Simulations of &amp;#x201C;atomistic&amp;#x201D; effects in nanoscale dopant profiling

2020

An adjoint-space optimization technique is presented for the large-scale optimization (i.e., optimization with over 104 design variables) of PEM fuel cell microstructure. The algorithm is based on evaluation of sensitivity functions of the cell discharge voltage under specified current conditions. The sensitivity functions are found by solving sparse linear systems of equations to find the Gâtaux derivatives of the discharge voltage with respect to the design variables. The optimization technique is applied to electrolyte distribution and carbon distributions within the cathode catalyst layer, to describe a profile of carbon, electrolyte, and porosity of a PEMFC cathode catalyst layer on a point-by-point basis.

Section: Numerical Computation Of the Sensitivity Function Of The Cel...mentioning

confidence: 99%

Designing the Ideal Catalyst Layer in PEMFCs

Lamb

2020

“…( ) [21] ( ) ( ) [22] where Pt m γ and V γ are the sensitivity functions of Pt m and V . Since the sensitivity function of Pt m is equal to 1 (in virtue of equations [3] and [5]), equations [20] and [22]…”

Section: Numerical Algorithm To Solve Problemmentioning

confidence: 99%

“…( ) Pt δµ r from [23] and inserting the result into eq. [21] allows us to compute λ as ( ) [25] Introducing the value of λ into [23] we find…”

Section: Computingmentioning

confidence: 99%

“…For this reason, next, we present a technique for the computation of sensitivity functions based on solving only one adjoint system of equations and performing a few matrix-vector multiplications. The technique presented below has been originally used for the analysis of variability and optimization of semiconductor devices (13)(14)(15)(16)(17)(18)(19) and has recently been applied by our group to solve inverse problems in dopant profiling (20,21). However, it should be noted that relatively similar approaches have been used before independently by the applied mathematics community to solve 1-D problems in fluid dynamics, climate, and heat transfer (22,23), and by the aerodynamic community to perform sensitivity analysis studies (24)(25)(26)(27).…”

Section: Numerical Computation Of the Catalyst Sensitivity Function O...mentioning

confidence: 99%

See 1 more Smart Citation

Mathematical Optimization of the Spatial Distribution of Platinum Particles in the Catalyst Layer of PEMFCs

Lamb

Mixon²,

2017

An adjoint-space technique is presented for the large-scale optimization (i.e. optimization with over 10 2 design variables) of the catalyst distribution in fuel cells. The algorithm is based on evaluating the catalyst sensitivity functions of the discharge voltage under specified current conditions. The catalyst sensitivity functions are computed efficiently using a gradient maximization algorithm, which requires solving a small number of sparse linear systems of equations to find the Gâtaux derivatives of the discharge current of the cell with respect to the design variables. It is shown that the optimum distribution of the catalyst varies with the discharge conditions, with the positions of landings and openings, as well as with the geometry and dimensions of the layers. It should be noted that our numerical algorithm can be used to describe the complete profile of the optimal catalyst by providing the full (mathematically exact) distribution of platinum particles in the catalyst layer.

“…For this reason, next, we present a technique for the computation of sensitivity functions based on solving only one adjoint system of equations and performing a few matrix-vector multiplications. The technique presented below has been originally developed for the analysis of variability and optimization of semiconductor devices (10)(11)(12)(13)(14)(15)(16) and has recently been applied by our group to solve inverse problems in dopant profiling (17,18). However, it should noted that relatively similar approaches have been used before independently by the applied mathematics community to solve 1-D problems in fluid dynamics, climate, and heat transfer (19,20), and by the aerodynamic community to perform sensitivity analysis studies (21)(22)(23)(24).…”

Section: Computation Of Catalyst Sensitivity Functionsmentioning

confidence: 99%

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

Mixon²,

Mehta

et al. 2015

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.