Buildings.Media.Air

Package with moist air model that decouples pressure and temperature

Information

This medium package models moist air using a gas law in which pressure and temperature are independent, which often leads to significantly faster and more robust computations. The specific heat capacities at constant pressure and at constant volume are constant. The air is assumed to be not saturated.

This medium uses the gas law

ρ/ρ_stp = p/p_stp,

where p_std and ρ_stp are constant reference temperature and density, rathern than the ideal gas law

ρ = p ⁄(R T),

where R is the gas constant and T is the temperature.

This formulation often leads to smaller systems of nonlinear equations because equations for pressure and temperature are decoupled. Therefore, if air inside a control volume such as room air is heated, it does not increase its specific volume. Consequently, merely heating or cooling a control volume does not affect the air flow calculations in a duct network that may be connected to that volume. Note that multizone air exchange simulation in which buoyancy drives the air flow is still possible as the models in Buildings.Airflow.Multizone compute the mass density using the function Buildings.Utilities.Psychrometrics.Functions.density_pTX in which density is a function of temperature.

Note that models in this package implement the equation for the internal energy as

u = h - p_stp ⁄ ρ_stp,

where u is the internal energy per unit mass, h is the enthalpy per unit mass, p_stp is the static pressure and ρ_stp is the mass density at standard pressure and temperature. The reason for this implementation is that in general,

h = u + p v,

from which follows that

u = h - p v = h - p ⁄ ρ = h - p_stp ⁄ ρ_std,

because p ⁄ ρ = p_stp ⁄ ρ_stp in this medium model.

The enthalpy is computed using the convention that h=0 if T=0 °C and no water vapor is present.

Extends from Modelica.Media.Interfaces.PartialCondensingGases (Base class for mixtures of condensing and non-condensing gases), Modelica.Icons.Package (Icon for standard packages).

