Description: "Package with moist air model that decouples pressure and temperature"

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## 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/ρstp = p/pstp,

where pstd and ρstp 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 - pstp ⁄ ρstp,

where u is the internal energy per unit mass, h is the enthalpy per unit mass, pstp is the static pressure and ρstp 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 - pstp ⁄ ρstd,

because p ⁄ ρ = pstp ⁄ ρstp 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

redeclare record extends ThermodynamicState "ThermodynamicState record for moist air" end ThermodynamicState;

## 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

Type | Name | Default | Description
--- | --- | --- | ---
Boolean | standardOrderComponents | true | If true, and reducedX = true, the last element of X will be computed from the other ones
Advanced
Boolean | preferredMediumStates | false | = true if StateSelect.prefer shall be used for the independent property variables of the medium

### Modelica definition

redeclare replaceable model extends BaseProperties( p(stateSelect=if preferredMediumStates then StateSelect.prefer else StateSelect.default), Xi(each stateSelect=if preferredMediumStates then StateSelect.prefer else StateSelect.default), final standardOrderComponents=true) "Base properties" protected constant Modelica.SIunits.MolarMass[2] MMX = {steam.MM,dryair.MM} "Molar masses of components"; MassFraction X_steam "Mass fraction of steam water"; MassFraction X_air "Mass fraction of air"; Modelica.SIunits.TemperatureDifference dT "Temperature difference used to compute enthalpy"; equation assert(T >= 200.0 and T <= 423.15, " Temperature T is not in the allowed range 200.0 K <= (T =" + String(T) + " K) <= 423.15 K required from medium model \"" + mediumName + "\"."); MM = 1/(Xi[Water]/MMX[Water]+(1.0-Xi[Water])/MMX[Air]); X_steam = Xi[Water]; // There is no liquid in this medium model X_air = 1-Xi[Water]; dT = T - reference_T; h = dT*dryair.cp * X_air + (dT * steam.cp + h_fg) * X_steam; R = dryair.R*X_air + steam.R*X_steam; // Equation for ideal gas, from h=u+p*v and R*T=p*v, from which follows that u = h-R*T. // u = h-R*T; // However, in this medium, the gas law is d/dStp=p/pStp, from which follows using h=u+pv that // u= h-p*v = h-p/d = h-pStp/dStp u = h-pStp/dStp; // In this medium model, the density depends only // on temperature, but not on pressure. // d = p/(R*T); d/dStp = p/pStp; state.p = p; state.T = T; state.X = X; end BaseProperties;

## Buildings.Media.Air.density

Gas density

### Information

Density is computed from pressure, temperature and composition in the thermodynamic state record applying the ideal gas law.

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

### Inputs

Type | Name | Default | Description
--- | --- | --- | ---
ThermodynamicState | state |  |

### Outputs

Type | Name | Description
--- | --- | ---
Density | d | Density [kg/m3]

### Modelica definition

redeclare function density "Gas density" extends Modelica.Icons.Function; input ThermodynamicState state; output Density d "Density"; algorithm d :=state.p*dStp/pStp; end density;

## 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

Type | Name | Default | Description
--- | --- | --- | ---
ThermodynamicState | state |  | Thermodynamic state record

### Outputs

Type | Name | Description
--- | --- | ---
DynamicViscosity | eta | Dynamic viscosity [Pa.s]

### Modelica definition

redeclare function extends dynamicViscosity "Return the dynamic viscosity of dry air" algorithm eta := 4.89493640395e-08 * state.T + 3.88335940547e-06; end dynamicViscosity;

## Buildings.Media.Air.enthalpyOfCondensingGas

Enthalpy of steam per unit mass of steam

### Information

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

### Inputs

Type | Name | Default | Description
--- | --- | --- | ---
Temperature | T |  | temperature [K]

### Outputs

Type | Name | Description
--- | --- | ---
SpecificEnthalpy | h | steam enthalpy [J/kg]

### Modelica definition

redeclare function enthalpyOfCondensingGas "Enthalpy of steam per unit mass of steam" annotation(derivative=der_enthalpyOfCondensingGas); extends Modelica.Icons.Function; input Temperature T "temperature"; output SpecificEnthalpy h "steam enthalpy"; algorithm h := (T-reference_T) * steam.cp + h_fg; end enthalpyOfCondensingGas;

## 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

Type | Name | Default | Description
--- | --- | --- | ---
Temperature | T |  | Temperature [K]
MassFraction | X[:] |  | Vector of mass fractions [kg/kg]

