FCSys.Species.H2O.Gas

H₂O gas

Information

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

Package Content

Name	Description
Fixed	Fixed properties

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FCSys.Species.H2O.Gas.Fixed

Fixed properties

Information

Assumptions:

1. The generalized resistivities (η, θ) are fixed (e.g., independent of thermodynamic state).
2. Ideal gas
3. The specific exchange currents (τ′) are zero. The rate of phase change is governed by the other configurations (liquid and ionomer).

The default resistivities (η = 1/(9.09e-6*U.Pa*U.s) and θ = U.m*U.K/(19.6e-3*U.W)) are of H₂O gas at saturation pressure and 300 K from Incropera and DeWitt [Table 1 lists the properties at saturation pressure and other temperatures. Table 2 lists the properties of H₂O gas at 1 atm. See also http://www.engineeringtoolbox.com/water-dynamic-kinematic-viscosity-d_596.html.

Table 1: Properties of H₂O gas at saturation pressure [Incropera2002, pp. 924–925].

T /U.K	cp*U.kg*U.K /(U.J*Data.m)	η *U.Pa*U.s	θ*U.W /(U.m*U.K)
273.15	1854	1/8.02e-6	1/18.2e-3
275	1855	1/8.09e-6	1/18.3e-3
280	1858	1/8.29e-6	1/18.6e-3
285	1861	1/8.49e-6	1/18.9e-3
290	1864	1/8.69e-6	1/19.3e-3
295	1868	1/8.89e-6	1/19.5e-3
300	1872	1/9.09e-6	1/19.6e-3
305	1877	1/9.29e-6	1/20.1e-3
310	1882	1/9.49e-6	1/20.4e-3
315	1888	1/9.69e-6	1/20.7e-3
320	1895	1/9.89e-6	1/21.0e-3
325	1903	1/10.09e-6	1/21.3e-3
330	1911	1/10.29e-6	1/21.7e-3
335	1920	1/10.49e-6	1/22.0e-3
340	1930	1/10.69e-6	1/22.3e-3
345	1941	1/10.89e-6	1/22.6e-3
350	1954	1/11.09e-6	1/23.0e-3
355	1968	1/11.29e-6	1/23.3e-3
360	1983	1/11.49e-6	1/23.7e-3
365	1999	1/11.69e-6	1/24.1e-3
370	2017	1/11.89e-6	1/24.5e-3
373.15	2029	1/12.02e-6	1/24.8e-3
375	2036	1/12.09e-6	1/24.9e-3
380	2057	1/12.29e-6	1/25.4e-3
385	2080	1/12.49e-6	1/25.8e-3
390	2104	1/12.69e-6	1/26.3e-3
400	2158	1/13.05e-6	1/27.2e-3
410	2221	1/13.42e-6	1/28.2e-3
420	2291	1/13.79e-6	1/29.8e-3
430	2369	1/14.14e-6	1/30.4e-3
440	2460	1/14.50e-6	1/31.7e-3
450	2560	1/14.85e-6	1/33.1e-3
460	2680	1/15.19e-6	1/34.6e-3
470	2790	1/15.54e-6	1/36.3e-3
480	2940	1/15.88e-6	1/38.1e-3
490	3100	1/16.23e-6	1/40.1e-3
500	3270	1/16.59e-6	1/42.3e-3
510	3470	1/16.95e-6	1/44.7e-3
520	3700	1/17.33e-6	1/47.5e-3
530	3960	1/17.72e-6	1/50.6e-3
540	4270	1/18.1e-6	1/54.0e-3
550	4640	1/18.6e-6	1/58.3e-3
560	5090	1/19.1e-6	1/63.7e-3
570	5670	1/19.7e-6	1/76.7e-3
580	6400	1/20.4e-6	1/76.7e-3
590	7350	1/21.5e-6	1/84.1e-3
600	8750	1/22.7e-6	1/92.9e-3
610	11100	1/24.1e-6	1/103e-3
620	15400	1/25.9e-6	1/114e-3
635	18300	1/27.0e-6	1/121e-3
630	22100	1/28.0e-6	1/130e-3
635	27600	1/30.0e-6	1/141e-3
640	42000	1/32.0e-6	1/155e-3

Table 2: Properties of H₂O gas at 1 atm [Incropera2002, p. 921].

T /U.K	cp*U.kg*U.K /(U.J*Data.m)	η *U.Pa*U.s	θ*U.W /(U.m*U.K)
380	2.060e3	1/127.1e-7	1/24.6e-3
400	2.014e3	1/134.4e-7	1/26.1e-3
450	1.980e3	1/152.5e-7	1/29.9e-3
500	1.985e3	1/170.4e-7	1/33.9e-3
550	1.997e3	1/188.4e-7	1/37.9e-3
600	2.206e3	1/206.7e-7	1/42.2e-3
650	2.056e3	1/224.7e-7	1/46.4e-3
700	2.085e3	1/242.6e-7	1/50.5e-3
750	2.119e3	1/260.4e-7	1/54.9e-3
800	2.152e3	1/278.6e-7	1/59.2e-3
850	2.186e3	1/296.9e-7	1/63.7e-3

The specific heat capacity is not fixed because it would affect the chemical potential and result in an incorrect cell potential.

