Publications

Chen, Ken S.; Hickner, Michael A.

Abstract not provided.

Proposed for publication in the International Journal of Energy Research.

Chen, Ken S.; Hickner, Michael A.; Noble, David R.

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.

Chen, Ken S.

This report documents the author's efforts in the deterministic modeling of copper-sulfidation corrosion on non-planar substrates such as diodes and electrical connectors. A new framework based on Goma was developed for multi-dimensional modeling of atmospheric copper-sulfidation corrosion on non-planar substrates. In this framework, the moving sulfidation front is explicitly tracked by treating the finite-element mesh as a pseudo solid with an arbitrary Lagrangian-Eulerian formulation and repeatedly performing re-meshing using CUBIT and re-mapping using MAPVAR. Three one-dimensional studies were performed for verifying the framework in asymptotic regimes. Limited model validation was also carried out by comparing computed copper-sulfide thickness with experimental data. The framework was first demonstrated in modeling one-dimensional copper sulfidation with charge separation. It was found that both the thickness of the space-charge layers and the electrical potential at the sulfidation surface decrease rapidly as the Cu{sub 2}S layer thickens initially but eventually reach equilibrium values as Cu{sub 2}S layer becomes sufficiently thick; it was also found that electroneutrality is a reasonable approximation and that the electro-migration flux may be estimated by using the equilibrium potential difference between the sulfidation and annihilation surfaces when the Cu{sub 2}S layer is sufficiently thick. The framework was then employed to model copper sulfidation in the solid-state-diffusion controlled regime (i.e. stage II sulfidation) on a prototypical diode until a continuous Cu{sub 2}S film was formed on the diode surface. The framework was also applied to model copper sulfidation on an intermittent electrical contact between a gold-plated copper pin and gold-plated copper pad; the presence of Cu{sub 2}S was found to raise the effective electrical resistance drastically. Lastly, future research needs in modeling atmospheric copper sulfidation are discussed.

Microsystem Technologies

Chen, Ken S.; Evans, Gregory H.

Two-dimensional processes of nickel electro-deposition in LIGA microfabrication were modeled using the finite-element method and a fully coupled implicit solution scheme via Newton's technique. Species concentrations, electrolyte potential, flow field, and positions of the moving deposition surfaces were computed by solving the species-mass, charge, and momentum conservation equations as well as pseudo-solid mesh-motion equations that employ an arbitrary Lagrangian-Eulerian (ALE) formulation. Coupling this ALE approach with repeated re-meshing and re-mapping makes it possible to track the entire transient deposition processes from start of deposition until the trenches are filled, thus enabling the computation of local current densities that influence the microstructure and functional/mechanical properties of the deposit.

Computational and Experimental Methods

Chen, Ken S.

A predictive multi-dimensional computer model, Lagrangian-Eulerian formulation developed for simulating electrodeposition in LIGA microfabrication was discussed. A Poisson equation that explicitly described electrolyte potential was derived by combining the species mass conservation equations and the electroneutrality constraint. It was observed that pseudo-solid mesh equations that employed an arbitrary-Lagrangian-Eulerian (ALE) formulation were solved in tracking the moving boundary that was present in a LIGA nickel electrodeposition process. By coupling the ALE approach it was easy to follow the entire transient deposition process from start of the deposition till the trench was completely filled up.

Hickner, Michael A.; Grossarth, Kevin R.; Chen, Ken S.; Noble, David R.

Abstract not provided.

Chen, Ken S.; Evans, Gregory H.

This report documents the efforts and accomplishments of the LIGA electrodeposition modeling project which was headed by the ASCI Materials and Physics Modeling Program. A multi-dimensional framework based on GOMA was developed for modeling time-dependent diffusion and migration of multiple charged species in a dilute electrolyte solution with reduction electro-chemical reactions on moving deposition surfaces. By combining the species mass conservation equations with the electroneutrality constraint, a Poisson equation that explicitly describes the electrolyte potential was derived. The set of coupled, nonlinear equations governing species transport, electric potential, velocity, hydrodynamic pressure, and mesh motion were solved in GOMA, using the finite-element method and a fully-coupled implicit solution scheme via Newton's method. By treating the finite-element mesh as a pseudo solid with an arbitrary Lagrangian-Eulerian formulation and by repeatedly performing re-meshing with CUBIT and re-mapping with MAPVAR, the moving deposition surfaces were tracked explicitly from start of deposition until the trenches were filled with metal, thus enabling the computation of local current densities that potentially influence the microstructure and frictional/mechanical properties of the deposit. The multi-dimensional, multi-species, transient computational framework was demonstrated in case studies of two-dimensional nickel electrodeposition in single and multiple trenches, without and with bath stirring or forced flow. Effects of buoyancy-induced convection on deposition were also investigated. To further illustrate its utility, the framework was employed to simulate deposition in microscreen-based LIGA molds. Lastly, future needs for modeling LIGA electrodeposition are discussed.

