Toward predictive PEFC simulation : the importance of thermal and electrical contact resistance

In computational models of polymer electrolyte fuel cells (PEFCs), thermal and electrical resistances between the different contacting material layers are commonly disregarded. Various experimental conductivity measurements have shown, though, that they can have a significant share in the overall through-plane resistance. Here, experimentally measured contact resistances between different MEA layers are implemented into a one-dimensional stationary two-phase PEFC model to demonstrate the importance of taking these effects into account in PEFC simulations that aim to be quantitatively predictive

Free open reference implementation of a two-phase PEM fuel cell model

In almost 30 years of PEM fuel cell modeling, countless numerical models have been developed in science and industrial applications, almost none of which have been fully disclosed to the public. There is a large need for standardization and establishing a common ground not only in experimental characterization of fuel cells, but also in the development of simulation codes, to prevent each research group from having to start anew from scratch. Here, we publish the first open standalone implementation of a full-blown, steady-state, non-isothermal two-phase model for low-temperature PEM fuel cells. It is based on macro-homogeneous modeling approaches and implements the most essential through-plane transport processes in a five-layer MEA. The focus is on code simplicity and compactness with only a few hundred lines of clearly readable code, providing a starting point for more complex model development. The model is implemented as a standalone MATLAB function, based on MATLAB's standard boundary value problem solver. The default simulation setup reflects wide-spread commercially available MEA materials. Operating conditions recommended for automotive applications by the European Commission are used to establish new fuel cell simulation base data, making our program a valuable candidate for model comparison, validation and benchmarking.Comment: 13 pages, 7 figures, 7 table

Orthotropic rotation-free thin shell elements

A method to simulate orthotropic behaviour in thin shell finite elements is proposed. The approach is based on the transformation of shape function derivatives, resulting in a new orthogonal basis aligned to a specified preferred direction for all elements. This transformation is carried out solely in the undeformed state leaving minimal additional impact on the computational effort expended to simulate orthotropic materials compared to isotropic, resulting in a straightforward and highly efficient implementation. This method is implemented for rotation-free triangular shells using the finite element framework built on the Kirchhoff--Love theory employing subdivision surfaces. The accuracy of this approach is demonstrated using the deformation of a pinched hemispherical shell (with a 18{\deg} hole) standard benchmark. To showcase the efficiency of this implementation, the wrinkling of orthotropic sheets under shear displacement is analyzed. It is found that orthotropic subdivision shells are able to capture the wrinkling behavior of sheets accurately for coarse meshes without the use of an additional wrinkling model.Comment: 10 pages, 8 figure

A new open-source PEMFC simulation tool for easy assessment of material parameterizations

After almost three decades of PEM fuel cell modelling, there is a large need for standardization and establishment of a common basis in the development of PEMFC models, not only for numerical simulation purposes, but also to test and validate MEA material parameterizations from experimental measurements. Until recently, there were only two open-source codes capable of simulating the state of the art in PEMFC modeling at the scale of single cells or MEAs: OpenFCST, a rather heavy FEM package consisting of more than 120 000 lines of C++ code (not counting library dependencies), and FAST-FC, a finite volume tool built on top of OpenFOAM, consisting of about 12 000 lines of code (not counting the required OpenFOAM). Albeit highly capable, these tools require significant effort and programming know-how to be set up and modified, and they are not well suited for easy substitution of material parameterizations or extensive parameter studies in sufficiently short computation times. We have recently developed the first open standalone MATLAB implementation of a full-blown, steady-state, non-isothermal, macro-homogeneous two-phase MEA model for low-temperature PEM fuel cells. It implements the most dominant through-plane transport processes in a 5-layer membrane electrode assembly: the transport of charge, energy, gas species and water. With a focus on code simplicity, compactness, portability, transparency, accessibility and free availability, our program is an ideal candidate for the assessment of new material parameterizations that may originate e.g. from experimental data. Thanks to the very short runtime of just a few seconds on an ordinary PC, extensive parameter studies and quick substitution of modeling assumptions or material properties are now possible with our tool without requiring deep programming knowledge or compilation of large software libraries. We demonstrate how the program may be used to quantitatively understand and evaluate PEM fuel cell material properties or measurement data