Package Content

Name	Description
Water=1	Index of water (in substanceNames, massFractions X, etc.)
Air=2	Index of air (in substanceNames, massFractions X, etc.)
pStp=reference_p	Pressure for which fluid density is defined
dStp=1.2	Fluid density at pressure pStp
ThermodynamicState	ThermodynamicState record for moist air
BaseProperties	Base properties
density	Gas density
dynamicViscosity	Return the dynamic viscosity of dry air
enthalpyOfCondensingGas	Enthalpy of steam per unit mass of steam
enthalpyOfGas	Enthalpy of gas mixture per unit mass of gas mixture
enthalpyOfLiquid	Enthalpy of liquid (per unit mass of liquid) which is linear in the temperature
enthalpyOfNonCondensingGas	Enthalpy of non-condensing gas per unit mass of steam
enthalpyOfVaporization	Enthalpy of vaporization of water
gasConstant	Return ideal gas constant as a function from thermodynamic state, only valid for phi<1
pressure	Returns pressure of ideal gas as a function of the thermodynamic state record
isobaricExpansionCoefficient	Isobaric expansion coefficient beta
isothermalCompressibility	Isothermal compressibility factor
saturationPressure	Saturation curve valid for 223.16 <= T <= 373.16 (and slightly outside with less accuracy)
specificEntropy	Return the specific entropy, only valid for phi<1
density_derp_T	Return the partial derivative of density with respect to pressure at constant temperature
density_derT_p	Return the partial derivative of density with respect to temperature at constant pressure
density_derX	Return the partial derivative of density with respect to mass fractions at constant pressure and temperature
specificHeatCapacityCp	Specific heat capacity of gas mixture at constant pressure
specificHeatCapacityCv	Specific heat capacity of gas mixture at constant volume
setState_dTX	Return thermodynamic state as function of density d, temperature T and composition X
setState_phX	Return thermodynamic state as function of pressure p, specific enthalpy h and composition X
setState_pTX	Return thermodynamic state as function of p, T and composition X or Xi
setState_psX	Return the thermodynamic state as function of p, s and composition X or Xi
specificEnthalpy	Compute specific enthalpy from pressure, temperature and mass fraction
specificEnthalpy_pTX	Specific enthalpy
specificGibbsEnergy	Specific Gibbs energy
specificHelmholtzEnergy	Specific Helmholtz energy
isentropicEnthalpy	Return the isentropic enthalpy
specificInternalEnergy	Specific internal energy
temperature	Return temperature of ideal gas as a function of the thermodynamic state record
molarMass	Return the molar mass
temperature_phX	Compute temperature from specific enthalpy and mass fraction
thermalConductivity	Thermal conductivity of dry air as a polynomial in the temperature
GasProperties	Coefficient data record for properties of perfect gases
dryair	Dry air properties
steam	Steam properties
k_mair=steam.MM/dryair.MM	Ratio of molar weights
MMX={steam.MM,dryair.MM}	Molar masses of components
h_fg=Buildings.Utilities.Psychrometrics.Constants.h_fg	Latent heat of evaporation of water
cpWatLiq=Buildings.Utilities.Psychrometrics.Constants.cpWatLiq	Specific heat capacity of liquid water
der_enthalpyOfLiquid	Temperature derivative of enthalpy of liquid per unit mass of liquid
der_enthalpyOfCondensingGas	Derivative of enthalpy of steam per unit mass of steam
enthalpyOfDryAir	Enthalpy of dry air per unit mass of dry air
der_enthalpyOfDryAir	Derivative of enthalpy of dry air per unit mass of dry air
der_enthalpyOfNonCondensingGas	Derivative of enthalpy of non-condensing gas per unit mass of steam
der_specificHeatCapacityCp	Derivative of specific heat capacity of gas mixture at constant pressure
der_specificHeatCapacityCv	Derivative of specific heat capacity of gas mixture at constant volume
Inherited
fluidConstants	Constant data for the fluid
moleToMassFractions	Return mass fractions X from mole fractions
massToMoleFractions	Return mole fractions from mass fractions X
ThermoStates	Enumeration type for independent variables
mediumName="unusablePartialMedium"	Name of the medium
substanceNames={mediumName}	Names of the mixture substances. Set substanceNames={mediumName} if only one substance.
extraPropertiesNames=fill("", 0)	Names of the additional (extra) transported properties. Set extraPropertiesNames=fill("",0) if unused
singleState	= true, if u and d are not a function of pressure
reducedX=true	= true if medium contains the equation sum(X) = 1.0; set reducedX=true if only one substance (see docu for details)
fixedX=false	= true if medium contains the equation X = reference_X
reference_p=101325	Reference pressure of Medium: default 1 atmosphere
reference_T=298.15	Reference temperature of Medium: default 25 deg Celsius
reference_X=fill(1/nX, nX)	Default mass fractions of medium
