2.6.2. Example: Optimization of an agglomerate cathode electrode¶
This folder contains the files used in order to reproduce the results reported in reference Secanell07b_.
The data is subdivided as follows:
- Directory
template/contains the main main.prm, data.prm and opt.prm file used in the simulations. In each of the sub-folders these files are extended - Directory
analysis/contains the data to run a single point in the polarization curve. It uses the data intemplate/directly without modifications. - Directory
parameteric/contains the data files used to compute a full polarization curve. To achieve this goal, only the main.prm is modified with respect to the template files by including information about the number of points needed in the polarization curve. The directory also includes an .ods file used to compare the data. The results, as of Feb. 2, 2014, OpenFCST Rev: 1817 match the article. - Directory
optimization/contains the main, data and optimization files necessary to run the optimization studies in section 4 of reference Secanell07b_.
Warning: This directory is not tested with regression tests, therefore it is possible that the parameter file has to be modified slightly in order to obtain the correct solution. The folder was last validated on Feb. 3, 2015 prior to openFCST release 0.2.
2.6.2.1. Polarization curve¶
2.6.2.1.1. The main.xml file¶
In order to perform a polarization curve, the same data file as for analysis case is used. The only difference in the main.xml file is specifying the polarization curve parameters, e.g.
Example:
######################################################################
# $Id: sample_main_param_file.prm 2011-02-09 secanell $
#
# This file is used to simulate an cathode and to obtain
# a single point on a polarisation curve. Use this file
# if you wish to perform a single analysis simulation.
#
#
# Copyright (C) 2011 by Marc Secanell
#
######################################################################
include ../template/main.prm
######################################################################
#
# The following parameters are modified in order to obtain a polarization
# curve with respect to the template file
#
######################################################################
subsection Simulator
set Analysis type = PolarizationCurve
################################################
subsection Polarization Curve
set Initial voltage [V] = 0.94
set Final voltage [V] = 0.19
set Increment [V] = 0.074
set Min. Increment [V] = 0.01
end
################################################
end
######################################################################
2.6.2.1.2. Results¶
Below is the polarization curve obtained from running the template file:
$ fuel_cell-2d.bin main.prm
Parameters: main.prm
//=====================================================================//
//
// OpenFCST: The open-source Fuel Cell Simulation Toolbox
//
// Version: 0.3, Nov. 2016
//
//=====================================================================//
//
// Current Developers
// ------------------
//
// Marc Secanell, 2006- (a): Framework, cathode, anode, PEM, (...)
// Alex Jarauta, 2016 (a): Local matrix info, enhancements
// Aslan Kosakian, 2014- (a): Transient simulations.
// Andreas Putz, 2012- (b): Framework
// Mayank Sabharwal (a), 2014-: Microscale simulations
// Jie Zhou (a), 2013-: Two-phase flow simuations
//
//
// Past Developers
// ---------------
//
// Chad Balen, 2014-16 (a): CMake, fluid flow and many enhancements
// Madhur Bhaiya, 2012-14 (a): Non-isothermal PEMFC
// Peter Dobson, 2009-11 (a): Least-square parameter estimation
// Michael Moore, 2010-12 (a): Double-trap ORR model
// Philip Wardlaw, 2012-14 (a): Micro-scale models and GUI
// Valentin N. Zingan, 2012-14 (a): Fluid flow and enhancements
//
// Other Contributors
// ------------------
//
// Kailyn Domican, 2012-14 (a): Optimization docs and enhancements.
// Simon Matterns, 2016-16 (a): Many GUI enhancements.
//
//
// a) Energy Systems Design Lab, University of Alberta
// b) Automotive Fuel Cell Cooperation (AFCC) Corp.
//
//
// (c) Copyright 2007-2016 by Energy Systems Design
// Laboratory, University of Alberta
//
// This software is distributed under the MIT License.
// For more information, see the README file in /doc/LICENSE
//
//=====================================================================//
//=====================================================================//
Running PolarizationCurve simulation
=============================================================================
== Polarization curve parameters: ==
Initial voltage [V] : 0.94
Final voltage [V] : 0.19
Increment [V] : 0.074
Adaptive Increment : 1
Min. Increment [V] : 0.01
== ==
=============================================================================
=============================================================================
Iteration : 0
Solving for...
Parameter name:
Cell param_value: 0.94
======
YOU ARE CURRENTLY SOLVING A CATHODE MODEL
Application->DoF->BlockMatrix->OptimizationBlockMatrix
->FuelCellShop::Equation::FicksTransportEquation
->FuelCellShop::Equation::FicksTransportEquation
->FuelCellShop::Equation::ElectronTransportEquation
->FuelCellShop::Equation::ProtonTransportEquation
->FuelCellShop::Equation::ReactionSourceTerms
->FuelCell::Application::AppCathode-2D
YOU ARE USING Newton3pp NEWTON SOLVER FOR STEADY-STATE PROBLEM
Application->Copy->Newton3ppBase->->AdaptiveRefinement
Parameters: data.prm
Line <28> of file <data.prm>: There is no such subsection to be entered: Fuel cell data.Cathode gas diffusion layer
subsection Fuel cell data
subsection Cathode gas diffusion layer
Line <29> of file <data.prm>: There is no such subsection to be entered: Fuel cell data.DesignFibrousGDL
subsection Fuel cell data
subsection DesignFibrousGDL
Line <31> of file <data.prm>: No such entry was declared:
Porosity
<Present subsection:
subsection Fuel cell data
>
Line <33> of file <data.prm>: There is no subsection to leave here!
Line <34> of file <data.prm>: There is no such subsection to be entered: Cathode catalyst layer
subsection Cathode catalyst layer
Line <35> of file <data.prm>: There is no such subsection to be entered: ConventionalCL
subsection ConventionalCL
Line <36> of file <data.prm>: No such entry was declared:
Platinum loading on support (%wt)
<Present subsection:
>
Line <37> of file <data.prm>: No such entry was declared:
Platinum loading per unit volume (mg/cm3)
<Present subsection:
>
Line <38> of file <data.prm>: No such entry was declared:
Electrolyte loading (%wt)
<Present subsection:
>
Line <39> of file <data.prm>: There is no subsection to leave here!
Line <40> of file <data.prm>: There is no subsection to leave here!
Line <41> of file <data.prm>: There is no subsection to leave here!
FESystem<2>[FE_Q<2>(2)^3]
name: CathodeMPL
Generating new grid...
Using FCST grid generator.
Levels:3
Cells:480
Dofs:6027(2009,2009,2009) sorting by component
name: DesignFibrousGDL
name: SGL24BC
Created a SGL24BC MPL
------------------------------
Parameters for Gas diffusion layer:
Material ids: 2
Constant porosity: 1
Constant permeability [cm^2]:
10000
0
0
10000
Square root of constant permeability [cm]:
100
0
0
100
Inverse of constant permeability [1/cm^2]:
0.0001
-0
-0
0.0001
Inverse of square root of constant permeability [1/cm]:
0.01
-0
-0
0.01
Constant Forchheimer permeability [1/cm]:
100
0
0
100
Constant tortuosity:
1
0
0
1
------------------------------
Parameters for Microporous layer:
Material ids: 1
Constant porosity: 1
Constant permeability [cm^2]:
10000
0
0
10000
Square root of constant permeability [cm]:
100
0
0
100
Inverse of constant permeability [1/cm^2]:
0.0001
-0
-0
0.0001
Inverse of square root of constant permeability [1/cm]:
0.01
-0
-0
0.01
Constant Forchheimer permeability [1/cm]:
100
0
0
100
Constant tortuosity:
1
0
0
1
======= CATALYST LAYER STRUCTURE ======
=== Catalyst layer === #:1 =====
Solid phase volume fraction:0.355265
Ionomer in the CL:0.539798
Porosity in the CL:0.104938
Active area in the CL:255044
---------------------------------------
Method to compute eff_property_electrolyte: Bruggemann
=======================================
-----Agglomerate for sub layer (1)-----
=========== CL MICROSTRUCTURE =========
Agglomerate Type: IonomerAgglomerateSun
Agglomerate Radius: 1000 [nm]
Agglomerate Porosity: 0.5
Agglomerate Thin Film: 80 [nm]
=======================================
---------------------------------------
Theoretical cell voltage: 1.2 V
Generating the initial guess
Cycle = 0 :
Generating the initial guess
Solving...