The relative humidities (RH and RH_boundaries), which are calculated as output variables, do not account for surface tension.

For more information, please see the Species model.

Extends from Fluid (Base model for a fluid species).

Parameters

Type	Name	Default	Description
Integer	n_inter	0	Number of exchange connections with other phases
Material properties
replaceable package Data		FCSys.Characteristics.H2O.Ga…	Characteristic data
Independence factors
NumberAbsolute	k_intra_Phi[n_intra, n_trans]	ones(n_intra, n_trans)	For translational exchange among species within the phase [1]
NumberAbsolute	k_intra_Q[n_intra]	ones(n_intra)	For thermal exchange among species within the phase [1]
Initialization
Velocity	phi.start[n_trans]	0	Velocity [L/T]
Current	I.start[n_trans]	0	Current [N/T]
Velocity	phi_boundaries.start[n_trans, Side]	0	Normal velocities at the boundaries [L/T]
Force	f.start[n_trans]	0	Total normal translational force on pairs of boundaries [L.M/T2]
Force	minusDeltaf.start[n_trans]	0	Dynamic and nonequilibrium compression forces [L.M/T2]
Geometry
Length	kL[:]	L[cartTrans]	Effective transport length [L]
Initialization
Init	initMaterial	Init.pressure	Method of initializing the material state
Init	initEnergy	Init.temperature	Method of initializing the thermal state
Amount	N_IC		Initial amount of material [N]
Density	rho_IC		Initial density [N/L3]
Volume	V_IC		Initial volume [L3]
PressureAbsolute	p_IC	environment.p_H2O	Initial pressure [M/(L.T2)]
TemperatureAbsolute	T_IC		Initial temperature [L2.M/(N.T2)]
Potential	h_IC		Initial specific enthalpy [L2.M/(N.T2)]
Potential	g_IC		Initial Gibbs potential [L2.M/(N.T2)]
Assumptions
Integer	n_trans	1	Number of transport axes
Integer	n_chem	2	Number of reaction and phase change processes
Formulation of the conservation equations
ConsThermo	consMaterial	ConsThermo.dynamic	Material
Boolean	consRot	false	Conserve rotational momentum
ConsTrans	consTransX	ConsTrans.dynamic	X-axis translational momentum
ConsTrans	consTransY	ConsTrans.dynamic	Y-axis translational momentum
ConsTrans	consTransZ	ConsTrans.dynamic	Z-axis translational momentum
ConsThermo	consEnergy	ConsThermo.dynamic	Energy
Axes with upstream discretization
Boolean	upstreamX	true	X
Boolean	upstreamY	true	Y
Boolean	upstreamZ	true	Z
Flow conditions
Boolean	approxVelocity	true	Calculate normal boundary velocities assuming uniform density
NumberAbsolute	Nu_Phi[Axis]	{4,4,4}	Translational Nusselt numbers [1]
NumberAbsolute	Nu_Q	1	Thermal Nusselt number [1]

Connectors

Type	Name	Description
Intra	intra[n_intra]	Connectors to exchange translational momentum and energy within the phase
Inter	inter[n_inter]	Connectors to exchange translational momentum and energy with all other species
Dalton	dalton	Connector for additivity of pressure
Boundary	boundaries[n_trans, Side]	Connectors for transport
Chemical	chemical[n_chem]	Connector for reactions and phase change
Material properties
replaceable package Data		Characteristic data

Modelica definition

model Fixed "Fixed properties"

  extends Fluid(
    redeclare replaceable package Data = FCSys.Characteristics.H2O.Gas (b_v=[1],
          n_v={-1,0}),
    redeclare parameter Q.Mobility mu=Data.mu(),
    redeclare parameter Q.TimeAbsolute nu=Data.nu(),
    redeclare parameter Q.Continuity zeta=Data.zeta(),
    redeclare parameter Q.Fluidity eta=1/(9.09e-6*U.Pa*U.s),
    redeclare parameter Q.ResistivityThermal theta=U.m*U.K/(19.6e-3*U.W),
    final tauprime,
    final N0,
    n_chem=2,
    p_IC=environment.p_H2O);

  // See the documentation for tables of values.

  output Q.NumberAbsolute RH(
    stateSelect=StateSelect.never,
    displayUnit="%") = p/Characteristics.H2O.p_sat(T) if environment.analysis 
    "Relative humidity (approximate)";
  output Q.NumberAbsolute RH_boundaries[n_trans, Side](
    each stateSelect=StateSelect.never,
    each displayUnit="%") = boundaries.p ./ Characteristics.H2O.p_sat(
    boundaries.T) if environment.analysis 
    "Relative humidity at the boundaries (approximate)";

end Fixed;