### Outputs

Type | Name | Description
--- | --- | ---
SpecificEnthalpy | h | Specific enthalpy [J/kg]

### Modelica definition

redeclare replaceable function extends enthalpyOfGas "Enthalpy of gas mixture per unit mass of gas mixture" algorithm h := enthalpyOfCondensingGas(T)*X[Water] + enthalpyOfDryAir(T)*(1.0-X[Water]); end enthalpyOfGas;

## 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

Type | Name | Default | Description
--- | --- | --- | ---
Temperature | T |  | Temperature [K]

### Outputs

Type | Name | Description
--- | --- | ---
SpecificEnthalpy | h | Liquid enthalpy [J/kg]

### Modelica definition

redeclare replaceable function extends enthalpyOfLiquid "Enthalpy of liquid (per unit mass of liquid) which is linear in the temperature" annotation(derivative=der_enthalpyOfLiquid); algorithm h := (T - reference_T)*cpWatLiq; end enthalpyOfLiquid;

## Buildings.Media.Air.enthalpyOfNonCondensingGas

Enthalpy of non-condensing gas per unit mass of steam

### Information

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

### Inputs

Type | Name | Default | Description
--- | --- | --- | ---
Temperature | T |  | temperature [K]

### Outputs

Type | Name | Description
--- | --- | ---
SpecificEnthalpy | h | enthalpy [J/kg]

### Modelica definition

redeclare function enthalpyOfNonCondensingGas "Enthalpy of non-condensing gas per unit mass of steam" annotation(derivative=der_enthalpyOfNonCondensingGas); extends Modelica.Icons.Function; input Temperature T "temperature"; output SpecificEnthalpy h "enthalpy"; algorithm h := enthalpyOfDryAir(T); end enthalpyOfNonCondensingGas;

## Buildings.Media.Air.enthalpyOfVaporization

Enthalpy of vaporization of water

### Information

Extends from (Return vaporization enthalpy of condensing fluid).

### Inputs

Type | Name | Default | Description
--- | --- | --- | ---
Temperature | T |  | Temperature [K]

### Outputs

Type | Name | Description
--- | --- | ---
SpecificEnthalpy | r0 | Vaporization enthalpy [J/kg]

### Modelica definition

redeclare function extends enthalpyOfVaporization "Enthalpy of vaporization of water" algorithm r0 := h_fg; end enthalpyOfVaporization;

## Buildings.Media.Air.gasConstant

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

### Information

The ideal gas constant for moist air is computed from thermodynamic state assuming that all water is in the gas phase.

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

### Inputs

Type | Name | Default | Description
--- | --- | --- | ---
ThermodynamicState | state |  | Thermodynamic state

### Outputs

Type | Name | Description
--- | --- | ---
SpecificHeatCapacity | R | Mixture gas constant [J/(kg.K)]

### Modelica definition

redeclare function extends gasConstant "Return ideal gas constant as a function from thermodynamic state, only valid for phi<1" algorithm R := dryair.R*(1 - state.X[Water]) + steam.R*state.X[Water]; end gasConstant;

## Buildings.Media.Air.pressure

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

### Information

Pressure is returned from the thermodynamic state record input as a simple assignment.

Extends from (Return pressure).

### Inputs

Type | Name | Default | Description
--- | --- | --- | ---
ThermodynamicState | state |  | Thermodynamic state record

### Outputs

Type | Name | Description
--- | --- | ---
AbsolutePressure | p | Pressure [Pa]

### Modelica definition

redeclare function extends pressure "Returns pressure of ideal gas as a function of the thermodynamic state record" algorithm p := state.p; end pressure;

## 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

βp = - 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

Type | Name | Default | Description
--- | --- | --- | ---
ThermodynamicState | state |  | Thermodynamic state record

### Outputs

Type | Name | Description
--- | --- | ---
IsobaricExpansionCoefficient | beta | Isobaric expansion coefficient [1/K]

### Modelica definition

redeclare function extends isobaricExpansionCoefficient "Isobaric expansion coefficient beta" algorithm beta := 0; end isobaricExpansionCoefficient;

## Buildings.Media.Air.isothermalCompressibility

Isothermal compressibility factor

### Information

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

κT = -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

Type | Name | Default | Description
--- | --- | --- | ---
ThermodynamicState | state |  | Thermodynamic state record

