FCSys.Regions.PEMs

Proton exchange membranes

Information

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

Package Content

Name	Description
PEM	Proton exchange membrane
DuPontN112	DuPont^TM Nafion® N-112
DuPontN115	DuPont^TM Nafion® N-115
DuPontN117	DuPont^TM Nafion® N-117
DuPontNE1110	DuPont^TM Nafion® NE-1110
DuPontNE1135	DuPont^TM Nafion® NE-1135
DuPontNRE211	DuPont^TM Nafion® NRE-1110
DuPontNRE212	DuPont^TM Nafion® NRE-1110

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:

There are no pores in the PEM. All H₂O is absorbed into the ionomer itself.
There is no cross-over of the reactant gases.

For more information, please see the Region model.

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

Parameters

Type Name Default Description

replaceable model Subregion FCSys.Subregions.SubregionIo… Base subregion model

Geometry

Length L_x[:] {40}*U.um Lengths along the x axis [L]

Length L_y[:] {8}*U.cm Lengths along the y axis [L]

Length L_z[:] {6.25}*U.cm Lengths across the z axis [L]

Assumptions

Included transport axes

Boolean inclTransX true X

Boolean inclTransY false Y

Boolean inclTransZ false Z

Type	Name	Default	Description
replaceable model Subregion	FCSys.Subregions.SubregionIo…	Base subregion model
Geometry
Length	L_x[:]	{40}*U.um	Lengths along the x axis [L]
Length	L_y[:]	{8}*U.cm	Lengths along the y axis [L]
Length	L_z[:]	{6.25}*U.cm	Lengths across the z axis [L]
Assumptions
Included transport axes
Boolean	inclTransX	true	X
Boolean	inclTransY	false	Y
Boolean	inclTransZ	false	Z

Connectors

Type Name Description

replaceable model Subregion Base subregion model

BoundaryBus xNegative[n_y, n_z] Negative boundary along the x axis

BoundaryBus xPositive[n_y, n_z] Positive boundary along the x axis

BoundaryBus yNegative[n_x, n_z] Negative boundary along the y axis

BoundaryBus yPositive[n_x, n_z] Positive boundary along the y axis

BoundaryBus zNegative[n_x, n_y] Negative boundary along the z axis

BoundaryBus zPositive[n_x, n_y] Positive boundary along the z axis

Type	Name	Description
replaceable model Subregion	Base subregion model
BoundaryBus	xNegative[n_y, n_z]	Negative boundary along the x axis
BoundaryBus	xPositive[n_y, n_z]	Positive boundary along the x axis
BoundaryBus	yNegative[n_x, n_z]	Negative boundary along the y axis
BoundaryBus	yPositive[n_x, n_z]	Positive boundary along the y axis
BoundaryBus	zNegative[n_x, n_y]	Negative boundary along the z axis
BoundaryBus	zPositive[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={40}*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=0.1*U.S/U.cm),
          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

DuPont^TM 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

Type Name Default Description

Geometry

Length L_x[:] {51*U.um} Lengths along the x axis [L]

Length L_y[:] {8}*U.cm Lengths along the y axis [L]

Length L_z[:] {6.25}*U.cm Lengths across the z axis [L]

Assumptions

Included transport axes

Boolean inclTransY false Y

Boolean inclTransZ false Z

Type	Name	Default	Description
Geometry
Length	L_x[:]	{51*U.um}	Lengths along the x axis [L]
Length	L_y[:]	{8}*U.cm	Lengths along the y axis [L]
Length	L_z[:]	{6.25}*U.cm	Lengths across the z axis [L]
Assumptions
Included transport axes
Boolean	inclTransY	false	Y
Boolean	inclTransZ	false	Z

Connectors

Type Name Description

BoundaryBus xNegative[n_y, n_z] Negative boundary along the x axis

BoundaryBus xPositive[n_y, n_z] Positive boundary along the x axis

BoundaryBus yNegative[n_x, n_z] Negative boundary along the y axis

BoundaryBus yPositive[n_x, n_z] Positive boundary along the y axis

BoundaryBus zNegative[n_x, n_y] Negative boundary along the z axis

BoundaryBus zPositive[n_x, n_y] Positive boundary along the z axis

Type	Name	Description
BoundaryBus	xNegative[n_y, n_z]	Negative boundary along the x axis
BoundaryBus	xPositive[n_y, n_z]	Positive boundary along the x axis
BoundaryBus	yNegative[n_x, n_z]	Negative boundary along the y axis
BoundaryBus	yPositive[n_x, n_z]	Positive boundary along the y axis
BoundaryBus	zNegative[n_x, n_y]	Negative boundary along the z axis
BoundaryBus	zPositive[n_x, n_y]	Positive boundary along the z axis

Modelica definition

model DuPontN112 "DuPont^TM 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

DuPont^TM 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

Type Name Default Description

Geometry

Length L_x[:] {127*U.um} Lengths along the x axis [L]

