Buildings.Media.Steam

Package with model for pure steam water vapor

Information

This medium package models water vapor (pure steam, region 2, quality=1).

Thermodynamic properties are calculated primarily in terms of pressure and temperature. For thermodynamic property functions, the IAPWS-IF97 formulations are adapted, and approximate relationships are provided for commonly used functions to improve computational efficiency and provide backward compatability.

Detailed functions from Modelica.Media.Water.WaterIF97_R2pT are generally used, except for Buildings.Media.Steam.specificEnthalpy and Buildings.Media.Steam.specificEntropy (both "forward" functions), as well as their "backward" inverse functions Buildings.Media.Steam.temperature_ph and Buildings.Media.Steam.temperature_ps, which are numerically consistent with the forward functions. The following modifications were made relative to the Modelica.Media.Water.WaterIF97_R2pT medium package:

Analytic expressions for the derivatives are provided for all thermodynamic property functions.
The implementation is generally simpler in order to increase the likelihood of more efficient simulations.

Limitations

The valid temperature range is 100°C ≤ T ≤ 160°C, and the valid pressure range is 100 kPa ≤ p ≤ 550 kPa.
When phase change is required, this model is to be used in combination with Buildings.Media.Water for the liquid phase (quality=0). Please note that the maximum temperature for liquid water is T_max=130°C. This is suitable for real-world condensate return and boiler feedwater systems, which are typically vented to the atmosphere with steam contained via steam traps (thus, T_max=100°C for the condensate or feedwater in properly functioning systems).

Applications

This model is intended for first generation district heating systems and other steam heating processes involving low and medium pressure steam.

References

W. Wagner et al., “The IAPWS industrial formulation 1997 for the thermodynamic properties of water and steam,” J. Eng. Gas Turbines Power, vol. 122, no. 1, pp. 150–180, 2000.

Kathryn Hinkelman, Saranya Anbarasu, Michael Wetter, Antoine Gautier, Wangda Zuo. 2022. “A Fast and Accurate Modeling Approach for Water and Steam Thermodynamics with Practical Applications in District Heating System Simulation,” Energy, 254(A), pp. 124227. 10.1016/j.energy.2022.124227

Kathryn Hinkelman, Saranya Anbarasu, Michael Wetter, Antoine Gautier, Baptiste Ravache, Wangda Zuo 2022. “Towards Open-Source Modelica Models For Steam-Based District Heating Systems.” Proc. of the 1st International Workshop On Open Source Modelling And Simulation Of Energy Systems (OSMSES 2022), Aachen, German, April 4-5, 2022. 10.1109/OSMSES54027.2022.9769121

Extends from Modelica.Media.Interfaces.PartialMedium (Partial medium properties (base package of all media packages)), Modelica.Icons.Package (Icon for standard packages).

Package Content

Name	Description
ThermodynamicState	Thermodynamic state variables
BaseProperties	Base properties (p, d, T, h, u, R, MM) of water
density	Returns density
dynamicViscosity	Return dynamic viscosity
molarMass	Return the molar mass of the medium
pressure	Return pressure
saturationPressure	Return saturation pressure of condensing fluid
saturationTemperature	Return saturation temperature
specificEnthalpy	Returns specific enthalpy
specificEntropy	Return specific entropy
specificInternalEnergy	Return specific internal energy
specificHeatCapacityCp	Specific heat capacity at constant pressure
specificHeatCapacityCv	Specific heat capacity at constant volume
specificGibbsEnergy	Specific Gibbs energy
specificHelmholtzEnergy	Specific Helmholtz energy
setState_dTX	Return the thermodynamic state as function of d and T
setState_pTX	Return the thermodynamic state as function of p and T
setState_phX	Return the thermodynamic state as function of p and h
setState_psX	Return the thermodynamic state as function of p and s
temperature	Return temperature
thermalConductivity	Return thermal conductivity
density_derh_p	Density derivative by specific enthalpy
density_derp_h	Density derivative by pressure
isentropicExponent	Return isentropic exponent
isothermalCompressibility	Isothermal compressibility of water
isobaricExpansionCoefficient	Isobaric expansion coefficient of water
isentropicEnthalpy	Isentropic enthalpy
GasProperties	Coefficient data record for properties of perfect gases
steam	Steam properties
g2	Gibbs function for region 2: g(p,T)
temperature_ph	Return temperature from p and h, inverse function of h(p,T)
temperature_ps	Return temperature from p and s, inverse function of s(p,T)
rho_pT	Density as function of temperature and pressure
pressure_dT	Computes pressure as a function of density and temperature
Inherited
ThermoStates=Modelica.Media.Interfaces.Choices.IndependentVariables.pTX	Enumeration type for independent variables
mediumName="steam"	Name of the medium
substanceNames={"water"}	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	= 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=true	= true if medium contains the equation X = reference_X
reference_p=101325	Reference pressure of Medium: default 1 atmosphere
reference_T=273.15	Reference temperature of Medium: default 25 deg Celsius
reference_X={1}	Default mass fractions of medium
p_default=100000	Default value for pressure of medium (for initialization)
T_default=Modelica.Units.Conversions.from_degC(100)	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)
C_default=fill(0, nC)	Default value for trace substances 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
velocityOfSound	Return velocity of sound
beta	Alias for isobaricExpansionCoefficient for user convenience
kappa	Alias of isothermalCompressibility for user convenience
density_derp_T	Return density derivative w.r.t. pressure at const temperature
density_derT_p	Return density derivative w.r.t. temperature at constant pressure
density_derX	Return density derivative w.r.t. mass fraction
specificEnthalpy_pTX	Return specific enthalpy from p, T, and X or Xi
specificEntropy_pTX	Return specific enthalpy from p, T, and X or Xi
density_pTX	Return density from p, T, and X or Xi
temperature_phX	Return temperature from p, h, 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 GasProperties steam(R=Modelica.Media.IdealGases.Common.SingleGasesData.H2O.R_s,
      MM=Modelica.Media.IdealGases.Common.SingleGasesData.H2O.MM)
    "Steam properties";