### Outputs

Type | Name | Description
--- | --- | ---
IsothermalCompressibility | kappa | Isothermal compressibility [1/Pa]

### Modelica definition

redeclare function extends isothermalCompressibility "Isothermal compressibility factor" algorithm kappa := -1/state.p; end isothermalCompressibility;

## 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

Type | Name | Default | Description
--- | --- | --- | ---
Temperature | Tsat |  | Saturation temperature [K]

### Outputs

Type | Name | Description
--- | --- | ---
AbsolutePressure | psat | Saturation pressure [Pa]

### Modelica definition

redeclare function extends saturationPressure "Saturation curve valid for 223.16 <= T <= 373.16 (and slightly outside with less accuracy)" algorithm psat := Buildings.Utilities.Psychrometrics.Functions.saturationPressure(Tsat); end saturationPressure;

## 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 = ss + sm,

where ss is the entropy change due to the state change (relative to the reference temperature) and sm 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

ss = cv ln(T/T0) + R ln(v/v0)
= cv ln(T/T0) + R ln(ρ0/ρ)

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

ss = cv ln(T/T0) + R ln(T/T0)
=cp ln(T/T0).

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

sm = -R ∑i( Xi ⁄ Mi ln(Yi 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

Type | Name | Default | Description
--- | --- | --- | ---
ThermodynamicState | state |  | Thermodynamic state record

### Outputs

Type | Name | Description
--- | --- | ---
SpecificEntropy | s | Specific entropy [J/(kg.K)]

### Modelica definition

redeclare function extends specificEntropy "Return the specific entropy, only valid for phi<1" protected Modelica.SIunits.MoleFraction[2] Y "Molar fraction"; algorithm Y := massToMoleFractions( state.X, {steam.MM,dryair.MM}); s := specificHeatCapacityCp(state) * Modelica.Math.log(state.T/reference_T) - Modelica.Constants.R * sum(state.X[i]/MMX[i]* Modelica.Math.log(max(Y[i], Modelica.Constants.eps)*state.p/reference_p) for i in 1:2); end specificEntropy;

## 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

Type | Name | Default | Description
--- | --- | --- | ---
ThermodynamicState | state |  | Thermodynamic state record

### Outputs

Type | Name | Description
--- | --- | ---
DerDensityByPressure | ddpT | Density derivative w.r.t. pressure [s2/m2]

### Modelica definition

redeclare function extends density_derp_T "Return the partial derivative of density with respect to pressure at constant temperature" algorithm ddpT := dStp/pStp; end density_derp_T;

## 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

Type | Name | Default | Description
--- | --- | --- | ---
ThermodynamicState | state |  | Thermodynamic state record

### Outputs

Type | Name | Description
--- | --- | ---
DerDensityByTemperature | ddTp | Density derivative w.r.t. temperature [kg/(m3.K)]

### Modelica definition

redeclare function extends density_derT_p "Return the partial derivative of density with respect to temperature at constant pressure" algorithm ddTp := 0; end density_derT_p;

## 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

Type | Name | Default | Description
--- | --- | --- | ---
ThermodynamicState | state |  | Thermodynamic state record

### Outputs

Type | Name | Description
--- | --- | ---
Density | dddX[nX] | Derivative of density w.r.t. mass fraction [kg/m3]

### Modelica definition

redeclare function extends density_derX "Return the partial derivative of density with respect to mass fractions at constant pressure and temperature" algorithm dddX := fill(0, nX); end density_derX;

## Buildings.Media.Air.specificHeatCapacityCp

Specific heat capacity of gas mixture at constant pressure

### Information

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

### Inputs

Type | Name | Default | Description
--- | --- | --- | ---
ThermodynamicState | state |  | Thermodynamic state record

### Outputs

Type | Name | Description
--- | --- | ---
SpecificHeatCapacity | cp | Specific heat capacity at constant pressure [J/(kg.K)]

### Modelica definition

redeclare replaceable function extends specificHeatCapacityCp "Specific heat capacity of gas mixture at constant pressure" annotation(derivative=der_specificHeatCapacityCp); algorithm cp := dryair.cp*(1-state.X[Water]) +steam.cp*state.X[Water]; end specificHeatCapacityCp;

## Buildings.Media.Air.specificHeatCapacityCv

Specific heat capacity of gas mixture at constant volume

### Information

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

### Inputs

Type | Name | Default | Description
--- | --- | --- | ---
ThermodynamicState | state |  | Thermodynamic state record

