Modellierung und Simulation der Dynamik von portablen Polymer-Elektrolyt-Membran-Brennstoffzellen

This thesis focuses on the modeling and simulation of the PEMFC.The physical and electrochemical fundamentals necessary for fuel cell modeling are introduced in Chapter 2.Planar self-breathing fuel cells in printed circuit board (PCB) technology are currently being developed at the Fraunhofer Institute for Solar Energy Systems.In order to analyze the operational behavior, a mathematical model of planar self-breathing fuel cells is developed and validated in Chapter 3.The multicomponent transport of the species is considered as well as the couplings between the transport processes of heat, charge, andmass and the electrochemical reactions. Furthermore, to explain the oxygen mass transport limitation in the porous electrode of the cathode side an agglomerate model for the oxygen reduction reaction is developed.The system of coupled partial differential equations (PDEs) is implemented in FEMLAB^TM. For the discretization of the PDEs the Galerkin finiteelement method is used. The resulting system of nonlinear equations is solved with the Newton method.The cell model is validated by comparison of the measured overall performance of a planar self-breathing fuel cellwith the predictions of the model.Based on the modeling results, a theoretical study of planar and self-breathing fuel cells is presented.The investigation of the operating behavior reveals the most important properties.In Chapter 4 the important issue of liquid water generation and transport in PEMFCs is addressed.One of the major tasks when operating this type of fuel cell is avoiding the complete flooding of the PEMFC during operation.A one-dimensional and isothermal model is developed that is based on a coupled system of partial differential equations.The model contains a dynamic and two-phase description of the proton exchange membrane fuel cell. The mass transport in the gas phase and in the liquid phase is considered as well as the phase transition between liquid water and water vapor. The transport of charges and the electrochemical reactions are part of the model. Flooding effects that are caused by liquid water accumulation are described by this model.Moreover, the model contains a time-dependent description of the membrane that accounts for Schroeder's paradox. The membrane model is coupled with the two-phase flow equations in the electrodes.The model is implemented in the software FEMLAB^TM.The time-dependent PDEs are discretized in space by using the Galerkin method with time-dependent nodal parameters.The resulting system of ordinary differential equations is solved using the implicit multistep solver ode15s of MATLAB^TM.The validity of the novel model approach for the membrane is shown by the comparison of the measured and the simulated cell resistance.The model is applied to simulate cyclic voltammograms.A hysteresis effect of the current-voltage relation and a time-dependent current density in the two-phase regime is found in both the simulation and the experiment.Chapter 5 is focused on the dynamic investigation of PEMFC stacks.Understanding the dynamic behavior of fuel cell stacks is important for the operation and control of fuel cell stacks.Using the single cell model of Chapter 3 and the dynamic model of Chapter 4 as basis, a mathematical modelof a PEMFC stack is developed. However, due to the complexity of a fuel cell stack, the spatial resolution and dynamic description of the liquid water transportare not accounted for. These restrictions allow for direct comparison between the solution variables of the model and measurement data and for the simulation ofhours of stack operation, which could otherwise not be achieved.The model is time-dependent and non-isothermal. It is based on energy and mass balance equations. Heat and mass transfer by convection and conduction within the stack, as well as changes due to the electrochemical reactions and the phase transition of water, are taken into account. The mass and heat transport equations are coupled with an electrical model that is based on the Tafel equation and a membrane model that accounts for the net-transfer of water through the membrane. The mathematical formulation of the model is a coupled differential algebraic equation system that contains ordinary differential equations in time describing the heat and mass transfer. An algebraic equation is used to describe the electrochemical reaction at the cathode.The model is implemented in MATLAB^TM. The system of equations is solved by using the implicit multistep solver ode15s.The mathematical stack model is capable of simulating arbitrary load profiles.These properties facilitate the application of the dynamic PEMFC stack model in system simulation and model-based control.The validity of the model approach is proven by comparing simulated and measured load profiles and stack temperatures