Kevin L Davies

Georgia Institute of Technology, Atlanta, Georgia USA

Christiaan J.J. Paredis

Georgia Institute of Technology, Atlanta, Georgia USA

Comas L. Haynes

Georgia Institute of Technology, Atlanta, Georgia USA

Published in: Proceedings of the 9th International MODELICA Conference; September 3-5; 2012; Munich; Germany

Linköping Electronic Conference Proceedings 76:10, s. 115-124

Published: 2012-11-19

ISBN: 978-91-7519-826-2

ISSN: 1650-3686 (print), 1650-3740 (online)

This paper describes the architecture and key equations of a library to model proton exchange membrane fuel cells (PEMFCs) in Modelica. The motivating goal of this work is to reconcile many of the published models of PEMFCs and combine them in a reconfigurable PEMFC model that is effective for a variety of uses. It is necessary to distill equations from fuel cell literature into forms that at once capture the essence of the physical interactions; are conducive to the physical modularity of the device; work within the constraints and take full advantage of the Modelica language.

Since the behavior of PEMFCs depends on both advection and diffusion; a suitable alternative to the Modelica Fluid library and the stream concept is necessary. The proposed solution uses a "mixing" scheme based on the exponential of the Peclet numbers for each transport process. Storage and transport processes are co-located in each subregion of a rectilinear grid-all in the same base model. The Onsager formulation is used; whereby the effort and flow rate are conjugates of the entropy flow rate associated with energy transfer.

The implementation is modular; it allows species to be enabled indendently for each region. In addition; the geometric axes may be independently enabled (up to 3D) and shearing (transverse momentum) may be optionally included. Chemical/electrochemical inteactions are communicated in a fully acausal manner through expandable connectors.

This paper focuses on the motivation; background; and approach. Future publications will describe the ongoing work to calibrate; validate; and utilize the model for particular case studies. The library is made available as open source.

PEMFC; three dimensional; fluid dynamics; electrochemistry; heat transfer; advection; diffusion; momentum; Onsager

[1] A. Bejan. Advanced Engineering Thermodynamics. John Wiley & Sons; 3rd edition; 2006.

[2] R. B. Bird; W. E. Stewart; and E. N. Lightfoot. Transport Phenomena. John Wiley & Sons; 2nd edition; 2002.

[3] W. Borutzky. Bond Graph Modelling of Engineering Systems: Theory; Applications and Software Support. Springer; 2011.

[4] K. A. Burke. Unitized regenerative fuel cell system development. NASA report TM—2003-212739; Glenn Research Center; Cleveland; OH; Dec. 2003.

[5] F. E. Cellier and J. Greifeneder. Modeling chemical reactions in modelica by use of chemo-bonds. In F. Casella; editor; Proc. 7th Int. Modelica Conf.; Como; Italy; Sep. 2009. Modelica Assoc.; Linköping University Electronic Press.

[6] E. L. . Cussler. Diffusion: Mass Transfer in Fluid Systems. Cambridge University Press; 2nd edition; 1997.

[7] K. L. Davies and R. M. Moore. Object-oriented fuel cell model library. Electrochem. Soc. T.; 11(1):797–808; Oct. 2007.

[8] K. L. Davies and R. M. Moore. PEMFCSim: A fuel cell model library in Modelica. In 31st Fuel Cell Seminar & Exposition; San Antonio; TX; Oct. 2007.

[9] K. L. Davies; R. M. Moore; and G. Bender. Model library of polymer electrolyte membrane fuel cells for system hardware and control design. In F. Casella; editor; Proc. 7th Int. Modelica Conf.; Como; Italy; Sep. 2009. Modelica Assoc.; Linköping University Electronic Press.

[10] K. L. Davies and C. J. Paredis. Natural unit representation in Modelica. In Proc. 9th Int. Modelica Conf.; Munich; Germany; Sep. 2012 (submitted). Modelica Assoc.

[11] J. H. Dymond; K. N. Marsh; R. C. Wilhoit; and K. C. Wong. Virial Coefficients of Pure Gases. Numerical Data and Functional Relationships in Science and Technology. Springer-Verlag; 2002.