Buildings.Media.Steam.ThermodynamicState

Thermodynamic state variables

Modelica definition

redeclare record ThermodynamicState "Thermodynamic state variables" AbsolutePressure p "Absolute pressure of medium"; Temperature T "Temperature of medium"; end ThermodynamicState;

Buildings.Media.Steam.BaseProperties

Base properties (p, d, T, h, u, R, MM) of water

Information

Extends from (Base properties (p, d, T, h, u, R_s, 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	true	= true if StateSelect.prefer shall be used for the independent property variables of the medium

Modelica definition

redeclare replaceable model extends BaseProperties( preferredMediumStates = true, final standardOrderComponents=true) "Base properties (p, d, T, h, u, R, MM) of water" equation MM = steam.MM; h = specificEnthalpy(state); d = density(state); u = h - p/d; R_s = steam.R; state.p = p; state.T = T; end BaseProperties;

Buildings.Media.Steam.density

Returns density

Information

Density is computed from temperature and pressure using the IAPWS-IF97 relationship via the Gibbs free energy for region 2.

Extends from (Return density).

Inputs

Type	Name	Default	Description
ThermodynamicState	state		Thermodynamic state record

Outputs

Type	Name	Description
Density	d	Density [kg/m3]

Modelica definition

redeclare replaceable function extends density "Returns density" algorithm d := rho_pT(state.p, state.T); end density;

Buildings.Media.Steam.dynamicViscosity

Return dynamic viscosity

Information

Dynamic viscosity is computed from density, temperature and pressure using the IAPWS-IF97 formulation.

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 replaceable function extends dynamicViscosity "Return dynamic viscosity" algorithm eta := Modelica.Media.Water.IF97_Utilities.dynamicViscosity( d=density(state), T=state.T, p=state.p); end dynamicViscosity;

Buildings.Media.Steam.molarMass

Return the molar mass of the medium

Information

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 replaceable function extends molarMass "Return the molar mass of the medium" algorithm MM := steam.MM; end molarMass;

Buildings.Media.Steam.pressure

Return pressure

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 "Return pressure" algorithm p := state.p; end pressure;

Buildings.Media.Steam.saturationPressure

Return saturation pressure of condensing fluid

Information

Saturation pressure is computed from temperature using the IAPWS-IF97 formulation.

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

Inputs

Type	Name	Default	Description
Temperature	Tsat		Saturation temperature [K]

Outputs

Type	Name	Description
AbsolutePressure	psat	Saturation pressure [Pa]

Modelica definition

replaceable function saturationPressure "Return saturation pressure of condensing fluid" extends Modelica.Icons.Function; input Temperature Tsat "Saturation temperature"; output AbsolutePressure psat "Saturation pressure"; algorithm psat := Modelica.Media.Water.IF97_Utilities.BaseIF97.Basic.psat(Tsat); end saturationPressure;

Buildings.Media.Steam.saturationTemperature

Return saturation temperature

Information

Saturation temperature is computed from pressure using the IAPWS-IF97 formulation.

Inputs

Type	Name	Default	Description
AbsolutePressure	psat		Saturation pressure [Pa]

Outputs

Type	Name	Description
Temperature	Tsat	Saturation temperature [K]

Modelica definition

replaceable function saturationTemperature "Return saturation temperature" input AbsolutePressure psat "Saturation pressure"; output Temperature Tsat "Saturation temperature"; algorithm Tsat := Modelica.Media.Water.IF97_Utilities.BaseIF97.Basic.tsat(psat); end saturationTemperature;

Buildings.Media.Steam.specificEnthalpy

Returns specific enthalpy

Information

Returns the specific enthalpy.

Implementation

The function is based on Modelica.Media.Water.WaterIF97_base.specificEnthalpy_pT. However, for the typical range of temperatures and pressures encountered in building and district energy applications, a linear function sufficies. This implementation is therefore a linear surface fit of the IF97 formulation h(p,T) in the ranges of 100°C ≤ T ≤ 160°C and 100 kPa ≤ p ≤ 550 kPa. The fit is scaled by the dataset's mean and standard deviation values to improve conditioning. The largest error of this linearization is 2.42 kJ/kg (0.09%), which occurs at 100.6°C and 100 kPa. The root mean square error (RMSE) is 0.76 kJ/kg.

