IEA EBC Annex 60

Annex60.Media.Specialized.Water.TemperatureDependentDensity

Package with model for liquid water with temperature-dependent density

Information

This medium package models liquid water.

The mass density is computed using a 3rd order polynomial, which yields the density as a function of temperature as shown in the figure below. Note, however, that computing density as a function of temperature can lead to considerably slower computing time compared to using Annex60.Media.Water in which the density is a constant. We therefore recommend to use Annex60.Media.Water for typical building energy simulations.

For the specific heat capacities at constant pressure and at constant volume, a constant value of 4184 J/(kg K), which corresponds to 20°C is used. The figure below shows the relative error of the specific heat capacity that is introduced by this simplification. Using a constant value for the specific heat capacity allows to compute temperature from enthalpy without having to solve an implicit equation, and therefore leads to faster simulation.

Thermal conductivity is calculated as a function of temperature as shown in the figure below. The correlation used to calculate the thermal conductivity is

λ(T) = λ(298.15 K) ⋅ (-1.48445+4.12292⋅(T/298.15)-1.63866⋅(T/298.15)²),

where λ(298.15 K) = 0.6065 W/(m ⋅ K) is the adopted standard value of the thermal conductivity of water at 298.15 K and 0.1 MPa.

Dynamic viscosity is calculated as the product of density and kinematic viscosity, both temperature dependent. However, the kinematic viscosity has its own temperture dependent correlation, implemented at Annex60.Media.Specialized.Water.TemperatureDependentDensity.kinematicViscosity. Results of the kinematic viscosity as a function of temperature are shown in the figure below.

The enthalpy is computed using the convention that h=0 if T=0 °C.

Limitations

Phase changes are not modeled.

Extends from Modelica.Media.Interfaces.PartialPureSubstance (Base class for pure substances of one chemical substance), Modelica.Icons.Package (Icon for standard packages).

Package Content

Name	Description
FluidConstants
ThermodynamicState	Thermodynamic state variables
cp_const=4184	Specific heat capacity at constant pressure
BaseProperties	Base properties
density	Return the density
dynamicViscosity	Return the dynamic viscosity
specificEnthalpy	Return the specific enthalpy
enthalpyOfLiquid	Return the specific enthalpy of liquid
specificInternalEnergy	Return the specific enthalpy
specificEntropy	Return the specific entropy
specificGibbsEnergy	Return the specific Gibbs energy
specificHelmholtzEnergy	Return the specific Helmholtz energy
isentropicEnthalpy	Return the isentropic enthalpy
isobaricExpansionCoefficient	Return the isobaric expansion coefficient
isothermalCompressibility	Return the isothermal compressibility factor
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	Return the specific heat capacity at constant pressure
specificHeatCapacityCv	Return the specific heat capacity at constant volume
thermalConductivity	Return the thermal conductivity
pressure	Return the pressure
temperature	Return the temperature
molarMass	Return the molar mass
setState_dTX	Return thermodynamic state from d, T, and X or Xi
setState_phX	Return the thermodynamic state as function of pressure p, specific enthalpy h and composition X or Xi
setState_pTX	Return the 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
cv_const=cp_const	Specific heat capacity at constant volume
a_const=1484	Constant velocity of sound
MM_const=0.018015268	Molar mass
der_specificHeatCapacityCp	Return the derivative of the specific heat capacity at constant pressure
der_enthalpyOfLiquid	Temperature derivative of enthalpy of liquid per unit mass of liquid
kinematicViscosity	Return the kinematic viscosity
Inherited
setState_pT	Return thermodynamic state from p and T
setState_ph	Return thermodynamic state from p and h
setState_ps	Return thermodynamic state from p and s
setState_dT	Return thermodynamic state from d and T
density_ph	Return density from p and h
temperature_ph	Return temperature from p and h
pressure_dT	Return pressure from d and T
specificEnthalpy_dT	Return specific enthalpy from d and T
specificEnthalpy_ps	Return specific enthalpy from p and s
temperature_ps	Return temperature from p and s
density_ps	Return density from p and s
specificEnthalpy_pT	Return specific enthalpy from p and T
density_pT	Return density from p and T
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
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
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 Modelica.SIunits.SpecificHeatCapacity cp_const = 4184
    "Specific heat capacity at constant pressure";

  final constant Modelica.SIunits.SpecificHeatCapacity cv_const = cp_const
    "Specific heat capacity at constant volume";

  constant Modelica.SIunits.VelocityOfSound a_const=1484
    "Constant velocity of sound";

  constant Modelica.SIunits.MolarMass MM_const=0.018015268 "Molar mass";

Annex60.Media.Specialized.Water.TemperatureDependentDensity.FluidConstants

Parameters

Modelica definition

Annex60.Media.Specialized.Water.TemperatureDependentDensity.ThermodynamicState

Thermodynamic state variables

Information

Extends from (Minimal variable set that is available as input argument to every medium function).

