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WOLFRAM SYSTEM MODELER

ReferenceMoistAir

ReferenceMoistAir: Detailed moist air model (143.15 ... 2000 K)

Package Contents

	ThermodynamicState ThermodynamicState record for moist air
	BaseProperties Moist air base properties record
	setState_pTX Return thermodynamic state as function of pressure p, temperature T and composition X
	setState_phX Return thermodynamic state as function of pressure p, specific enthalpy h and composition X
	setState_psX Return thermodynamic state as function of pressure p, specific enthalpy h and composition X
	setState_dTX Return thermodynamic state as function of density d, temperature T and composition X
	setSmoothState Return thermodynamic state so that it smoothly approximates: if x > 0 then state_a else state_b
	Xsaturation Return absolute humidity per unit mass of moist air at saturation as a function of the thermodynamic state record
	xsaturation Return absolute humidity per unit mass of dry air at saturation as a function of the thermodynamic state record
	massFraction_pTphi Return mass fractions as a function of pressure, temperature and relative humidity
	massFractionWaterVapor Return mass fraction of water vapor
	massFractionWaterNonVapor Return mass fraction of liquid and solid water
	massFractionSaturation Return saturation mass fractions
	massFractionSaturation_ppsat Return mass fvraction at saturation boundary given pressure and saturation pressure
	massFraction_waterContent Return mass fractions as a function of pressure, temperature and absolute humidity in kg(water)/kg(dry air)
	waterContent_X Return water content in kg(water)/kg(dry air) given mass fractions
	relativeHumidity Return relative humidity
	gasConstant Return ideal gas constant as a function from thermodynamic state, only valid for phi<1
	saturationPressureLiquid Return saturation pressure of water as a function of temperature T
	sublimationPressureIce Return sublimation pressure of water as a function of temperature T between 223.16 and 273.16 K
	saturationPressure Return saturation pressure of condensing fluid
	saturationTemperature Return saturation temperature of condensing fluid
	enthalpyOfVaporization Return enthalpy of vaporization of water
	enthalpyOfLiquid Return enthalpy of liquid water
	enthalpyOfGas Return specific enthalpy of gas (air and steam)
	enthalpyOfCondensingGas Return specific enthalpy of steam
	enthalpyOfNonCondensingGas Return specific enthalpy of dry air
	enthalpyOfDryAir Return specific enthalpy of dry air
	enthalpyOfWater Return specific enthalpy of water (solid + liquid + steam)
	enthalpyOfWaterVapor Return specific enthalpy of steam
	enthalpyOfWaterNonVapor Return enthalpy of liquid and solid water
	pressure Returns pressure of ideal gas as a function of the thermodynamic state record
	temperature Return temperature of ideal gas as a function of the thermodynamic state record
	density Returns density as a function of the thermodynamic state record
	specificEnthalpy Return specific enthalpy of moist air as a function of the thermodynamic state record
	specificInternalEnergy Return specific internal energy of moist air as a function of the thermodynamic state record
	specificEntropy Return specific entropy from thermodynamic state record, only valid for phi<1
	specificGibbsEnergy Return specific Gibbs energy as a function of the thermodynamic state record, only valid for phi<1
	specificHelmholtzEnergy Return specific Helmholtz energy as a function of the thermodynamic state record, only valid for phi<1
	specificHeatCapacityCp Return specific heat capacity at constant pressure as a function of the thermodynamic state record
	specificHeatCapacityCv Return specific heat capacity at constant volume as a function of the thermodynamic state record
	isentropicExponent Return isentropic exponent
	isentropicEnthalpy Return isentropic enthalpy
	velocityOfSound Return velocity of sound
	molarMass Return the molar mass of the medium
	dynamicViscosity Return dynamic viscosity as a function of the thermodynamic state record, valid from 73.15 K to 373.15 K
	thermalConductivity Return thermal conductivity as a function of the thermodynamic state record, valid from 73.15 K to 373.15 K
	Utilities Utility package for moist air

Package Constants (29)