Solving the linear system using UMFPACK
Overall residual at iteration 1 = 0.000419717
Residual for equation 0 is: 7.69004e-10
Residual for equation 1 is: 0.000296779
Residual for equation 2 is: 0.000296791
Solving the linear system using UMFPACK
Overall residual at iteration 2 = 1.14177e-06
Residual for equation 0 is: 2.0919e-12
Residual for equation 1 is: 8.07352e-07
Residual for equation 2 is: 8.07352e-07
Solving the linear system using UMFPACK
Overall residual at iteration 3 = 9.90169e-12
Residual for equation 0 is: 1.80606e-17
Residual for equation 1 is: 6.97022e-12
Residual for equation 2 is: 7.03275e-12
Solution: 3: 2009 2009 2009
Cycle = 1 :
Entering estimate...
Exited estimate
LOOP i=0
Levels:4
Cells:915
Dofs:11637(3879,3879,3879) sorting by component
Exited remesh
Solving...
Solving the linear system using UMFPACK
Overall residual at iteration 1 = 9.50588e-13
Residual for equation 0 is: 2.45372e-19
Residual for equation 1 is: 9.30935e-14
Residual for equation 2 is: 9.46019e-13
Solution: 3: 3879 3879 3879
sorting by component
Response current is : -0.0844989
Current density: 0.0844989 at cell param_value 0.94
=============================================================================
=============================================================================
=============================================================================
Iteration : 1
Solving for...
Parameter name:
Cell param_value: 0.866
======
YOU ARE CURRENTLY SOLVING A CATHODE MODEL
Application->DoF->BlockMatrix->OptimizationBlockMatrix
->FuelCellShop::Equation::FicksTransportEquation
->FuelCellShop::Equation::FicksTransportEquation
->FuelCellShop::Equation::ElectronTransportEquation
->FuelCellShop::Equation::ProtonTransportEquation
->FuelCellShop::Equation::ReactionSourceTerms
->FuelCell::Application::AppCathode-2D
YOU ARE USING Newton3pp NEWTON SOLVER FOR STEADY-STATE PROBLEM
Application->Copy->Newton3ppBase->->AdaptiveRefinement
Parameters: data.prm
Line <28> of file <data.prm>: There is no such subsection to be entered: Fuel cell data.Cathode gas diffusion layer
subsection Fuel cell data
subsection Cathode gas diffusion layer
Line <29> of file <data.prm>: There is no such subsection to be entered: Fuel cell data.DesignFibrousGDL
subsection Fuel cell data
subsection DesignFibrousGDL
Line <31> of file <data.prm>: No such entry was declared:
Porosity
<Present subsection:
subsection Fuel cell data
>
Line <33> of file <data.prm>: There is no subsection to leave here!
Line <34> of file <data.prm>: There is no such subsection to be entered: Cathode catalyst layer
subsection Cathode catalyst layer
Line <35> of file <data.prm>: There is no such subsection to be entered: ConventionalCL
subsection ConventionalCL
Line <36> of file <data.prm>: No such entry was declared:
Platinum loading on support (%wt)
<Present subsection:
>
Line <37> of file <data.prm>: No such entry was declared:
Platinum loading per unit volume (mg/cm3)
<Present subsection:
>
Line <38> of file <data.prm>: No such entry was declared:
Electrolyte loading (%wt)
<Present subsection:
>
Line <39> of file <data.prm>: There is no subsection to leave here!
Line <40> of file <data.prm>: There is no subsection to leave here!
Line <41> of file <data.prm>: There is no subsection to leave here!
FESystem<2>[FE_Q<2>(2)^3]
name: CathodeMPL
Generating new grid...
Using FCST grid generator.
Levels:3
Cells:480
Dofs:6027(2009,2009,2009) sorting by component
name: DesignFibrousGDL
name: SGL24BC
Created a SGL24BC MPL
------------------------------
Parameters for Gas diffusion layer:
Material ids: 2
Constant porosity: 1
Constant permeability [cm^2]:
10000
0
0
10000
Square root of constant permeability [cm]:
100
0
0
100
Inverse of constant permeability [1/cm^2]:
0.0001
-0
-0
0.0001
Inverse of square root of constant permeability [1/cm]:
0.01
-0
-0
0.01
Constant Forchheimer permeability [1/cm]:
100
0
0
100
Constant tortuosity:
1
0
0
1
------------------------------
Parameters for Microporous layer:
Material ids: 1
Constant porosity: 1
Constant permeability [cm^2]:
10000
0
0
10000
Square root of constant permeability [cm]:
100
0
0
100
Inverse of constant permeability [1/cm^2]:
0.0001
-0
-0
0.0001
Inverse of square root of constant permeability [1/cm]:
0.01
-0
-0
0.01
Constant Forchheimer permeability [1/cm]:
100
0
0
100
Constant tortuosity:
1
0
0
1
======= CATALYST LAYER STRUCTURE ======
=== Catalyst layer === #:1 =====
Solid phase volume fraction:0.355265
Ionomer in the CL:0.539798
Porosity in the CL:0.104938
Active area in the CL:255044
---------------------------------------
Method to compute eff_property_electrolyte: Bruggemann
=======================================
-----Agglomerate for sub layer (1)-----
=========== CL MICROSTRUCTURE =========
Agglomerate Type: IonomerAgglomerateSun
Agglomerate Radius: 1000 [nm]
Agglomerate Porosity: 0.5
Agglomerate Thin Film: 80 [nm]
=======================================
---------------------------------------
Theoretical cell voltage: 1.2 V
Generating the initial guess
Cycle = 0 :
Correcting the initial guess
Solving...
Solving the linear system using UMFPACK
Overall residual at iteration 1 = 0.000485971
Residual for equation 0 is: 8.94222e-10
Residual for equation 1 is: 0.000342143
Residual for equation 2 is: 0.000345117
Solving the linear system using UMFPACK
Overall residual at iteration 2 = 1.66968e-06
Residual for equation 0 is: 3.05912e-12
Residual for equation 1 is: 1.18064e-06
Residual for equation 2 is: 1.18064e-06
Solving the linear system using UMFPACK
Overall residual at iteration 3 = 2.50835e-11
Residual for equation 0 is: 4.59362e-17
Residual for equation 1 is: 1.77287e-11
Residual for equation 2 is: 1.77447e-11
Solution: 3: 2009 2009 2009
Cycle = 1 :
Entering estimate...
Exited estimate
LOOP i=0
Levels:4
Cells:915
Dofs:11616(3872,3872,3872) sorting by component
Exited remesh
Solving...
Solving the linear system using UMFPACK
Overall residual at iteration 1 = 5.45924e-12
Residual for equation 0 is: 9.8423e-18
Residual for equation 1 is: 3.79268e-12
Residual for equation 2 is: 3.9267e-12
Solution: 3: 3872 3872 3872
sorting by component
Response current is : -0.236935
Current density: 0.236935 at cell param_value 0.866
=============================================================================
=============================================================================
=============================================================================
Iteration : 2
Solving for...
Parameter name:
Cell param_value: 0.792
======
YOU ARE CURRENTLY SOLVING A CATHODE MODEL
Application->DoF->BlockMatrix->OptimizationBlockMatrix
->FuelCellShop::Equation::FicksTransportEquation
->FuelCellShop::Equation::FicksTransportEquation
->FuelCellShop::Equation::ElectronTransportEquation
->FuelCellShop::Equation::ProtonTransportEquation
->FuelCellShop::Equation::ReactionSourceTerms
->FuelCell::Application::AppCathode-2D
YOU ARE USING Newton3pp NEWTON SOLVER FOR STEADY-STATE PROBLEM
Application->Copy->Newton3ppBase->->AdaptiveRefinement
Parameters: data.prm
Line <28> of file <data.prm>: There is no such subsection to be entered: Fuel cell data.Cathode gas diffusion layer
subsection Fuel cell data
subsection Cathode gas diffusion layer
Line <29> of file <data.prm>: There is no such subsection to be entered: Fuel cell data.DesignFibrousGDL
subsection Fuel cell data
subsection DesignFibrousGDL
Line <31> of file <data.prm>: No such entry was declared:
Porosity
<Present subsection:
subsection Fuel cell data
>
Line <33> of file <data.prm>: There is no subsection to leave here!
