Asymptotically Reduced Model for a Proton Exchange Membrane Fuel Cell Stack: Automated Model Generation and Verification

A proton exchange membrane fuel cell (PEMFC) stack can comprise a large number of cells and coolant plates; the former, in turn, contain further functional layers and groups. The large number of transport phenomena that occur at differing length scales throughout the stack pose a challenging problem for mathematical modeling. In this context, we present a "bottom-up" approach to overcome the difficulties in the mathematical modeling of a PEMFC stack; in short, a fast and memory-efficient reduced model for a single PEMFC derived earlier is coupled to a model for heat and charge transfer in a coolant plate to form a numerical building block, which can be replicated to form a virtual stack having the required number of cells. This procedure is automated to avoid the time-consuming task of manually creating the stack, as well as to remove the possibility of human error during the setup phase. The automated, reduced stack model is verified for a 10-cell stack with the full set of equations; good agreement is found when perturbations between cells are "small." We then study the computational efficiency of the reduced model for stacks comprising up to 400 cells: A typical run for a 10-cell and a 100-cell stack takes around 20 s and 3-4 min and requires 0.6 and 1.2 GB of random access memory, respectively. Finally, extensions to include the effects of perturbed flow, additional physics, external manifolds, and other types of flow fields are discussed.

[1]  Christoph Ziegler,et al.  Computationally efficient modeling of the dynamic behavior of a portable PEM fuel cell stack , 2008 .

[2]  Song-Yul Choe,et al.  Unsteady 2D PEM fuel cell modeling for a stack emphasizing thermal effects , 2007 .

[3]  Ramana G. Reddy,et al.  Materials and design development for bipolar/end plates in fuel cells , 2004 .

[4]  Biswa R. Padhy,et al.  Performance of DMFC with SS 316 bipolar/end plates , 2006 .

[5]  Hyunchul Ju,et al.  Nonisothermal Modeling of Polymer Electrolyte Fuel Cells I. Experimental Validation , 2005 .

[6]  François Maréchal,et al.  Energy balance model of a SOFC cogenerator operated with biogas , 2003 .

[7]  Michael Vynnycky,et al.  Reduced Two-Phase Model for Analysis of the Anode of a DMFC , 2004 .

[8]  Hee Chun Lim,et al.  Pressure and flow distribution in internal gas manifolds of a fuel-cell stack , 2003 .

[9]  Jun Li,et al.  A reduced 1D dynamic model of a planar direct internal reforming solid oxide fuel cell for system research , 2009 .

[10]  P. Lin,et al.  A high efficient assembly technique for large PEMFC stacks: Part I. Theory , 2009 .

[11]  P. Rodatz,et al.  Operational aspects of a large PEFC stack under practical conditions , 2004 .

[12]  Bradley P. Ladewig,et al.  Analysis of the Ripple Current in a 5 kW Polymer Electrolyte Membrane Fuel Cell Stack , 2009 .

[13]  Steven Beale,et al.  Computer methods for performance prediction in fuel cells , 2003 .

[14]  Ramana G. Reddy,et al.  Modeling of polymer electrolyte membrane fuel cell with metal foam in the flow-field of the bipolar/end plates , 2003 .

[15]  Michael Vynnycky,et al.  Analysis of a Two-Phase Non-Isothermal Model for a PEFC , 2005 .

[16]  Shiauh-Ping Jung,et al.  Flow distribution in the manifold of PEM fuel cell stack , 2007 .

[17]  Weirong Chen,et al.  Nonlinear robust control of proton exchange membrane fuel cell by state feedback exact linearization , 2009 .

[18]  W. M. Taama,et al.  One-dimensional thermal model for direct methanol fuel cell stacks. Part II. Model based parametric analysis and predicted temperature profiles , 1999 .

[19]  Chengwei Wu,et al.  A high efficient assembly technique for large proton exchange membrane fuel cell stacks: Part II. Applications , 2010 .

[20]  I. Celik,et al.  A numerical study of cell-to-cell variations in a SOFC stack , 2004 .

[21]  A. Fedorov,et al.  Reduced-order transient thermal modeling for SOFC heating and cooling , 2006 .

[22]  J. I. Gazzarri,et al.  Short-stack modeling of degradation in solid oxide fuel cells: Part I. Contact degradation , 2008 .

[23]  Michael Vynnycky,et al.  A Two‐Phase Non‐Isothermal PEFC Model: Theory and Validation , 2004 .

[24]  P. Sui,et al.  Cell Interaction Phenomena in Polymer Electrolyte Fuel Cell Stacks , 2008 .

[25]  Raghunathan Rengaswamy,et al.  A two-dimensional steady state model including the effect of liquid water for a PEM fuel cell cathode , 2007 .

[26]  A. A. Kulikovsky,et al.  Mirroring of Current-Free Spots in a Fuel Cell Stack , 2007 .

[27]  M. Han,et al.  Characterization of gas diffusion layers for PEMFC , 2008 .

[28]  Jari Ihonen,et al.  Modelling compression pressure distribution in fuel cell stacks , 2009 .

[29]  William W. Clark,et al.  Effects of cell-to-cell fuel mal-distribution on fuel cell performance and a means to reduce mal-distribution using MEMS micro-valves , 2007 .