Modelica definition

Annex60.Media.Specialized.Water.TemperatureDependentDensity.BaseProperties

Base properties

Information

Base properties of the medium.

Extends from .

Parameters

Modelica definition

Annex60.Media.Specialized.Water.TemperatureDependentDensity.density

Return the density

Information

This function computes the density as a function of temperature.

Implementation

The function is based on the IDA implementation in therpro.nmf, which implements

d := 1000.12 + 1.43711e-2*T_degC -
 5.83576e-3*T_degC^2 + 1.5009e-5*T_degC^3;
 

This has been converted to Kelvin, which resulted in the above expression. In addition, below 5 °C and above 100 °C, the density is replaced by a linear function to avoid inflection points. This linear extension is such that the density is once continuously differentiable.

Extends from (Return density).

Inputs

Outputs

Modelica definition

Annex60.Media.Specialized.Water.TemperatureDependentDensity.dynamicViscosity

Return the dynamic viscosity

Information

This function computes the dynamic viscosity.

Extends from (Return dynamic viscosity).

Inputs

Outputs

Modelica definition

Annex60.Media.Specialized.Water.TemperatureDependentDensity.specificEnthalpy

Return the specific enthalpy

Information

This function computes the specific enthalpy.

Extends from (Return specific enthalpy).

Inputs

Outputs

Modelica definition

Annex60.Media.Specialized.Water.TemperatureDependentDensity.enthalpyOfLiquid

Return the specific enthalpy of liquid

Information

This function computes the specific enthalpy of liquid water.

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

Inputs

Outputs

Modelica definition

Annex60.Media.Specialized.Water.TemperatureDependentDensity.specificInternalEnergy

Return the specific enthalpy

Information

This function computes the specific internal energy.

Extends from (Return specific internal energy).

Inputs

Outputs

Modelica definition

Annex60.Media.Specialized.Water.TemperatureDependentDensity.specificEntropy

Return the specific entropy

Information

This function computes the specific entropy.

To obtain the state for a given pressure, entropy and mass fraction, use Annex60.Media.Air.setState_psX.

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

Inputs

Outputs

Modelica definition

Annex60.Media.Specialized.Water.TemperatureDependentDensity.specificGibbsEnergy

Return the specific Gibbs energy

Information

This function computes the specific Gibbs energy.

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

Inputs

Outputs

Modelica definition

Annex60.Media.Specialized.Water.TemperatureDependentDensity.specificHelmholtzEnergy

Return the specific Helmholtz energy

Information

This function computes the specific Helmholtz energy.

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

Inputs

Outputs

Modelica definition

Annex60.Media.Specialized.Water.TemperatureDependentDensity.isentropicEnthalpy

Return the isentropic enthalpy

Information

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

Extends from (Return isentropic enthalpy).

Inputs

Outputs

Modelica definition

Annex60.Media.Specialized.Water.TemperatureDependentDensity.isobaricExpansionCoefficient

Return the isobaric expansion coefficient

Information

This function returns the isobaric expansion coefficient,

β_p = - 1 ⁄ v   (∂ v ⁄ ∂ T)_p,

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

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

Inputs

Outputs

Modelica definition

Annex60.Media.Specialized.Water.TemperatureDependentDensity.isothermalCompressibility

Return the isothermal compressibility factor

Information

This function returns the isothermal compressibility coefficient, which is zero as this medium is incompressible. The isothermal compressibility is defined as

κ_T = - 1 ⁄ v   (∂ v ⁄ ∂ p)_T,

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

Extends from (Return overall the isothermal compressibility factor).

Inputs

Outputs

Modelica definition

Annex60.Media.Specialized.Water.TemperatureDependentDensity.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, which is zero as the medium is incompressible.

