FCSys.Subregions.Examples

Examples

Information

Extends from Modelica.Icons.ExamplesPackage (Icon for packages containing runnable examples).

Package Content

Name	Description
PhaseChange	Examples of phase change
Reactions	Examples of phase change
AirColumn	Gas in a vertical array of subregions, affected by gravity
BinaryDiffusion	Pressure-driven flow of H₂, dragging H₂O
Echo	Two regions of gas with an initial pressure difference
EchoCentral	Two regions of gas with an initial pressure difference, with central difference scheme
ElectricalConduction	Migration of e^- through C⁺
InternalFlow	Internal, laminar flow of liquid water
Subregion	Single subregion, with H₂ by default
Subregions	Horizontal array of subregions with an initial pressure difference (H₂ included by default)
ThermalConduction	Thermal conduction (through solid)
ThermalConductionConvection	Thermal conduction through a solid alongside conduction and convection through a gas

FCSys.Subregions.Examples.AirColumn

Gas in a vertical array of subregions, affected by gravity FCSys.Subregions.Examples.AirColumn

Information

This is a model of a vertical column of 10 × 10 × 10 m regions with N₂ gas. The upper boundary is held at 1 bar and the lower boundary has zero velocity. The initial pressure difference is zero, but a gas enters the upper boundary and a pressure difference develops due to gravity. There are oscillations due to the inertance and compression of the gas. After about 1.5 s, the pressure difference settles to L_y a_y m ρ as expected.

A temperature gradient is created due to the thermodynamics of the expanding and contracting gases. It takes much longer (over a year!) for the temperatures to equalize due to the size of the system and the low thermal conductivity of the gas. With a stiff solver, the model should simulate at this time scale as well.

The damping factor (k) can be used to scale the continuity (ζ) of the gas in the regions. The oscillations are dampened considerably at k = 100. However, with high values of the factor, the boundary pressures are decoupled from the pressures in the region because the nonequilibrium force is considerable.

Assumptions:

The central difference scheme is used (no upstream discretization).

Extends from Modelica.Icons.Example (Icon for runnable examples).

Parameters

Type Name Default Description

Integer n_y 3 Number of discrete subregions along the y axis, besides the 2 boundary subregions

Pressure Deltap_IC 0 Initial pressure difference [M/(L.T2)]

NumberAbsolute k 5 Damping factor [1]

Type	Name	Default	Description
Integer	n_y	3	Number of discrete subregions along the y axis, besides the 2 boundary subregions
Pressure	Deltap_IC	0	Initial pressure difference [M/(L.T2)]
NumberAbsolute	k	5	Damping factor [1]

Modelica definition

model AirColumn 
  "Gas in a vertical array of subregions, affected by gravity"
  import FCSys.Utilities.round;
  extends Modelica.Icons.Example;

  parameter Integer n_y=3 
    "Number of discrete subregions along the y axis, besides the 2 boundary subregions";
  parameter Q.Pressure Deltap_IC=0 "Initial pressure difference";

  output Q.Pressure Deltap=subregion2.gas.N2.p - subregion1.gas.N2.p 
    "Measured pressure difference";
  output Q.Pressure Deltap_ex=-(n_y + 1)*10*U.m*environment.a[Axis.y]*
      Characteristics.N2.Gas.m*subregions[round(n_y/2)].gas.N2.rho 
    "Expected pressure difference";

  parameter Q.NumberAbsolute k=5 "Damping factor";

  inner Conditions.Environment environment(p=U.bar);
  FCSys.Subregions.Subregion subregion1(
    L={10,10,10}*U.m,
    inclTransX=false,
    inclTransY=true,
    inclTransZ=false,
    gas(inclN2=true, N2(
        zeta=k*FCSys.Characteristics.H2.Gas.zeta(),
        p_IC=environment.p - Deltap_IC/2,
        upstreamY=false)));

  FCSys.Subregions.Subregion subregions[n_y](
    each L={10,10,10}*U.m,
    each inclTransZ=false,
    gas(each inclN2=true, N2(
        each zeta=k*FCSys.Characteristics.H2.Gas.zeta(),
        p_IC={environment.p - Deltap_IC/2 - i*Deltap_IC/(n_y + 1) for i in 1:
            n_y},
        each upstreamY=false)),
    each inclTransX=false,
    each inclTransY=true) if n_y > 0;

  FCSys.Subregions.Subregion subregion2(
    L={10,10,10}*U.m,
    inclTransZ=false,
    inclTransX=false,
    inclTransY=true,
    gas(inclN2=true, N2(
        zeta=k*FCSys.Characteristics.H2.Gas.zeta(),
        p_IC=environment.p + Deltap_IC/2,
        upstreamY=false)));