### Outputs

Type | Name | Description
--- | --- | ---
SpecificHeatCapacity | cv | Specific heat capacity at constant volume [J/(kg.K)]

### Modelica definition

redeclare replaceable function extends specificHeatCapacityCv "Specific heat capacity of gas mixture at constant volume" annotation(derivative=der_specificHeatCapacityCv); algorithm cv:= dryair.cv*(1-state.X[Water]) +steam.cv*state.X[Water]; end specificHeatCapacityCv;

## 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

Type | Name | Default | Description
--- | --- | --- | ---
Density | d |  | Density [kg/m3]
Temperature | T |  | Temperature [K]
MassFraction | X[:] | reference_X | Mass fractions [kg/kg]

### Outputs

Type | Name | Description
--- | --- | ---
ThermodynamicState | state | Thermodynamic state

### Modelica definition

redeclare function setState_dTX "Return thermodynamic state as function of density d, temperature T and composition X" extends Modelica.Icons.Function; input Density d "Density"; input Temperature T "Temperature"; input MassFraction X[:]=reference_X "Mass fractions"; output ThermodynamicState state "Thermodynamic state"; algorithm // Note that d/dStp = p/pStp, hence p = d*pStp/dStp state := if size(X, 1) == nX then ThermodynamicState(p=d*pStp/dStp, T=T, X=X) else ThermodynamicState(p=d*pStp/dStp, T=T, X=cat(1, X, {1 - sum(X)})); end setState_dTX;

## Buildings.Media.Air.setState_phX

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

### Information

The thermodynamic state record is computed from pressure p, specific enthalpy h and composition X.

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

### Inputs

Type | Name | Default | Description
--- | --- | --- | ---
AbsolutePressure | p |  | Pressure [Pa]
SpecificEnthalpy | h |  | Specific enthalpy [J/kg]
MassFraction | X[:] | reference_X | Mass fractions [kg/kg]

### Outputs

Type | Name | Description
--- | --- | ---
ThermodynamicState | state | Thermodynamic state record

### Modelica definition

redeclare function extends setState_phX "Return thermodynamic state as function of pressure p, specific enthalpy h and composition X" algorithm state := if size(X, 1) == nX then ThermodynamicState(p=p, T=temperature_phX(p, h, X), X=X) else ThermodynamicState(p=p, T=temperature_phX(p, h, X), X=cat(1, X, {1 - sum(X)})); end setState_phX;

## Buildings.Media.Air.setState_pTX

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

### Information

The thermodynamic state record is computed from pressure p, temperature T and composition X.

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

### Inputs

Type | Name | Default | Description
--- | --- | --- | ---
AbsolutePressure | p |  | Pressure [Pa]
Temperature | T |  | Temperature [K]
MassFraction | X[:] | reference_X | Mass fractions [kg/kg]

### Outputs

Type | Name | Description
--- | --- | ---
ThermodynamicState | state | Thermodynamic state record

### Modelica definition

redeclare function extends setState_pTX "Return thermodynamic state as function of p, T and composition X or Xi" algorithm state := if size(X, 1) == nX then ThermodynamicState(p=p, T=T, X=X) else ThermodynamicState(p=p, T=T, X=cat(1, X, {1 - sum(X)})); end setState_pTX;

## 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

Type | Name | Default | Description
--- | --- | --- | ---
AbsolutePressure | p |  | Pressure [Pa]
SpecificEntropy | s |  | Specific entropy [J/(kg.K)]
MassFraction | X[:] | reference_X | Mass fractions [kg/kg]

### Outputs

Type | Name | Description
--- | --- | ---
ThermodynamicState | state | Thermodynamic state record

### Modelica definition

redeclare function extends setState_psX "Return the thermodynamic state as function of p, s and composition X or Xi" protected Modelica.SIunits.MassFraction[2] X_int= if size(X, 1) == nX then X else cat(1, X, {1 - sum(X)}) "Mass fraction"; Modelica.SIunits.MoleFraction[2] Y "Molar fraction"; Modelica.SIunits.Temperature T "Temperature"; algorithm Y := massToMoleFractions( X_int, {steam.MM,dryair.MM}); // The next line is obtained from symbolic solving the // specificEntropy function for T. // In this formulation, we can set T to any value when calling // specificHeatCapacityCp as cp does not depend on T. T := 273.15 * Modelica.Math.exp((s + Modelica.Constants.R * sum(X_int[i]/MMX[i]* Modelica.Math.log(max(Y[i], Modelica.Constants.eps)) for i in 1:2)) / specificHeatCapacityCp(setState_pTX(p=p, T=273.15, X=X_int))); state := ThermodynamicState(p=p, T=T, X=X_int); end setState_psX;

## Buildings.Media.Air.specificEnthalpy

Compute specific enthalpy from pressure, temperature and mass fraction

### Information

Extends from (Return specific enthalpy).

