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Research Papers

Adjoint-Based Sensitivity Analysis and Error Correction Methods Applied to Solid Oxide Fuel Cells

[+] Author and Article Information
S. Kapadia

 UT SimCenter at Chattanooga, 701 East ML King Boulevard, Chattanooga, TN 37403sagar-kapadia@utc.edu

W. K. Anderson

 UT SimCenter at Chattanooga, 701 East ML King Boulevard, Chattanooga, TN 37403kyle-anderson@utc.edu

L. Elliott

 UT SimCenter at Chattanooga, 701 East ML King Boulevard, Chattanooga, TN 37403louie-elliott@utc.edu

C. Burdyshaw

 UT SimCenter at Chattanooga, 701 East ML King Boulevard, Chattanooga, TN 37403chad-burdyshaw@utc.edu

J. Fuel Cell Sci. Technol 6(2), 021010 (Feb 25, 2009) (10 pages) doi:10.1115/1.3005579 History: Received June 16, 2007; Revised December 14, 2007; Published February 25, 2009

Sensitivity analysis and design optimization of solid oxide fuel cells are presented. Multispecies diffusion, low speed convection, and chemical kinetics are included in a two-dimensional numerical model, and sensitivity derivatives are computed using both discrete adjoint method and direct differentiation. The implementation of the discrete adjoint method is validated by comparing sensitivity derivatives obtained using the adjoint with results obtained using direct differentiation and finite-difference methods. For optimization, cost functions describing hydrogen concentration along the anode-electrolyte interface, hydrogen concentration at the channel outlet, and standard deviation of temperature inside the anode are considered. Material properties of the anode, operating conditions, and a shape parameter are selected as design variables. The development of an initial design environment to automate the flowfield solution, sensitivity computation, optimization, and mesh movement is also described. Finally, an adjoint-based error correction method is implemented and demonstrated to provide accurate estimations for a desired objective function on a fine mesh by combining information obtained from analysis and adjoint solutions on a coarser one.

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Copyright © 2009 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Solid oxide fuel cell components

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Figure 2

Computational domain and boundary conditions

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Figure 3

Hydrogen mole fraction obtained using original design variables (Table 5)

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Figure 4

Hydrogen mole fraction obtained using optimized design variables for Cost-1 (Table 6)

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Figure 5

Hydrogen mole fraction obtained using optimized design variables for Cost-2 (Table 7)

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Figure 6

Temperature contours obtained using original design variables (Table 5)

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Figure 7

Temperature contours obtained using optimized design variables for Cost-3 (Table 8)

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Figure 8

Error estimation performed for a cost function of percentage methane utilization

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