p_default=101325	Default value for pressure of medium (for initialization)
T_default=Modelica.SIunits.Conversions.from_degC(20)	Default value for temperature of medium (for initialization)
h_default=specificEnthalpy_pTX(p_default, T_default, X_default)	Default value for specific enthalpy of medium (for initialization)
X_default=reference_X	Default value for mass fractions of medium (for initialization)
nS=size(substanceNames, 1)	Number of substances
nX=nS	Number of mass fractions
nXi=if fixedX then 0 else if reducedX then nS - 1 else nS	Number of structurally independent mass fractions (see docu for details)
nC=size(extraPropertiesNames, 1)	Number of extra (outside of standard mass-balance) transported properties
C_nominal=1.0e-6*ones(nC)	Default for the nominal values for the extra properties
FluidConstants	Critical, triple, molecular and other standard data of fluid
setSmoothState	Return thermodynamic state so that it smoothly approximates: if x > 0 then state_a else state_b
prandtlNumber	Return the Prandtl number
heatCapacity_cp	Alias for deprecated name
heatCapacity_cv	Alias for deprecated name
isentropicExponent	Return isentropic exponent
velocityOfSound	Return velocity of sound
beta	Alias for isobaricExpansionCoefficient for user convenience
kappa	Alias of isothermalCompressibility for user convenience
density_derp_h	Return density derivative w.r.t. pressure at const specific enthalpy
density_derh_p	Return density derivative w.r.t. specific enthalpy at constant pressure
specificEntropy_pTX	Return specific enthalpy from p, T, and X or Xi
density_pTX	Return density from p, T, and X or Xi
density_phX	Return density from p, h, and X or Xi
temperature_psX	Return temperature from p,s, and X or Xi
density_psX	Return density from p, s, and X or Xi
specificEnthalpy_psX	Return specific enthalpy from p, s, and X or Xi
MassFlowRate	Type for mass flow rate with medium specific attributes
AbsolutePressure	Type for absolute pressure with medium specific attributes
Density	Type for density with medium specific attributes
DynamicViscosity	Type for dynamic viscosity with medium specific attributes
EnthalpyFlowRate	Type for enthalpy flow rate with medium specific attributes
MassFraction	Type for mass fraction with medium specific attributes
MoleFraction	Type for mole fraction with medium specific attributes
MolarMass	Type for molar mass with medium specific attributes
MolarVolume	Type for molar volume with medium specific attributes
IsentropicExponent	Type for isentropic exponent with medium specific attributes
SpecificEnergy	Type for specific energy with medium specific attributes
SpecificInternalEnergy	Type for specific internal energy with medium specific attributes
SpecificEnthalpy	Type for specific enthalpy with medium specific attributes
SpecificEntropy	Type for specific entropy with medium specific attributes
SpecificHeatCapacity	Type for specific heat capacity with medium specific attributes
SurfaceTension	Type for surface tension with medium specific attributes
Temperature	Type for temperature with medium specific attributes
ThermalConductivity	Type for thermal conductivity with medium specific attributes
PrandtlNumber	Type for Prandtl number with medium specific attributes
VelocityOfSound	Type for velocity of sound with medium specific attributes
ExtraProperty	Type for unspecified, mass-specific property transported by flow
CumulativeExtraProperty	Type for conserved integral of unspecified, mass specific property
ExtraPropertyFlowRate	Type for flow rate of unspecified, mass-specific property
IsobaricExpansionCoefficient	Type for isobaric expansion coefficient with medium specific attributes
DipoleMoment	Type for dipole moment with medium specific attributes
DerDensityByPressure	Type for partial derivative of density with respect to pressure with medium specific attributes
DerDensityByEnthalpy	Type for partial derivative of density with respect to enthalpy with medium specific attributes
DerEnthalpyByPressure	Type for partial derivative of enthalpy with respect to pressure with medium specific attributes
DerDensityByTemperature	Type for partial derivative of density with respect to temperature with medium specific attributes
DerTemperatureByPressure	Type for partial derivative of temperature with respect to pressure with medium specific attributes
SaturationProperties	Saturation properties of two phase medium
FluidLimits	Validity limits for fluid model
FixedPhase	Phase of the fluid: 1 for 1-phase, 2 for two-phase, 0 for not known, e.g., interactive use
Basic	The most basic version of a record used in several degrees of detail
IdealGas	The ideal gas version of a record used in several degrees of detail
TwoPhase	The two phase fluid version of a record used in several degrees of detail