### Inputs

Type | Name | Default | Description
--- | --- | --- | ---
ThermodynamicState | state |  | Thermodynamic state record

### Outputs

Type | Name | Description
--- | --- | ---
SpecificEnthalpy | h | Specific enthalpy [J/kg]

### Modelica definition

redeclare replaceable function extends specificEnthalpy "Compute specific enthalpy from pressure, temperature and mass fraction" algorithm h := (state.T - reference_T)*dryair.cp * (1 - state.X[Water]) + ((state.T-reference_T) * steam.cp + h_fg) * state.X[Water]; end specificEnthalpy;

## Buildings.Media.Air.specificEnthalpy_pTX

Specific enthalpy

### Information

Specific enthalpy as a function of temperature and species concentration. The pressure is input for compatibility with the medium models, but the specific enthalpy is independent of the pressure.

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

### Inputs

Type | Name | Default | Description
--- | --- | --- | ---
Pressure | p |  | Pressure [Pa]
Temperature | T |  | Temperature [K]
MassFraction | X[:] |  | Mass fractions of moist air [1]

### Outputs

Type | Name | Description
--- | --- | ---
SpecificEnthalpy | h | Specific enthalpy at p, T, X [J/kg]

### Modelica definition

redeclare replaceable function specificEnthalpy_pTX "Specific enthalpy" extends Modelica.Icons.Function; input Modelica.SIunits.Pressure p "Pressure"; input Modelica.SIunits.Temperature T "Temperature"; input Modelica.SIunits.MassFraction X[:] "Mass fractions of moist air"; output Modelica.SIunits.SpecificEnthalpy h "Specific enthalpy at p, T, X"; algorithm h := specificEnthalpy(setState_pTX(p, T, X)); end specificEnthalpy_pTX;

## Buildings.Media.Air.specificGibbsEnergy

Specific Gibbs energy

### Information

Extends from (Return specific Gibbs energy).

### Inputs

Type | Name | Default | Description
--- | --- | --- | ---
ThermodynamicState | state |  | Thermodynamic state record

### Outputs

Type | Name | Description
--- | --- | ---
SpecificEnergy | g | Specific Gibbs energy [J/kg]

### Modelica definition

redeclare replaceable function extends specificGibbsEnergy "Specific Gibbs energy" algorithm g := specificEnthalpy(state) - state.T*specificEntropy(state); end specificGibbsEnergy;

## Buildings.Media.Air.specificHelmholtzEnergy

Specific Helmholtz energy

### Information

Extends from (Return specific Helmholtz energy).

### Inputs

Type | Name | Default | Description
--- | --- | --- | ---
ThermodynamicState | state |  | Thermodynamic state record

### Outputs

Type | Name | Description
--- | --- | ---
SpecificEnergy | f | Specific Helmholtz energy [J/kg]

### Modelica definition

redeclare replaceable function extends specificHelmholtzEnergy "Specific Helmholtz energy" algorithm f := specificEnthalpy(state) - gasConstant(state)*state.T - state.T*specificEntropy(state); end specificHelmholtzEnergy;

## 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

Type | Name | Default | Description
--- | --- | --- | ---
AbsolutePressure | p_downstream |  | Downstream pressure [Pa]
ThermodynamicState | refState |  | Reference state for entropy

### Outputs

Type | Name | Description
--- | --- | ---
SpecificEnthalpy | h_is | Isentropic enthalpy [J/kg]

### Modelica definition

redeclare function extends isentropicEnthalpy "Return the isentropic enthalpy" algorithm h_is := specificEnthalpy(setState_psX( p=p_downstream, s=specificEntropy(refState), X=refState.X)); end isentropicEnthalpy;

## Buildings.Media.Air.specificInternalEnergy

Specific internal energy

### Information

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

### Inputs

Type | Name | Default | Description
--- | --- | --- | ---
ThermodynamicState | state |  | Thermodynamic state record

### Outputs

Type | Name | Description
--- | --- | ---
SpecificEnergy | u | Specific internal energy [J/kg]

### Modelica definition

redeclare function extends specificInternalEnergy "Specific internal energy" extends Modelica.Icons.Function; algorithm u := specificEnthalpy(state) - pStp/dStp; end specificInternalEnergy;

## Buildings.Media.Air.temperature

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

### Information

Temperature is returned from the thermodynamic state record input as a simple assignment.