Line <34> of file <data.prm>: There is no such subsection to be entered: Cathode catalyst layer
subsection Cathode catalyst layer
Line <35> of file <data.prm>: There is no such subsection to be entered: ConventionalCL
subsection ConventionalCL
Line <36> of file <data.prm>: No such entry was declared:
Platinum loading on support (%wt)
<Present subsection:
>
Line <37> of file <data.prm>: No such entry was declared:
Platinum loading per unit volume (mg/cm3)
<Present subsection:
>
Line <38> of file <data.prm>: No such entry was declared:
Electrolyte loading (%wt)
<Present subsection:
>
Line <39> of file <data.prm>: There is no subsection to leave here!
Line <40> of file <data.prm>: There is no subsection to leave here!
Line <41> of file <data.prm>: There is no subsection to leave here!
FESystem<2>[FE_Q<2>(2)^3]
name: CathodeMPL
Generating new grid...
Using FCST grid generator.
Levels:3
Cells:480
Dofs:6027(2009,2009,2009) sorting by component
name: DesignFibrousGDL
name: SGL24BC
Created a SGL24BC MPL
------------------------------
Parameters for Gas diffusion layer:
Material ids: 2
Constant porosity: 1
Constant permeability [cm^2]:
10000
0
0
10000
Square root of constant permeability [cm]:
100
0
0
100
Inverse of constant permeability [1/cm^2]:
0.0001
-0
-0
0.0001
Inverse of square root of constant permeability [1/cm]:
0.01
-0
-0
0.01
Constant Forchheimer permeability [1/cm]:
100
0
0
100
Constant tortuosity:
1
0
0
1
------------------------------
Parameters for Microporous layer:
Material ids: 1
Constant porosity: 1
Constant permeability [cm^2]:
10000
0
0
10000
Square root of constant permeability [cm]:
100
0
0
100
Inverse of constant permeability [1/cm^2]:
0.0001
-0
-0
0.0001
Inverse of square root of constant permeability [1/cm]:
0.01
-0
-0
0.01
Constant Forchheimer permeability [1/cm]:
100
0
0
100
Constant tortuosity:
1
0
0
1
======= CATALYST LAYER STRUCTURE ======
=== Catalyst layer === #:1 =====
Solid phase volume fraction:0.355265
Ionomer in the CL:0.539798
Porosity in the CL:0.104938
Active area in the CL:255044
---------------------------------------
Method to compute eff_property_electrolyte: Bruggemann
=======================================
-----Agglomerate for sub layer (1)-----
=========== CL MICROSTRUCTURE =========
Agglomerate Type: IonomerAgglomerateSun
Agglomerate Radius: 1000 [nm]
Agglomerate Porosity: 0.5
Agglomerate Thin Film: 80 [nm]
=======================================
---------------------------------------
Theoretical cell voltage: 1.2 V
Generating the initial guess
Cycle = 0 :
Correcting the initial guess
Solving...
Solving the linear system using UMFPACK
Overall residual at iteration 1 = 0.000182679
Residual for equation 0 is: 3.35153e-10
Residual for equation 1 is: 0.000128997
Residual for equation 2 is: 0.000129349
Solving the linear system using UMFPACK
Overall residual at iteration 2 = 1.18312e-07
Residual for equation 0 is: 2.16768e-13
Residual for equation 1 is: 8.36588e-08
Residual for equation 2 is: 8.36599e-08
Solving the linear system using UMFPACK
Overall residual at iteration 3 = 6.95988e-13
Residual for equation 0 is: 9.92577e-20
Residual for equation 1 is: 3.79772e-14
Residual for equation 2 is: 6.94951e-13
Solution: 3: 2009 2009 2009
Cycle = 1 :
Entering estimate...
Exited estimate
LOOP i=0
Levels:4
Cells:915
Dofs:11616(3872,3872,3872) sorting by component
Exited remesh
Solving...
Solving the linear system using UMFPACK
Overall residual at iteration 1 = 4.56071e-11
Residual for equation 0 is: 8.35555e-17
Residual for equation 1 is: 3.22389e-11
Residual for equation 2 is: 3.22593e-11
Solution: 3: 3872 3872 3872
sorting by component
Response current is : -0.451976
Current density: 0.451976 at cell param_value 0.792
=============================================================================
=============================================================================
=============================================================================
Iteration : 3
Solving for...
Parameter name:
Cell param_value: 0.718
======
YOU ARE CURRENTLY SOLVING A CATHODE MODEL
Application->DoF->BlockMatrix->OptimizationBlockMatrix
->FuelCellShop::Equation::FicksTransportEquation
->FuelCellShop::Equation::FicksTransportEquation
->FuelCellShop::Equation::ElectronTransportEquation
->FuelCellShop::Equation::ProtonTransportEquation
->FuelCellShop::Equation::ReactionSourceTerms
->FuelCell::Application::AppCathode-2D
YOU ARE USING Newton3pp NEWTON SOLVER FOR STEADY-STATE PROBLEM
Application->Copy->Newton3ppBase->->AdaptiveRefinement
Parameters: data.prm
Line <28> of file <data.prm>: There is no such subsection to be entered: Fuel cell data.Cathode gas diffusion layer
subsection Fuel cell data
subsection Cathode gas diffusion layer
Line <29> of file <data.prm>: There is no such subsection to be entered: Fuel cell data.DesignFibrousGDL
subsection Fuel cell data
subsection DesignFibrousGDL
Line <31> of file <data.prm>: No such entry was declared:
Porosity
<Present subsection:
subsection Fuel cell data
>
Line <33> of file <data.prm>: There is no subsection to leave here!
Line <34> of file <data.prm>: There is no such subsection to be entered: Cathode catalyst layer
subsection Cathode catalyst layer
Line <35> of file <data.prm>: There is no such subsection to be entered: ConventionalCL
subsection ConventionalCL
Line <36> of file <data.prm>: No such entry was declared:
Platinum loading on support (%wt)
<Present subsection:
>
Line <37> of file <data.prm>: No such entry was declared:
Platinum loading per unit volume (mg/cm3)
<Present subsection:
>
Line <38> of file <data.prm>: No such entry was declared:
Electrolyte loading (%wt)
<Present subsection:
>
Line <39> of file <data.prm>: There is no subsection to leave here!
Line <40> of file <data.prm>: There is no subsection to leave here!
Line <41> of file <data.prm>: There is no subsection to leave here!
FESystem<2>[FE_Q<2>(2)^3]
name: CathodeMPL
Generating new grid...
Using FCST grid generator.
Levels:3
Cells:480
Dofs:6027(2009,2009,2009) sorting by component
name: DesignFibrousGDL
name: SGL24BC
Created a SGL24BC MPL
------------------------------
Parameters for Gas diffusion layer:
Material ids: 2
Constant porosity: 1
Constant permeability [cm^2]:
10000
0
0
10000
Square root of constant permeability [cm]:
100
0
0
100
Inverse of constant permeability [1/cm^2]:
0.0001
-0
-0
0.0001
Inverse of square root of constant permeability [1/cm]:
0.01
-0
-0
0.01
Constant Forchheimer permeability [1/cm]:
100
0
0
100
Constant tortuosity:
1
0
0
1
------------------------------
Parameters for Microporous layer:
Material ids: 1
Constant porosity: 1
Constant permeability [cm^2]:
10000
0
0
10000
Square root of constant permeability [cm]:
100
0
0
100
Inverse of constant permeability [1/cm^2]:
0.0001
-0
-0
0.0001
Inverse of square root of constant permeability [1/cm]:
0.01
-0
-0
0.01
Constant Forchheimer permeability [1/cm]:
100
0
0
100
Constant tortuosity:
1
0
0
1
======= CATALYST LAYER STRUCTURE ======
=== Catalyst layer === #:1 =====
Solid phase volume fraction:0.355265
Ionomer in the CL:0.539798
Porosity in the CL:0.104938
Active area in the CL:255044
---------------------------------------
Method to compute eff_property_electrolyte: Bruggemann
=======================================
-----Agglomerate for sub layer (1)-----
=========== CL MICROSTRUCTURE =========
Agglomerate Type: IonomerAgglomerateSun
Agglomerate Radius: 1000 [nm]
Agglomerate Porosity: 0.5
Agglomerate Thin Film: 80 [nm]
=======================================
---------------------------------------
Theoretical cell voltage: 1.2 V
Generating the initial guess
Cycle = 0 :
Correcting the initial guess
Solving...