[30]  François Maréchal,et al.  Generalized model of planar SOFC repeat element for design optimization , 2004 .

[31]  Félix Barreras,et al.  Study of the distribution of air flow in a proton exchange membrane fuel cell stack , 2009 .

[32]  M. Verbrugge,et al.  Mathematical model of a gas diffusion electrode bonded to a polymer electrolyte , 1991 .

[33]  Sreenivas Jayanti,et al.  Flow distribution and pressure drop in parallel-channel configurations of planar fuel cells , 2005 .

[34]  A. A. Kulikovsky,et al.  Voltage loss in bipolar plates in a fuel cell stack , 2006 .

[35]  Chaoyang Wang,et al.  An approach to measuring spatially resolved water crossover coefficient in a polymer electrolyte fuel cell , 2007 .

[36]  Tero Hottinen,et al.  Modeling of Polymer Electrolyte Membrane Fuel Cell Stack End Plates , 2008 .

[37]  Michael Vynnycky,et al.  Validated Reduction and Accelerated Numerical Computation of a Model for the Proton Exchange Membrane Fuel Cell , 2009 .

[38]  Michael Vynnycky,et al.  Reduced Two-Dimensional One-Phase Model for Analysis of the Anode of a DMFC , 2003 .

[39]  C. Siegel.  Review of computational heat and mass transfer modeling in polymer-electrolyte-membrane (PEM) fuel cells , 2008 .

[40]  Keith Scott,et al.  One-dimensional thermal model for direct methanol fuel cell stacks. Part I. Model development , 1999 .

[41]  J. Kim,et al.  Development of porous carbon foam polymer electrolyte membrane fuel cell , 2010 .

[42]  A. Kulikovsky.  Model of a Direct Methanol Fuel Cell Stack Resistive “Spots” and Stack Performance , 2006 .

[43]  A. Parthasarathy,et al.  Temperature Dependence of the Electrode Kinetics of Oxygen Reduction at the Platinum/Nafion® Interface—A Microelectrode Investigation , 1992 .

[44]  T. Springer,et al.  Polymer Electrolyte Fuel Cell Model , 1991 .

[45]  A. Kulikovsky.  Optimal temperature for DMFC stack operation , 2008 .

[46]  Michael Vynnycky,et al.  A quantitative study of the effect of flow-distributor geometry in the cathode of a PEM fuel cell , 2006 .

[47]  Michael Vynnycky,et al.  Asymptotic Reduction for Numerical Modeling of Polymer Electrolyte Fuel Cells , 2009, SIAM J. Appl. Math..

[48]  Weilin Zhuge,et al.  Numerical simulation of a mini PEMFC stack , 2006 .

[49]  Michael Vynnycky,et al.  Analysis of a Model for Multicomponent Mass Transfer in the Cathode of a Polymer Electrolyte Fuel Cell , 2003, SIAM J. Appl. Math..

[50]  B. Wetton,et al.  Flow distribution in proton exchange membrane fuel cell stacks , 2006 .

[51]  Chih-Yung Wen,et al.  Experimental study of clamping effects on the performances of a single proton exchange membrane fuel cell and a 10-cell stack , 2009 .

[52]  Christopher Hebling,et al.  Experimental and numerical studies of portable PEMFC stack , 2009 .

[53]  Yosuke Matsukuma,et al.  Numerical analysis of relative humidity distribution in polymer electrolyte fuel cell stack including cooling water , 2006 .

[54]  S. G. Choi,et al.  Development of 1 kW class polymer electrolyte membrane fuel cell power generation system , 2002 .

[55]  Jack Brouwer,et al.  Quasi-three dimensional dynamic model of a proton exchange membrane fuel cell for system and controls development , 2007 .

[56]  Keith Promislow,et al.  Reduced dimensional computational models of polymer electrolyte membrane fuel cell stacks , 2007, J. Comput. Phys..

[57]  Adrian Bejan,et al.  Constructal PEM fuel cell stack design , 2005 .

[58]  Daniel Hissel,et al.  Characterisation and modelling of a 5 kW PEMFC for transportation applications , 2006 .

[59]  P. Cheng,et al.  Transport Phenomena Analysis in Proton Exchange Membrane Fuel Cells , 2005 .

[60]  Steven Beale,et al.  A Distributed Resistance Analogy for Solid Oxide Fuel Cells , 2005 .

[61]  S. Kandlikar,et al.  Thermal management issues in a PEMFC stack – A brief review of current status , 2009 .

[62]  Dimos Poulikakos,et al.  Polymer Electrolyte Fuel Cells With Porous Materials as Fluid Distributors and Comparisons With Traditional Channeled Systems , 2004 .

[63]  Sunhoe Kim,et al.  Effects of humidity and temperature on a proton exchange membrane fuel cell (PEMFC) stack , 2008 .

[64]  Steven Beale,et al.  Performance predictions in solid oxide fuel cells , 2006 .

[65]  Norman Munroe,et al.  Review and comparison of approaches to proton exchange membrane fuel cell modeling , 2005 .

[66]  B. M. Suleiman,et al.  Dynamic plane source technique for simultaneous determination of specific heat, thermal conductivity and thermal diffusivity of metallic samples , 1991 .