American Society of Mechanical Engineers, Heat Transfer Division, (Publication) HTD

Noble, D.R.; Chen, Ken S.

The process of removing liquid water droplets in polymer electrolyte fuel cells (PEFC) is examined using a simple analytical model and two-dimensional simulations. Specifically, the stability of a droplet adhering to the wall of the cathode flow channel is examined as a function of the geometry of the flow channel, the applied pressure gradient, and the wetting properties. The result is a prediction of the critical droplet size as a function of the difference between the advancing and receding contact angles, or contact angle hysteresis. The analytical model is shown to qualitatively predict this stability limit when compared to two-dimensional simulation results. The simulations are performed using both Arbitrary Lagrangian Eulerian (ALE) methods and level set methods. The ALE and level set predictions are shown to be in good agreement. Copyright © 2004 by ASME.

Braithwaite, J.W.; Braithwaite, J.W.; Sorensen, Neil R.; Robinson, David G.; Chen, Ken S.; Bogdan, Carolyn W.

An analytical capability is being developed that can be used to predict the effect of corrosion on the performance of electrical circuits and systems. The availability of this ''toolset'' will dramatically improve our ability to influence device and circuit design, address and remediate field occurrences, and determine real limits for circuit service life. In pursuit of this objective, we have defined and adopted an iterative, statistical-based, top-down approach that will permit very formidable and real obstacles related to both the development and use of the toolset to be resolved as effectively as possible. An important component of this approach is the direct incorporation of expert opinion. Some of the complicating factors to be addressed involve the code/model complexity, the existence of large number of possible degradation processes, and an incompatibility between the length scales associated with device dimensions and the corrosion processes. Two of the key aspects of the desired predictive toolset are (1) a direct linkage of an electrical-system performance model with mechanistic-based, deterministic corrosion models, and (2) the explicit incorporation of a computational framework to quantify the effects of non-deterministic parameters (uncertainty). The selected approach and key elements of the toolset are first described in this paper. These descriptions are followed by some examples of how this toolset development process is being implemented.

Journal of the Electrochemical Society

Um, Sukkee; Wang, C.Y.; Chen, Ken S.

A transient, multidimensional model has been developed to simulate proton exchange membrane fuel cells. The model accounts simultaneously for electrochemical kinetics, current distribution, hydrodynamics, and multicomponent transport. A single set of conservation equations valid for flow channels, gas-diffusion electrodes, catalyst layers, and the membrane region are developed and numerically solved using a finite-volume-based computational fluid dynamics technique. The numerical model is validated against published experimental data with good agreement. Subsequently, the model is applied to explore hydrogen dilution effects in the anode feed. The predicted polarization curves under hydrogen dilution conditions are in qualitative agreement with recent experiments reported in the literature. The detailed two-dimensional electrochemical and flow/transport simulations further reveal that in the presence of hydrogen dilution in the fuel stream, hydrogen is depleted at the reaction surface, resulting in substantial anode mass transport polarization and hence a lower current density that is limited by hydrogen transport from the fuel stream to the reaction site. Finally, a transient simulation of the cell current density response to a step change in cell voltage is reported.

Journal of Electrochemical Society

Chen, Ken S.; Chen, Ken S.

Two-phase flow and transport of reactants and products in the air cathode of proton exchange membrane (PEM) fuel cells is studied analytically and numerically. Four regimes of water distribution and transport are classified by defining three threshold current densities and a maximum current density. They correspond to first appearance of liquid water at the membrane/cathode interface, extension of the gas-liquid two-phase zone to the cathode/channel interface, saturated moist air exiting the gas channel, and complete consumption of oxygen by the electrochemical reaction. When the cell operates above the first threshold current density, liquid water appears and a two-phase zone forms within the porous cathode. A two-phase, multi-component mixture model in conjunction with a finite-volume-based computational fluid dynamics (CFD) technique is applied to simulate the cathode operation in this regime. The model is able to handle the situation where a single-phase region co-exists with a two-phase zone in the air cathode. For the first time, the polarization curve as well as water and oxygen concentration distributions encompassing both single- and two-phase regimes of the air cathode are presented. Capillary action is found to be the dominant mechanism for water transport inside the two-phase zone. The liquid water saturation within the cathode is predicted to reach 6.3% at 1.4 A/cm{sup 2}.

Chen, Ken S.; Evans, Gregory H.; Larson, Richard S.; Noble, David R.; Houf, William G.

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.