Solving the linear system using UMFPACK
Overall residual at iteration 1 = 0.000251548
Residual for equation 0 is: 4.6442e-10
Residual for equation 1 is: 0.000176493
Residual for equation 2 is: 0.000179239
Solving the linear system using UMFPACK
Overall residual at iteration 2 = 1.65273e-07
Residual for equation 0 is: 3.0281e-13
Residual for equation 1 is: 1.16864e-07
Residual for equation 2 is: 1.16867e-07
Solving the linear system using UMFPACK
Overall residual at iteration 3 = 5.89477e-13
Residual for equation 0 is: 1.90142e-19
Residual for equation 1 is: 7.31793e-14
Residual for equation 2 is: 5.84917e-13
Solution: 3: 2009 2009 2009
Cycle = 1 :
Entering estimate...
Exited estimate
LOOP i=0
Levels:4
Cells:915
Dofs:11634(3878,3878,3878) sorting by component
Exited remesh
Solving...
Solving the linear system using UMFPACK
Overall residual at iteration 1 = 1.13357e-10
Residual for equation 0 is: 2.07707e-16
Residual for equation 1 is: 8.01543e-11
Residual for equation 2 is: 8.01573e-11
Solution: 3: 3878 3878 3878
sorting by component
Response current is : -0.643129
Current density: 0.643129 at cell param_value 0.718
=============================================================================
=============================================================================
=============================================================================
Iteration : 4
Solving for...
Parameter name:
Cell param_value: 0.644
======
YOU ARE CURRENTLY SOLVING A CATHODE MODEL
Application->DoF->BlockMatrix->OptimizationBlockMatrix
->FuelCellShop::Equation::FicksTransportEquation
->FuelCellShop::Equation::FicksTransportEquation
->FuelCellShop::Equation::ElectronTransportEquation
->FuelCellShop::Equation::ProtonTransportEquation
->FuelCellShop::Equation::ReactionSourceTerms
->FuelCell::Application::AppCathode-2D
YOU ARE USING Newton3pp NEWTON SOLVER FOR STEADY-STATE PROBLEM
Application->Copy->Newton3ppBase->->AdaptiveRefinement
Parameters: data.prm
Line <28> of file <data.prm>: There is no such subsection to be entered: Fuel cell data.Cathode gas diffusion layer
subsection Fuel cell data
subsection Cathode gas diffusion layer
Line <29> of file <data.prm>: There is no such subsection to be entered: Fuel cell data.DesignFibrousGDL
subsection Fuel cell data
subsection DesignFibrousGDL
Line <31> of file <data.prm>: No such entry was declared:
Porosity
<Present subsection:
subsection Fuel cell data
>
Line <33> of file <data.prm>: There is no subsection to leave here!
Line <34> of file <data.prm>: There is no such subsection to be entered: Cathode catalyst layer
subsection Cathode catalyst layer
Line <35> of file <data.prm>: There is no such subsection to be entered: ConventionalCL
subsection ConventionalCL
Line <36> of file <data.prm>: No such entry was declared:
Platinum loading on support (%wt)
<Present subsection:
>
Line <37> of file <data.prm>: No such entry was declared:
Platinum loading per unit volume (mg/cm3)
<Present subsection:
>
Line <38> of file <data.prm>: No such entry was declared:
Electrolyte loading (%wt)
<Present subsection:
>
Line <39> of file <data.prm>: There is no subsection to leave here!
Line <40> of file <data.prm>: There is no subsection to leave here!
Line <41> of file <data.prm>: There is no subsection to leave here!
FESystem<2>[FE_Q<2>(2)^3]
name: CathodeMPL
Generating new grid...
Using FCST grid generator.
Levels:3
Cells:480
Dofs:6027(2009,2009,2009) sorting by component
name: DesignFibrousGDL
name: SGL24BC
Created a SGL24BC MPL
------------------------------
Parameters for Gas diffusion layer:
Material ids: 2
Constant porosity: 1
Constant permeability [cm^2]:
10000
0
0
10000
Square root of constant permeability [cm]:
100
0
0
100
Inverse of constant permeability [1/cm^2]:
0.0001
-0
-0
0.0001
Inverse of square root of constant permeability [1/cm]:
0.01
-0
-0
0.01
Constant Forchheimer permeability [1/cm]:
100
0
0
100
Constant tortuosity:
1
0
0
1
------------------------------
Parameters for Microporous layer:
Material ids: 1
Constant porosity: 1
Constant permeability [cm^2]:
10000
0
0
10000
Square root of constant permeability [cm]:
100
0
0
100
Inverse of constant permeability [1/cm^2]:
0.0001
-0
-0
0.0001
Inverse of square root of constant permeability [1/cm]:
0.01
-0
-0
0.01
Constant Forchheimer permeability [1/cm]:
100
0
0
100
Constant tortuosity:
1
0
0
1
======= CATALYST LAYER STRUCTURE ======
=== Catalyst layer === #:1 =====
Solid phase volume fraction:0.355265
Ionomer in the CL:0.539798
Porosity in the CL:0.104938
Active area in the CL:255044
---------------------------------------
Method to compute eff_property_electrolyte: Bruggemann
=======================================
-----Agglomerate for sub layer (1)-----
=========== CL MICROSTRUCTURE =========
Agglomerate Type: IonomerAgglomerateSun
Agglomerate Radius: 1000 [nm]
Agglomerate Porosity: 0.5
Agglomerate Thin Film: 80 [nm]
=======================================
---------------------------------------
Theoretical cell voltage: 1.2 V
Generating the initial guess
Cycle = 0 :
Correcting the initial guess
Solving...
Solving the linear system using UMFPACK
Overall residual at iteration 1 = 0.000307979
Residual for equation 0 is: 5.66764e-10
Residual for equation 1 is: 0.000216805
Residual for equation 2 is: 0.000218738
Solving the linear system using UMFPACK
Overall residual at iteration 2 = 1.21794e-07
Residual for equation 0 is: 2.2315e-13
Residual for equation 1 is: 8.612e-08
Residual for equation 2 is: 8.61226e-08
Solving the linear system using UMFPACK
Overall residual at iteration 3 = 6.29501e-13
Residual for equation 0 is: 4.98556e-20
Residual for equation 1 is: 1.85389e-14
Residual for equation 2 is: 6.29228e-13
Solution: 3: 2009 2009 2009
Cycle = 1 :
Entering estimate...
Exited estimate
LOOP i=0
Levels:4
Cells:915
Dofs:11640(3880,3880,3880) sorting by component
Exited remesh
Solving...
Solving the linear system using UMFPACK
Overall residual at iteration 1 = 1.42194e-10
Residual for equation 0 is: 2.60541e-16
Residual for equation 1 is: 1.00547e-10
Residual for equation 2 is: 1.00546e-10
Solution: 3: 3880 3880 3880
sorting by component
Response current is : -0.777879
Current density: 0.777879 at cell param_value 0.644
=============================================================================
=============================================================================
=============================================================================
Iteration : 5
Solving for...
Parameter name:
Cell param_value: 0.57
======
YOU ARE CURRENTLY SOLVING A CATHODE MODEL
Application->DoF->BlockMatrix->OptimizationBlockMatrix
->FuelCellShop::Equation::FicksTransportEquation
->FuelCellShop::Equation::FicksTransportEquation
->FuelCellShop::Equation::ElectronTransportEquation
->FuelCellShop::Equation::ProtonTransportEquation
->FuelCellShop::Equation::ReactionSourceTerms
->FuelCell::Application::AppCathode-2D
YOU ARE USING Newton3pp NEWTON SOLVER FOR STEADY-STATE PROBLEM
Application->Copy->Newton3ppBase->->AdaptiveRefinement
Parameters: data.prm
Line <28> of file <data.prm>: There is no such subsection to be entered: Fuel cell data.Cathode gas diffusion layer
subsection Fuel cell data
subsection Cathode gas diffusion layer
Line <29> of file <data.prm>: There is no such subsection to be entered: Fuel cell data.DesignFibrousGDL
subsection Fuel cell data
subsection DesignFibrousGDL
Line <31> of file <data.prm>: No such entry was declared:
Porosity
<Present subsection:
subsection Fuel cell data
>
Line <33> of file <data.prm>: There is no subsection to leave here!