  Conditions.ByConnector.BoundaryBus.Single.Sink BC(gas(inclN2=true, N2(
          materialSet(y=environment.p))));

equation 
  connect(subregion1.yPositive, subregions[1].yNegative);

  for i in 1:n_y - 1 loop
    connect(subregions[1:n_y - 1].yPositive, subregions[2:n_y].yNegative) 
      "Not shown in the diagram";
  end for;
  if n_y == 0 then
    connect(subregion1.yPositive, subregion2.yNegative) 
      "Not shown in the diagram";
  end if;
  connect(subregions[n_y].yPositive, subregion2.yNegative);

  connect(BC.boundary, subregion2.yPositive);
end AirColumn;

FCSys.Subregions.Examples.BinaryDiffusion

Pressure-driven flow of H₂, dragging H₂O FCSys.Subregions.Examples.BinaryDiffusion

Information

Extends from Subregion (Single subregion, with H₂ by default).

Parameters

Type Name Default Description

Species

Boolean 'inclC+' true Carbon plus (C⁺)

Boolean 'inclSO3-' false Nafion sulfonate (C₁₉HF₃₇O₅S^-, abbreviated as SO₃^-)

Boolean 'incle-' false Electrons (e^-)

Boolean 'inclH+' false Protons (H⁺)

Boolean inclH2 true Hydrogen (H₂)

Boolean inclH2O true Water vapor (H₂O)

Boolean inclN2 false Nitrogen (N₂)

Boolean inclO2 false Oxygen (O₂)

Type	Name	Default	Description
Species
Boolean	'inclC+'	true	Carbon plus (C⁺)
Boolean	'inclSO3-'	false	Nafion sulfonate (C₁₉HF₃₇O₅S^-, abbreviated as SO₃^-)
Boolean	'incle-'	false	Electrons (e^-)
Boolean	'inclH+'	false	Protons (H⁺)
Boolean	inclH2	true	Hydrogen (H₂)
Boolean	inclH2O	true	Water vapor (H₂O)
Boolean	inclN2	false	Nitrogen (N₂)
Boolean	inclO2	false	Oxygen (O₂)

Modelica definition

model BinaryDiffusion 
  "Pressure-driven flow of H₂, dragging H₂O"
  extends Subregion(
    inclH2O=true,
    'inclC+'=true,
    subregion(common(k_Phi={1e-5,1e-5,1e-5}),gas(
        common(k_Phi={1e4,1e4,1e4}),
        H2(T(stateSelect=StateSelect.always), phi(each stateSelect=StateSelect.always)),

        H2O(initEnergy=Init.none, boundaries(Ndot(each stateSelect=StateSelect.always))))),

    environment(RH=0.6));

  Conditions.ByConnector.BoundaryBus.Single.Source source(gas(
      inclH2=true,
      inclH2O=true,
      H2(
        thermalSet(y=environment.T),
        redeclare function materialSpec = Conditions.ByConnector.Boundary.Single.Material.pressure,

        redeclare Modelica.Blocks.Sources.Ramp materialSet(
          height=-U.Pa,
          offset=environment.p_dry,
          duration=10)),
      H2O(
        redeclare function materialSpec = Conditions.ByConnector.Boundary.Single.Material.pressure,

        materialSet(y=environment.p_H2O),
        thermalSet(y=environment.T))));

  Conditions.ByConnector.BoundaryBus.Single.Source sink(gas(
      inclH2=true,
      inclH2O=true,
      H2(materialSet(y=-source.gas.H2.boundary.Ndot), thermalSet(y=environment.T)),

      H2O(
        redeclare function materialSpec = Conditions.ByConnector.Boundary.Single.Material.pressure,

        materialSet(y=environment.p_H2O),
        thermalSet(y=environment.T))));

equation 
  connect(source.boundary, subregion.xNegative);
  connect(subregion.xPositive, sink.boundary);
end BinaryDiffusion;

FCSys.Subregions.Examples.Echo

Two regions of gas with an initial pressure difference FCSys.Subregions.Examples.Echo

Information

Extends from Subregions (Horizontal array of subregions with an initial pressure difference (H₂ included by default)).