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 "Returns specific enthalpy" protected constant Real a[:] = {2.749e+06,-9118,2.752e+04} "Regression coefficients"; constant AbsolutePressure pMean = 2.50427896656637E+05 "Mean pressure"; constant Temperature TMean = 4.15555698340926E+02 "Mean temperature"; constant Real pSD = 1.13236055019318E+05 "Normalization value"; constant Real TSD = 1.32971013463839E+01 "Normalization value"; Modelica.Units.SI.PressureDifference pHat; Modelica.Units.SI.TemperatureDifference THat; algorithm pHat := (state.p - pMean)/pSD; THat := (state.T - TMean)/TSD; h := a[1] + a[2]*pHat + a[3]*THat; end specificEnthalpy;

Buildings.Media.Steam.specificEntropy

Return specific entropy

Information

Returns the specific entropy.

Implementation

The function is based on Modelica.Media.Water.WaterIF97_base.specificEntropy. However, for the typical range of temperatures and pressures encountered in building and district energy applications, an invertible polynomial fit sufficies. This implementation is therefore a polynomial fit (quadratic in pressure, linear in temperature) of the IF97 formulation s(p,T) in the ranges of 100°C ≤ T ≤ 160°C and 100 kPa ≤ p ≤ 550 kPa. The fit is scaled by the dataset's mean and standard deviation values to improve conditioning. The largest error of this approximation is 0.047 kJ/kg-K (0.70%), which occurs at 160°C and 550 kPa. The root mean square error (RMSE) is 12.56 J/kg-K.

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 replaceable function extends specificEntropy "Return specific entropy" protected constant Real a[:] = {7135,-252.4,70.03,40.6,4.953} "Regression coefficients"; constant AbsolutePressure pMean = 2.50427896656637E+05 "Mean pressure"; constant Temperature TMean = 4.15555698340926E+02 "Mean temperature"; constant Real pSD = 1.13236055019318E+05 "Normalization value"; constant Real TSD = 1.32971013463839E+01 "Normalization value"; Modelica.Units.SI.PressureDifference pHat; Modelica.Units.SI.TemperatureDifference THat; algorithm pHat := (state.p - pMean)/pSD; THat := (state.T - TMean)/TSD; s := a[1] + a[2]*pHat + a[3]*THat + pHat*(a[4]*pHat + a[5]*THat); end specificEntropy;

Buildings.Media.Steam.specificInternalEnergy

Return specific internal energy

Information

Returns the specific internal energy for a given state.

Extends from (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 replaceable function extends specificInternalEnergy "Return specific internal energy" algorithm u := specificEnthalpy(state) - state.p/density(state); end specificInternalEnergy;

Buildings.Media.Steam.specificHeatCapacityCp

Specific heat capacity at constant pressure

Information

Specific heat at constant pressure is computed from temperature and pressure using the IAPWS-IF97 relationship via the Gibbs free energy for region 2.

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 at constant pressure" protected Modelica.Media.Common.GibbsDerivs g "Dimensionless Gibbs function and derivatives w.r.t. pi and tau"; SpecificHeatCapacity R "Specific gas constant of water vapor"; algorithm R := Modelica.Media.Water.IF97_Utilities.BaseIF97.data.RH2O; // Region 2 properties g := g2(state.p, state.T); cp := -R*g.tau*g.tau*g.gtautau; end specificHeatCapacityCp;

Buildings.Media.Steam.specificHeatCapacityCv

Specific heat capacity at constant volume

Information

Specific heat at constant volume is computed from temperature and pressure using the IAPWS-IF97 relationship via the Gibbs free energy for region 2.

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 at constant volume" protected Modelica.Media.Common.GibbsDerivs g "Dimensionless Gibbs function and derivatives w.r.t. pi and tau"; SpecificHeatCapacity R "Specific gas constant of water vapor"; algorithm R := Modelica.Media.Water.IF97_Utilities.BaseIF97.data.RH2O; // Region 2 properties g := g2(state.p, state.T); cv := R*(-g.tau*g.tau*g.gtautau + ((g.gpi - g.tau*g.gtaupi)*(g.gpi - g.tau*g.gtaupi)/g.gpipi)); end specificHeatCapacityCv;

Buildings.Media.Steam.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.Steam.specificHelmholtzEnergy

Specific Helmholtz energy

Information

Returns the specific Helmholtz energy for a given state.

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) - steam.R*state.T - state.T*specificEntropy(state); end specificHelmholtzEnergy;

Buildings.Media.Steam.setState_dTX

Return the thermodynamic state as function of d and T

Information

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

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

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 record

Modelica definition

redeclare replaceable function extends setState_dTX "Return the thermodynamic state as function of d and T" algorithm state := ThermodynamicState(p=pressure_dT(d,T), T=T); end setState_dTX;

Buildings.Media.Steam.setState_pTX

Return the thermodynamic state as function of p and T

Information

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

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 replaceable function extends setState_pTX "Return the thermodynamic state as function of p and T" algorithm state := ThermodynamicState(p=p, T=T); end setState_pTX;

Buildings.Media.Steam.setState_phX

Return the thermodynamic state as function of p and h

Information

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

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 replaceable function extends setState_phX "Return the thermodynamic state as function of p and h" algorithm state := ThermodynamicState(p=p, T=temperature_ph(p,h)); end setState_phX;

Buildings.Media.Steam.setState_psX

Return the thermodynamic state as function of p and s

Information

The thermodynamic state record is computed from pressure p and specific entropy s.