Extends from (Return temperature).

### Inputs

Type | Name | Default | Description
--- | --- | --- | ---
ThermodynamicState | state |  | Thermodynamic state record

### Outputs

Type | Name | Description
--- | --- | ---
Temperature | T | Temperature [K]

### Modelica definition

redeclare function extends temperature "Return temperature of ideal gas as a function of the thermodynamic state record" algorithm T := state.T; end temperature;

## 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

Type | Name | Default | Description
--- | --- | --- | ---
ThermodynamicState | state |  | Thermodynamic state record

### Outputs

Type | Name | Description
--- | --- | ---
MolarMass | MM | Mixture molar mass [kg/mol]

### Modelica definition

redeclare function extends molarMass "Return the molar mass" algorithm MM := 1/(state.X[Water]/MMX[Water]+(1.0-state.X[Water])/MMX[Air]); end molarMass;

## Buildings.Media.Air.temperature_phX

Compute temperature from specific enthalpy and mass fraction

### Information

Temperature as a function of specific enthalpy and species concentration. The pressure is input for compatibility with the medium models, but the temperature is independent of the pressure.

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

### Inputs

Type | Name | Default | Description
--- | --- | --- | ---
AbsolutePressure | p |  | Pressure [Pa]
SpecificEnthalpy | h |  | specific enthalpy [J/kg]
MassFraction | X[:] |  | mass fractions of composition [kg/kg]

### Outputs

Type | Name | Description
--- | --- | ---
Temperature | T | temperature [K]

### Modelica definition

redeclare replaceable function temperature_phX "Compute temperature from specific enthalpy and mass fraction" extends Modelica.Icons.Function; input AbsolutePressure p "Pressure"; input SpecificEnthalpy h "specific enthalpy"; input MassFraction[:] X "mass fractions of composition"; output Temperature T "temperature"; algorithm T := reference_T + (h - h_fg * X[Water]) /((1 - X[Water])*dryair.cp + X[Water] * steam.cp); end temperature_phX;

## Buildings.Media.Air.thermalConductivity

Thermal conductivity of dry air as a polynomial in the temperature

### Information

Extends from (Return thermal conductivity).

### Inputs

Type | Name | Default | Description
--- | --- | --- | ---
ThermodynamicState | state |  | Thermodynamic state record

### Outputs

Type | Name | Description
--- | --- | ---
ThermalConductivity | lambda | Thermal conductivity [W/(m.K)]

### Modelica definition

redeclare function extends thermalConductivity "Thermal conductivity of dry air as a polynomial in the temperature" algorithm lambda := Modelica.Media.Incompressible.TableBased.Polynomials_Temp.evaluate( {(-4.8737307422969E-008), 7.67803133753502E-005, 0.0241814385504202}, Modelica.SIunits.Conversions.to_degC(state.T)); end thermalConductivity;

## 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

record GasProperties "Coefficient data record for properties of perfect gases" extends Modelica.Icons.Record; Modelica.SIunits.MolarMass MM "Molar mass"; Modelica.SIunits.SpecificHeatCapacity R "Gas constant"; Modelica.SIunits.SpecificHeatCapacity cp "Specific heat capacity at constant pressure"; Modelica.SIunits.SpecificHeatCapacity cv = cp-R "Specific heat capacity at constant volume"; end GasProperties;

## 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

Type | Name | Default | Description
--- | --- | --- | ---
Temperature | T |  | Temperature [K]
Real | der_T |  | Temperature derivative

### Outputs

Type | Name | Description
--- | --- | ---
Real | der_h | Derivative of liquid enthalpy

### Modelica definition

replaceable function der_enthalpyOfLiquid "Temperature derivative of enthalpy of liquid per unit mass of liquid" extends Modelica.Icons.Function; input Temperature T "Temperature"; input Real der_T "Temperature derivative"; output Real der_h "Derivative of liquid enthalpy"; algorithm der_h := cpWatLiq*der_T; end der_enthalpyOfLiquid;