Parameters

Type Name Default Description

NumberAbsolute k 1 Damping factor [1]

Integer n_x 0 Number of discrete subregions along the x axis, besides the 2 side subregions

Pressure Deltap_IC -100*U.Pa Initial pressure difference [M/(L.T2)]

Species

Boolean 'inclC+' false Carbon plus (C⁺)

Boolean 'inclSO3-' false Nafion sulfonate (C₁₉HF₃₇O₅S)

Boolean 'incle-' false Electrons (e^-)

Boolean 'inclH+' false Protons (H⁺)

Boolean inclH2 true Hydrogen (H₂)

Boolean inclH2O false Water vapor (H₂O)

Boolean inclN2 false Nitrogen (N₂)

Boolean inclO2 false Oxygen (O₂)

Type	Name	Default	Description
NumberAbsolute	k	1	Damping factor [1]
Integer	n_x	0	Number of discrete subregions along the x axis, besides the 2 side subregions
Pressure	Deltap_IC	-100*U.Pa	Initial pressure difference [M/(L.T2)]
Species
Boolean	'inclC+'	false	Carbon plus (C⁺)
Boolean	'inclSO3-'	false	Nafion sulfonate (C₁₉HF₃₇O₅S)
Boolean	'incle-'	false	Electrons (e^-)
Boolean	'inclH+'	false	Protons (H⁺)
Boolean	inclH2	true	Hydrogen (H₂)
Boolean	inclH2O	false	Water vapor (H₂O)
Boolean	inclN2	false	Nitrogen (N₂)
Boolean	inclO2	false	Oxygen (O₂)

Modelica definition

model Echo "Two regions of gas with an initial pressure difference"
  parameter Q.NumberAbsolute k=1 "Damping factor";

  extends Subregions(subregion1(gas(H2(zeta=k*Characteristics.H2.Gas.zeta()))),
      subregion2(gas(H2(zeta=k*FCSys.Characteristics.H2.Gas.zeta()))));

end Echo;

FCSys.Subregions.Examples.EchoCentral

Two regions of gas with an initial pressure difference, with central difference scheme FCSys.Subregions.Examples.EchoCentral

Information

Extends from Echo (Two regions of gas with an initial pressure difference).

Parameters

Type	Name	Default	Description
NumberAbsolute	k	1	Damping factor [1]
Integer	n_x	0	Number of discrete subregions along the x axis, besides the 2 side subregions
Pressure	Deltap_IC	-100*U.Pa	Initial pressure difference [M/(L.T2)]
Species
Boolean	'inclC+'	false	Carbon plus (C⁺)
Boolean	'inclSO3-'	false	Nafion sulfonate (C₁₉HF₃₇O₅S)
Boolean	'incle-'	false	Electrons (e^-)
Boolean	'inclH+'	false	Protons (H⁺)
Boolean	inclH2	true	Hydrogen (H₂)
Boolean	inclH2O	false	Water vapor (H₂O)
Boolean	inclN2	false	Nitrogen (N₂)
Boolean	inclO2	false	Oxygen (O₂)

Modelica definition

model EchoCentral 
  "Two regions of gas with an initial pressure difference, with central difference scheme"
  extends Echo(
    subregion1(gas(
        H2(upstreamX=false),
        H2O(upstreamX=false),
        N2(upstreamX=false),
        O2(upstreamX=false))),
    subregions(gas(
        H2(each upstreamX=false),
        H2O(each upstreamX=false),
        N2(each upstreamX=false),
        O2(each upstreamX=false))),
    subregion2(gas(
        H2(upstreamX=false),
        H2O(upstreamX=false),
        N2(upstreamX=false),
        O2(upstreamX=false))));

end EchoCentral;

FCSys.Subregions.Examples.ElectricalConduction

Migration of e^- through C⁺ FCSys.Subregions.Examples.ElectricalConduction

Information

This is an example of Ohm's law. The 1 cm × 1 mm × 1 mm subregion contains carbon (C⁺) and electrons. An electrical current of 50 mA (5 A/cm²) is delivered into the negative boundary and exits the positive boundary. Due to the finite mobility of the electrons a force is required to support the current; this maps directly to electrical potential. The example shows that the measured resistance is R = L/(A ρ μ) as expected, where ρ is electronic density and μ is electronic mobility.

The measured rate of heat generation (subregion.graphite.'e-'.Edot_DT) is equal to P = (zI)² R as expected, where zI = 50 mA is the electrical current. This heat is conducted through the carbon to the boundaries, which are held at 25 °C. The measured steady state temperature is T = T₀ + θ L P/(4 A) as expected, where T₀ = 25 °C is the boundary temperature and θ is the thermal resistance. The factor of one fourth is due to the boundary conditions; the conduction length is half of the total length and the heat is rejected to both sides. There is no thermal convection or radiation—only conduction to the sides.

Extends from Examples.Subregion (Single subregion, with H₂ by default).

