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Research Papers

# Impact of the Temperature Profile on Thermal Stress in a Tubular Solid Oxide Fuel Cell

[+] Author and Article Information
Katharina Fischer

Institute of Turbomachinery and Fluid Dynamics, Leibniz Universität Hannover, Appelstrasse 9, D-30167 Hannover, Germanyk.fischer@tfd.uni-hannover.de

Joerg R. Seume

Institute of Turbomachinery and Fluid Dynamics, Leibniz Universität Hannover, Appelstrasse 9, D-30167 Hannover, Germanyseume@tfd.uni-hannover.de

J. Fuel Cell Sci. Technol 6(1), 011017 (Nov 12, 2008) (9 pages) doi:10.1115/1.2971132 History: Received June 14, 2007; Revised May 10, 2008; Published November 12, 2008

## Abstract

The knowledge of the stress distribution in the ceramic components of a solid oxide fuel cell (SOFC) is a prerequisite for assessing the risk of failure due to crack formation as well as for predicting its durability. Due to the high temperature span associated with thermal cycles, high thermal gradients, and the mismatch of thermal and mechanical properties of the ceramic components, thermomechanical stress is of particular importance in SOFC. A finite-element mechanical model of a tubular SOFC is developed and combined with a 2D thermo-electrochemical model in order to provide realistic temperature profiles to the finite-element analysis of the ceramic SOFC membrane-electrode assembly (MEA). The resulting simulation tool is employed for three different analyses: In the first analysis, temperature profiles provided by the thermo-electrochemical model are used to show the impact of direct versus indirect internal reformation of methane on thermomechanical stress in the MEA. In order to clarify the contribution of temperature level and thermal gradients to the emergence of stress, the second analysis systematically investigates the stress distribution with assumed temperature profiles. In the third analysis, particular attention is given to the influence of thermal model accuracy on the results. For this purpose, three modeling cases are provided: (i) Heat sources resulting from the anodic and cathodic half-reactions are considered separately in thermal modeling. (ii) According to a frequently used simplification in SOFC modeling, all heat released by the reaction of hydrogen and oxygen is assigned to the anode/electrolyte interface. (iii) The temperature profile is averaged in the radial direction. The results reveal a strong dependence of thermomechanical stress on the methane reforming strategy, which confirms the importance of a careful control of operating conditions. The effect of temperature level on maximum tensile thermomechanical stress is found to dominate by one order of magnitude over that of typical thermal gradients occurring in the SOFC during operation. In contrast to the high relevance commonly ascribed to thermal gradients, the results show that in the tubular SOFC thermal gradients play only a minor role for the emergence of stress. Concerning model accuracy, the separate consideration of half-reactions at the electrodes is found to be not necessary, while the results clearly emphasize the importance of radially discretized thermal modeling for the model-based prediction of thermal stress.

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## Figures

Figure 1

Geometry and dimensions of the tubular SOFC (adopted from Ref. 13)

Figure 2

Longitudinal distributions of reactants, temperature, and thermal gradients for operation on completely reformed (left) and partially reformed natural gas (right)

Figure 3

Distribution of thermomechanical stress for operation on completely (a) and partially (b) reformed natural gas

Figure 4

Implementation of the longitudinal thermal gradient (case (v)) in the finite-element mechanical SOFC model

Figure 5

Distribution of thermomechanical stress in the MEA subject to a homogeneous temperature T=298 K (i), a radial thermal gradient δT/δr=500 K/m (iii) or δT/δr=−5000 K/m (iv), and a longitudinal thermal gradient δT/δz=500 K/m (v)

Figure 6

Maximum tensile stress caused by the assumed temperature profiles and in a real operating point

Figure 7

Radial temperature profiles calculated with (solid line) and without (dashed line) a separate inclusion of the single-electrode reactions compared with the radial mean temperature (dotted line)

Figure 8

Radial temperature gradients in an internally reforming SOFC calculated with (i) and without (ii) a separate consideration of the single-electrode reactions

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