Investigation of Heat Distribution in SOC-Stacks By Multiphysical Modeling
Authors: Zhang Shidong , Peters Roland , Kruse Nicolas , Deja R. , Kunz Felix , Eichel Rüdiger-A. 
Published: November 2022

In the scope of clean energy, the solid oxide cell (SOC) offers a promising solution for different applications. The electrolyte, the air electrode and the fuel electrode of an SOC are typically based on yttrium stabilized zirconia (YSZ), lanthanum strontium cobaltite (LSC) or manganite (LSM) and nickel cermet, respectively. It typically operates in a temperature range of 600 – 1000 oC and can be operated as a fuel cell (SOFC), an electrolysis cell (SOEC) or reversibly (rSOC).
An SOC-stacks consists of several repeating units, each of which is assembled by various components. Among them, the sealants are important to maintain the reliability and long-term operations of a stack. Several issues lead to high stress in the sealants, including the mechanical load, mismatch of thermal expansion coefficients, and thermal gradients 1. It was indicated that a small temperature gradient near the manifolds results in excessively high tensile stress. This may lead to glass ceramics sealing failure, which is critical in SOC designs 2. Therefore, the authors carry out the elastic stress simulations in an operating SOC-stack due to non-uniform temperature distributions.
A previously introduced CFD model 3 is further developed to address coupled chemical and electrochemical reactions in rSOC-stacks. This model has been implemented in the open-source library, OpenFOAM. It considers the major multiphysical phenomena e.g. heat, mass, momentum and charge transport as well as heat radiation and electrochemical reactions and employs a volume-averaged approach 4. The computational requirements can be greatly reduced, which offers the possibility to simulate large stacks in reduced computing time. The temperature distributions derived from the stack simulation are used as inputs for thermal stress analysis, by mapping the interconnect temperatures to the detailed repeating unit. An open-source, finite element method (FEM) based software, Calculix, is applied to simulate the stress distributions. It is assumed all layers are tightly connected without slipping.
The SOC-stack design considered in the multiphysical simulation as well as the FEM stress analysis is an in-house design, Mark-F20. It consists of 18 repeating units, each with an active area of approximately 320 cm2. The stack operates in the furnace condition, at a temperature of 700 oC, with CH4 mixture being supplied to the anode in the SOFC-mode (i=0.5 A/cm², U=0.8 V). The flow is in a counter-flow regime. A comparison of temperature distributions in interconnect is conducted between simulation and experiment. A maximum deviation of 10 K can be observed near the fuel inlet. It is acceptable providing the overall temperature variations of 80 K and the uncertainties in the measurements. This low-temperature zone results from the fast endothermic methane steam reforming reaction. The zone near the fuel outlet is cooled down by the inlet airflow on the cathode side. The stress-free temperature is 800 oC. It can be found that the maximum stress appears around the fuel inlet manifold with a magnitude of 100 MPa. The stress is also large near the air inlet manifold with a magnitude of 70 MPa. These areas show higher possibilities of mechanical failure.
Consequentially, the stack model that has been developed enables to investigate the heat distribution in SOC-stacks. By comparing temperature distribution and the IV-curve predicted by the model with experimental measurements, good agreements were found.
In the future, the sealant failure will be investigated 2 and attention has to be paid to future stack designs.
References
(1) Blum, L.; Groß, S. M.; Malzbender, J.; Pabst, U.; Peksen, M.; Peters, R.; Vinke, I. C. Investigation of Solid Oxide Fuel Cell Sealing Behavior under Stack Relevant Conditions at Forschungszentrum Jülich. Journal of Power Sources
2011, 196 (17), 7175–7181.
(2) Bremm, S.; Dölling, S.; Becker, W.; Blum, L.; Peters, Ro.; Malzbender, J.; Stolten, D. A Methodological Contribution to Failure Prediction of Glass Ceramics Sealings in High-Temperature Solid Oxide Fuel Cell Stacks. Journal of Power Sources
2021, 507, 230301.
(3) Zhang, S.; Peters, R.; Varghese, B. A.; Deja, R.; Kruse, N.; Beale, S. B.; Blum, L.; Peters, R. Modeling of Reversible Solid Oxide Cell Stacks with an Open-Source Library. ECS Trans.
2021, 103 (1), 569.
(4) Beale, S. B.; Zhubrin, S. V. A Distributed Resistance Analogy for Solid Oxide Fuel Cells. Numerical Heat Transfer, Part B: Fundamentals
2005, 47, 573–591.

Figure 1