Parameters

Type Name Default Description

Species

Boolean 'inclC+' true Carbon plus (C⁺)

Boolean 'inclSO3-' false Nafion sulfonate (C₁₉HF₃₇O₅S^-, abbreviated as SO₃^-)

Boolean 'incle-' true Electrons (e^-)

Boolean 'inclH+' false Protons (H⁺)

Boolean inclH2 false Hydrogen (H₂)

Boolean inclH2O false Water vapor (H₂O)

Boolean inclN2 false Nitrogen (N₂)

Boolean inclO2 false Oxygen (O₂)

Type	Name	Default	Description
Species
Boolean	'inclC+'	true	Carbon plus (C⁺)
Boolean	'inclSO3-'	false	Nafion sulfonate (C₁₉HF₃₇O₅S^-, abbreviated as SO₃^-)
Boolean	'incle-'	true	Electrons (e^-)
Boolean	'inclH+'	false	Protons (H⁺)
Boolean	inclH2	false	Hydrogen (H₂)
Boolean	inclH2O	false	Water vapor (H₂O)
Boolean	inclN2	false	Nitrogen (N₂)
Boolean	inclO2	false	Oxygen (O₂)

Modelica definition

model ElectricalConduction 
  "Migration of e^- through C⁺"

  output Q.Potential w=subregion.graphite.'e-'.Deltag[1] "Electrical potential";
  output Q.Current zI=-subregion.graphite.'e-'.I[1] "Electrical current";
  output Q.ResistanceElectrical R=w/zI "Measured electrical resistance";
  output Q.ResistanceElectrical R_ex=subregion.L[Axis.x]/(subregion.graphite.
      'e-'.sigma*subregion.A[Axis.x]) "Expected electrical resistance";
  output Q.Power P=subregion.graphite.'e-'.Edot_AT 
    "Measured rate of heat generation";
  output Q.Power P_ex=zI^2*R "Expected rate of heat generation";
  output Q.TemperatureAbsolute T=subregion.graphite.'C+'.T 
    "Measured temperature";
  output Q.TemperatureAbsolute T_ex=environment.T + subregion.graphite.'C+'.theta
      *U.cm*P/(4*subregion.A[Axis.x]) "Expected temperature";

  extends Examples.Subregion(
    'inclC+'=true,
    'incle-'=true,
    inclH2=false,
    subregion(L={U.cm,U.mm,U.mm}, graphite('C+'(epsilon=1),'e-'(sigma=1e2*U.S/U.m))));

  Conditions.ByConnector.BoundaryBus.Single.Source BC1(graphite(
      'incle-'='incle-',
      'inclC+'=true,
      'C+'(set(y=environment.T)),
      'e-'(
        materialSet(y=-0.05*U.A),
        redeclare function thermalSpec = Conditions.ByConnector.Boundary.Single.Thermal.heatRate,

        thermalSet(y=0))));

  Conditions.ByConnector.BoundaryBus.Single.Sink BC2(graphite(
      'inclC+'=true,
      'incle-'='incle-',
      redeclare Conditions.ByConnector.ThermalDiffusive.Single.Temperature 'C+'
        (set(y=environment.T))));

equation 
  connect(BC1.boundary, subregion.xNegative);

  connect(subregion.xPositive, BC2.boundary);

end ElectricalConduction;

FCSys.Subregions.Examples.InternalFlow

Internal, laminar flow of liquid water FCSys.Subregions.Examples.InternalFlow

Information

A small-signal variation is added to the time-average flow rate in order to demonstrate the effects of inertance.

Note that the temperature increases due to viscous dissipation, but the increase is limited by thermal convection. The walls are adiabatic.

Extends from Examples.Subregion (Single subregion, with H₂ by default).

Parameters

Type Name Default Description

VolumeRate Vdot_large -1.5*U.cc/U.s Prescribed large signal volumetric flow rate [L3/T]

Species

Boolean 'inclC+' false Carbon plus (C⁺)

Boolean 'inclSO3-' false Nafion sulfonate (C₁₉HF₃₇O₅S^-, abbreviated as SO₃^-)

Boolean 'incle-' false Electrons (e^-)

Boolean 'inclH+' false Protons (H⁺)

Boolean inclH2 false Hydrogen (H₂)

Boolean inclH2O false Water vapor (H₂O)

Boolean inclN2 false Nitrogen (N₂)

Boolean inclO2 false Oxygen (O₂)

Type	Name	Default	Description
VolumeRate	Vdot_large	-1.5*U.cc/U.s	Prescribed large signal volumetric flow rate [L3/T]
Species
Boolean	'inclC+'	false	Carbon plus (C⁺)
Boolean	'inclSO3-'	false	Nafion sulfonate (C₁₉HF₃₇O₅S^-, abbreviated as SO₃^-)
Boolean	'incle-'	false	Electrons (e^-)
Boolean	'inclH+'	false	Protons (H⁺)
Boolean	inclH2	false	Hydrogen (H₂)
Boolean	inclH2O	false	Water vapor (H₂O)
Boolean	inclN2	false	Nitrogen (N₂)
Boolean	inclO2	false	Oxygen (O₂)

