Design of the Catalyst Layers in PEMFCs Using an Adjoint Sensitivity Analysis Approach

Abstract

A numerical algorithm is presented for the large-scale optimization of catalyst distribution in proton exchange membrane fuel cells (PEMFCs). The algorithm is based on the evaluation of catalyst sensitivity functions, which show how much the cell voltage or discharge current are increasing when a small amount of catalyst is added at given locations inside the catalyst layers. The catalyst sensitivity functions are evaluated with relatively low computational cost using an adjoint space approach. Using the proposed algorithm one can compute the exact, optimum, three-dimensional (3-D) distribution of platinum particles inside the catalyst layers in order to maximize the overall power density of the cell. It is shown that the optimum distribution depends on the discharge conditions, on the positions of landings and openings, and on the geometry and dimensions of the layers. In general, the optimum catalyst density in the cathode catalyst layer should be larger at the membrane than at the gas diffusion layer interface. In addition, the catalyst density should be slightly larger under the gas channel and smaller under landings.

Adjoint Method for the Optimization of the Catalyst Distribution in Proton Exchange Membrane Fuel Cells

“…For more details about the transport and electrochemical model we recommend the literature. 43,60 Hydrogen gas diffuses from the gas channels to the surface of the agglomerates in the anode CL and, then, through the ionomer to the reaction sites. Similarly, the oxygen diffuses from the gas channels to the surface of the agglomerates in the cathode CL and, then, through the ionomer to the reaction sites.…”

Adjoint Method for Increasing the Breakdown Voltage and Reducing the On-State Resistance in Wide Band Gap Power Transistors

“…The algorithm is based on applying the first-order necessary conditions to these equations and deriving an equation for the optimum (infinitesimal) change of the doping concentration. The mathematical algorithm presented below is relatively similar to the technique presented in (16) for the optimization of the catalyst of proton exchange membrane fuel cells and in (18) for suppressing random dopant induced fluctuations in nanoscale transistors.…”

“…With this constraint, the optimization problem becomes where δω is a small parameter limiting the maximum amount of doping variation. Problem [15] can be solved by defining Lagrangean [16] where ,0 ON R is the initial on-state resistance and λ and ON λ are Lagrange multipliers, and calculating the extreme points of [16]. Indeed, by introducing [11] into [16] we obtain ( ) [17] Writing the first-order necessary conditions (Kuhn-Tucker conditions) we get the following system of equations…”

“…One should notice that adjoint methods have been used before by the applied mathematics community to solve 1-D problems in fluid dynamics, climate, and heat transfer (2,3), and by the aerodynamic community to perform sensitivity analysis studies (4-7). Our group has also used adjoint methods for the analysis of random doping and oxide roughness induced variability in semiconductor devices (8)(9)(10)(11)(12)(13)(14) and has recently applied it to solve inverse problems in dopant profiling (15), and optimize the catalyst distribution in proton exchange membrane fuel cells (16). This article is structured as follows.…”

Analysis of Sensitivity of PEMFC Parameters to Non-Uniform Platinum Deposition

“…The length of vectors x and P t μ are equal to the total number of vertexes of the finite element discretization (which is of the order of 10 4 for 2-D discretizations and 10 5 -10 6 for 3-D discretizations). For more details about the transport model we recommend (19). x .…”