Line <34> of file <data.prm>: There is no such subsection to be entered: Cathode catalyst layer
subsection Cathode catalyst layer
Line <35> of file <data.prm>: There is no such subsection to be entered: ConventionalCL
subsection ConventionalCL
Line <36> of file <data.prm>: No such entry was declared:
Platinum loading on support (%wt)
<Present subsection:
>
Line <37> of file <data.prm>: No such entry was declared:
Platinum loading per unit volume (mg/cm3)
<Present subsection:
>
Line <38> of file <data.prm>: No such entry was declared:
Electrolyte loading (%wt)
<Present subsection:
>
Line <39> of file <data.prm>: There is no subsection to leave here!
Line <40> of file <data.prm>: There is no subsection to leave here!
Line <41> of file <data.prm>: There is no subsection to leave here!
FESystem<2>[FE_Q<2>(2)^3]
name: CathodeMPL
Generating new grid...
Using FCST grid generator.
Levels:3
Cells:480
Dofs:6027(2009,2009,2009) sorting by component
name: DesignFibrousGDL
name: SGL24BC
Created a SGL24BC MPL
------------------------------
Parameters for Gas diffusion layer:
Material ids: 2
Constant porosity: 1
Constant permeability [cm^2]:
10000
0
0
10000
Square root of constant permeability [cm]:
100
0
0
100
Inverse of constant permeability [1/cm^2]:
0.0001
-0
-0
0.0001
Inverse of square root of constant permeability [1/cm]:
0.01
-0
-0
0.01
Constant Forchheimer permeability [1/cm]:
100
0
0
100
Constant tortuosity:
1
0
0
1
------------------------------
Parameters for Microporous layer:
Material ids: 1
Constant porosity: 1
Constant permeability [cm^2]:
10000
0
0
10000
Square root of constant permeability [cm]:
100
0
0
100
Inverse of constant permeability [1/cm^2]:
0.0001
-0
-0
0.0001
Inverse of square root of constant permeability [1/cm]:
0.01
-0
-0
0.01
Constant Forchheimer permeability [1/cm]:
100
0
0
100
Constant tortuosity:
1
0
0
1
======= CATALYST LAYER STRUCTURE ======
=== Catalyst layer === #:1 =====
Solid phase volume fraction:0.355265
Ionomer in the CL:0.539798
Porosity in the CL:0.104938
Active area in the CL:255044
---------------------------------------
Method to compute eff_property_electrolyte: Bruggemann
=======================================
-----Agglomerate for sub layer (1)-----
=========== CL MICROSTRUCTURE =========
Agglomerate Type: IonomerAgglomerateSun
Agglomerate Radius: 1000 [nm]
Agglomerate Porosity: 0.5
Agglomerate Thin Film: 80 [nm]
=======================================
---------------------------------------
Theoretical cell voltage: 1.2 V
Generating the initial guess
Cycle = 0 :
Correcting the initial guess
Solving...
Solving the linear system using UMFPACK
Overall residual at iteration 1 = 0.000248588
Residual for equation 0 is: 4.56746e-10
Residual for equation 1 is: 0.000175278
Residual for equation 2 is: 0.000176277
Solving the linear system using UMFPACK
Overall residual at iteration 2 = 4.48377e-08
Residual for equation 0 is: 8.21513e-14
Residual for equation 1 is: 3.17045e-08
Residual for equation 2 is: 3.17056e-08
Solving the linear system using UMFPACK
Overall residual at iteration 3 = 5.63011e-13
Residual for equation 0 is: 1.33704e-20
Residual for equation 1 is: 1.67318e-15
Residual for equation 2 is: 5.63009e-13
Solution: 3: 2009 2009 2009
Cycle = 1 :
Entering estimate...
Exited estimate
LOOP i=0
Levels:4
Cells:915
Dofs:11673(3891,3891,3891) sorting by component
Exited remesh
Solving...
Solving the linear system using UMFPACK
Overall residual at iteration 1 = 1.18511e-10
Residual for equation 0 is: 2.17119e-16
Residual for equation 1 is: 8.37916e-11
Residual for equation 2 is: 8.38083e-11
Solution: 3: 3891 3891 3891
sorting by component
Response current is : -0.861166
Current density: 0.861166 at cell param_value 0.57
=============================================================================
=============================================================================
=============================================================================
Iteration : 6
Solving for...
Parameter name:
Cell param_value: 0.496
======
YOU ARE CURRENTLY SOLVING A CATHODE MODEL
Application->DoF->BlockMatrix->OptimizationBlockMatrix
->FuelCellShop::Equation::FicksTransportEquation
->FuelCellShop::Equation::FicksTransportEquation
->FuelCellShop::Equation::ElectronTransportEquation
->FuelCellShop::Equation::ProtonTransportEquation
->FuelCellShop::Equation::ReactionSourceTerms
->FuelCell::Application::AppCathode-2D
YOU ARE USING Newton3pp NEWTON SOLVER FOR STEADY-STATE PROBLEM
Application->Copy->Newton3ppBase->->AdaptiveRefinement
Parameters: data.prm
Line <28> of file <data.prm>: There is no such subsection to be entered: Fuel cell data.Cathode gas diffusion layer
subsection Fuel cell data
subsection Cathode gas diffusion layer
Line <29> of file <data.prm>: There is no such subsection to be entered: Fuel cell data.DesignFibrousGDL
subsection Fuel cell data
subsection DesignFibrousGDL
Line <31> of file <data.prm>: No such entry was declared:
Porosity
<Present subsection:
subsection Fuel cell data
>
Line <33> of file <data.prm>: There is no subsection to leave here!
Line <34> of file <data.prm>: There is no such subsection to be entered: Cathode catalyst layer
subsection Cathode catalyst layer
Line <35> of file <data.prm>: There is no such subsection to be entered: ConventionalCL
subsection ConventionalCL
Line <36> of file <data.prm>: No such entry was declared:
Platinum loading on support (%wt)
<Present subsection:
>
Line <37> of file <data.prm>: No such entry was declared:
Platinum loading per unit volume (mg/cm3)
<Present subsection:
>
Line <38> of file <data.prm>: No such entry was declared:
Electrolyte loading (%wt)
<Present subsection:
>
Line <39> of file <data.prm>: There is no subsection to leave here!
Line <40> of file <data.prm>: There is no subsection to leave here!
Line <41> of file <data.prm>: There is no subsection to leave here!
FESystem<2>[FE_Q<2>(2)^3]
name: CathodeMPL
Generating new grid...
Using FCST grid generator.
Levels:3
Cells:480
Dofs:6027(2009,2009,2009) sorting by component
name: DesignFibrousGDL
name: SGL24BC
Created a SGL24BC MPL
------------------------------
Parameters for Gas diffusion layer:
Material ids: 2
Constant porosity: 1
Constant permeability [cm^2]:
10000
0
0
10000
Square root of constant permeability [cm]:
100
0
0
100
Inverse of constant permeability [1/cm^2]:
0.0001
-0
-0
0.0001
Inverse of square root of constant permeability [1/cm]:
0.01
-0
-0
0.01
Constant Forchheimer permeability [1/cm]:
100
0
0
100
Constant tortuosity:
1
0
0
1
------------------------------
Parameters for Microporous layer:
Material ids: 1
Constant porosity: 1
Constant permeability [cm^2]:
10000
0
0
10000
Square root of constant permeability [cm]:
100
0
0
100
Inverse of constant permeability [1/cm^2]:
0.0001
-0
-0
0.0001
Inverse of square root of constant permeability [1/cm]:
0.01
-0
-0
0.01
Constant Forchheimer permeability [1/cm]:
100
0
0
100
Constant tortuosity:
1
0
0
1
======= CATALYST LAYER STRUCTURE ======
=== Catalyst layer === #:1 =====
Solid phase volume fraction:0.355265
Ionomer in the CL:0.539798
Porosity in the CL:0.104938
Active area in the CL:255044
---------------------------------------
Method to compute eff_property_electrolyte: Bruggemann
=======================================
-----Agglomerate for sub layer (1)-----
=========== CL MICROSTRUCTURE =========
Agglomerate Type: IonomerAgglomerateSun
Agglomerate Radius: 1000 [nm]
Agglomerate Porosity: 0.5
Agglomerate Thin Film: 80 [nm]
=======================================
---------------------------------------
Theoretical cell voltage: 1.2 V
Generating the initial guess
Cycle = 0 :
Correcting the initial guess
Solving...