Modelica definition

model InternalFlow "Internal, laminar flow of liquid water"
  import FCSys.Utilities.Delta;
  final parameter Q.Area A=subregion.A[Axis.x] "Cross-sectional area";

  // Conditions
  parameter Q.VolumeRate Vdot_large=-1.5*U.cc/U.s 
    "Prescribed large signal volumetric flow rate";

  // Measurements
  output Q.Pressure Deltap=Delta(subregion.liquid.H2O.boundaries[1, :].p) 
    "Measured pressure difference";
  output Q.Length D=2*A/(subregion.L[Axis.y] + subregion.L[Axis.z]);
  output Q.Number Re=subregion.liquid.H2O.phi[Axis.x]*D*subregion.liquid.H2O.eta
      *subregion.liquid.H2O.Data.m*subregion.liquid.H2O.rho if environment.analysis
    "Reynolds number";
  output Q.Pressure Deltap_Poiseuille=-32*subregion.L[Axis.x]*subregion.liquid.H2O.phi[
      Axis.x]/(D^2*subregion.liquid.H2O.eta) 
    "Pressure difference according to Poiseuille's law";
  Real x=Deltap_Poiseuille/Deltap;

  output Q.Power Qdot_gen_Poiseuille=-Deltap_Poiseuille*Vdot 
    "Rate of heat generation according to Poiseuille's law";
  output Q.VolumeRate Vdot=BC1.liquid.H2O.materialSet.y 
    "Total volumetric flow rate";

  extends Examples.Subregion(inclH2=false, subregion(
      L={U.m,U.mm,U.mm},
      inclTransY=true,
      inclTransZ=true,
      liquid(inclH2O=true, H2O(initMaterial=Init.none))));

  Conditions.ByConnector.BoundaryBus.Single.Source BC1(liquid(inclH2O=true, H2O(
        redeclare Modelica.Blocks.Sources.Sine materialSet(
          amplitude=0.2*Vdot_large,
          offset=Vdot_large,
          freqHz=1),
        redeclare function materialSpec = Conditions.ByConnector.Boundary.Single.Material.volumeRate
            (redeclare package Data = FCSys.Characteristics.H2O.Liquid),
        thermalSet(y=environment.T))));

  Conditions.ByConnector.BoundaryBus.Single.Sink BC2(liquid(inclH2O=true, H2O(
          materialSet(y=U.atm))));

  Conditions.ByConnector.BoundaryBus.Single.Source BC3(liquid(inclH2O=true, H2O(
          redeclare function thermalSpec = Conditions.ByConnector.Boundary.Single.Thermal.heatRate,
          thermalSet(y=0))));

  Conditions.ByConnector.BoundaryBus.Single.Source BC4(liquid(inclH2O=true, H2O(
          redeclare function thermalSpec = Conditions.ByConnector.Boundary.Single.Thermal.heatRate,
          thermalSet(y=0))));

  Conditions.ByConnector.BoundaryBus.Single.Source BC5(liquid(inclH2O=true, H2O(
          redeclare function thermalSpec = Conditions.ByConnector.Boundary.Single.Thermal.heatRate,
          thermalSet(y=0))));

  Conditions.ByConnector.BoundaryBus.Single.Source BC6(liquid(inclH2O=true, H2O(
          redeclare function thermalSpec = Conditions.ByConnector.Boundary.Single.Thermal.heatRate,
          thermalSet(y=0))));

equation 
  connect(BC1.boundary, subregion.xNegative);

  connect(BC2.boundary, subregion.xPositive);

  connect(subregion.yNegative, BC3.boundary);
  connect(BC4.boundary, subregion.yPositive);

  connect(subregion.zPositive, BC6.boundary);

  connect(subregion.zNegative, BC5.boundary);
end InternalFlow;

FCSys.Subregions.Examples.Subregion

Single subregion, with H₂ by default FCSys.Subregions.Examples.Subregion

Information

This model is boring. It just establishes a single subregion with H₂ by default. There are no boundary conditions other than those implied by the open connectors (no diffusion current, no forces, no thermal conduction). Other examples in this package extend from this one.

Extends from Modelica.Icons.Example (Icon for runnable examples).

