FCSys.Regions.PEMs

Proton exchange membranes

Information

Extends from Modelica.Icons.Package (Icon for standard packages).

Package Content

NameDescription
FCSys.Regions.PEMs.PEM PEM Proton exchange membrane
FCSys.Regions.PEMs.DuPontN112 DuPontN112 DuPontTM Nafion® N-112
FCSys.Regions.PEMs.DuPontN115 DuPontN115 DuPontTM Nafion® N-115
FCSys.Regions.PEMs.DuPontN117 DuPontN117 DuPontTM Nafion® N-117
FCSys.Regions.PEMs.DuPontNE1110 DuPontNE1110 DuPontTM Nafion® NE-1110
FCSys.Regions.PEMs.DuPontNE1135 DuPontNE1135 DuPontTM Nafion® NE-1135
FCSys.Regions.PEMs.DuPontNRE211 DuPontNRE211 DuPontTM Nafion® NRE-1110
FCSys.Regions.PEMs.DuPontNRE212 DuPontNRE212 DuPontTM Nafion® NRE-1110

FCSys.Regions.PEMs.PEM FCSys.Regions.PEMs.PEM

Proton exchange membrane FCSys.Regions.PEMs.PEM

Information

This model represents the proton exchange membrane of a PEMFC. The x axis extends from the anode to the cathode. By default, the cross-sectional area in the yz plane is 50 cm2.

The transport of protons includes inertance or inductance (i.e., translational momentum is stored) in the x direction in the subregions with index (x = 1, y > 1, z > 1). This is for numerical reasons, although in reality there is inductance.

Assumptions:

  1. There are no pores in the PEM. All H2O is absorbed into the ionomer itself.
  2. There is no cross-over of the reactant gases.
  3. There is no cross-over of the reactant gases.
  4. For more information, please see the Region model.

    Extends from Region (Base model for a 3D array of subregions).

    Parameters

    TypeNameDefaultDescription
    replaceable model SubregionFCSys.Subregions.SubregionIo…Base subregion model
    Geometry
    LengthL_x[:]{100}*U.umLengths along the x axis [L]
    LengthL_y[:]{8}*U.cmLengths along the y axis [L]
    LengthL_z[:]{6.25}*U.cmLengths across the z axis [L]
    Assumptions
    Included transport axes
    BooleaninclTransXtrueX
    BooleaninclTransYfalseY
    BooleaninclTransZfalseZ

    Connectors

    TypeNameDescription
    replaceable model SubregionBase subregion model
    BoundaryBusxNegative[n_y, n_z]Negative boundary along the x axis
    BoundaryBusxPositive[n_y, n_z]Positive boundary along the x axis
    BoundaryBusyNegative[n_x, n_z]Negative boundary along the y axis
    BoundaryBusyPositive[n_x, n_z]Positive boundary along the y axis
    BoundaryBuszNegative[n_x, n_y]Negative boundary along the z axis
    BoundaryBuszPositive[n_x, n_y]Positive boundary along the z axis

    Modelica definition

    model PEM "Proton exchange membrane"
      // extends FCSys.Icons.Names.Top4;
    
      // Note:  Extensions of PEM should be placed directly in the PEMs
      // package rather than subpackages (e.g., by manufacturer) so that
      // __Dymola_choicesFromPackage can be used.  Dymola 7.4 launches the
      // parameter dialogs too slowly when __Dymola_choicesAllMatching is
      // used.
    
      extends Region(
        L_x={100}*U.um,
        L_y={8}*U.cm,
        L_z={6.25}*U.cm,
        final inclTransX=true,
        inclTransY=false,
        inclTransZ=false,
        redeclare replaceable model Subregion = FCSys.Subregions.SubregionIonomer (
              ionomer(
              'inclSO3-'=true,
              'inclH+'=true,
              inclH2O=true,
              'SO3-'(final mu=0,final epsilon=1),
              'H+'(initEnergy=Init.none, sigma=40*U.S/U.m),
              H2O(initEnergy=Init.none,upstreamX=false))),
        subregions(ionomer('H+'(consTransX={{{if x > 1 or (y == 1 and z == 1) then 
                  ConsTrans.steady else ConsTrans.dynamic for z in 1:n_z} for y in 1
                  :n_y} for x in 1:n_x}))));
    
    protected 
      Q.Current I_states_1[:](
        each stateSelect=StateSelect.always,
        each start=0,
        each fixed=true) = subregions[1, 2:n_y, 1].ionomer.'H+'.I[1] if n_y > 1 
        "Forced states, set #1";
      Q.Current I_states_2[:, :](
        each stateSelect=StateSelect.always,
        each start=0,
        each fixed=true) = subregions[1, :, 2:n_z].ionomer.'H+'.I[1] if n_z > 1 
        "Forced states, set #2";
      // Note:  These variables avoid dynamic state selection in Dymola 2014.
    