## 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

Type | Name | Default | Description
--- | --- | --- | ---
Temperature | T |  | Temperature [K]
Real | der_T |  | Temperature derivative

### Outputs

Type | Name | Description
--- | --- | ---
Real | der_h | Derivative of steam enthalpy

### Modelica definition

function der_enthalpyOfCondensingGas "Derivative of enthalpy of steam per unit mass of steam" extends Modelica.Icons.Function; input Temperature T "Temperature"; input Real der_T "Temperature derivative"; output Real der_h "Derivative of steam enthalpy"; algorithm der_h := steam.cp*der_T; end der_enthalpyOfCondensingGas;

## Buildings.Media.Air.enthalpyOfDryAir

Enthalpy of dry air per unit mass of dry air

### Information

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

### Inputs

Type | Name | Default | Description
--- | --- | --- | ---
Temperature | T |  | Temperature [K]

### Outputs

Type | Name | Description
--- | --- | ---
SpecificEnthalpy | h | Dry air enthalpy [J/kg]

### Modelica definition

replaceable function enthalpyOfDryAir "Enthalpy of dry air per unit mass of dry air" annotation(derivative=der_enthalpyOfDryAir); extends Modelica.Icons.Function; input Temperature T "Temperature"; output SpecificEnthalpy h "Dry air enthalpy"; algorithm h := (T - reference_T)*dryair.cp; end enthalpyOfDryAir;

## 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

Type | Name | Default | Description
--- | --- | --- | ---
Temperature | T |  | Temperature [K]
Real | der_T |  | Temperature derivative

### Outputs

Type | Name | Description
--- | --- | ---
Real | der_h | Derivative of dry air enthalpy

### Modelica definition

replaceable function der_enthalpyOfDryAir "Derivative of enthalpy of dry air per unit mass of dry air" extends Modelica.Icons.Function; input Temperature T "Temperature"; input Real der_T "Temperature derivative"; output Real der_h "Derivative of dry air enthalpy"; algorithm der_h := dryair.cp*der_T; end der_enthalpyOfDryAir;

## 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

Type | Name | Default | Description
--- | --- | --- | ---
Temperature | T |  | Temperature [K]
Real | der_T |  | Temperature derivative

### Outputs

Type | Name | Description
--- | --- | ---
Real | der_h | Derivative of steam enthalpy

### Modelica definition

replaceable function der_enthalpyOfNonCondensingGas "Derivative of enthalpy of non-condensing gas per unit mass of steam" extends Modelica.Icons.Function; input Temperature T "Temperature"; input Real der_T "Temperature derivative"; output Real der_h "Derivative of steam enthalpy"; algorithm der_h := der_enthalpyOfDryAir(T, der_T); end der_enthalpyOfNonCondensingGas;

## 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

Type | Name | Default | Description
--- | --- | --- | ---
ThermodynamicState | state |  | Thermodynamic state
ThermodynamicState | der_state |  | Derivative of thermodynamic state

### Outputs

Type | Name | Description
--- | --- | ---
Real | der_cp | Derivative of specific heat capacity [J/(kg.K.s)]

### Modelica definition

replaceable function der_specificHeatCapacityCp "Derivative of specific heat capacity of gas mixture at constant pressure" extends Modelica.Icons.Function; input ThermodynamicState state "Thermodynamic state"; input ThermodynamicState der_state "Derivative of thermodynamic state"; output Real der_cp(unit="J/(kg.K.s)") "Derivative of specific heat capacity"; algorithm der_cp := (steam.cp-dryair.cp)*der_state.X[Water]; end der_specificHeatCapacityCp;

## 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

Type | Name | Default | Description
--- | --- | --- | ---
ThermodynamicState | state |  | Thermodynamic state
ThermodynamicState | der_state |  | Derivative of thermodynamic state

### Outputs

Type | Name | Description
--- | --- | ---
Real | der_cv | Derivative of specific heat capacity [J/(kg.K.s)]

### Modelica definition

replaceable function der_specificHeatCapacityCv "Derivative of specific heat capacity of gas mixture at constant volume" extends Modelica.Icons.Function; input ThermodynamicState state "Thermodynamic state"; input ThermodynamicState der_state "Derivative of thermodynamic state"; output Real der_cv(unit="J/(kg.K.s)") "Derivative of specific heat capacity"; algorithm der_cv := (steam.cv-dryair.cv)*der_state.X[Water]; end der_specificHeatCapacityCv;