Parameters

Type Name Default Description

Species

Boolean 'inclC+' false Carbon plus (C⁺)

Boolean 'inclSO3-' false Nafion sulfonate (C₁₉HF₃₇O₅S^-, abbreviated as SO₃^-)

Boolean 'incle-' false Electrons (e^-)

Boolean 'inclH+' false Protons (H⁺)

Boolean inclH2 true Hydrogen (H₂)

Boolean inclH2O false Water vapor (H₂O)

Boolean inclN2 false Nitrogen (N₂)

Boolean inclO2 false Oxygen (O₂)

Type	Name	Default	Description
Species
Boolean	'inclC+'	false	Carbon plus (C⁺)
Boolean	'inclSO3-'	false	Nafion sulfonate (C₁₉HF₃₇O₅S^-, abbreviated as SO₃^-)
Boolean	'incle-'	false	Electrons (e^-)
Boolean	'inclH+'	false	Protons (H⁺)
Boolean	inclH2	true	Hydrogen (H₂)
Boolean	inclH2O	false	Water vapor (H₂O)
Boolean	inclN2	false	Nitrogen (N₂)
Boolean	inclO2	false	Oxygen (O₂)

Modelica definition

model Subregion 
  "Single subregion, with H₂ by default"

  extends Modelica.Icons.Example;

  parameter Boolean 'inclC+'=false "Carbon plus (C⁺)";
  parameter Boolean 'inclSO3-'=false 
    "Nafion sulfonate (C₁₉HF₃₇O₅S^-, abbreviated as SO₃^-)";
  parameter Boolean 'incle-'=false "Electrons (e^-)";
  parameter Boolean 'inclH+'=false "Protons (H⁺)";
  parameter Boolean inclH2=true "Hydrogen (H₂)";
  parameter Boolean inclH2O=false "Water vapor (H₂O)";
  parameter Boolean inclN2=false "Nitrogen (N₂)";
  parameter Boolean inclO2=false "Oxygen (O₂)";

  inner Conditions.Environment environment(RH=0);

  FCSys.Subregions.Subregion subregion(
    L={1,1,1}*U.cm,
    inclTransY=false,
    inclTransZ=false,
    graphite(final 'inclC+'='inclC+', final 'incle-'='incle-'),
    ionomer(final 'inclSO3-'='inclSO3-', final 'inclH+'='inclH+'),
    gas(
      final inclH2=inclH2,
      final inclH2O=inclH2O,
      final inclN2=inclN2,
      final inclO2=inclO2));

end Subregion;

FCSys.Subregions.Examples.Subregions

Horizontal array of subregions with an initial pressure difference (H₂ included by default) FCSys.Subregions.Examples.Subregions

Information

Extends from Modelica.Icons.Example (Icon for runnable examples).

Parameters

Type Name Default Description

Integer n_x 0 Number of discrete subregions along the x axis, besides the 2 side subregions

Pressure Deltap_IC -100*U.Pa Initial pressure difference [M/(L.T2)]

Species

Boolean 'inclC+' false Carbon plus (C⁺)

Boolean 'inclSO3-' false Nafion sulfonate (C₁₉HF₃₇O₅S)

Boolean 'incle-' false Electrons (e^-)

Boolean 'inclH+' false Protons (H⁺)

Boolean inclH2 true Hydrogen (H₂)

Boolean inclH2O false Water vapor (H₂O)

Boolean inclN2 false Nitrogen (N₂)

Boolean inclO2 false Oxygen (O₂)

Type	Name	Default	Description
Integer	n_x	0	Number of discrete subregions along the x axis, besides the 2 side subregions
Pressure	Deltap_IC	-100*U.Pa	Initial pressure difference [M/(L.T2)]
Species
Boolean	'inclC+'	false	Carbon plus (C⁺)
Boolean	'inclSO3-'	false	Nafion sulfonate (C₁₉HF₃₇O₅S)
Boolean	'incle-'	false	Electrons (e^-)
Boolean	'inclH+'	false	Protons (H⁺)
Boolean	inclH2	true	Hydrogen (H₂)
Boolean	inclH2O	false	Water vapor (H₂O)
Boolean	inclN2	false	Nitrogen (N₂)
Boolean	inclO2	false	Oxygen (O₂)

Modelica definition

model Subregions 
  "Horizontal array of subregions with an initial pressure difference (H₂ included by default)"
  extends Modelica.Icons.Example;

  parameter Integer n_x=0 
    "Number of discrete subregions along the x axis, besides the 2 side subregions";
  parameter Q.Pressure Deltap_IC=-100*U.Pa "Initial pressure difference";
  parameter Boolean 'inclC+'=false "Carbon plus (C⁺)";
  parameter Boolean 'inclSO3-'=false 
    "Nafion sulfonate (C₁₉HF₃₇O₅S)";
  parameter Boolean 'incle-'=false "Electrons (e^-)";
  parameter Boolean 'inclH+'=false "Protons (H⁺)";
  parameter Boolean inclH2=true "Hydrogen (H₂)";
  parameter Boolean inclH2O=false "Water vapor (H₂O)";
  parameter Boolean inclN2=false "Nitrogen (N₂)";
  parameter Boolean inclO2=false "Oxygen (O₂)";

