Modeling of Reversible Solid Oxide Cell Stacks with an Open-Source Library
Authors: Zhang Shidong , Peters Roland , Varghese Bob Austin , Deja Robert , Kruse Nicolas , Beale Steven B. , Blum Ludger , Peters Ralf 
Published: July 2021

Fuel cells are potential contenders of the traditional internal combustion engines, with relative high efficiency and low/no emission of pollution and greenhouse gases. Electrolyzers convert electricity into chemical energy, e.g. hydrogen, and in case of high-temperature electrolyzers in syngas, e.g. hydrogen and carbon-monoxide, etc. A reversible solid oxide cell (rSOC) is able to operate in both modes. This represents a promising electrochemical device for future applications. Comprehensive experimental investigations on rSOCs are typically expensive and time-consuming. These may be conveniently augmented by numerical models to improve and optimize and enable the provision of more rapid prototypes. These models usually consider some or all of the underlying physical processes, e.g. heat and mass transfer (including thermal radiation), structural analysis, etc. They range from zero-dimensional (0-D) and 1-D models in system-level models1, 2 to coupled 3-D models in cell/stack-level applications.3–5 Stack/system level models are attracting more and more attention due to their practical applications to commercial/industrial designs.
In this work, a steady-state, 3-D, non-isothermal, and homogenized stack model has been developed from an extension of previous studies4–6 and implemented into the open-source library, OpenFOAM.7 It addresses all major physical processes, including fluid flow, heat and mass transfer (including thermal radiation), and electrochemical reactions. The model strategy applies a multi-region approach to consider every unit-cell as different sub-regions, namely, cathode, anode, electrolyte, and interconnect. Inter region heat and mass transfer is prescribed during the calculations. The micro-structures within the subregions are treated using volume-averaging method, in which case, the flow distribution can be easily described by replacing the viscous losses with a drag or friction term in the governing momentum equation(s). This greatly decreases the computational effort,6 and predicts quite similar results to those from experimental measurements.5 In the present work a surface-to-surface (S2S) model, also referred to as a viewFactor model, is utilized to simulate the external thermal radiations. Internal radiation is neglected due to its relative unimportance.
Figure 1: Comparisons of temperature variations between experimental measurements and simulations, i = 0.5 A cm−2 .
The present model is applied to investigate the performance of an in-house designed rSOC stack, the key component of a 5/15kW-class rSOC system.8 A 1-D simulation is also performed with a previous developed Simulink model.1 The stack consists of four 10-layer sub-stacks with an active cell area per layer of 320 cm2. It operates in both fuel cell and electrolysis modes, in a temperature range of 600 – 800 ◦C. To reduce heat losses to adjacent components and ambient environment, it is surrounded by insulating plates. More details can be found in the recent publication.8 As shown by Figure 1, temperature variations are compared between experimental measurements and numerical predictions, at a mean current density of 0.5 A cm-2 . In fuel cell mode, the cell voltages are 0.818 V, 0.821 V, and 0.824 V, for the experiment, Simulink, and stack model, respectively. In the electrolysis mode, the values are 1.240 V, 1.234 V, and 1.260 V, respectively. These results indicate fairly good agreement between the predictions and experiments. It can be found that the stack model predicts smaller temperature deviations than is seen in the experiments and the Simulink predictions. However, the former consumes approximately 1 hour for every run, while the later costs only several minutes. In future work, thermal stresses, which play important roles in design optimization, will be considered. Considering the 3-D nature of the stress distribution, the coupling between present model and a structural analysis program/solver would be a promising topic.
References
[1] M. Engelbracht, R. Peters, L. Blum, and D. Stolten. Journal of the Electrochemical Society 162(9), F982 (2015).
[2] R. Peters, R. Deja, Q. Fang, V. N. Nguyen, P. Preuster, L. Blum, P. Wasserscheid, and D. Stolten. International Journal of Hydrogen Energy 44(26), 13794–13806 (2019).
[3] M. Peksen. International Journal of Hydrogen Energy 36(18), 11914–11928 (2011).
[4] S. B. Beale, H.-W. Choi, J. G. Pharoah, H. K. Roth, H. Jasak, and D. H. Jeon. Computer Physics Communications 200, 15 – 26 (2016).
[5] R. Nishida, S. Beale, J. Pharoah, L. de Haart, and L. Blum. Journal of Power Sources 373, 203–210 (2018).
[6] M. Navasa, X.-Y. Miao, and H. L. Frandsen. International Journal of Hydrogen Energy 44(41), 23330–23347 (2019).
[7] OpenFOAM-v2012. https://www.openfoam.com/. Accessed date: 01-02-2021.
[8] R. Peters, M. Frank, W. Tiedemann, I. Hoven, R. Deja, N. Kruse, Q. Fang, L. Blum, and R. Peters. Journal of the Electrochemical Society (2021).

Figure 1