Types and constants

  constant Integer Water=1 
  "Index of water (in substanceNames, massFractions X, etc.)";

  constant Integer Air=2 
  "Index of air (in substanceNames, massFractions X, etc.)";

  constant AbsolutePressure pStp = reference_p 
  "Pressure for which fluid density is defined";

  constant Density dStp = 1.2 "Fluid density at pressure pStp";

  constant GasProperties dryair(
    R =    Modelica.Media.IdealGases.Common.SingleGasesData.Air.R,
    MM =   Modelica.Media.IdealGases.Common.SingleGasesData.Air.MM,
    cp =   Buildings.Utilities.Psychrometrics.Constants.cpAir,
    cv =   Buildings.Utilities.Psychrometrics.Constants.cpAir
             -Modelica.Media.IdealGases.Common.SingleGasesData.Air.R) 
  "Dry air properties";

  constant GasProperties steam(
    R =    Modelica.Media.IdealGases.Common.SingleGasesData.H2O.R,
    MM =   Modelica.Media.IdealGases.Common.SingleGasesData.H2O.MM,
    cp =   Buildings.Utilities.Psychrometrics.Constants.cpSte,
    cv =   Buildings.Utilities.Psychrometrics.Constants.cpSte
             -Modelica.Media.IdealGases.Common.SingleGasesData.H2O.R) 
  "Steam properties";

  constant Real k_mair =  steam.MM/dryair.MM "Ratio of molar weights";

  constant Modelica.SIunits.MolarMass[2] MMX={steam.MM,dryair.MM} 
  "Molar masses of components";

  constant Modelica.SIunits.SpecificEnergy h_fg=
    Buildings.Utilities.Psychrometrics.Constants.h_fg 
  "Latent heat of evaporation of water";

  constant Modelica.SIunits.SpecificHeatCapacity cpWatLiq=
    Buildings.Utilities.Psychrometrics.Constants.cpWatLiq 
  "Specific heat capacity of liquid water";

Buildings.Media.Air.ThermodynamicState

ThermodynamicState record for moist air

Information

Extends from (Thermodynamic state variables).

Modelica definition

Buildings.Media.Air.BaseProperties

Base properties

Information

Extends from (Base properties (p, d, T, h, u, R, MM and, if applicable, X and Xi) of a medium).

Parameters

Modelica definition

Buildings.Media.Air.density

Gas density

Information

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Outputs

Modelica definition

Buildings.Media.Air.dynamicViscosity

Return the dynamic viscosity of dry air

Information

This function returns the dynamic viscosity.

Implementation

The function is based on the 5th order polynomial of Modelica.Media.Air.MoistAir.dynamicViscosity. However, for the typical range of temperatures encountered in building applications, a linear function sufficies. This implementation is therefore the above 5th order polynomial, linearized around 20°C. The relative error of this linearization is 0.4% at -20°C, and less then 0.2% between -5°C and +50°C.

Extends from (Return dynamic viscosity).

Inputs

Outputs

Modelica definition

Buildings.Media.Air.enthalpyOfCondensingGas

Enthalpy of steam per unit mass of steam

Information

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Outputs

Modelica definition

Buildings.Media.Air.enthalpyOfGas

Enthalpy of gas mixture per unit mass of gas mixture

Information

Extends from (Return enthalpy of non-condensing gas mixture).

Inputs

Outputs

Modelica definition

Buildings.Media.Air.enthalpyOfLiquid

Enthalpy of liquid (per unit mass of liquid) which is linear in the temperature

Information

Extends from (Return liquid enthalpy of condensing fluid).

Inputs

Outputs

Modelica definition

Buildings.Media.Air.enthalpyOfNonCondensingGas

Enthalpy of non-condensing gas per unit mass of steam

Information

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Outputs

Modelica definition

Buildings.Media.Air.enthalpyOfVaporization

Enthalpy of vaporization of water

Information

Extends from (Return vaporization enthalpy of condensing fluid).

Inputs

Outputs

Modelica definition

Buildings.Media.Air.gasConstant

Return ideal gas constant as a function from thermodynamic state, only valid for phi<1

Information

Extends from (Return the gas constant of the mixture (also for liquids)).

Inputs

Outputs

Modelica definition

Buildings.Media.Air.pressure

Returns pressure of ideal gas as a function of the thermodynamic state record

Information

Extends from (Return pressure).

Inputs

Outputs

Modelica definition

Buildings.Media.Air.isobaricExpansionCoefficient

Isobaric expansion coefficient beta

Information

This function returns the isobaric expansion coefficient at constant pressure, which is zero for this medium. The isobaric expansion coefficient at constant pressure is

β_p = - 1 ⁄ v   (∂ v ⁄ ∂ T)_p = 0,

where v is the specific volume, T is the temperature and p is the pressure.

