Michael Vynnycky

Analysis of a Two-Phase Non-Isothermal Model for a PEFC

A non-isothermal, two-phase model for a polymer electrolyte fuel cell (PEFC) is presented, analyzed, and solved numerically under three different thermal, and two hydrodynamic, modeling assumptions ...

Finite-difference methods with increased accuracy and correct initialization for one-dimensional Stefan problems

Although the numerical solution of one-dimensional phase-change, or Stefan, problems is well documented, a review of the most recent literature indicates that there are still unresolved issues regarding the start-up of a computation for a region that initially has zero thickness, as well as how to determine the location of the moving boundary thereafter. This paper considers the so-called boundary immobilization method for four benchmark melting problems, in tandem with three finite-difference discretization schemes. We demonstrate a combined analytical and numerical approach that eliminates completely the ad hoc treatment of the starting solution that is often used, and is numerically second-order accurate in both time and space, a point that has been consistently overlooked for this type of moving-boundary problem.

Reduced Two-Dimensional One-Phase Model for Analysis of the Anode of a DMFC

An isothermal two-dimensional liquid phase model for the conservation of mass, momentum, and species in the anode of a direct methanol fuel cell (DMFC) is presented and analyzed. The inherent electrochemistry in the DMFC anode active layer is reduced to boundary conditions via parameter adaption. The model is developed for the case when the geometry aspect ratio is small, and it is shown that, under realistic operating conditions, a reduced model, which nonetheless describes all the essential physics of the full model, can be derived. The significant benefits of this approach are that physical trends become much more apparent than in the full model and that there is considerable reduction in the time required to compute numerical solutions, a fact especially useful for wide-ranging parameter studies. Such a study is then performed in terms of the three nondimensional parameters that emerge from the analysis, and we subsequently interpret our results in terms of the dimensional design and operating parameters. In particular, we highlight their effect on methanol mass transfer in the flow channel and on the current density. The results indicate the relative importance of mass-transfer resistance in both the flow channel and the adjacent porous backing.

Reduced Two-Phase Model for Analysis of the Anode of a DMFC

An isothermal two-phase ternary mixture model that takes into account conservation of momentum, mass, and species in the anode of a direct methanol fuel cell (DMFC) is presented and analyzed. The slenderness of the anode allows a considerable reduction of the mathematical formulation, without sacrificing the essential physics. The reduced model is then verified and validated against data obtained from an experimental DMFC outfitted with a transparent end plate. Good agreement is achieved. The effect of mass-transfer resistances in the flow field and porous backing are highlighted. The presence of a gas phase is shown to improve the mass transfer of methanol at higher temperatures (>30 degreesC). It is also found that at a temperature of around 30 degreesC, a one-phase model predicts the same current density distribution as a more sophisticated two-phase model. Analysis of the results from the two-phase model, in combination with the experiments, results in a suggestion for an optimal flow field for the liquid-fed DMFC.

An accurate numerical solution for the transient heating of an evaporating spherical droplet

A recently derived numerical algorithm for one-dimensional time-dependent Stefan problems is extended for the purposes of solving a moving boundary problem for the transient heating of an evaporating spherical droplet. The Keller box finite-difference scheme is used, in tandem with the so-called boundary immobilization method. An important component of the work is the careful use of variable transformations that must be built into the numerical algorithm in order to preserve second-order accuracy in both time and space – an issue not previously discussed in relation to this widely-used scheme. In addition, we demonstrate that our solution is in close agreement with the solution obtained using an alternative numerical scheme that employs an analytic solution of the heat conduction equation inside the droplet, for which the droplet radius was assumed to be a piecewise linear function of time. The advantages of the new method are discussed.

An accurate finite-difference method for ablation-type Stefan problems

A recently derived numerical algorithm for one-dimensional time-dependent Stefan problems is extended for the purpose of solving one-phase ablation-type moving boundary problems; in tandem with the Keller box finite-difference scheme, the so-called boundary immobilization method is used. An important component of the work is the use of variable transformations that must be built into the numerical algorithm in order to preserve second-order accuracy in both time and space. The analysis also determines that the ablation front initially moves as the time raised to the power 3/2; hence, it evolves considerably more slowly than the phase-change front in the classical Stefan problem with isothermal cooling.

A Mathematical Model for the Electrochemical Pickling of Steel

In industrial electrolytic pickling, a steel strip with oxidized surfaces is passed through an aqueous electrolyte between a configuration of electrodes, across which a potential difference is appl ...

On the modelling of two-phase flow in the cathode gas diffusion layer of a polymer electrolyte fuel cell

A front-tracking approach is derived for the numerical solution of the equations arising in the multi-fluid model for isothermal multiphase multicomponent flow in the gas diffusion layer of the cathode of a polymer electrolyte fuel cell under conditions of local thermodynamic equilibrium. The method is able to find the location of the one-phase/two-phase interface explicitly and without need for the artificial diffusion, smoothing and ad hoc source terms that are required in existing formulations. Also, the analysis indicates the presence of a previously unidentified integrable singularity, which can be removed provided that the dependent variables are chosen correctly. For quantitative comparison, a benchmark example is implemented using both approaches in the commercially available finite-element software Comsol Multiphysics.

Impedance as a Tool for Investigating Aging in Lithium-Ion Porous Electrodes II. Positive Electrode Examination

High-power positive LixNi0.8Co0.15Al0.05O2 composite porous electrodes are known to be the main source of impedance increase in batteries based on GEN2 chemistry. The impedance of positive electrod ...

On the numerical solution of two-phase Stefan problems with heat-flux boundary conditions

A recently derived numerical algorithm for one-dimensional one-phase Stefan problems is extended for the purpose of two-phase moving boundary problems in which the second phase first appears only after a finite delay time; this can occur if the phase change is caused by a heat-flux boundary condition. In tandem with the Keller box finite-difference scheme, the so-called boundary immobilization method is used. An important component of the work is the use of variable transformations that must be built into the numerical algorithm to resolve the boundary-condition discontinuity that is associated with the onset of phase change. This allows the delay time until solidification begins to be determined, and gives second-order accuracy in both time and space.