Experimental parameter uncertainty in PEM fuel cell modeling. Part I: Scatter in material parameterization

Ever since modeling has become a mature part of proton exchange membrane fuel cell (PEMFC) research and development, it has been plagued by significant uncertainty lying in the detailed knowledge of material properties required. Experimental data published on several transport coefficients are scattered over orders of magnitude, even for the most extensively studied materials such as Nafion membranes, for instance. For PEMFC performance models to become predictive, high-quality input data is essential. In this bipartite paper series, we determine the most critical transport parameters for which accurate experimental characterization is required in order to enable performance prediction with sufficient confidence from small to large current densities. In the first part, a macro-homogeneous two-phase membrane-electrode assembly model is furnished with a comprehensive set of material parameterizations from the experimental and modeling literature. The computational model is applied to demonstrate the large spread in performance prediction resulting from experimentally measured or validated material parameterizations alone. The result of this is a ranking list of material properties, sorted by induced spread in the fuel cell performance curve. The three most influential parameters in this list stem from membrane properties: The Fickean diffusivity of dissolved water, the protonic conductivity and the electro-osmotic drag coefficient.Comment: 19 pages, 8 figures, 10 table

Free open reference implementation of a two-phase PEM fuel cell model

In almost 30 years of PEM fuel cell modeling, countless numerical models have been developed in science and industrial applications, almost none of which have been fully disclosed to the public. There is a large need for standardization and establishing a common ground not only in experimental characterization of fuel cells, but also in the development of simulation codes, to prevent each research group from having to start anew from scratch. Here, we publish the first open standalone implementation of a full-blown, steady-state, non-isothermal two-phase model for low-temperature PEM fuel cells. It is based on macro-homogeneous modeling approaches and implements the most essential through-plane transport processes in a five-layer MEA. The focus is on code simplicity and compactness with only a few hundred lines of clearly readable code, providing a starting point for more complex model development. The model is implemented as a standalone MATLAB function, based on MATLAB's standard boundary value problem solver. The default simulation setup reflects wide-spread commercially available MEA materials. Operating conditions recommended for automotive applications by the European Commission are used to establish new fuel cell simulation base data, making our program a valuable candidate for model comparison, validation and benchmarking.Comment: 13 pages, 7 figures, 7 table

Experimental parameter uncertainty in PEM fuel cell modeling. Part II: Sensitivity analysis and importance ranking

Numerical modeling of proton exchange membrane fuel cells is at the verge of becoming predictive. A crucial requisite for this, though, is that material properties of the membrane-electrode assembly and their functional dependence on the conditions of operation are known with high precision. In this bipartite paper series we determine the most critical transport parameters for which accurate experimental characterization is required in order to enable the simulation of fuel cell operation with sufficient confidence from small to large current densities. In Part II, we employ the two-phase model developed in Part I to carry out extensive forward uncertainty propagation analyses. These include the study of local parameter sensitivity in the vicinity of a baseline parameter set, and a global sensitivity analysis in which a broad range of operating conditions and material properties is covered. A comprehensive ranking list of model parameters is presented, sorted by impact on predicted fuel cell properties such as the current-voltage characteristics and water balance. The top five in this list are, in this order: The membrane hydration isotherm, the electro-osmotic drag coefficient, the membrane thickness, the water diffusivity in the ionomer and its ionic conductivity.Comment: 9 pages, 5 figures, 4 table