      outer Conditions.Environment environment "Environmental conditions";
    
    end PEM;
    

    FCSys.Regions.PEMs.DuPontN112 FCSys.Regions.PEMs.DuPontN112

    DuPontTM Nafion® N-112 FCSys.Regions.PEMs.DuPontN112

    Information

    The default properties are based on [DuPont2004N].

    For more information, please see the PEM model.

    Extends from PEM (Proton exchange membrane).

    Parameters

    TypeNameDefaultDescription
    Geometry
    LengthL_x[:]{51*U.um}Lengths along the x axis [L]
    LengthL_y[:]{8}*U.cmLengths along the y axis [L]
    LengthL_z[:]{6.25}*U.cmLengths across the z axis [L]
    Assumptions
    Included transport axes
    BooleaninclTransYfalseY
    BooleaninclTransZfalseZ

    Connectors

    TypeNameDescription
    BoundaryBusxNegative[n_y, n_z]Negative boundary along the x axis
    BoundaryBusxPositive[n_y, n_z]Positive boundary along the x axis
    BoundaryBusyNegative[n_x, n_z]Negative boundary along the y axis
    BoundaryBusyPositive[n_x, n_z]Positive boundary along the y axis
    BoundaryBuszNegative[n_x, n_y]Negative boundary along the z axis
    BoundaryBuszPositive[n_x, n_y]Positive boundary along the z axis

    Modelica definition

    model DuPontN112 "DuPontTM Nafion® N-112"
      extends PEM(L_x={51*U.um},Subregion(ionomer('H+'(sigma=0.083*U.S/U.cm))));
      // Additional properties not yet incorporated [DuPont2004N]:
      //     Density:  (100 g/m2)/(51 um) = 1.9608 g/cm3
    
    end DuPontN112;
    

    FCSys.Regions.PEMs.DuPontN115 FCSys.Regions.PEMs.DuPontN115

    DuPontTM Nafion® N-115 FCSys.Regions.PEMs.DuPontN115

    Information

    The default properties are based on [DuPont2004N].

    For more information, please see the PEM model.

    Extends from PEM (Proton exchange membrane).

    Parameters

    TypeNameDefaultDescription
    Geometry
    LengthL_x[:]{127*U.um}Lengths along the x axis [L]
    LengthL_y[:]{8}*U.cmLengths along the y axis [L]
    LengthL_z[:]{6.25}*U.cmLengths across the z axis [L]
    Assumptions
    Included transport axes
    BooleaninclTransYfalseY
    BooleaninclTransZfalseZ

    Connectors

    TypeNameDescription
    BoundaryBusxNegative[n_y, n_z]Negative boundary along the x axis
    BoundaryBusxPositive[n_y, n_z]Positive boundary along the x axis
    BoundaryBusyNegative[n_x, n_z]Negative boundary along the y axis
    BoundaryBusyPositive[n_x, n_z]Positive boundary along the y axis
    BoundaryBuszNegative[n_x, n_y]Negative boundary along the z axis
    BoundaryBuszPositive[n_x, n_y]Positive boundary along the z axis

    Modelica definition

    model DuPontN115 "DuPontTM Nafion® N-115"
      extends PEM(L_x={127*U.um},Subregion(ionomer('H+'(sigma=0.083*U.S/U.cm))));
      // Additional properties not yet incorporated [DuPont2004N] and [DuPont2005]:
      //     Density:  (250 g/m2)/(127 um) = 1.9685 g/cm3
    
    end DuPontN115;
    

    FCSys.Regions.PEMs.DuPontN117 FCSys.Regions.PEMs.DuPontN117

    DuPontTM Nafion® N-117 FCSys.Regions.PEMs.DuPontN117

    Information

    The default properties are based on [DuPont2004N].

    For more information, please see the PEM model.

    Extends from PEM (Proton exchange membrane).

