Jürgen Fuhrmann

Performance Modeling of a Direct Methanol Fuel Cell

A new two-dimensional model of a direct methanol fuel cell (DMFC) has been developed and numerically tested. In complement to the existing developments, this model regards the diffusion layers as water-gas systems in the pore space with saturation and permeability varying according to capillary effects. The presence of hydrophilic and hydrophobic pores has been taken into account by introducing a new parametrization of the relationship between capillary pressure and saturation. Thus, mass transport occurs in parallel in the two phases, gas and liquid. The exchange between these phases is due to condensation and evaporation with rates given by the available exchange surface and the temperature. The gas transport is governed by the Stefan-Maxwell equations incorporated into the two-phase flow modeling approach. Instead of the often used Tafel and Butler-Volmer equations which are insufficient in the case of catalytic methanol oxidation and oxygen reduction, according to recent investigations, the electrochemical reactions are split up into reaction chains involving the covering of the catalysts with the various intermediate species. The main advantage of this approach is that it incorporates the effects of the limitation of the reaction rates due to the limited number of catalyst sites in a natural manner. The resulting system of transport and reaction equations is discretized in time by the backward Euler method and in space by a finite volume technique with proper upwinding.

A finite volume scheme for nonlinear parabolic equations derived from one-dimensional local dirichlet problems

In this paper, we propose a new method to compute the numerical flux of a finite volume scheme, used for the approximation of the solution of the nonlinear partial differential equation ut+div(qf(u))−ΔΦ(u)=0 in a 1D, 2D or 3D domain. The function Φ is supposed to be strictly increasing, but some values s such that Φ′(s)=0 can exist. The method is based on the solution, at each interface between two control volumes, of the nonlinear elliptic two point boundary value problem (qf(υ)+(Φ(υ))′)′=0 with Dirichlet boundary conditions given by the values of the discrete approximation in both control volumes. We prove the existence of a solution to this two point boundary value problem. We show that the expression for the numerical flux can be yielded without referring to this solution. Furthermore, we prove that the so designed finite volume scheme has the expected stability properties and that its solution converges to the weak solution of the continuous problem. Numerical results show the increase of accuracy due to the use of this scheme, compared to some other schemes.

Hybrid Finite-Volume/Finite-Element Schemes for p(x)-Laplace Thermistor Models

We introduce an empirical PDE model for the electrothermal description of organic semiconductor devices by means of current and heat flow. The current flow equation is of p(x)-Laplace type, where the piecewise constant exponent p(x) takes the non-Ohmic behavior of the organic layers into account. Moreover, the electrical conductivity contains an Arrhenius-type temperature law. We present a hybrid finite-volume/finite-element discretization scheme for the coupled system, discuss a favorite discretization of the p(x)-Laplacian at hetero interfaces, and explain how path following methods are applied to simulate S-shaped current-voltage relations resulting from the interplay of self-heating and heat flow.

On modifications of the Scharfetter-Gummel scheme for drift-diffusion equations with Fermi-like statistical distribution functions

Driven by applications in fields like organic semiconductors there is an increased interest in numerical simulations based on drift-diffusion models with general statistical distribution functions. It is important to keep the well known qualitative properties of the Scharfetter-Gummel finite volume scheme, like positivity of solutions, dissipativity and consistency with thermodynamic equilibrium. A proper generalization to general statistical distribution functions is a topic of current research. The paper presents different state-of-the-art approaches to solve this problem. Their issues and advantages are discussed, and their practical performance is evaluated for real device structures.

Electro-thermal modeling of organic semiconductors describing negative differential resistance induced by self-heating

We discuss self-heating of organic semiconductor devices based on Arrhenius-like conductivity laws. The self-consistent calculation of charge and heat transport explains thermal switching, bistability, and hysteresis resulting from S-shaped current-voltage curves with regions of negative differential resistance (NDR). For large area thin film organic devices we study the appearance of a spatially localized NDR region and the spatial evolution of this NDR region in dependence on the total current. We propose that in organic light emitting diodes (OLEDs) these effects are responsible for spatially inhomogeneous current flow and inhomogeneous luminance at high power.

A Multigrid Method for the Solution of a Convection — Diffusion Equation with Rapidly Varying Coefficients

Consider the following equations n n

Comparison of Scharfetter-Gummel Flux Discretizations Under Blakemore Statistics

- div,(gradn, - ,n,grad,psi), = ,f

Self-heating effects in organic semiconductor crossbar structures with small active area

n nand (for u = e −ψ n) n n