulerian formulation for determining the liquid/gas interface position are also performed to assess the simplified cylindrical-droplet model. Necessary conditions for preventing fully grown droplets from lodging in the flow channel are derived using the simplified models. It is found that droplet removal can be enhanced by increasing flow channel length or mean gas flow velocity, decreasing channel height or contact angle hysteresis, or making the GDL/GFC interface more hydrophobic.
Solidification and blood flow seemingly have little in common, but each involves a fluid in contact with a deformable solid. In these systems, the solid-fluid interface moves as the solid advects and deforms, often traversing the entire domain of interest. Currently, these problems cannot be simulated without innumerable expensive remeshing steps, mesh manipulations or decoupling the solid and fluid motion. Despite the wealth of progress recently made in mechanics modeling, this glaring inadequacy persists. We propose a new technique that tracks the interface implicitly and circumvents the need for remeshing and remapping the solution onto the new mesh. The solid-fluid boundary is tracked with a level set algorithm that changes the equation type dynamically depending on the phases present. This novel approach to coupled mechanics problems promises to give accurate stresses, displacements and velocities in both phases, simultaneously.
In many micro-scale fluid dynamics problems, molecular-level processes can control the interfacial energy and viscoelastic properties at a liquid-solid interface. This leads to a flow behavior that is very different from those similar fluid dynamics problems at the macro-scale. Presently, continuum modeling fails to capture this flow behavior. Molecular dynamics simulations have been applied to investigate these complex fluid-wall interactions at the nano-scale. Results show that the influence of the wall crystal lattice orientation on the fluid-wall interactions can be very important. To address those problems involving interactions of multiple length scales, a coupled atomistic-continuum model has been developed and applied to analyze flow in channels with atomically smooth walls. The present coupling strategy uses the molecular dynamics technique to probe the non-equilibrium flow near the channel walls and applies constraints to the fluid particle motion, which is coupled to the continuum flow modeling in the interior region. We have applied this new methodology to investigate Couette flow in micro-channels.
Processes that involve particle-laden fluids are common in geomechanics and especially in the petroleum industry. Understanding the physics of these processes and the ability to predict their behavior requires the development of coupled fluid-flow and particle-motion computational methods. This paper outlines an accurate and robust coupled computational scheme using the lattice-Boltzmann method for fluid flow and the discrete-element method for solid particle motion. Results from several two-dimensional validation simulations are presented. Simulations reported include the sedimentation of an ellipse, a disc and two interacting discs in a closed column of fluid. The recently discovered phenomenon of drafting, kissing, and tumbling is fully reproduced in the two-disc simulation.
A phenomenological model was developed for multicomponent transport of charged species with simultaneous electrochemical reactions in concentrated solutions, and was applied to model processes in a thermal battery cell. A new general framework was formulated and implemented in GOMA (a multidimensional, multiphysics, finite-element computer code developed and being enhanced at Sandia) for modeling multidimensional, multicomponent transport of neutral and charged species in concentrated solutions. The new framework utilizes the Stefan-Maxwell equations that describe multicomponent diffusion of interacting species using composition-insensitive binary diffusion coefficients. The new GOMA capability for modeling multicomponent transport of neutral species was verified and validated using the model problem of ternary gaseous diffusion in a Stefan tube. The new GOMA-based thermal battery computer model was verified using an idealized battery cell in which concentration gradients are absent; the full model was verified by comparing with that of Bernardi and Newman (1987) and validated using limited thermal battery discharge-performance data from the open literature (Dunning 1981) and from Sandia (Guidotti 1996). Moreover, a new Liquid Chemkin Software Package was developed, which allows the user to handle manly aspects of liquid-phase kinetics, thermodynamics, and transport (particularly in terms of computing properties). Lastly, a Lattice-Boltzmann-based capability was developed for modeling pore- or micro-scale phenomena involving convection, diffusion, and simplified chemistry; this capability was demonstrated by modeling phenomena in the cathode region of a thermal battery cell.
Evaporation is a classical physics problem which, because of its significant importance for many engineering applications, has drawn considerable attention by previous researchers. Classical theoretical models [Ta. I. Frenkel, Kinetic Theory of Liquids, Clarendon Press, Oxford, 1946] represent evaporation in a simplistic way as the escape of atoms with highest velocities from a potential well with the depth determined by the atomic binding energy. The processes taking place in the gas phase above the rapidly evaporating surface have also been studied in great detail [S.I.Anisimov and V. A. Khokhlov, Instabilities in Lasser-Matter Interaction, CRC Press, Boca Raton, 1995]. The description of evaporation utilizing these models is known to adequately characterize drilling with high beam intensity, e.g., >10{sup 7} W/cm{sup 2}. However, the interaction regimes when beam intensity is relatively low, such as during welding or cutting, lack both theoretical and experimental consideration of the evaporation. It was shown recently that if the evaporation is treated in accordance with Anisimov et.al.'s approach, then predicted evaporation recoil should be a substantial factor influencing melt flow and related heat transfer during laser beam welding and cutting. To verify the applicability of this model for low beam intensity interaction, the authors compared the results of measurements and calculations of recoil pressure generated during laser beam irradiation of a target. The target material used was water ice at {minus}10 C. The displacement of a target supported in a nearly frictionless air bearing under irradiation by a defocused laser beam from a 14 kW CO{sub 2} laser was recorded and Newton's laws of motion used to derive the recoil pressure.