Extends from (Return overall the isobaric expansion coefficient beta).

Inputs

Outputs

Modelica definition

Buildings.Media.Air.isothermalCompressibility

Isothermal compressibility factor

Information

This function returns the isothermal compressibility coefficient. The isothermal compressibility is

κ_T = -1 ⁄ v   (∂ v ⁄ ∂ p)_T = -1 ⁄ p,

where v is the specific volume, T is the temperature and p is the pressure.

Extends from (Return overall the isothermal compressibility factor).

Inputs

Outputs

Modelica definition

Buildings.Media.Air.saturationPressure

Saturation curve valid for 223.16 <= T <= 373.16 (and slightly outside with less accuracy)

Information

Extends from (Return saturation pressure of condensing fluid).

Inputs

Outputs

Modelica definition

Buildings.Media.Air.specificEntropy

Return the specific entropy, only valid for phi<1

Information

This function computes the specific entropy.

The specific entropy of the mixture is obtained from

s = s_s + s_m,

where s_s is the entropy change due to the state change (relative to the reference temperature) and s_m is the entropy change due to mixing of the dry air and water vapor.

The entropy change due to change in state is obtained from

s_s = c_v ln(T/T₀) + R ln(v/v₀)
= c_v ln(T/T₀) + R ln(ρ₀/ρ)

If we assume ρ = p₀/(R T), and because c_p = c_v + R, we can write

s_s = c_v ln(T/T₀) + R ln(T/T₀)
=c_p ln(T/T₀).

Next, the entropy of mixing is obtained from a reversible isothermal expansion process. Hence,

s_m = -R ∑_i( X_i ⁄ M_i ln(Y_i p/p₀)),

where R is the gas constant, X is the mass fraction, M is the molar mass, and Y is the mole fraction.

To obtain the state for a given pressure, entropy and mass fraction, use Buildings.Media.Air.setState_psX.

Limitations

This function is only valid for a relative humidity below 100%.

Extends from (Return specific entropy).

Inputs

Outputs

Modelica definition

Buildings.Media.Air.density_derp_T

Return the partial derivative of density with respect to pressure at constant temperature

Information

This function returns the partial derivative of density with respect to pressure at constant temperature.

Extends from (Return density derivative w.r.t. pressure at const temperature).

Inputs

Outputs

Modelica definition

Buildings.Media.Air.density_derT_p

Return the partial derivative of density with respect to temperature at constant pressure

Information

This function computes the derivative of density with respect to temperature at constant pressure.

Extends from (Return density derivative w.r.t. temperature at constant pressure).

Inputs

Outputs

Modelica definition

Buildings.Media.Air.density_derX

Return the partial derivative of density with respect to mass fractions at constant pressure and temperature

Information

This function returns the partial derivative of density with respect to mass fraction. This value is zero because in this medium, density is proportional to pressure, but independent of the species concentration.

Extends from (Return density derivative w.r.t. mass fraction).

Inputs

Outputs

Modelica definition

Buildings.Media.Air.specificHeatCapacityCp

Specific heat capacity of gas mixture at constant pressure

Information

Extends from (Return specific heat capacity at constant pressure).

Inputs

Outputs

Modelica definition

Buildings.Media.Air.specificHeatCapacityCv

Specific heat capacity of gas mixture at constant volume

Information

Extends from (Return specific heat capacity at constant volume).

Inputs

Outputs

Modelica definition

Buildings.Media.Air.setState_dTX

Return thermodynamic state as function of density d, temperature T and composition X

Information

The thermodynamic state record is computed from density d, temperature T and composition X.

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Outputs

Modelica definition

Buildings.Media.Air.setState_phX

Return thermodynamic state as function of pressure p, specific enthalpy h and composition X

Information

Extends from (Return thermodynamic state as function of p, h and composition X or Xi).