[12] Dynasim AB. Dymola: Dynamic Modeling Laboratory; Mar. 2010. Ver. 7.4.

[13] F. P. Incropera and D. P. DeWitt. Fundamentals of Heat and Mass Transfer. John Wiley & Sons; 5th edition; 2002.

[14] J. Larminie and A. Dicks. Fuel Cell Systems Explained. John Wiley & Sons; 2nd edition; 2003.

[15] C. Mattiussi. The finite volume; finite element; and finite difference methods as numerical methods for physical field problems. volume 113 of Advances in Imaging and Electron Physics; pages 1–146. Elsevier Academic Press; 2000.

[16] B. J. McBride; M. J. Zehe; and S. Gordon. NASA Glenn coefficients for calculating thermodynamic properties of individual species. NASA report TP—2002-211556; Glenn Research Center; Cleveland; OH; Sep. 2002.

[17] B. A. McCain; A. G. Stefanopoulou; and K. R. Butts. A study toward minimum spatial discretization of a fuel cell dynamics model. In Proc. Int. Mech. Eng. Congr. Exposition (IMECE2006); number IMECE2006-14509; Chicago; IL; Nov. 2006. ASME.

[18] D. A. McKay; W. T. Ott; and A. G. Stefanopoulou. Modeling; parameter identification; and validation of water dynamics for a fuel cell stack. In Conf. on Fuel Cell Science; Engineering and Technology; Orlando; FL; Nov. 2005.ASME. FUELCELL2005-81484.

[19] Modelica Association. Modelica Standard Library. http://www.modelica.org/libraries/Modelica; Dec. 2009. Ver.3.1.

[20] M. J. Moran and H. N. Shapiro. Fundamentals of Engineering Thermodynamics. John Wiley & Sons; 6th edition; 2008.

[21] R. D. Present. Kinetic Theory of Gases. McGraw-Hill; 1958.

[22] M. A. Rubio; A. Urquia; L. Gonzá¡lez; D. Guinea; and S. Dormido. FuelCellLib: A modelica library for modeling of fuel cells. In Proc. 4th Int. Modelica Conf.; Hamburg-Harburg; Germany; Mar. 2005. Modelica Association.

[23] M. A. Rubio; A. Urquiaa; and S. Dormidoa. Dynamic modelling of PEM fuel cells using the FuelCellLib Modelica library. Math. Comp. Model. Dyn.; 16(3):165–194; Jun. 2010. doi: 10.1080/13873954.2010.506758.

[24] A. Salogni and P. Colonna. Modeling of solid oxide fuel cells for dynamic simulations of integrated systems. Appl. Therm. Eng.; 30(5):464–477; 2010. doi: 10.1016/j.applthermaleng.2009.10.007.

[25] R. A. Svehla. Transport coefficients for the nasa lewis chemical equilibrium program. NASA Technical Memorandum NASA; Lewis Research Center; Cleveland; OH; Apr. 1995.

[26] U.S. Department of Energy. Hydrogen; fuel cells & infrastructure technologies program: Multiyear research; development and demonstration plan. Technical report; Energy Efficiency and Renewable Energy; Oct. 2007. Section 3.4: Fuel Cells.

[27] N. Wagner; W. Schnurnberger; B. Mueller; and M. Lang. Electrochemical impedance spectra of solid-oxide fuel cells and polymer membrane fuel cells. Electrochim. Acta; 43(24):3785–3793; 1998. doi: 10.1016/S0013-4686(98)00138-8.

[28] A. Z. Weber; R. M. Darling; and J. S. Newman. Modeling two-phase behavior in PEFCs. J. Electrochem. Soc.; 151(10):A1715–A1727; 2004. doi: 10.1149/1.1792891.

[29] K. W. Woo and S. I. Yeo. Dalton’s Law vs. Amagat’s Law for the mixture of real gases. SNU J. Educ. Res.; 5:127–134; 1995.