Solving the linear system using UMFPACK
Overall residual at iteration 1 = 0.00016468
Residual for equation 0 is: 3.02306e-10
Residual for equation 1 is: 0.000116219
Residual for equation 2 is: 0.000116673
Solving the linear system using UMFPACK
Overall residual at iteration 2 = 1.41059e-08
Residual for equation 0 is: 2.58445e-14
Residual for equation 1 is: 9.97425e-09
Residual for equation 2 is: 9.97447e-09
Solving the linear system using UMFPACK
Overall residual at iteration 3 = 4.08666e-13
Residual for equation 0 is: 1.27315e-20
Residual for equation 1 is: 1.86914e-16
Residual for equation 2 is: 4.08666e-13
Solution: 3: 2009 2009 2009
Cycle = 1 :
Entering estimate...
Exited estimate
LOOP i=0
Levels:4
Cells:915
Dofs:11691(3897,3897,3897) sorting by component
Exited remesh
Solving...
Solving the linear system using UMFPACK
Overall residual at iteration 1 = 7.64356e-11
Residual for equation 0 is: 1.40055e-16
Residual for equation 1 is: 5.40511e-11
Residual for equation 2 is: 5.40452e-11
Solution: 3: 3897 3897 3897
sorting by component
Response current is : -0.907746
Current density: 0.907746 at cell param_value 0.496
=============================================================================
=============================================================================
=============================================================================
Iteration : 7
Solving for...
Parameter name:
Cell param_value: 0.422
======
YOU ARE CURRENTLY SOLVING A CATHODE MODEL
Application->DoF->BlockMatrix->OptimizationBlockMatrix
->FuelCellShop::Equation::FicksTransportEquation
->FuelCellShop::Equation::FicksTransportEquation
->FuelCellShop::Equation::ElectronTransportEquation
->FuelCellShop::Equation::ProtonTransportEquation
->FuelCellShop::Equation::ReactionSourceTerms
->FuelCell::Application::AppCathode-2D
YOU ARE USING Newton3pp NEWTON SOLVER FOR STEADY-STATE PROBLEM
Application->Copy->Newton3ppBase->->AdaptiveRefinement
Parameters: data.prm
Line <28> of file <data.prm>: There is no such subsection to be entered: Fuel cell data.Cathode gas diffusion layer
subsection Fuel cell data
subsection Cathode gas diffusion layer
Line <29> of file <data.prm>: There is no such subsection to be entered: Fuel cell data.DesignFibrousGDL
subsection Fuel cell data
subsection DesignFibrousGDL
Line <31> of file <data.prm>: No such entry was declared:
Porosity
<Present subsection:
subsection Fuel cell data
>
Line <33> of file <data.prm>: There is no subsection to leave here!
Line <34> of file <data.prm>: There is no such subsection to be entered: Cathode catalyst layer
subsection Cathode catalyst layer
Line <35> of file <data.prm>: There is no such subsection to be entered: ConventionalCL
subsection ConventionalCL
Line <36> of file <data.prm>: No such entry was declared:
Platinum loading on support (%wt)
<Present subsection:
>
Line <37> of file <data.prm>: No such entry was declared:
Platinum loading per unit volume (mg/cm3)
<Present subsection:
>
Line <38> of file <data.prm>: No such entry was declared:
Electrolyte loading (%wt)
<Present subsection:
>
Line <39> of file <data.prm>: There is no subsection to leave here!
Line <40> of file <data.prm>: There is no subsection to leave here!
Line <41> of file <data.prm>: There is no subsection to leave here!
FESystem<2>[FE_Q<2>(2)^3]
name: CathodeMPL
Generating new grid...
Using FCST grid generator.
Levels:3
Cells:480
Dofs:6027(2009,2009,2009) sorting by component
name: DesignFibrousGDL
name: SGL24BC
Created a SGL24BC MPL
------------------------------
Parameters for Gas diffusion layer:
Material ids: 2
Constant porosity: 1
Constant permeability [cm^2]:
10000
0
0
10000
Square root of constant permeability [cm]:
100
0
0
100
Inverse of constant permeability [1/cm^2]:
0.0001
-0
-0
0.0001
Inverse of square root of constant permeability [1/cm]:
0.01
-0
-0
0.01
Constant Forchheimer permeability [1/cm]:
100
0
0
100
Constant tortuosity:
1
0
0
1
------------------------------
Parameters for Microporous layer:
Material ids: 1
Constant porosity: 1
Constant permeability [cm^2]:
10000
0
0
10000
Square root of constant permeability [cm]:
100
0
0
100
Inverse of constant permeability [1/cm^2]:
0.0001
-0
-0
0.0001
Inverse of square root of constant permeability [1/cm]:
0.01
-0
-0
0.01
Constant Forchheimer permeability [1/cm]:
100
0
0
100
Constant tortuosity:
1
0
0
1
======= CATALYST LAYER STRUCTURE ======
=== Catalyst layer === #:1 =====
Solid phase volume fraction:0.355265
Ionomer in the CL:0.539798
Porosity in the CL:0.104938
Active area in the CL:255044
---------------------------------------
Method to compute eff_property_electrolyte: Bruggemann
=======================================
-----Agglomerate for sub layer (1)-----
=========== CL MICROSTRUCTURE =========
Agglomerate Type: IonomerAgglomerateSun
Agglomerate Radius: 1000 [nm]
Agglomerate Porosity: 0.5
Agglomerate Thin Film: 80 [nm]
=======================================
---------------------------------------
Theoretical cell voltage: 1.2 V
Generating the initial guess
Cycle = 0 :
Correcting the initial guess
Solving...
Solving the linear system using UMFPACK
Overall residual at iteration 1 = 9.50716e-05
Residual for equation 0 is: 1.74448e-10
Residual for equation 1 is: 6.71247e-05
Residual for equation 2 is: 6.73267e-05
Solving the linear system using UMFPACK
Overall residual at iteration 2 = 3.03412e-09
Residual for equation 0 is: 5.55902e-15
Residual for equation 1 is: 2.14543e-09
Residual for equation 2 is: 2.14547e-09
Solution: 3: 2009 2009 2009
Cycle = 1 :
Entering estimate...
Exited estimate
LOOP i=0
Levels:4
Cells:915
Dofs:11691(3897,3897,3897) sorting by component
Exited remesh
Solving...
Solving the linear system using UMFPACK
Overall residual at iteration 1 = 4.2541e-11
Residual for equation 0 is: 7.79398e-17
Residual for equation 1 is: 3.00792e-11
Residual for equation 2 is: 3.00828e-11
Solution: 3: 3897 3897 3897
sorting by component
Response current is : -0.932032
Current density: 0.932032 at cell param_value 0.422
=============================================================================
=============================================================================
=============================================================================
Iteration : 8
Solving for...
Parameter name:
Cell param_value: 0.348
======
YOU ARE CURRENTLY SOLVING A CATHODE MODEL
Application->DoF->BlockMatrix->OptimizationBlockMatrix
->FuelCellShop::Equation::FicksTransportEquation
->FuelCellShop::Equation::FicksTransportEquation
->FuelCellShop::Equation::ElectronTransportEquation
->FuelCellShop::Equation::ProtonTransportEquation
->FuelCellShop::Equation::ReactionSourceTerms
->FuelCell::Application::AppCathode-2D
YOU ARE USING Newton3pp NEWTON SOLVER FOR STEADY-STATE PROBLEM
Application->Copy->Newton3ppBase->->AdaptiveRefinement
Parameters: data.prm
Line <28> of file <data.prm>: There is no such subsection to be entered: Fuel cell data.Cathode gas diffusion layer
subsection Fuel cell data
subsection Cathode gas diffusion layer
Line <29> of file <data.prm>: There is no such subsection to be entered: Fuel cell data.DesignFibrousGDL
subsection Fuel cell data
subsection DesignFibrousGDL
Line <31> of file <data.prm>: No such entry was declared:
Porosity
<Present subsection:
subsection Fuel cell data
>
Line <33> of file <data.prm>: There is no subsection to leave here!