  inner Conditions.Environment environment;
  FCSys.Subregions.Subregion subregion1(
    L={1,1,1}*U.cm,
    inclTransY=false,
    inclTransZ=false,
    gas(
      final inclH2=inclH2,
      final inclH2O=inclH2O,
      final inclN2=inclN2,
      final inclO2=inclO2,
      H2(p_IC=environment.p - Deltap_IC/2, phi(each stateSelect=StateSelect.always,
            each fixed=true)),
      H2O(p_IC=environment.p - Deltap_IC/2, phi(each stateSelect=StateSelect.always,
            each fixed=true)),
      N2(p_IC=environment.p - Deltap_IC/2, phi(each stateSelect=StateSelect.always,
            each fixed=true)),
      O2(p_IC=environment.p - Deltap_IC/2, phi(each stateSelect=StateSelect.always,
            each fixed=true))),
    graphite(final 'inclC+'='inclC+', final 'incle-'='incle-'),
    ionomer(final 'inclSO3-'='inclSO3-', final 'inclH+'='inclH+'),
    liquid(H2O(epsilon_IC=0.25)));

  FCSys.Subregions.Subregion subregions[n_x](
    each L={1,1,1}*U.cm,
    each inclTransY=false,
    each inclTransZ=false,
    gas(
      each final inclH2=inclH2,
      each final inclH2O=inclH2O,
      each final inclN2=inclN2,
      each final inclO2=inclO2,
      H2(p_IC={environment.p - Deltap_IC/2 - i*Deltap_IC/(n_x + 1) for i in 1:
            n_x}, each phi(each stateSelect=StateSelect.always, each fixed=true)),

      H2O(p_IC={environment.p - Deltap_IC/2 - i*Deltap_IC/(n_x + 1) for i in 1:
            n_x}, each phi(each stateSelect=StateSelect.always, each fixed=true)),

      N2(p_IC={environment.p - Deltap_IC/2 - i*Deltap_IC/(n_x + 1) for i in 1:
            n_x}, each phi(each stateSelect=StateSelect.always, each fixed=true)),

      O2(p_IC={environment.p - Deltap_IC/2 - i*Deltap_IC/(n_x + 1) for i in 1:
            n_x}, each phi(each stateSelect=StateSelect.always, each fixed=true))),

    graphite(each final 'inclC+'='inclC+', each final 'incle-'='incle-'),
    ionomer(each final 'inclSO3-'='inclSO3-', each final 'inclH+'='inclH+'),
    liquid(H2O(each epsilon_IC=0.25))) if n_x > 0;

  FCSys.Subregions.Subregion subregion2(
    L={1,1,1}*U.cm,
    inclTransY=false,
    inclTransZ=false,
    gas(
      final inclH2=inclH2,
      final inclH2O=inclH2O,
      final inclN2=inclN2,
      final inclO2=inclO2,
      H2(p_IC=environment.p + Deltap_IC/2),
      H2O(p_IC=environment.p + Deltap_IC/2),
      N2(p_IC=environment.p + Deltap_IC/2),
      O2(p_IC=environment.p + Deltap_IC/2)),
    graphite(final 'inclC+'='inclC+', final 'incle-'='incle-'),
    ionomer(final 'inclSO3-'='inclSO3-', final 'inclH+'='inclH+'),
    liquid(H2O(each epsilon_IC=0.25)));

equation 
  connect(subregion1.xPositive, subregions[1].xNegative);

  for i in 1:n_x - 1 loop
    connect(subregions[i].xPositive, subregions[i + 1].xNegative) 
      "Not shown in the diagram";
  end for;
  if n_x == 0 then
    connect(subregion1.xPositive, subregion2.xNegative) 
      "Not shown in the diagram";
  end if;
  connect(subregions[n_x].xPositive, subregion2.xNegative);

end Subregions;

FCSys.Subregions.Examples.ThermalConduction

Thermal conduction (through solid) FCSys.Subregions.Examples.ThermalConduction

Information

Extends from Examples.Subregions (Horizontal array of subregions with an initial pressure difference (H₂ included by default)).

Parameters

Type Name Default Description

Integer n_x 6 Number of discrete subregions along the x axis, besides the 2 side subregions

Pressure Deltap_IC -100*U.Pa Initial pressure difference [M/(L.T2)]

Species

Boolean 'inclC+' true Carbon plus (C⁺)

Boolean 'inclSO3-' false Nafion sulfonate (C₁₉HF₃₇O₅S)

Boolean 'incle-' false Electrons (e^-)

Boolean 'inclH+' false Protons (H⁺)

Boolean inclH2 false Hydrogen (H₂)

Boolean inclH2O false Water vapor (H₂O)

Boolean inclN2 false Nitrogen (N₂)

Boolean inclO2 false Oxygen (O₂)