Length L_y[:] {8}*U.cm Lengths along the y axis [L]

Length L_z[:] {6.25}*U.cm Lengths across the z axis [L]

Assumptions

Included transport axes

Boolean inclTransY false Y

Boolean inclTransZ false Z

Type	Name	Default	Description
Geometry
Length	L_x[:]	{127*U.um}	Lengths along the x axis [L]
Length	L_y[:]	{8}*U.cm	Lengths along the y axis [L]
Length	L_z[:]	{6.25}*U.cm	Lengths across the z axis [L]
Assumptions
Included transport axes
Boolean	inclTransY	false	Y
Boolean	inclTransZ	false	Z

Connectors

Type	Name	Description
BoundaryBus	xNegative[n_y, n_z]	Negative boundary along the x axis
BoundaryBus	xPositive[n_y, n_z]	Positive boundary along the x axis
BoundaryBus	yNegative[n_x, n_z]	Negative boundary along the y axis
BoundaryBus	yPositive[n_x, n_z]	Positive boundary along the y axis
BoundaryBus	zNegative[n_x, n_y]	Negative boundary along the z axis
BoundaryBus	zPositive[n_x, n_y]	Positive boundary along the z axis

Modelica definition

model DuPontN115 "DuPont^TM 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

DuPont^TM 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

Type Name Default Description

Geometry

Length L_x[:] {183*U.um} Lengths along the x axis [L]

Length L_y[:] {8}*U.cm Lengths along the y axis [L]

Length L_z[:] {6.25}*U.cm Lengths across the z axis [L]

Assumptions

Included transport axes

Boolean inclTransY false Y

Boolean inclTransZ false Z

Type	Name	Default	Description
Geometry
Length	L_x[:]	{183*U.um}	Lengths along the x axis [L]
Length	L_y[:]	{8}*U.cm	Lengths along the y axis [L]
Length	L_z[:]	{6.25}*U.cm	Lengths across the z axis [L]
Assumptions
Included transport axes
Boolean	inclTransY	false	Y
Boolean	inclTransZ	false	Z

Connectors

Type	Name	Description
BoundaryBus	xNegative[n_y, n_z]	Negative boundary along the x axis
BoundaryBus	xPositive[n_y, n_z]	Positive boundary along the x axis
BoundaryBus	yNegative[n_x, n_z]	Negative boundary along the y axis
BoundaryBus	yPositive[n_x, n_z]	Positive boundary along the y axis
BoundaryBus	zNegative[n_x, n_y]	Negative boundary along the z axis
BoundaryBus	zPositive[n_x, n_y]	Positive boundary along the z axis

Modelica definition

model DuPontN117 "DuPont^TM 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

DuPont^TM 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

Type Name Default Description

Geometry

Length L_x[:] {254*U.um} Lengths along the x axis [L]

Length L_y[:] {8}*U.cm Lengths along the y axis [L]

Length L_z[:] {6.25}*U.cm Lengths across the z axis [L]

Assumptions

Included transport axes

Boolean inclTransY false Y

Boolean inclTransZ false Z

Type	Name	Default	Description
Geometry
Length	L_x[:]	{254*U.um}	Lengths along the x axis [L]
Length	L_y[:]	{8}*U.cm	Lengths along the y axis [L]
Length	L_z[:]	{6.25}*U.cm	Lengths across the z axis [L]
Assumptions
Included transport axes
Boolean	inclTransY	false	Y
Boolean	inclTransZ	false	Z

Connectors

Type	Name	Description
BoundaryBus	xNegative[n_y, n_z]	Negative boundary along the x axis
BoundaryBus	xPositive[n_y, n_z]	Positive boundary along the x axis
BoundaryBus	yNegative[n_x, n_z]	Negative boundary along the y axis
BoundaryBus	yPositive[n_x, n_z]	Positive boundary along the y axis
BoundaryBus	zNegative[n_x, n_y]	Negative boundary along the z axis
BoundaryBus	zPositive[n_x, n_y]	Positive boundary along the z axis

Modelica definition

model DuPontNE1110 
  "DuPont^TM 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

DuPont^TM 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

Type Name Default Description

Geometry

Length L_x[:] {89*U.um} Lengths along the x axis [L]

Length L_y[:] {8}*U.cm Lengths along the y axis [L]

Length L_z[:] {6.25}*U.cm Lengths across the z axis [L]

Assumptions

Included transport axes

Boolean inclTransY false Y

Boolean inclTransZ false Z

Type	Name	Default	Description
Geometry
Length	L_x[:]	{89*U.um}	Lengths along the x axis [L]
Length	L_y[:]	{8}*U.cm	Lengths along the y axis [L]
Length	L_z[:]	{6.25}*U.cm	Lengths across the z axis [L]
Assumptions
Included transport axes
Boolean	inclTransY	false	Y
Boolean	inclTransZ	false	Z