Line <34> of file <data.prm>: There is no such subsection to be entered: Cathode catalyst layer
subsection Cathode catalyst layer
Line <35> of file <data.prm>: There is no such subsection to be entered: ConventionalCL
subsection ConventionalCL
Line <36> of file <data.prm>: No such entry was declared:
Platinum loading on support (%wt)
<Present subsection:
>
Line <37> of file <data.prm>: No such entry was declared:
Platinum loading per unit volume (mg/cm3)
<Present subsection:
>
Line <38> of file <data.prm>: No such entry was declared:
Electrolyte loading (%wt)
<Present subsection:
>
Line <39> of file <data.prm>: There is no subsection to leave here!
Line <40> of file <data.prm>: There is no subsection to leave here!
Line <41> of file <data.prm>: There is no subsection to leave here!
FESystem<2>[FE_Q<2>(2)^3]
name: CathodeMPL
Generating new grid...
Using FCST grid generator.
Levels:3
Cells:480
Dofs:6027(2009,2009,2009) sorting by component
name: DesignFibrousGDL
name: SGL24BC
Created a SGL24BC MPL
------------------------------
Parameters for Gas diffusion layer:
Material ids: 2
Constant porosity: 1
Constant permeability [cm^2]:
10000
0
0
10000
Square root of constant permeability [cm]:
100
0
0
100
Inverse of constant permeability [1/cm^2]:
0.0001
-0
-0
0.0001
Inverse of square root of constant permeability [1/cm]:
0.01
-0
-0
0.01
Constant Forchheimer permeability [1/cm]:
100
0
0
100
Constant tortuosity:
1
0
0
1
------------------------------
Parameters for Microporous layer:
Material ids: 1
Constant porosity: 1
Constant permeability [cm^2]:
10000
0
0
10000
Square root of constant permeability [cm]:
100
0
0
100
Inverse of constant permeability [1/cm^2]:
0.0001
-0
-0
0.0001
Inverse of square root of constant permeability [1/cm]:
0.01
-0
-0
0.01
Constant Forchheimer permeability [1/cm]:
100
0
0
100
Constant tortuosity:
1
0
0
1
======= CATALYST LAYER STRUCTURE ======
=== Catalyst layer === #:1 =====
Solid phase volume fraction:0.355265
Ionomer in the CL:0.539798
Porosity in the CL:0.104938
Active area in the CL:255044
---------------------------------------
Method to compute eff_property_electrolyte: Bruggemann
=======================================
-----Agglomerate for sub layer (1)-----
=========== CL MICROSTRUCTURE =========
Agglomerate Type: IonomerAgglomerateSun
Agglomerate Radius: 1000 [nm]
Agglomerate Porosity: 0.5
Agglomerate Thin Film: 80 [nm]
=======================================
---------------------------------------
Theoretical cell voltage: 1.2 V
Generating the initial guess
Cycle = 0 :
Correcting the initial guess
Solving...
Solving the linear system using UMFPACK
Overall residual at iteration 1 = 5.02346e-05
Residual for equation 0 is: 9.21567e-11
Residual for equation 1 is: 3.54753e-05
Residual for equation 2 is: 3.55671e-05
Solving the linear system using UMFPACK
Overall residual at iteration 2 = 4.75811e-10
Residual for equation 0 is: 8.71766e-16
Residual for equation 1 is: 3.36447e-10
Residual for equation 2 is: 3.36452e-10
Solution: 3: 2009 2009 2009
Cycle = 1 :
Entering estimate...
Exited estimate
LOOP i=0
Levels:4
Cells:915
Dofs:11694(3898,3898,3898) sorting by component
Exited remesh
Solving...
Solving the linear system using UMFPACK
Overall residual at iteration 1 = 2.2162e-11
Residual for equation 0 is: 4.05915e-17
Residual for equation 1 is: 1.56655e-11
Residual for equation 2 is: 1.56764e-11
Solution: 3: 3898 3898 3898
sorting by component
Response current is : -0.94416
Current density: 0.94416 at cell param_value 0.348
=============================================================================
=============================================================================
=============================================================================
Iteration : 9
Solving for...
Parameter name:
Cell param_value: 0.274
======
YOU ARE CURRENTLY SOLVING A CATHODE MODEL
Application->DoF->BlockMatrix->OptimizationBlockMatrix
->FuelCellShop::Equation::FicksTransportEquation
->FuelCellShop::Equation::FicksTransportEquation
->FuelCellShop::Equation::ElectronTransportEquation
->FuelCellShop::Equation::ProtonTransportEquation
->FuelCellShop::Equation::ReactionSourceTerms
->FuelCell::Application::AppCathode-2D
YOU ARE USING Newton3pp NEWTON SOLVER FOR STEADY-STATE PROBLEM
Application->Copy->Newton3ppBase->->AdaptiveRefinement
Parameters: data.prm
Line <28> of file <data.prm>: There is no such subsection to be entered: Fuel cell data.Cathode gas diffusion layer
subsection Fuel cell data
subsection Cathode gas diffusion layer
Line <29> of file <data.prm>: There is no such subsection to be entered: Fuel cell data.DesignFibrousGDL
subsection Fuel cell data
subsection DesignFibrousGDL
Line <31> of file <data.prm>: No such entry was declared:
Porosity
<Present subsection:
subsection Fuel cell data
>
Line <33> of file <data.prm>: There is no subsection to leave here!
Line <34> of file <data.prm>: There is no such subsection to be entered: Cathode catalyst layer
subsection Cathode catalyst layer
Line <35> of file <data.prm>: There is no such subsection to be entered: ConventionalCL
subsection ConventionalCL
Line <36> of file <data.prm>: No such entry was declared:
Platinum loading on support (%wt)
<Present subsection:
>
Line <37> of file <data.prm>: No such entry was declared:
Platinum loading per unit volume (mg/cm3)
<Present subsection:
>
Line <38> of file <data.prm>: No such entry was declared:
Electrolyte loading (%wt)
<Present subsection:
>
Line <39> of file <data.prm>: There is no subsection to leave here!
Line <40> of file <data.prm>: There is no subsection to leave here!
Line <41> of file <data.prm>: There is no subsection to leave here!
FESystem<2>[FE_Q<2>(2)^3]
name: CathodeMPL
Generating new grid...
Using FCST grid generator.
Levels:3
Cells:480
Dofs:6027(2009,2009,2009) sorting by component
name: DesignFibrousGDL
name: SGL24BC
Created a SGL24BC MPL
------------------------------
Parameters for Gas diffusion layer:
Material ids: 2
Constant porosity: 1
Constant permeability [cm^2]:
10000
0
0
10000
Square root of constant permeability [cm]:
100
0
0
100
Inverse of constant permeability [1/cm^2]:
0.0001
-0
-0
0.0001
Inverse of square root of constant permeability [1/cm]:
0.01
-0
-0
0.01
Constant Forchheimer permeability [1/cm]:
100
0
0
100
Constant tortuosity:
1
0
0
1
------------------------------
Parameters for Microporous layer:
Material ids: 1
Constant porosity: 1
Constant permeability [cm^2]:
10000
0
0
10000
Square root of constant permeability [cm]:
100
0
0
100
Inverse of constant permeability [1/cm^2]:
0.0001
-0
-0
0.0001
Inverse of square root of constant permeability [1/cm]:
0.01
-0
-0
0.01
Constant Forchheimer permeability [1/cm]:
100
0
0
100
Constant tortuosity:
1
0
0
1
======= CATALYST LAYER STRUCTURE ======
=== Catalyst layer === #:1 =====
Solid phase volume fraction:0.355265
Ionomer in the CL:0.539798
Porosity in the CL:0.104938
Active area in the CL:255044
---------------------------------------
Method to compute eff_property_electrolyte: Bruggemann
=======================================
-----Agglomerate for sub layer (1)-----
=========== CL MICROSTRUCTURE =========
Agglomerate Type: IonomerAgglomerateSun
Agglomerate Radius: 1000 [nm]
Agglomerate Porosity: 0.5
Agglomerate Thin Film: 80 [nm]
=======================================
---------------------------------------
Theoretical cell voltage: 1.2 V
Generating the initial guess
Cycle = 0 :
Correcting the initial guess
Solving...