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

Inputs

Outputs

Modelica definition

Annex60.Media.Specialized.Water.TemperatureDependentDensity.density_derT_p

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

Information

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

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

Inputs

Outputs

Modelica definition

Annex60.Media.Specialized.Water.TemperatureDependentDensity.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, which is zero as the medium is a single substance.

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

Inputs

Outputs

Modelica definition

Annex60.Media.Specialized.Water.TemperatureDependentDensity.specificHeatCapacityCp

Return the specific heat capacity at constant pressure

Information

This function returns the specific heat capacity at constant pressure.

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

Inputs

Outputs

Modelica definition

Annex60.Media.Specialized.Water.TemperatureDependentDensity.specificHeatCapacityCv

Return the specific heat capacity at constant volume

Information

This function computes the specific heat capacity at constant volume.

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

Inputs

Outputs

Modelica definition

Annex60.Media.Specialized.Water.TemperatureDependentDensity.thermalConductivity

Return the thermal conductivity

Information

This function returns the thermal conductivity. The expression is obtained from Ramires et al. (1995).

References

Ramires, Maria L. V. and Nieto de Castro, Carlos A. and Nagasaka, Yuchi and Nagashima, Akira and Assael, Marc J. and Wakeham, William A. Standard Reference Data for the Thermal Conductivity of Water. Journal of Physical and Chemical Reference Data, 24, p. 1377-1381, 1995. DOI:10.1063/1.555963.

Extends from (Return thermal conductivity).

Inputs

Outputs

Modelica definition

Annex60.Media.Specialized.Water.TemperatureDependentDensity.pressure

Return the pressure

Information

This function returns the pressure.

Extends from (Return pressure).

Inputs

Outputs

Modelica definition

Annex60.Media.Specialized.Water.TemperatureDependentDensity.temperature

Return the temperature

Information

This function returns the temperature.

Extends from (Return temperature).

Inputs

Outputs

Modelica definition

Annex60.Media.Specialized.Water.TemperatureDependentDensity.molarMass

Return the molar mass

Information

This function returns the molar mass, which is assumed to be constant.

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

Inputs

Outputs

Modelica definition

Annex60.Media.Specialized.Water.TemperatureDependentDensity.setState_dTX

Return thermodynamic state from d, T, and X or Xi

Information

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

Inputs

Outputs

Modelica definition

Annex60.Media.Specialized.Water.TemperatureDependentDensity.setState_phX

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

Information

This function returns the thermodynamic state for a given pressure, specific enthalpy and composition.

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

Inputs

Outputs

Modelica definition

Annex60.Media.Specialized.Water.TemperatureDependentDensity.setState_pTX

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

Information

This function returns the thermodynamic state for a given pressure, temperature and composition.

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

Inputs

Outputs

Modelica definition

Annex60.Media.Specialized.Water.TemperatureDependentDensity.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 Annex60.Media.Specialized.Water.TemperatureDependentDensity.specificEntropy for temperature.

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

Inputs

Outputs

Modelica definition

Annex60.Media.Specialized.Water.TemperatureDependentDensity.der_specificHeatCapacityCp

Return the derivative of the specific heat capacity at constant pressure

Information

This function computes the derivative of the specific heat capacity at constant pressure with respect to the state.

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

Inputs

Outputs

Modelica definition

Annex60.Media.Specialized.Water.TemperatureDependentDensity.der_enthalpyOfLiquid

Temperature derivative of enthalpy of liquid per unit mass of liquid

Information

This function computes the temperature derivative of the enthalpy of liquid water per unit mass.

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

Inputs

Outputs

Modelica definition

Annex60.Media.Specialized.Water.TemperatureDependentDensity.kinematicViscosity

Return the kinematic viscosity

Information

This function computes the kinematic viscosity as a function of temperature.

Implementation

The function is based on the IDA implementation in therpro.nmf. The original equation is

kinVis :=1E-6*Modelica.Math.exp(0.577449 - 3.253945e-2*T_degC + 2.17369e-4*
      T_degC^2 - 7.22111e-7*T_degC^3);
      

This has been converted to Kelvin, which resulted in the above expression. In addition, at 5 °C the kinematic viscosity is linearly extrapolated to avoid a large gradient at very low temperatures. We selected the same point for the linearization as we used for the density, as the density and the kinematic viscosity are combined in Annex60.Media.Specialized.Water.TemperatureDependentDensity.dynamicViscosity.

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

Inputs

Outputs

Modelica definition