Connectors

Type	Name	Description
BoundaryBus	xNegative[n_y, n_z]	Negative boundary along the x axis
BoundaryBus	xPositive[n_y, n_z]	Positive boundary along the x axis
BoundaryBus	yNegative[n_x, n_z]	Negative boundary along the y axis
BoundaryBus	yPositive[n_x, n_z]	Positive boundary along the y axis
BoundaryBus	zNegative[n_x, n_y]	Negative boundary along the z axis
BoundaryBus	zPositive[n_x, n_y]	Positive boundary along the z axis

Modelica definition

model DuPontNE1135 
  "DuPont^TM 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

DuPont^TM 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 DuPont^TM Nafion® N and NE series [DuPont2004N]. It is not listed for DuPont^TM Nafion® NRE-211 in [DuPont2004NRE].

For more information, please see the PEM model.

Extends from PEM (Proton exchange membrane).

Parameters

Type Name Default Description

Geometry

Length L_x[:] {25.4*U.um} Lengths along the x axis [L]

Length L_y[:] {8}*U.cm Lengths along the y axis [L]

Length L_z[:] {6.25}*U.cm Lengths across the z axis [L]

Assumptions

Included transport axes

Boolean inclTransY false Y

Boolean inclTransZ false Z

Type	Name	Default	Description
Geometry
Length	L_x[:]	{25.4*U.um}	Lengths along the x axis [L]
Length	L_y[:]	{8}*U.cm	Lengths along the y axis [L]
Length	L_z[:]	{6.25}*U.cm	Lengths across the z axis [L]
Assumptions
Included transport axes
Boolean	inclTransY	false	Y
Boolean	inclTransZ	false	Z

Connectors

Type	Name	Description
BoundaryBus	xNegative[n_y, n_z]	Negative boundary along the x axis
BoundaryBus	xPositive[n_y, n_z]	Positive boundary along the x axis
BoundaryBus	yNegative[n_x, n_z]	Negative boundary along the y axis
BoundaryBus	yPositive[n_x, n_z]	Positive boundary along the y axis
BoundaryBus	zNegative[n_x, n_y]	Negative boundary along the z axis
BoundaryBus	zPositive[n_x, n_y]	Positive boundary along the z axis

Modelica definition

model DuPontNRE211 
  "DuPont^TM 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

DuPont^TM Nafion® NRE-1110 FCSys.Regions.PEMs.DuPontNRE212

Information

For more information, please see the PEM model.

Extends from PEM (Proton exchange membrane).

Parameters

Type Name Default Description

Geometry

Length L_x[:] {50.8*U.um} Lengths along the x axis [L]

Length L_y[:] {8}*U.cm Lengths along the y axis [L]

Length L_z[:] {6.25}*U.cm Lengths across the z axis [L]

Assumptions

Included transport axes

Boolean inclTransY false Y

Boolean inclTransZ false Z

Type	Name	Default	Description
Geometry
Length	L_x[:]	{50.8*U.um}	Lengths along the x axis [L]
Length	L_y[:]	{8}*U.cm	Lengths along the y axis [L]
Length	L_z[:]	{6.25}*U.cm	Lengths across the z axis [L]
Assumptions
Included transport axes
Boolean	inclTransY	false	Y
Boolean	inclTransZ	false	Z

Connectors

Type	Name	Description
BoundaryBus	xNegative[n_y, n_z]	Negative boundary along the x axis
BoundaryBus	xPositive[n_y, n_z]	Positive boundary along the x axis
BoundaryBus	yNegative[n_x, n_z]	Negative boundary along the y axis
BoundaryBus	yPositive[n_x, n_z]	Positive boundary along the y axis
BoundaryBus	zNegative[n_x, n_y]	Negative boundary along the z axis
BoundaryBus	zPositive[n_x, n_y]	Positive boundary along the z axis

Modelica definition

model DuPontNRE212 
  "DuPont^TM 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;

FCSys

Table of Contents

Download

FCSys.Regions.PEMs

Information

Package Content

FCSys.Regions.PEMs.PEM

Information

Parameters

Connectors

Modelica definition

FCSys.Regions.PEMs.DuPontN112

Information

Parameters

Connectors

Modelica definition

FCSys.Regions.PEMs.DuPontN115

Information

Parameters

Connectors

Modelica definition

FCSys.Regions.PEMs.DuPontN117

Information

Parameters

Connectors

Modelica definition

FCSys.Regions.PEMs.DuPontNE1110

Information

Parameters

Connectors

Modelica definition

FCSys.Regions.PEMs.DuPontNE1135

Information

Parameters

Connectors

Modelica definition

FCSys.Regions.PEMs.DuPontNRE211

Information

Parameters

Connectors

Modelica definition

FCSys.Regions.PEMs.DuPontNRE212

Information

Parameters

Connectors

Modelica definition