A fundamental model exhibiting nonlinear oscillatory dynamics in solid oxide fuel cells

Abstract

In this paper, we address the phenomenon of temporal, self-sustained oscillations which have been observed under quite general conditions in solid oxide fuel cells. Our objective is to uncover the fundamental mechanisms giving rise to the observed oscillations. To this end, we develop a model based on the fundamental chemical kinetics and transfer processes which take place within the fuel cell. This leads to a three-dimensional dynamical system, which, under typical operating conditions, is rationally reducible to a planar dynamical system. The structural dynamics of the planar dynamical system are studied in detail. Self-sustained oscillations are shown to arise through Hopf bifurcations in this planar dynamical system, and the key parameter ranges for the occurrence of such oscillations are identified.

Current Oscillations in Solid Oxide Fuel Cells under Weakly Humidified Conditions

“…The system of coupled nonlinear ordinary differential equations governing the reaction dynamics and transfer at the anode is given as (see [1]),…”

“…The first term of each rate equation represents the transfer of the particular species into the reaction zone A, whilst the remaining terms represent the production/consumption of the species as given by the reduced reaction scheme (8) and (9). The system (15)-(17) is then nondimensionalised and rationally reduced to the planar dynamical system (see [1]),…”

“…The parameter ā 0 represents the ratio of inlet concentration to the scaled concentration of methane (a s ). The bifurcation analysis of the system (18)- (19), which will be referred to as [D-S], is given in [1]. Some figures from [1] will be reproduced in Section (5) in order to compare the model with the experimental results.…”

“…The analysis of this planar dynamical system was then split into two cases, namely, a weakly humidified, and a fully humidified fuel stream. The case of a weakly humidified fuel stream was examined in detail in [1]. The model exhibited multiple steady states and autonomous nonlinear oscillations in the phase 3 plane.…”

“…A series of experiments have been conducted in order to investigate the oscillatory phenomena occurring in standard methane fuelled SOFCs with a Ni/YSZ anode. In this paper the results of this experimental programme are presented, and we compare them with the results of the model presented in [1]. To begin with, the model is briefly summarised and the notation is introduced.…”