ThermoStates	Value: Modelica.Media.Interfaces.Choices.IndependentVariables.pTX Type: IndependentVariables Description: Enumeration type for independent variables
mediumName	Value: "Moist air" Type: String Description: Name of the medium
substanceNames	Value: {"Water", "Air"} Type: String[:] Description: Names of the mixture substances. Set substanceNames={mediumName} if only one substance.
extraPropertiesNames	Value: fill("", 0) Type: String[:] Description: Names of the additional (extra) transported properties. Set extraPropertiesNames=fill("",0) if unused
singleState	Value: false Type: Boolean Description: = true, if u and d are not a function of pressure
reducedX	Value: true Type: Boolean Description: = true if medium contains the equation sum(X) = 1.0; set reducedX=true if only one substance (see docu for details)
fixedX	Value: false Type: Boolean Description: = true if medium contains the equation X = reference_X
reference_p	Value: 101325 Type: AbsolutePressure (Pa) Description: Reference pressure of Medium: default 1 atmosphere
reference_T	Value: 298.15 Type: Temperature (K) Description: Reference temperature of Medium: default 25 deg Celsius
reference_X	Value: {0.01, 0.99} Type: MassFraction[nX] (kg/kg) Description: Default mass fractions of medium
p_default	Value: 101325 Type: AbsolutePressure (Pa) Description: Default value for pressure of medium (for initialization)
T_default	Value: Modelica.Units.Conversions.from_degC(20) Type: Temperature (K) Description: Default value for temperature of medium (for initialization)
h_default	Value: specificEnthalpy_pTX(p_default, T_default, X_default) Type: SpecificEnthalpy (J/kg) Description: Default value for specific enthalpy of medium (for initialization)
X_default	Value: reference_X Type: MassFraction[nX] (kg/kg) Description: Default value for mass fractions of medium (for initialization)
C_default	Value: fill(0, nC) Type: ExtraProperty[nC] Description: Default value for trace substances of medium (for initialization)
nS	Value: size(substanceNames, 1) Type: Integer Description: Number of substances
nX	Value: nS Type: Integer Description: Number of mass fractions
nXi	Value: if fixedX then 0 else if reducedX then nS - 1 else nS Type: Integer Description: Number of structurally independent mass fractions (see docu for details)
nC	Value: size(extraPropertiesNames, 1) Type: Integer Description: Number of extra (outside of standard mass-balance) transported properties
C_nominal	Value: 1.0e-6 * ones(nC) Type: Real[nC] Description: Default for the nominal values for the extra properties
fluidConstants	Value: {Utilities.Water95_Utilities.waterConstants, Modelica.Media.Air.ReferenceAir.airConstants} Type: FluidConstants[nS] Description: Constant data for the fluid
Water	Value: 1 Type: Integer Description: Index of water (in substanceNames, massFractions X, etc.)
Air	Value: 2 Type: Integer Description: Index of air (in substanceNames, massFractions X, etc.)
useEnhancementFactor	Value: false Type: Boolean Description: Use the enhancement factor in the calculations
useDissociation	Value: true Type: Boolean Description: Take dissociation into account for high temperatures
k_mair	Value: steam.MM / dryair.MM Type: Real Description: Ratio of molar weights
dryair	Value: ReferenceAir.Air_Utilities.Basic.Constants Type: FundamentalConstants Description: Constants of the medium
steam	Value: Utilities.Water95_Utilities.Constants Type: FundamentalConstants Description: Constants of the medium
MMX	Value: {steam.MM, dryair.MM} Type: MolarMass[2] (kg/mol) Description: Molar masses of components

Information

This information is part of the Modelica Standard Library maintained by the Modelica Association.

Calculation of fluid properties for moist air in the region from 143.15 Kelvin to 2000 Kelvin at pressures up to 10 MPa. This model of moist air is based on the diploma thesis of Hellriegel [10] with small modifications. Moist air is treated as an ideal mixture of the real fluids air and water.

Restriction

The functions provided by this package shall be used inside of the restricted limits according to the referenced literature.

611.2 Pa ≤ p ≤ 10 MPa
143.15 K ≤ T ≤ 2000 K

Usage

The package MoistAir can be used as any other medium model (see User's Guide of Media Library for further information). The package defines two boolean constants useEnhancementFactor and useDissociation, which give the user fine grained control of the calculations.

Constant	Default Value	Meaning
useEnhancementFactor	false	The enhancement factor is used in the calculation of the saturation partial pressure of water in moist air. It is always very close to 1 except for high pressures (>2 MPa) and low temperatures (<233.15 K). For pressures less than 1 MPa this factor can be safely set to 1. Its calculation is very expensive, since it can only be calculated by an iterative method.
useDissociation	true	The effect of dissociation is taken into account for temperatures greater than 773.15 K.

Calculation algorithms

Nomenclature

p	Mixture pressure in Pa
T	Temperature in K
x_w	Absolute humidity in kg(water)/kg(dry air)
x_ws	Absolute humidity on saturation boundary in kg(water)/kg(dry air)
φ	Relative humidity (only defined for unsaturated humid air)

Unsaturated and saturated humid air (0 ≤ x_w ≤ x_ws)

Ideal mixture of dry air and steam

Dry air:
- d,h,u,s,c_p from [1]
- λ, η from [2]
Steam:
- d,h,u,s,c_p from [4]
- λ, η for 273.15 K ≤ T ≤ 1073.15 K from [5] and [6]
- λ, η for T < 273.15 K or T > 1073.15 K from [12]

Supersaturated humid air (liquid fog and ice fog)