Collapse of orthotropic spherical shells

We report on the buckling and subsequent collapse of orthotropic elastic spherical shells under volume and pressure control. Going far beyond what is known for isotropic shells, a rich morphological phase space with three distinct regimes emerges upon variation of shell slenderness and degree of orthotropy. Our extensive numerical simulations are in agreement with experiments using fabricated polymer shells. The shell buckling pathways and corresponding strain energy evolution are shown to depend strongly on material orthotropy. We find surprisingly robust orthotropic structures with strong similarities to stomatocytes and tricolpate pollen grains, suggesting that the shape of several of Nature's collapsed shells could be understood from the viewpoint of material orthotropy.Comment: 7 pages, 5 figure

Subdivision Shell Elements with Anisotropic Growth

A thin shell finite element approach based on Loop's subdivision surfaces is proposed, capable of dealing with large deformations and anisotropic growth. To this end, the Kirchhoff-Love theory of thin shells is derived and extended to allow for arbitrary in-plane growth. The simplicity and computational efficiency of the subdivision thin shell elements is outstanding, which is demonstrated on a few standard loading benchmarks. With this powerful tool at hand, we demonstrate the broad range of possible applications by numerical solution of several growth scenarios, ranging from the uniform growth of a sphere, to boundary instabilities induced by large anisotropic growth. Finally, it is shown that the problem of a slowly and uniformly growing sheet confined in a fixed hollow sphere is equivalent to the inverse process where a sheet of fixed size is slowly crumpled in a shrinking hollow sphere in the frictionless, quasi-static, elastic limit.Comment: 20 pages, 12 figures, 1 tabl

Analysis and extension of a PEMFC model

A stationary, macro-homogeneous 1D through-plane model of a membrane electrode assembly (MEA) has been developed by Vetter and Schumacher [1]. In this work, a sensitivity analysis for various parameters of this MEA model is carried out. 48 parameters are identified that impact the model behaviour through the parameterization of transport properties, electrochemistry and through operating conditions. All parameters have been varied over a decade and compared to the initial value to study the impact on the simulated I-V characteristic. If the variation outranged physically reasonable limits, the latter are applied as variation boundaries. In Fig.1 the variation of the electrical conductivity of the GDL sigma_e is shown as exemplary simulation result. The value is varied between 130 and 1300 S/m to account for data of different products types, e.g. from SGL Carbon [2], Toray [3], Freudenberg [4] and Ballard [5]. Fig.1 (a) depicts the polarisation curve with cell voltage U in V plotted over the current density i in A/cm². Two reference points at static cell voltages of Uref = 0.8 V with iref = 0.3 A/cm² (partial load) and Uref = 0.6 V with iref = 2.3 A/cm² (full load) are used in order to evaluate the specific parameter sensitivity. The colour legend depicts the varied parameter values. It can be seen that a higher electrical conductivity leads to a higher current density at equal cell voltage. In Fig.1 (b), the relative deviation of the current density at static cell voltage CCD = (i-iref)/iref is plotted over the varied parameter range. Passing the 0-line indicates passing the default parameter value. Thus, positive deviation stands for an increase and negative deviation for a decrease in performance. The relative deviation at 0.6 V reaches from -0.1 to 0.2, indicating a high sensitivity of the model to sigma_e at full load operation. For partial load conditions, the influence of sigma_e is lower than at full load, as expected from the domination of activation losses over ohmic losses at low current densities. 1. R. Vetter, J. O. Schumacher. Free open reference implementation of a two-phase PEM fuel cell model. Manuscript in preparation for Computer Physics Communications 2. SIGRACET® Gas Diffusion Layers for PEM Fuel Cells, Electrolyzers and Batteries. White Paper. SGL CARBON GmbH. Aug. 2016. 3. Toray Carbon Fiber Paper TGP-H. Technical Data. Accessed: 12. February 2018. FUEL CELL Store. 4. Freudenberg Gas Diffusion Layers for PEMFC DMFC. Technical Data. Freudenberg. Dec. 2014. 5. AvCarb Gas Diffusion Systems for Fuel Cells. Technical Data. AvCarb. Feb. 2013