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 replaceable function extends setState_psX "Return the thermodynamic state as function of p and s" algorithm state := ThermodynamicState(p=p, T=temperature_ps(p,s)); end setState_psX;

Buildings.Media.Steam.temperature

Return temperature

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" algorithm T := state.T; end temperature;

Buildings.Media.Steam.thermalConductivity

Return thermal conductivity

Information

Thermal conductivity is computed from density, temperature and pressure using the IAPWS-IF97 formulation.

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 replaceable function extends thermalConductivity "Return thermal conductivity" algorithm lambda := Modelica.Media.Water.IF97_Utilities.thermalConductivity( density(state), state.T, state.p); end thermalConductivity;

Buildings.Media.Steam.density_derh_p

Density derivative by specific enthalpy

Information

Returns the partial derivative of density with respect to specific enthalpy at constant pressure using the IAPWS-IF97 formulation.

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

Inputs

Type	Name	Default	Description
ThermodynamicState	state		Thermodynamic state record

Outputs

Type	Name	Description
DerDensityByEnthalpy	ddhp	Density derivative w.r.t. specific enthalpy [kg.s2/m5]

Modelica definition

redeclare function extends density_derh_p "Density derivative by specific enthalpy" algorithm ddhp := Modelica.Media.Water.IF97_Utilities.ddhp( p = state.p, h = specificEnthalpy(state), phase = 1, region = 2); end density_derh_p;

Buildings.Media.Steam.density_derp_h

Density derivative by pressure

Information

Returns the partial derivative of density with respect to pressure at constant specific enthalpy using the IAPWS-IF97 formulation.

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

Inputs

Type	Name	Default	Description
ThermodynamicState	state		Thermodynamic state record

Outputs

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

Modelica definition

redeclare function extends density_derp_h "Density derivative by pressure" algorithm ddph := Modelica.Media.Water.IF97_Utilities.ddph( p = state.p, h = specificEnthalpy(state), phase = 1, region = 2); end density_derp_h;

Buildings.Media.Steam.isentropicExponent

Return isentropic exponent

Information

Isentropic exponent is computed from temperature and pressure using the IAPWS-IF97 formulation.

Extends from (Return isentropic exponent).

Inputs

Type	Name	Default	Description
ThermodynamicState	state		Thermodynamic state record

Outputs

Type	Name	Description
IsentropicExponent	gamma	Isentropic exponent [1]

Modelica definition

redeclare replaceable function extends isentropicExponent "Return isentropic exponent" algorithm gamma := Modelica.Media.Water.IF97_Utilities.isentropicExponent_pT( p = state.p, T = state.T, region = 2); end isentropicExponent;

Buildings.Media.Steam.isothermalCompressibility

Isothermal compressibility of water

Information

Isothermal compressibility is computed from temperature and pressure using the IAPWS-IF97 formulation.

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 replaceable function extends isothermalCompressibility "Isothermal compressibility of water" algorithm kappa := Modelica.Media.Water.IF97_Utilities.kappa_pT( p = state.p, T = state.T, region = 2); end isothermalCompressibility;

Buildings.Media.Steam.isobaricExpansionCoefficient

Isobaric expansion coefficient of water

Information

Isobaric expansion coefficient is computed from temperature and pressure using the IAPWS-IF97 formulation.

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 replaceable function extends isobaricExpansionCoefficient "Isobaric expansion coefficient of water" algorithm beta := Modelica.Media.Water.IF97_Utilities.beta_pT( p = state.p, T = state.T, region = 2); end isobaricExpansionCoefficient;

Buildings.Media.Steam.isentropicEnthalpy

Isentropic enthalpy

Information

Isentropic enthalpy is computed using the IAPWS-IF97 formulation:

A medium is in a particular state, refState.
The enthalpy at another state h_is shall be computed under the assumption that the state transformation from refState to h_is is performed with a change of specific entropy ds = 0 and the pressure of state h_is is p_downstream and the composition X upstream and downstream is assumed to be the same.

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 replaceable function extends isentropicEnthalpy "Isentropic enthalpy" algorithm h_is := Modelica.Media.Water.IF97_Utilities.isentropicEnthalpy( p = p_downstream, s = specificEntropy(refState), phase = 0); // phase 0 means unknown end isentropicEnthalpy;

Buildings.Media.Steam.GasProperties

Coefficient data record for properties of perfect gases

Information

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.Units.SI.MolarMass MM "Molar mass"; Modelica.Units.SI.SpecificHeatCapacity R "Gas constant"; end GasProperties;

Buildings.Media.Steam.g2

Gibbs function for region 2: g(p,T)

Information

This function is identical to Modelica.Media.Water.IF97_Utilities.BaseIF97.Basic.g2 except that

it contains the smoothOrder annotation, and
it removes the assertions on the temperature and pressure because the applicability of this medium is steam heating which has medium states that are inside these values.

The smoothOrder is needed for Optimica to differentiate the specific heat capacity, which is used in Buildings.Media.Examples.SteamDerivativeCheck. The function is differentiable except at p=0, which is far away from the state for which this function is used.