Type	Name	Default	Description
Integer	n_x	6	Number of discrete subregions along the x axis, besides the 2 side subregions
Pressure	Deltap_IC	-100*U.Pa	Initial pressure difference [M/(L.T2)]
Species
Boolean	'inclC+'	true	Carbon plus (C⁺)
Boolean	'inclSO3-'	false	Nafion sulfonate (C₁₉HF₃₇O₅S)
Boolean	'incle-'	false	Electrons (e^-)
Boolean	'inclH+'	false	Protons (H⁺)
Boolean	inclH2	false	Hydrogen (H₂)
Boolean	inclH2O	false	Water vapor (H₂O)
Boolean	inclN2	false	Nitrogen (N₂)
Boolean	inclO2	false	Oxygen (O₂)

Modelica definition

model ThermalConduction "Thermal conduction (through solid)"
  extends Examples.Subregions(
    n_x=6,
    'inclC+'=true,
    inclH2=false,
    subregion1(graphite('C+'(T_IC=environment.T + 30*U.K, epsilon=1))),
    subregions(each graphite('C+'(epsilon=1))),
    subregion2(graphite('C+'(epsilon=1))));

end ThermalConduction;

FCSys.Subregions.Examples.ThermalConductionConvection

Thermal conduction through a solid alongside conduction and convection through a gas FCSys.Subregions.Examples.ThermalConductionConvection

Information

Extends from ThermalConduction (Thermal conduction (through solid)).

Parameters

Type Name Default Description

Integer n_x 6 Number of discrete subregions along the x axis, besides the 2 side subregions

Pressure Deltap_IC -100*U.Pa Initial pressure difference [M/(L.T2)]

Species

Boolean 'inclC+' true Carbon plus (C⁺)

Boolean 'inclSO3-' false Nafion sulfonate (C₁₉HF₃₇O₅S)

Boolean 'incle-' false Electrons (e^-)

Boolean 'inclH+' false Protons (H⁺)

Boolean inclH2 false Hydrogen (H₂)

Boolean inclH2O false Water vapor (H₂O)

Boolean inclN2 true Nitrogen (N₂)

Boolean inclO2 false Oxygen (O₂)

Type	Name	Default	Description
Integer	n_x	6	Number of discrete subregions along the x axis, besides the 2 side subregions
Pressure	Deltap_IC	-100*U.Pa	Initial pressure difference [M/(L.T2)]
Species
Boolean	'inclC+'	true	Carbon plus (C⁺)
Boolean	'inclSO3-'	false	Nafion sulfonate (C₁₉HF₃₇O₅S)
Boolean	'incle-'	false	Electrons (e^-)
Boolean	'inclH+'	false	Protons (H⁺)
Boolean	inclH2	false	Hydrogen (H₂)
Boolean	inclH2O	false	Water vapor (H₂O)
Boolean	inclN2	true	Nitrogen (N₂)
Boolean	inclO2	false	Oxygen (O₂)

Modelica definition

model ThermalConductionConvection 
  "Thermal conduction through a solid alongside conduction and convection through a gas"

  extends ThermalConduction(
    inclN2=true,
    subregion1(gas(N2(
          T_IC=subregion1.graphite.'C+'.T_IC,
          phi(stateSelect=StateSelect.always, displayUnit="mm/s"),
          phi_boundaries(each displayUnit="mm/s"))), graphite('C+'(epsilon=0.5))),

    subregions(
      common(each k_Phi={10,10,10}),
      gas(N2(each phi(each stateSelect=StateSelect.always, displayUnit="mm/s"),
            each phi_boundaries(each displayUnit="mm/s"))),
      each graphite('C+'(epsilon=0.5))),
    subregion2(gas(N2(phi(displayUnit="mm/s"), phi_boundaries(each displayUnit="mm/s"))),
        graphite('C+'(epsilon=0.5))),
    environment(psi_O2_dry=0, RH=0));

end ThermalConductionConvection;

FCSys

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FCSys.Subregions.Examples

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FCSys.Subregions.Examples.AirColumn

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Modelica definition

FCSys.Subregions.Examples.BinaryDiffusion

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Modelica definition

FCSys.Subregions.Examples.Echo

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Parameters

Modelica definition

FCSys.Subregions.Examples.EchoCentral

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Modelica definition

FCSys.Subregions.Examples.ElectricalConduction

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Parameters

Modelica definition

FCSys.Subregions.Examples.InternalFlow

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Modelica definition

FCSys.Subregions.Examples.Subregion

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Parameters

Modelica definition

FCSys.Subregions.Examples.Subregions

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Parameters

Modelica definition

FCSys.Subregions.Examples.ThermalConduction

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Parameters

Modelica definition

FCSys.Subregions.Examples.ThermalConductionConvection

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Parameters

Modelica definition