Inputs

Outputs

Modelica definition

Buildings.Media.Air.setState_pTX

Return thermodynamic state as function of p, T and composition X or Xi

Information

Extends from (Return thermodynamic state as function of p, T and composition X or Xi).

Inputs

Outputs

Modelica definition

Buildings.Media.Air.setState_psX

Return the thermodynamic state as function of p, s and composition X or Xi

Information

This function returns the thermodynamic state based on pressure, specific entropy and mass fraction.

The state is computed by symbolically solving Buildings.Media.Air.specificEntropy for temperature.

Extends from (Return thermodynamic state as function of p, s and composition X or Xi).

Inputs

Outputs

Modelica definition

Buildings.Media.Air.specificEnthalpy

Compute specific enthalpy from pressure, temperature and mass fraction

Information

Extends from (Return specific enthalpy).

Inputs

Outputs

Modelica definition

Buildings.Media.Air.specificEnthalpy_pTX

Specific enthalpy

Information

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Outputs

Modelica definition

Buildings.Media.Air.specificGibbsEnergy

Specific Gibbs energy

Information

Extends from (Return specific Gibbs energy).

Inputs

Outputs

Modelica definition

Buildings.Media.Air.specificHelmholtzEnergy

Specific Helmholtz energy

Information

Extends from (Return specific Helmholtz energy).

Inputs

Outputs

Modelica definition

Buildings.Media.Air.isentropicEnthalpy

Return the isentropic enthalpy

Information

This function computes the specific enthalpy for an isentropic state change from the temperature that corresponds to the state refState to reference_T.

Extends from (Return isentropic enthalpy).

Inputs

Outputs

Modelica definition

Buildings.Media.Air.specificInternalEnergy

Specific internal energy

Information

Extends from Modelica.Icons.Function (Icon for functions), (Return specific internal energy).

Inputs

Outputs

Modelica definition

Buildings.Media.Air.temperature

Return temperature of ideal gas as a function of the thermodynamic state record

Information

Extends from (Return temperature).

Inputs

Outputs

Modelica definition

Buildings.Media.Air.molarMass

Return the molar mass

Information

This function returns the molar mass.

Extends from (Return the molar mass of the medium).

Inputs

Outputs

Modelica definition

Buildings.Media.Air.temperature_phX

Compute temperature from specific enthalpy and mass fraction

Information

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Outputs

Modelica definition

Buildings.Media.Air.thermalConductivity

Thermal conductivity of dry air as a polynomial in the temperature

Information

Extends from (Return thermal conductivity).

Inputs

Outputs

Modelica definition

Buildings.Media.Air.GasProperties

Coefficient data record for properties of perfect gases

Information

This data record contains the coefficients for perfect gases.

Extends from Modelica.Icons.Record (Icon for records).

Modelica definition

Buildings.Media.Air.der_enthalpyOfLiquid

Temperature derivative of enthalpy of liquid per unit mass of liquid

Information

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Outputs

Modelica definition

Buildings.Media.Air.der_enthalpyOfCondensingGas

Derivative of enthalpy of steam per unit mass of steam

Information

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Outputs

Modelica definition

Buildings.Media.Air.enthalpyOfDryAir

Enthalpy of dry air per unit mass of dry air

Information

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Outputs

Modelica definition

Buildings.Media.Air.der_enthalpyOfDryAir

Derivative of enthalpy of dry air per unit mass of dry air

Information

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Outputs

Modelica definition

Buildings.Media.Air.der_enthalpyOfNonCondensingGas

Derivative of enthalpy of non-condensing gas per unit mass of steam

Information

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Outputs

Modelica definition

Buildings.Media.Air.der_specificHeatCapacityCp

Derivative of specific heat capacity of gas mixture at constant pressure

Information

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Outputs

Modelica definition

Buildings.Media.Air.der_specificHeatCapacityCv

Derivative of specific heat capacity of gas mixture at constant volume

Information

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Outputs

Modelica definition