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

Inputs

Type	Name	Default	Description
Pressure	p		Pressure [Pa]
Temperature	T		Temperature (K) [K]

Outputs

Type	Name	Description
GibbsDerivs	g	Dimensionless Gibbs function and derivatives w.r.t. pi and tau

Modelica definition

function g2 "Gibbs function for region 2: g(p,T)" extends Modelica.Icons.Function; input Modelica.Units.SI.Pressure p "Pressure"; input Modelica.Units.SI.Temperature T "Temperature (K)"; output Modelica.Media.Common.GibbsDerivs g "Dimensionless Gibbs function and derivatives w.r.t. pi and tau"; protected Real tau2 "Dimensionless temperature"; Real[55] o "Vector of auxiliary variables"; algorithm g.p := p; g.T := T; g.R_s := Modelica.Media.Water.IF97_Utilities.BaseIF97.data.RH2O; // assert(p > 0.0, // "IF97 medium function g2 called with too low pressure\n" + "p = " + // String(p) + " Pa <= 0.0 Pa"); // assert(p <= 100.0e6, "IF97 medium function g2: the input pressure (= " // + String(p) + " Pa) is higher than 100 Mpa"); // assert(T >= 273.15, "IF97 medium function g2: the temperature (= " + // String(T) + " K) is lower than 273.15 K!"); // assert(T <= 1073.15, // "IF97 medium function g2: the input temperature (= " + String(T) + // " K) is higher than the limit of 1073.15 K"); g.pi := p/Modelica.Media.Water.IF97_Utilities.BaseIF97.data.PSTAR2; g.tau := Modelica.Media.Water.IF97_Utilities.BaseIF97.data.TSTAR2/T; tau2 := -0.5 + g.tau; o[1] := tau2*tau2; o[2] := o[1]*tau2; o[3] := -0.050325278727930*o[2]; o[4] := -0.057581259083432 + o[3]; o[5] := o[4]*tau2; o[6] := -0.045996013696365 + o[5]; o[7] := o[6]*tau2; o[8] := -0.0178348622923580 + o[7]; o[9] := o[8]*tau2; o[10] := o[1]*o[1]; o[11] := o[10]*o[10]; o[12] := o[11]*o[11]; o[13] := o[10]*o[11]*o[12]*tau2; o[14] := o[1]*o[10]*tau2; o[15] := o[10]*o[11]*tau2; o[16] := o[1]*o[12]*tau2; o[17] := o[1]*o[11]*tau2; o[18] := o[1]*o[10]*o[11]; o[19] := o[10]*o[11]*o[12]; o[20] := o[1]*o[10]; o[21] := g.pi*g.pi; o[22] := o[21]*o[21]; o[23] := o[21]*o[22]; o[24] := o[10]*o[12]*tau2; o[25] := o[12]*o[12]; o[26] := o[11]*o[12]*o[25]*tau2; o[27] := o[10]*o[12]; o[28] := o[1]*o[10]*o[11]*tau2; o[29] := o[10]*o[12]*o[25]*tau2; o[30] := o[1]*o[10]*o[25]*tau2; o[31] := o[1]*o[11]*o[12]; o[32] := o[1]*o[12]; o[33] := g.tau*g.tau; o[34] := o[33]*o[33]; o[35] := -0.000053349095828174*o[13]; o[36] := -0.087594591301146 + o[35]; o[37] := o[2]*o[36]; o[38] := -0.0078785554486710 + o[37]; o[39] := o[1]*o[38]; o[40] := -0.00037897975032630 + o[39]; o[41] := o[40]*tau2; o[42] := -0.000066065283340406 + o[41]; o[43] := o[42]*tau2; o[44] := 5.7870447262208e-6*tau2; o[45] := -0.301951672367580*o[2]; o[46] := -0.172743777250296 + o[45]; o[47] := o[46]*tau2; o[48] := -0.091992027392730 + o[47]; o[49] := o[48]*tau2; o[50] := o[1]*o[11]; o[51] := o[10]*o[11]; o[52] := o[11]*o[12]*o[25]; o[53] := o[10]*o[12]*o[25]; o[54] := o[1]*o[10]*o[25]; o[55] := o[11]*o[12]*tau2; g.g := g.pi*(-0.00177317424732130 + o[9] + g.pi*(tau2*(-0.000033032641670203 + (-0.000189489875163150 + o[1]*(-0.0039392777243355 + (-0.043797295650573 - 0.0000266745479140870*o[13])*o[2]))*tau2) + g.pi*( 2.04817376923090e-8 + (4.3870667284435e-7 + o[1]*(-0.000032277677238570 + (-0.00150339245421480 - 0.040668253562649*o[13])*o[2]))*tau2 + g.pi *(g.pi*(2.29220763376610e-6*o[14] + g.pi*((-1.67147664510610e-11 + o[ 15]*(-0.00211714723213550 - 23.8957419341040*o[16]))*o[2] + g.pi*(-5.9059564324270e-18 + o[17]*(-1.26218088991010e-6 - 0.038946842435739*o[18]) + g.pi*(o[ 11]*(1.12562113604590e-11 - 8.2311340897998*o[19]) + g.pi*( 