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WOLFRAM SYSTEM MODELER

MoistAir

Air: Moist air model (190 ... 647 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_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
	xsaturation_pT Return absolute humidity per unit mass of dry air at saturation as a function of pressure p and temperature T
	massFraction_pTphi Return steam mass fraction as a function of relative humidity phi and temperature T
	relativeHumidity_pTX Return relative humidity as a function of pressure p, temperature T and composition X
	relativeHumidity Return relative humidity as a function of the thermodynamic state record
	gasConstant Return ideal gas constant as a function from thermodynamic state, only valid for phi<1
	gasConstant_X Return ideal gas constant as a function from composition X
	saturationPressureLiquid Return saturation pressure of water as a function of temperature T in the range of 273.16 to 647.096 K
	saturationPressureLiquid_der Derivative function for 'saturationPressureLiquid'
	sublimationPressureIce Return sublimation pressure of water as a function of temperature T between 190 and 273.16 K
	sublimationPressureIce_der Derivative function for 'sublimationPressureIce'
	saturationPressure Return saturation pressure of water as a function of temperature T between 190 and 647.096 K
	saturationPressure_der Derivative function for 'saturationPressure'
	saturationTemperature Return saturation temperature of water as a function of (partial) pressure p
	enthalpyOfVaporization Return enthalpy of vaporization of water as a function of temperature T, 273.16 to 647.096 K
	HeatCapacityOfWater Return specific heat capacity of water (liquid only) as a function of temperature T
	enthalpyOfLiquid Return enthalpy of liquid water as a function of temperature T(use enthalpyOfWater instead)
	enthalpyOfGas Return specific enthalpy of gas (air and steam) as a function of temperature T and composition X
	enthalpyOfCondensingGas Return specific enthalpy of steam as a function of temperature T
	enthalpyOfNonCondensingGas Return specific enthalpy of dry air as a function of temperature T
	enthalpyOfWater Computes specific enthalpy of water (solid/liquid) near atmospheric pressure from temperature T
	enthalpyOfWater_der Derivative function of enthalpyOfWater
	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
	T_phX Return temperature as a function of pressure p, specific enthalpy h and composition X
	density Returns density of ideal gas as a function of the thermodynamic state record
	specificEnthalpy Return specific enthalpy of moist air as a function of the thermodynamic state record
	h_pTX Return specific enthalpy of moist air as a function of pressure p, temperature T and composition X
	h_pTX_der Derivative function of h_pTX
	isentropicExponent Return isentropic exponent (only for gas fraction!)
	isentropicEnthalpyApproximation Approximate calculation of h_is from upstream properties, downstream pressure, gas part only
	specificInternalEnergy Return specific internal energy of moist air as a function of the thermodynamic state record
	specificInternalEnergy_pTX Return specific internal energy of moist air as a function of pressure p, temperature T and composition X
	specificInternalEnergy_pTX_der Derivative function for specificInternalEnergy_pTX
	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
	dynamicViscosity Return dynamic viscosity as a function of the thermodynamic state record, valid from 123.15 K to 1273.15 K
	thermalConductivity Return thermal conductivity as a function of the thermodynamic state record, valid from 123.15 K to 1273.15 K
	velocityOfSound
	isobaricExpansionCoefficient
	isothermalCompressibility
	density_derp_h
	density_derh_p
	density_derp_T
	density_derT_p
	density_derX
	molarMass
	T_psX Return temperature as a function of pressure p, specific entropy s and composition X
	setState_psX
	s_pTX Return specific entropy of moist air as a function of pressure p, temperature T and composition X (only valid for phi<1)
	s_pTX_der Return specific entropy of moist air as a function of pressure p, temperature T and composition X (only valid for phi<1)
	isentropicEnthalpy Isentropic enthalpy (only valid for phi<1)
	Utilities Utility functions

Package Constants (27)

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: {IdealGases.Common.FluidData.H2O, IdealGases.Common.FluidData.N2} 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.)
k_mair	Value: steam.MM / dryair.MM Type: Real Description: Ratio of molar weights
dryair	Value: IdealGases.Common.SingleGasesData.Air Type: DataRecord Description: Coefficient data record for properties of ideal gases based on NASA source
steam	Value: IdealGases.Common.SingleGasesData.H2O Type: DataRecord Description: Coefficient data record for properties of ideal gases based on NASA source
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.

Thermodynamic Model

This package provides a full thermodynamic model of moist air including the fog region and temperatures below zero degC. The governing assumptions in this model are:

the perfect gas law applies
water volume other than that of steam is neglected

All extensive properties are expressed in terms of the total mass in order to comply with other media in this library. However, for moist air it is rather common to express the absolute humidity in terms of mass of dry air only, which has advantages when working with charts. In addition, care must be taken, when working with mass fractions with respect to total mass, that all properties refer to the same water content when being used in mathematical operations (which is always the case if based on dry air only). Therefore two absolute humidities are computed in the BaseProperties model: X denotes the absolute humidity in terms of the total mass while x denotes the absolute humidity per unit mass of dry air. In addition, the relative humidity phi is also computed.

At the triple point temperature of water of 0.01 °C or 273.16 K and a relative humidity greater than 1 fog may be present as liquid and as ice resulting in a specific enthalpy somewhere between those of the two isotherms for solid and liquid fog, respectively. For numerical reasons a coexisting mixture of 50% solid and 50% liquid fog is assumed in the fog region at the triple point in this model.

Range of validity

From the assumptions mentioned above it follows that the pressure should be in the region around atmospheric conditions or below (a few bars may still be fine though). Additionally a very high water content at low temperatures would yield incorrect densities, because the volume of the liquid or solid phase would not be negligible anymore. The model does not provide information on limits for water drop size in the fog region or transport information for the actual condensation or evaporation process in combination with surfaces. All excess water which is not in its vapour state is assumed to be still present in the air regarding its energy but not in terms of its spatial extent.

The thermodynamic model may be used for temperatures ranging from 190 ... 647 K. This holds for all functions unless otherwise stated in their description. However, although the model works at temperatures above the saturation temperature it is questionable to use the term "relative humidity" in this region. Please note, that although several functions compute pure water properties, they are designed to be used within the moist air medium model where properties are dominated by air and steam in their vapor states, and not for pure liquid water applications.

Transport Properties

Several additional functions that are not needed to describe the thermodynamic system, but are required to model transport processes, like heat and mass transfer, may be called. They usually neglect the moisture influence unless otherwise stated.

Application

The model's main area of application is all processes that involve moist air cooling under near atmospheric pressure with possible moisture condensation. This is the case in all domestic and industrial air conditioning applications. Another large domain of moist air applications covers all processes that deal with dehydration of bulk material using air as a transport medium. Engineering tasks involving moist air are often performed (or at least visualized) by using charts that contain all relevant thermodynamic data for a moist air system. These so called psychrometric charts can be generated from the medium properties in this package. The model PsychrometricData may be used for this purpose in order to obtain data for figures like those below (the plotting itself is not part of the model though).

Legend: blue - constant specific enthalpy, red - constant temperature, black - constant relative humidity

Wolfram Language

In[1]:=

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

Out[1]:=

Extended by (4)

	Medium Modelica.Media.Examples.PsychrometricData Used medium package
	Medium Modelica.Media.Examples.MoistAir Medium model
	Medium Modelica.Fluid.Examples.TraceSubstances.RoomCO2WithControls
	Medium Modelica.Fluid.Examples.TraceSubstances.RoomCO2