Liquid fog (x_w > x_wsw) and T ≥ 273.16 K

Ideal mixture of saturated humid air and water

Saturated humid air (see above)
d,h,u,s of liquid droplets from [4]
c_p is not defined
λ, η of liquid droplets from [5] and [6]

Ice fog (x_w > x_wsw) and T < 273.16 K

Ideal mixture of saturated humid air and ice

Saturated humid air (see above)
d,h,u,s of ice crystals from [7]
c_p is not defined
λ of ice as constant value
η of ice is neglected

Saturation pressure of water in moist air

The saturation pressure p_ds of water in moist air is calculated by p_ds = f*p_sat, where

f is the enhancement factor from [9] and [3]
p_sat for T ≥ 273.16 K is the saturation pressure from [4]
p_sat for T < 273.16 K is the saturation pressure from [8]

Dissociation

For temperatures above 773.15 K effects of dissociation are taken into account. Dissociation is modeled according to [11]. For high temperatures the calculated values for moist air with 0 kg(water)/kg(dry air) (i.e. dry air) may differ from those calculated by the package Modelica.Media.Air.ReferenceAir, because there no dissociation is considered.

References

[1] Thermodynamic Properties of Air and Mixtures of Nitrogen, Argon, and Oxygen From 60 to 2000 K at Pressures to 2000 MPa. J. Phys. Chem. Ref. Data, Vol. 29, No. 3, 2000.

[2] Viscosity and Thermal Conductivity Equations for Nitrogen, Oxygen, Argon, and Air. International Journal of Thermophysics, Vol. 25, No. 1, January 2004

[3] Revised Release on the IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use. 2009 International Association for the Properties of Water and Steam.

[4] Revised Release on the IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam. 2007 International Association for the Properties of Water and Steam.

[5] Release on the IAPWS Formulation 2008 for the Viscosity of Ordinary Water Substance. 2008 International Association for the Properties of Water and Steam

[6] Release on the IAPWS Formulation 2011 for the Thermal Conductivity of Ordinary Water Substance. 2011 International Association for the Properties of Water and Steam.

[7] Revised Release on the Equation of State 2006 for H2O Ice Ih. 2009 International Association for the Properties of Water and Steam.

[8] Revised Release on the Pressure along the Melting and Sublimation Curves of Ordinary Water Substance. 2011 International Association for the Properties of Water and Steam.

[9] Determination of Thermodynamic and Transport Properties of Humid Air for Power-Cycle Calculations. 2009 PTB, Braunschweig, Germany.

[10] Berechnung der thermodynamischen Zustandsfunktionen von feuchter Luft in energietechnischen Prozessmodellierungen. 2001 Diplomarbeit, Zittau.

[11] Thermodynamische Stoffwerte von feuchter Luft und Verbrennungsgasen. 2003 VDI-Richtlinie 4670.

[12] Wärmeübertragung in Dampferzeugern und Wärmetauschern. 1985 FDBR-Fachbuchreihe, Bd. 2, Vulkan Verlag Essen.

References

Lemmon, E. W., Jacobsen, R. T., Penoncello, S. G., Friend, D. G.:: Thermodynamic Properties of Air and Mixtures of Nitrogen, Argon, and Oxygen From 60 to 2000 K at Pressures to 2000 MPa. J. Phys. Chem. Ref. Data, Vol. 29, No. 3, 2000.
Lemmon, E. W., Jacobsen, R. T.:: Viscosity and Thermal Conductivity Equations for Nitrogen, Oxygen, Argon, and Air. International Journal of Thermophysics, Vol. 25, No. 1, January 2004

Verification

The verification report for the development of this library is provided here.

Acknowledgment

This library was developed by XRG Simulation GmbH as part of the Clean Sky JTI project (Project title: MoMoLib-Modelica Model Library Development for Media, Magnetic Systems and Wavelets; Project number: 296369; Theme: JTI-CS-2011-1-SGO-02-026: Modelica Model Library Development Part I). The partial financial support for the development of this library by the European Union is highly appreciated.

Some parts of this library refer to the ThermoFluid library developed at Lund University (http://thermofluid.sourceforge.net).

Wolfram Language

In[1]:=

SystemModel["Modelica.Media.Air.ReferenceMoistAir"]

Out[1]:=

Extended by (1)

Medium

Modelica.Media.Examples.ReferenceAir.MoistAir

Medium model

Package Contents

Package Constants (29)

Information

Restriction

Usage

Calculation algorithms

Nomenclature

Unsaturated and saturated humid air (0 ≤ xw ≤ xws)

Supersaturated humid air (liquid fog and ice fog)

Saturation pressure of water in moist air

Dissociation

References

References

Verification

Acknowledgment

Wolfram Language

Extended by (1)

Unsaturated and saturated humid air (0 ≤ x_w ≤ x_ws)