1.98097128020880e-8*o[15] + g.pi*(o[10]*(1.04069652101740e-19 + (-1.02347470959290e-13 - 1.00181793795110e-9*o[10])*o[20]) + o[23]*(o[13]*(-8.0882908646985e-11 + 0.106930318794090*o[24]) + o[21]*(-0.33662250574171*o[26] + o[21]* (o[27]*(8.9185845355421e-25 + (3.06293168762320e-13 - 4.2002467698208e-6*o[15])*o[28]) + g.pi*(-5.9056029685639e-26*o[24] + g.pi*(3.7826947613457e-6*o[29] + g.pi*(-1.27686089346810e-15*o[30] + o[31]*(7.3087610595061e-29 + o[18]*(5.5414715350778e-17 - 9.4369707241210e-7*o[32]))*g.pi)))))))))))) + tau2*(-7.8847309559367e-10 + (1.27907178522850e-8 + 4.8225372718507e-7*tau2)*tau2))))) + (-0.0056087911830200 + g.tau*(0.071452738814550 + g.tau*(-0.40710498239280 + g.tau*( 1.42408197144400 + g.tau*(-4.3839511194500 + g.tau*(-9.6927686002170 + g.tau*(10.0866556801800 + (-0.284086326077200 + 0.0212684635330700 *g.tau)*g.tau) + Modelica.Math.log(g.pi)))))))/(o[34]*g.tau); g.gpi := (1.00000000000000 + g.pi*(-0.00177317424732130 + o[9] + g.pi*( o[43] + g.pi*(6.1445213076927e-8 + (1.31612001853305e-6 + o[1]*(-0.000096833031715710 + (-0.0045101773626444 - 0.122004760687947*o[13])*o[2]))*tau2 + g.pi *(g.pi*(0.0000114610381688305*o[14] + g.pi*((-1.00288598706366e-10 + o[15]*(-0.0127028833928130 - 143.374451604624*o[16]))*o[2] + g.pi*(-4.1341695026989e-17 + o[17]*(-8.8352662293707e-6 - 0.272627897050173*o[18]) + g.pi*(o[11] *(9.0049690883672e-11 - 65.849072718398*o[19]) + g.pi*( 1.78287415218792e-7*o[15] + g.pi*(o[10]*(1.04069652101740e-18 + (-1.02347470959290e-12 - 1.00181793795110e-8*o[10])*o[20]) + o[23]*(o[13]*(-1.29412653835176e-9 + 1.71088510070544*o[24]) + o[21]*(-6.0592051033508*o[26] + o[21]*(o[ 27]*(1.78371690710842e-23 + (6.1258633752464e-12 - 0.000084004935396416*o[15])*o[28]) + g.pi*(-1.24017662339842e-24*o[24] + g.pi*(0.000083219284749605*o[29] + g.pi*(-2.93678005497663e-14*o[ 30] + o[31]*(1.75410265428146e-27 + o[18]*(1.32995316841867e-15 - 0.0000226487297378904*o[32]))*g.pi)))))))))))) + tau2*(-3.15389238237468e-9 + (5.1162871409140e-8 + 1.92901490874028e-6*tau2)*tau2))))))/g.pi; g.gpipi := (-1.00000000000000 + o[21]*(o[43] + g.pi*( 1.22890426153854e-7 + (2.63224003706610e-6 + o[1]*(-0.000193666063431420 + (-0.0090203547252888 - 0.244009521375894*o[13])*o[2]))*tau2 + g.pi *(g.pi*(0.000045844152675322*o[14] + g.pi*((-5.0144299353183e-10 + o[ 15]*(-0.063514416964065 - 716.87225802312*o[16]))*o[2] + g.pi*(-2.48050170161934e-16 + o[17]*(-0.000053011597376224 - 1.63576738230104*o[18]) + g.pi*(o[ 11]*(6.3034783618570e-10 - 460.94350902879*o[19]) + g.pi*( 1.42629932175034e-6*o[15] + g.pi*(o[10]*(9.3662686891566e-18 + (-9.2112723863361e-12 - 9.0163614415599e-8*o[10])*o[20]) + o[23]*(o[13]*(-1.94118980752764e-8 + 25.6632765105816*o[24]) + o[21]*(-103.006486756963*o[26] + o[21]*( o[27]*(3.3890621235060e-22 + (1.16391404129682e-10 - 0.00159609377253190*o[15])*o[28]) + g.pi*(-2.48035324679684e-23*o[24] + g.pi*(0.00174760497974171*o[29] + g.pi*(-6.4609161209486e-13*o[30] + o[31]*(4.0344361048474e-26 + o[18]*(3.05889228736295e-14 - 0.00052092078397148*o[32]))*g.pi)))))))))))) + tau2*(-9.4616771471240e-9 + (1.53488614227420e-7 + o[44])*tau2)))))/o[21]; g.gtau := (0.0280439559151000 + g.tau*(-0.285810955258200 + g.tau*( 1.22131494717840 + g.tau*(-2.84816394288800 + g.tau*(4.3839511194500 + o[33]*(10.0866556801800 + (-0.56817265215440 + 0.063805390599210*g.tau) *g.tau))))))/(o[33]*o[34]) + g.pi*(-0.0178348622923580 + o[49] + g.pi *(-0.000033032641670203 + (-0.00037897975032630 + o[1]*(-0.0157571108973420 + (-0.306581069554011 - 0.00096028372490713*o[13])*o[2]))*tau2 + g.pi *(4.3870667284435e-7 + o[1]*(-0.000096833031715710 + (-0.0090203547252888 - 1.42338887469272*o[13])*o[2]) + g.pi*(-7.8847309559367e-10 + g.pi* (0.0000160454534363627*o[20] + g.pi*(o[1]*(-5.0144299353183e-11 + o[ 15]*(-0.033874355714168 - 836.35096769364*o[16])) + g.pi*((-0.0000138839897890111 - 0.97367106089347*o[18])*o[50] + g.pi*(o[14]*(9.0049690883672e-11 - 296.320827232793*o[19]) + g.pi*(2.57526266427144e-7*o[51] + g.pi*( o[2]*(4.1627860840696e-19 + (-1.02347470959290e-12 - 1.40254511313154e-8*o[10])*o[20]) + o[23]*(o[19]*(-2.34560435076256e-9 + 5.3465159397045*o[24]) + o[21]*(-19.1874828272775*o[52] + o[21]*(o[ 16]*(1.78371690710842e-23 + (1.07202609066812e-11 - 0.000201611844951398*o[15])*o[28]) + g.pi*(-1.24017662339842e-24*o[27] + g.pi*(0.000200482822351322*o[53] + g.pi*(-4.9797574845256e-14*o[54] + (1.90027787547159e-27 + o[18]*(2.21658861403112e-15 - 0.000054734430199902*o[32]))*o[55]*g.pi)))))))))))) + ( 2.55814357045700e-8 + 1.44676118155521e-6*tau2)*tau2)))); g.gtautau := (-0.168263735490600 + g.tau*(1.42905477629100 + g.tau*(-4.8852597887136 + g.tau*(8.5444918286640 + g.tau*(-8.7679022389000 + o[33]*(-0.56817265215440 + 0.127610781198420*g.tau)*g.tau)))))/(o[33]*o[34]*g.tau) + g.pi*(-0.091992027392730 + (-0.34548755450059 - 1.50975836183790*o[2])*tau2 + g.pi*(-0.00037897975032630 + o[1]*(-0.047271332692026 + (-1.83948641732407 - 0.033609930371750* o[13])*o[2]) + g.pi*((-0.000193666063431420 + (-0.045101773626444 - 48.395221739552*o[13])*o[2])*tau2 + g.pi*(2.55814357045700e-8 + 2.89352236311042e-6*tau2 + g.pi*(0.000096272720618176*o[10]*tau2 + g.pi *((-1.00288598706366e-10 + o[15]*(-0.50811533571252 - 28435.9329015838*o[16]))*tau2 + g.pi*(o[11]*(-0.000138839897890111 - 23.3681054614434*o[18])*tau2 + g.pi*((6.3034783618570e-10 - 10371.2289531477*o[19])*o[20] + g.pi*(3.09031519712573e-6*o[17] + g.pi *(o[1]*(1.24883582522088e-18 + (-9.2112723863361e-12 - 1.82330864707100e-7*o[10])*o[20]) + o[23]*(o[1]*o[11]*o[12]*(-6.5676921821352e-8 + 261.979281045521*o[24])*tau2 + o[21]*(-1074.49903832754*o[1]*o[10] *o[12]*o[25]*tau2 + o[21]*((3.3890621235060e-22 + ( 3.6448887082716e-10 - 0.0094757567127157*o[15])*o[28])*o[32] + g.pi*( -2.48035324679684e-23*o[16] + g.pi*(0.0104251067622687*o[1]*o[12]*o[ 25]*tau2 + g.pi*(o[11]*o[12]*(4.7506946886790e-26 + o[18]*( 8.6446955947214e-14 - 0.00311986252139440*o[32]))*g.pi - 1.89230784411972e-12*o[10]*o[25]*tau2)))))))))))))))); g.gtaupi := -0.0178348622923580 + o[49] + g.pi*(-0.000066065283340406 + (-0.00075795950065260 + o[1]*(-0.0315142217946840 + (-0.61316213910802 - 0.00192056744981426*o[13])*o[2]))*tau2 + g.pi*(1.31612001853305e-6 + o[1]*(-0.000290499095147130 + (-0.0270610641758664 - 4.2701666240781*o[13])*o[2]) + g.pi*(-3.15389238237468e-9 + g.pi*( 0.000080227267181813*o[20] + g.pi*(o[1]*(-3.00865796119098e-10 + o[15] *(-0.203246134285008 - 5018.1058061618*o[16])) + g.pi*((-0.000097187928523078 - 6.8156974262543*o[18])*o[50] + g.pi*(o[14]*(7.2039752706938e-10 - 2370.56661786234*o[19]) + g.pi*(2.31773639784430e-6*o[51] + g.pi*(o[2] *(4.1627860840696e-18 + (-1.02347470959290e-11 - 1.40254511313154e-7* o[10])*o[20]) + o[23]*(o[19]*(-3.7529669612201e-8 + 85.544255035272*o[ 24]) + o[21]*(-345.37469089099*o[52] + o[21]*(o[16]*( 3.5674338142168e-22 + (2.14405218133624e-10 - 0.0040322368990280*o[15]) *o[28]) + g.pi*(-2.60437090913668e-23*o[27] + g.pi*( 0.0044106220917291*o[53] + g.pi*(-1.14534422144089e-12*o[54] + ( 4.5606669011318e-26 + o[18]*(5.3198126736747e-14 - 0.00131362632479764*o[32]))*o[55]*g.pi)))))))))))) + ( 1.02325742818280e-7 + o[44])*tau2))); end g2;