    Parameters

    TypeNameDefaultDescription
    Geometry
    LengthL_x[:]{183*U.um}Lengths along the x axis [L]
    LengthL_y[:]{8}*U.cmLengths along the y axis [L]
    LengthL_z[:]{6.25}*U.cmLengths across the z axis [L]
    Assumptions
    Included transport axes
    BooleaninclTransYfalseY
    BooleaninclTransZfalseZ

    Connectors

    TypeNameDescription
    BoundaryBusxNegative[n_y, n_z]Negative boundary along the x axis
    BoundaryBusxPositive[n_y, n_z]Positive boundary along the x axis
    BoundaryBusyNegative[n_x, n_z]Negative boundary along the y axis
    BoundaryBusyPositive[n_x, n_z]Positive boundary along the y axis
    BoundaryBuszNegative[n_x, n_y]Negative boundary along the z axis
    BoundaryBuszPositive[n_x, n_y]Positive boundary along the z axis

    Modelica definition

    model DuPontN117 "DuPontTM Nafion® N-117"
      extends PEM(L_x={183*U.um},Subregion(ionomer('H+'(sigma=0.083*U.S/U.cm))));
      // Additional properties not yet incorporated [DuPont2004N] and [DuPont2005]:
      //     Density:  (360 g/m2)/(183 um) = 1.9672 g/cm3
    
    end DuPontN117;
    

    FCSys.Regions.PEMs.DuPontNE1110 FCSys.Regions.PEMs.DuPontNE1110

    DuPontTM Nafion® NE-1110 FCSys.Regions.PEMs.DuPontNE1110

    Information

    The default properties are based on [DuPont2004N].

    For more information, please see the PEM model.

    Extends from PEM (Proton exchange membrane).

    Parameters

    TypeNameDefaultDescription
    Geometry
    LengthL_x[:]{254*U.um}Lengths along the x axis [L]
    LengthL_y[:]{8}*U.cmLengths along the y axis [L]
    LengthL_z[:]{6.25}*U.cmLengths across the z axis [L]
    Assumptions
    Included transport axes
    BooleaninclTransYfalseY
    BooleaninclTransZfalseZ

    Connectors

    TypeNameDescription
    BoundaryBusxNegative[n_y, n_z]Negative boundary along the x axis
    BoundaryBusxPositive[n_y, n_z]Positive boundary along the x axis
    BoundaryBusyNegative[n_x, n_z]Negative boundary along the y axis
    BoundaryBusyPositive[n_x, n_z]Positive boundary along the y axis
    BoundaryBuszNegative[n_x, n_y]Negative boundary along the z axis
    BoundaryBuszPositive[n_x, n_y]Positive boundary along the z axis

    Modelica definition

    model DuPontNE1110 
      "DuPontTM Nafion® NE-1110"
      extends PEM(L_x={254*U.um},Subregion(ionomer('H+'(sigma=0.083*U.S/U.cm))));
      // Additional properties not yet incorporated [DuPont2004N] and [DuPont2005]:
      //     Density:  (500 g/m2)/(254 um) = 1.9685 g/cm3
    
    end DuPontNE1110;
    

    FCSys.Regions.PEMs.DuPontNE1135 FCSys.Regions.PEMs.DuPontNE1135

    DuPontTM Nafion® NE-1135 FCSys.Regions.PEMs.DuPontNE1135

    Information

    The default properties are based on [DuPont2004N].

    For more information, please see the PEM model.

    Extends from PEM (Proton exchange membrane).

    Parameters

    TypeNameDefaultDescription
    Geometry
    LengthL_x[:]{89*U.um}Lengths along the x axis [L]
    LengthL_y[:]{8}*U.cmLengths along the y axis [L]
    LengthL_z[:]{6.25}*U.cmLengths across the z axis [L]
    Assumptions
    Included transport axes
    BooleaninclTransYfalseY
    BooleaninclTransZfalseZ

    Connectors

    TypeNameDescription
    BoundaryBusxNegative[n_y, n_z]Negative boundary along the x axis
    BoundaryBusxPositive[n_y, n_z]Positive boundary along the x axis
    BoundaryBusyNegative[n_x, n_z]Negative boundary along the y axis
    BoundaryBusyPositive[n_x, n_z]Positive boundary along the y axis
    BoundaryBuszNegative[n_x, n_y]Negative boundary along the z axis
    BoundaryBuszPositive[n_x, n_y]Positive boundary along the z axis