Solving the linear system using UMFPACK
Overall residual at iteration 1 = 2.52255e-05
Residual for equation 0 is: 4.62723e-11
Residual for equation 1 is: 1.78159e-05
Residual for equation 2 is: 1.78584e-05
Solving the linear system using UMFPACK
Overall residual at iteration 2 = 6.20537e-11
Residual for equation 0 is: 1.13699e-16
Residual for equation 1 is: 4.38806e-11
Residual for equation 2 is: 4.38766e-11
Solution: 3: 2009 2009 2009
Cycle = 1 :
Entering estimate...
Exited estimate
LOOP i=0
Levels:4
Cells:915
Dofs:11694(3898,3898,3898) sorting by component
Exited remesh
Solving...
Solving the linear system using UMFPACK
Overall residual at iteration 1 = 1.09601e-11
Residual for equation 0 is: 2.00669e-17
Residual for equation 1 is: 7.74438e-12
Residual for equation 2 is: 7.75549e-12
Solution: 3: 3898 3898 3898
sorting by component
Response current is : -0.950075
Current density: 0.950075 at cell param_value 0.274
=============================================================================
=============================================================================
=============================================================================
Iteration : 10
Solving for...
Parameter name:
Cell param_value: 0.2
======
YOU ARE CURRENTLY SOLVING A CATHODE MODEL
Application->DoF->BlockMatrix->OptimizationBlockMatrix
->FuelCellShop::Equation::FicksTransportEquation
->FuelCellShop::Equation::FicksTransportEquation
->FuelCellShop::Equation::ElectronTransportEquation
->FuelCellShop::Equation::ProtonTransportEquation
->FuelCellShop::Equation::ReactionSourceTerms
->FuelCell::Application::AppCathode-2D
YOU ARE USING Newton3pp NEWTON SOLVER FOR STEADY-STATE PROBLEM
Application->Copy->Newton3ppBase->->AdaptiveRefinement
Parameters: data.prm
Line <28> of file <data.prm>: There is no such subsection to be entered: Fuel cell data.Cathode gas diffusion layer
subsection Fuel cell data
subsection Cathode gas diffusion layer
Line <29> of file <data.prm>: There is no such subsection to be entered: Fuel cell data.DesignFibrousGDL
subsection Fuel cell data
subsection DesignFibrousGDL
Line <31> of file <data.prm>: No such entry was declared:
Porosity
<Present subsection:
subsection Fuel cell data
>
Line <33> of file <data.prm>: There is no subsection to leave here!
Line <34> of file <data.prm>: There is no such subsection to be entered: Cathode catalyst layer
subsection Cathode catalyst layer
Line <35> of file <data.prm>: There is no such subsection to be entered: ConventionalCL
subsection ConventionalCL
Line <36> of file <data.prm>: No such entry was declared:
Platinum loading on support (%wt)
<Present subsection:
>
Line <37> of file <data.prm>: No such entry was declared:
Platinum loading per unit volume (mg/cm3)
<Present subsection:
>
Line <38> of file <data.prm>: No such entry was declared:
Electrolyte loading (%wt)
<Present subsection:
>
Line <39> of file <data.prm>: There is no subsection to leave here!
Line <40> of file <data.prm>: There is no subsection to leave here!
Line <41> of file <data.prm>: There is no subsection to leave here!
FESystem<2>[FE_Q<2>(2)^3]
name: CathodeMPL
Generating new grid...
Using FCST grid generator.
Levels:3
Cells:480
Dofs:6027(2009,2009,2009) sorting by component
name: DesignFibrousGDL
name: SGL24BC
Created a SGL24BC MPL
------------------------------
Parameters for Gas diffusion layer:
Material ids: 2
Constant porosity: 1
Constant permeability [cm^2]:
10000
0
0
10000
Square root of constant permeability [cm]:
100
0
0
100
Inverse of constant permeability [1/cm^2]:
0.0001
-0
-0
0.0001
Inverse of square root of constant permeability [1/cm]:
0.01
-0
-0
0.01
Constant Forchheimer permeability [1/cm]:
100
0
0
100
Constant tortuosity:
1
0
0
1
------------------------------
Parameters for Microporous layer:
Material ids: 1
Constant porosity: 1
Constant permeability [cm^2]:
10000
0
0
10000
Square root of constant permeability [cm]:
100
0
0
100
Inverse of constant permeability [1/cm^2]:
0.0001
-0
-0
0.0001
Inverse of square root of constant permeability [1/cm]:
0.01
-0
-0
0.01
Constant Forchheimer permeability [1/cm]:
100
0
0
100
Constant tortuosity:
1
0
0
1
======= CATALYST LAYER STRUCTURE ======
=== Catalyst layer === #:1 =====
Solid phase volume fraction:0.355265
Ionomer in the CL:0.539798
Porosity in the CL:0.104938
Active area in the CL:255044
---------------------------------------
Method to compute eff_property_electrolyte: Bruggemann
=======================================
-----Agglomerate for sub layer (1)-----
=========== CL MICROSTRUCTURE =========
Agglomerate Type: IonomerAgglomerateSun
Agglomerate Radius: 1000 [nm]
Agglomerate Porosity: 0.5
Agglomerate Thin Film: 80 [nm]
=======================================
---------------------------------------
Theoretical cell voltage: 1.2 V
Generating the initial guess
Cycle = 0 :
Correcting the initial guess
Solving...
Solving the linear system using UMFPACK
Overall residual at iteration 1 = 1.23309e-05
Residual for equation 0 is: 2.26181e-11
Residual for equation 1 is: 8.70928e-06
Residual for equation 2 is: 8.72925e-06
Solving the linear system using UMFPACK
Overall residual at iteration 2 = 7.35279e-12
Residual for equation 0 is: 1.34683e-17
Residual for equation 1 is: 5.19789e-12
Residual for equation 2 is: 5.20052e-12
Solution: 3: 2009 2009 2009
Cycle = 1 :
Entering estimate...
Exited estimate
LOOP i=0
Levels:4
Cells:915
Dofs:11694(3898,3898,3898) sorting by component
Exited remesh
Solving...
Solving the linear system using UMFPACK
Overall residual at iteration 1 = 5.31645e-12
Residual for equation 0 is: 9.72925e-18
Residual for equation 1 is: 3.75477e-12
Residual for equation 2 is: 3.76382e-12
Solution: 3: 3898 3898 3898
sorting by component
Response current is : -0.952925
Current density: 0.952925 at cell param_value 0.2
=============================================================================
=============================================================================
The program was executed in: 11.5218 seconds
=============== END ====================
To plot the polarization curves we use the plotting utility available in PythonFCST and compare the simulation results with the reference results.
$ fcst_plot_polcurve.py polarization_curve.dat polarization_curve_reference.dat --label Current Reference --output article
==================================================
= Creates postprocessing plots from the tabular output file of the fcst polcurve sweep
==================================================
--------------------------------------------------
= - Parse Commandline
--------------------------------------------------
= - Parse file polarization_curve.dat
Column header: ['Cell voltage [V]', 'Cathode current [A/cm2]']
Rows: 11
--------------------------------------------------
= - Parse file polarization_curve_reference.dat
Column header: ['Cell voltage [V]', 'Cathode current [A/cm2]']
Rows: 6
Save figure polcurve
2.6.2.2. Optimization study¶
In order to perform an optimization study, several changes are necessary in the main.prm (.xml) file. Also, a new file is need to provide information to the optimizer.
2.6.2.2.1. The main.xml file¶
The main.xml file needs to be modified as follows:
- In section Simulator, set Analysis type to Optimization
- In section Simulator, subsection Optimization specify the optimization file in optimization parameter file name
Example:
######################################################################
include ../template/main.prm
######################################################################
subsection Simulator
set Analysis type = Optimization
subsection Optimization
set optimization parameter file name = opt.prm
set Dakota direct = true
end
end
######################################################################
2.6.2.2.2. The opt.xml file¶
The opt.xml is used to specify the optimization number of design variables, and its initial value, upper and lower bounds. It also specifies the number of objectives and constraints and if they are equality or inequality constraints. Finally, it specifies the type of optimizer to use. In the article case, the file is:
######################################################################
#
# This file is used to run multi-dimensional parametric studies.
# See end of file for a list of possible design variables.
#
# Copyright (C) 2013, Kailyn Domican
#
######################################################################
include ../template/opt.prm