Buildings.Media.Steam.temperature_ph

Return temperature from p and h, inverse function of h(p,T)

Information

Returns temperature from specific enthalpy and pressure.

Implementation

This linear approximation is the inverse or backward function of Buildings.Media.Steam.specificEnthalpy and is numerically consistent with that forward function.

The largest error of this linearization is 1.17°C (0.31%), which occurs at 100°C and 100 kPa.

Inputs

Type	Name	Default	Description
AbsolutePressure	p		Pressure [Pa]
SpecificEnthalpy	h		Specific Enthalpy [J/kg]

Outputs

Type	Name	Description
Temperature	T	Temperature [K]

Modelica definition

function temperature_ph "Return temperature from p and h, inverse function of h(p,T)" input AbsolutePressure p "Pressure"; input SpecificEnthalpy h "Specific Enthalpy"; output Temperature T "Temperature"; protected constant Real a[:] = {2.749e+06,-9118,2.752e+04} "Coefficients from forward function h(p,T)"; constant Real b[:] = {-a[1]*TSD/a[3]+TMean, -a[2]*TSD/a[3], TSD/a[3]} "Regression coefficients"; constant AbsolutePressure pMean = 2.50427896656637E+05 "Mean pressure"; constant Temperature TMean = 4.15555698340926E+02 "Mean temperature"; constant Real pSD = 1.13236055019318E+05 "Normalization value"; constant Real TSD = 1.32971013463839E+01 "Normalization value"; Modelica.Units.SI.PressureDifference pHat; algorithm pHat := (p - pMean)/pSD; T := b[1] + b[2]*pHat + b[3]*h; end temperature_ph;

Buildings.Media.Steam.temperature_ps

Return temperature from p and s, inverse function of s(p,T)

Information

Returns temperature from specific entropy and pressure.

Implementation

This polynomial approximation is the inverse or backward function of Buildings.Media.Steam.specificEntropy and is numerically consistent with that forward function.

The largest error of this linearization is 7.70°C (1.86%), which occurs at 137.4°C and 100 kPa.

Inputs

Type	Name	Default	Description
AbsolutePressure	p		Pressure [Pa]
SpecificEntropy	s		Specific Entropy [J/(kg.K)]

Outputs

Type	Name	Description
Temperature	T	Temperature [K]

Modelica definition

function temperature_ps "Return temperature from p and s, inverse function of s(p,T)" input AbsolutePressure p "Pressure"; input SpecificEntropy s "Specific Entropy"; output Temperature T "Temperature"; protected constant Real a[:] = {7135,-252.4,70.03,40.6,4.953} "Coefficients from forward function s(p,T)"; constant AbsolutePressure pMean = 2.50427896656637E+05 "Mean pressure"; constant Temperature TMean = 4.15555698340926E+02 "Mean temperature"; constant Real pSD = 1.13236055019318E+05 "Normalization value"; constant Real TSD = 1.32971013463839E+01 "Normalization value"; Modelica.Units.SI.PressureDifference pHat; Modelica.Units.SI.TemperatureDifference THat; algorithm pHat := (p - pMean)/pSD; THat := (s - a[1] - pHat*(a[2] + a[4]*pHat))/(a[3] + a[5]*pHat); T := THat*TSD + TMean; end temperature_ps;

Buildings.Media.Steam.rho_pT

Density as function of temperature and pressure

Information

Density is computed from temperature and pressure using the IAPWS-IF97 relationship via the Gibbs free energy for region 2.

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

Inputs

Type	Name	Default	Description
AbsolutePressure	p		Pressure [Pa]
Temperature	T		Temperature [K]

Outputs

Type	Name	Description
Density	rho	Density [kg/m3]

Modelica definition

function rho_pT "Density as function of temperature and pressure" extends Modelica.Icons.Function; input AbsolutePressure p "Pressure"; input Temperature T "Temperature"; output Density rho "Density"; protected Modelica.Media.Common.GibbsDerivs g "Dimensionless Gibbs function and derivatives w.r.t. pi and tau"; SpecificHeatCapacity R "Specific gas constant of water vapor"; function g2_smooth extends Modelica.Media.Water.IF97_Utilities.BaseIF97.Basic.g2; end g2_smooth; algorithm R := Modelica.Media.Water.IF97_Utilities.BaseIF97.data.RH2O; // Region 2 properties g := g2_smooth(p, T); rho := p/(R*T*g.pi*g.gpi); end rho_pT;

Buildings.Media.Steam.pressure_dT

Computes pressure as a function of density and temperature

Inputs

Type	Name	Default	Description
Density	d		Density [kg/m3]
Temperature	T		Temperature [K]

Outputs

Type	Name	Description
AbsolutePressure	p	Pressure [Pa]

Modelica definition

function pressure_dT "Computes pressure as a function of density and temperature" input Density d "Density"; input Temperature T "Temperature"; output AbsolutePressure p "Pressure"; algorithm p := Modelica.Media.Water.IF97_Utilities.BaseIF97.Inverses.pofdt125( d=d, T=T, reldd=1.0e-8, region=2); end pressure_dT;