    Modelica definition

    model DuPontNE1135 
      "DuPontTM Nafion® NE-1135"
      extends PEM(L_x={89*U.um},Subregion(ionomer('H+'(sigma=0.083*U.S/U.cm))));
      // Additional properties not yet incorporated [DuPont2004N] and [DuPont2005]:
      //     Density:  (190 g/m2)/(89 um) = 2.1348 g/cm3
    
    end DuPontNE1135;
    

    FCSys.Regions.PEMs.DuPontNRE211 FCSys.Regions.PEMs.DuPontNRE211

    DuPontTM Nafion® NRE-1110 FCSys.Regions.PEMs.DuPontNRE211

    Information

    The default properties are based on [DuPont2004N], except that the default value of protonic conductivity (σ = 0.083*U.S/U.cm) is for the DuPontTM Nafion® N and NE series [DuPont2004N]. It is not listed for DuPontTM Nafion® NRE-211 in [DuPont2004NRE].

    For more information, please see the PEM model.

    Extends from PEM (Proton exchange membrane).

    Parameters

    TypeNameDefaultDescription
    Geometry
    LengthL_x[:]{25.4*U.um}Lengths along the x axis [L]
    LengthL_y[:]{8}*U.cmLengths along the y axis [L]
    LengthL_z[:]{6.25}*U.cmLengths across the z axis [L]
    Assumptions
    Included transport axes
    BooleaninclTransYfalseY
    BooleaninclTransZfalseZ

    Connectors

    TypeNameDescription
    BoundaryBusxNegative[n_y, n_z]Negative boundary along the x axis
    BoundaryBusxPositive[n_y, n_z]Positive boundary along the x axis
    BoundaryBusyNegative[n_x, n_z]Negative boundary along the y axis
    BoundaryBusyPositive[n_x, n_z]Positive boundary along the y axis
    BoundaryBuszNegative[n_x, n_y]Negative boundary along the z axis
    BoundaryBuszPositive[n_x, n_y]Positive boundary along the z axis

    Modelica definition

    model DuPontNRE211 
      "DuPontTM Nafion® NRE-1110"
      extends PEM(L_x={25.4*U.um},Subregion(ionomer('H+'(sigma=0.083*U.S/U.cm))));
      // Additional properties not yet incorporated [DuPont2004NRE]:
      //     Density:  (50 g/m2)/(25.4 um) = 1.9685 g/cm3
    
    end DuPontNRE211;
    

    FCSys.Regions.PEMs.DuPontNRE212 FCSys.Regions.PEMs.DuPontNRE212

    DuPontTM Nafion® NRE-1110 FCSys.Regions.PEMs.DuPontNRE212

    Information

    The default properties are based on [DuPont2004N], except that the default value of protonic conductivity (σ = 0.083*U.S/U.cm) is for the DuPontTM Nafion® N and NE series [DuPont2004N]. It is not listed for DuPontTM Nafion® NRE-212 in [DuPont2004NRE].

    For more information, please see the PEM model.

    Extends from PEM (Proton exchange membrane).

    Parameters

    TypeNameDefaultDescription
    Geometry
    LengthL_x[:]{50.8*U.um}Lengths along the x axis [L]
    LengthL_y[:]{8}*U.cmLengths along the y axis [L]
    LengthL_z[:]{6.25}*U.cmLengths across the z axis [L]
    Assumptions
    Included transport axes
    BooleaninclTransYfalseY
    BooleaninclTransZfalseZ

    Connectors

    TypeNameDescription
    BoundaryBusxNegative[n_y, n_z]Negative boundary along the x axis
    BoundaryBusxPositive[n_y, n_z]Positive boundary along the x axis
    BoundaryBusyNegative[n_x, n_z]Negative boundary along the y axis
    BoundaryBusyPositive[n_x, n_z]Positive boundary along the y axis
    BoundaryBuszNegative[n_x, n_y]Negative boundary along the z axis
    BoundaryBuszPositive[n_x, n_y]Positive boundary along the z axis

    Modelica definition

    model DuPontNRE212 
      "DuPontTM Nafion® NRE-1110"
      extends PEM(L_x={50.8*U.um},Subregion(ionomer('H+'(sigma=0.083*U.S/U.cm))));
      // Additional properties not yet incorporated [DuPont2004NRE]:
      //     Density:  (100 g/m2)/(50.8 um) = 1.9685 g/cm3
    
    end DuPontNRE212;