Modelica.Media.Incompressible.TableBased

Incompressible medium properties based on tables

Information

This is the base package for medium models of incompressible fluids based on tables. The minimal data to provide for a useful medium description is tables of density and heat capacity as functions of temperature.

It should be noted that incompressible media only have 1 state per control volume (usually T), but have both T and p as inputs for fully correct properties. The error of using only T-dependent properties is small, therefore a Boolean flag enthalpyOfT exists. If it is true, the enumeration Choices.independentVariables is set to Choices.independentVariables.T otherwise it is set to Choices.independentVariables.pT.

Using the package TableBased

To implement a new medium model, create a package that extends TableBased and provides one or more of the constant tables:

tableDensity        = [T, d];
tableHeatCapacity   = [T, Cp];
tableConductivity   = [T, lam];
tableViscosity      = [T, eta];
tableVaporPressure  = [T, pVap];

The table data is used to fit constant polynomials of order npol, the temperature data points do not need to be same for different properties. Properties like enthalpy, inner energy and entropy are calculated consistently from integrals and derivatives of d(T) and Cp(T). The minimal data for a useful medium model is thus density and heat capacity. Transport properties and vapor pressure are optional, if the data tables are empty the corresponding function calls can not be used.

Extends from Modelica.Media.Interfaces.PartialMedium (Partial medium properties (base package of all media packages)).

Package Content

Name	Description
enthalpyOfT=true	True if enthalpy is approximated as a function of T only, (p-dependence neglected)
densityOfT=size(tableDensity, 1) > 1	True if density is a function of temperature
T_min	Minimum temperature valid for medium model
T_max	Maximum temperature valid for medium model
T0=273.15	Reference Temperature
h0=0	Reference enthalpy at T0, reference_p
s0=0	Reference entropy at T0, reference_p
MM_const=0.1	Molar mass
npol=2	Degree of polynomial used for fitting
npolDensity=npol	Degree of polynomial used for fitting rho(T)
npolHeatCapacity=npol	Degree of polynomial used for fitting Cp(T)
npolViscosity=npol	Degree of polynomial used for fitting eta(T)
npolVaporPressure=npol	Degree of polynomial used for fitting pVap(T)
npolConductivity=npol	Degree of polynomial used for fitting lambda(T)
neta=size(tableViscosity, 1)	Number of data points for viscosity
tableDensity	Table for rho(T)
tableHeatCapacity	Table for Cp(T)
tableViscosity	Table for eta(T)
tableVaporPressure	Table for pVap(T)
tableConductivity	Table for lambda(T)
TinK	True if T[K],Kelvin used for table temperatures
hasDensity=not (size(tableDensity, 1) == 0)	True if table tableDensity is present
hasHeatCapacity=not (size(tableHeatCapacity, 1) == 0)	True if table tableHeatCapacity is present
hasViscosity=not (size(tableViscosity, 1) == 0)	True if table tableViscosity is present
hasVaporPressure=not (size(tableVaporPressure, 1) == 0)	True if table tableVaporPressure is present
invTK=if size(tableViscosity, 1) > 0 then (if TinK then 1 ./ tableViscosity[:, 1] else 1 ./ Cv.from_degC(tableViscosity[:, 1])) else fill(0, neta)
poly_rho=if hasDensity then Poly.fitting(tableDensity[:, 1], tableDensity[:, 2], npolDensity) else zeros(npolDensity + 1)
poly_Cp=if hasHeatCapacity then Poly.fitting(tableHeatCapacity[:, 1], tableHeatCapacity[:, 2], npolHeatCapacity) else zeros(npolHeatCapacity + 1)
poly_eta=if hasViscosity then Poly.fitting(invTK, Math.log(tableViscosity[:, 2]), npolViscosity) else zeros(npolViscosity + 1)
poly_pVap=if hasVaporPressure then Poly.fitting(tableVaporPressure[:, 1], tableVaporPressure[:, 2], npolVaporPressure) else zeros(npolVaporPressure + 1)
poly_lam=if size(tableConductivity, 1) > 0 then Poly.fitting(tableConductivity[:, 1], tableConductivity[:, 2], npolConductivity) else zeros(npolConductivity + 1)
invertTemp	Function to invert temperatures
BaseProperties	Base properties of T dependent medium
setState_pTX	Returns state record, given pressure and temperature
setState_dTX	Returns state record, given pressure and temperature
setState_pT	Returns state record as function of p and T
setState_phX	Returns state record, given pressure and specific enthalpy
setState_ph	Returns state record as function of p and h
setState_psX	Returns state record, given pressure and specific entropy
setState_ps	Returns state record as function of p and s
setSmoothState	Return thermodynamic state so that it smoothly approximates: if x > 0 then state_a else state_b
specificHeatCapacityCv	Specific heat capacity at constant volume (or pressure) of medium
specificHeatCapacityCp	Specific heat capacity at constant volume (or pressure) of medium
dynamicViscosity	Return dynamic viscosity as a function of the thermodynamic state record
thermalConductivity	Return thermal conductivity as a function of the thermodynamic state record
s_T	Compute specific entropy
specificEntropy	Return specific entropy as a function of the thermodynamic state record
h_T	Compute specific enthalpy from temperature
h_T_der	Compute specific enthalpy from temperature
h_pT	Compute specific enthalpy from pressure and temperature
density_T	Return density as function of temperature
temperature	Return temperature as a function of the thermodynamic state record
pressure	Return pressure as a function of the thermodynamic state record
density	Return density as a function of the thermodynamic state record
specificEnthalpy	Return specific enthalpy as a function of the thermodynamic state record
specificInternalEnergy	Return specific internal energy as a function of the thermodynamic state record
T_ph	Compute temperature from pressure and specific enthalpy
T_ps	Compute temperature from pressure and specific enthalpy
Polynomials_Temp	Temporary Functions operating on polynomials (including polynomial fitting); only to be used in Modelica.Media.Incompressible.TableBased
Inherited
ThermoStates=if enthalpyOfT then Modelica.Media.Interfaces.Choices.IndependentVariables.T else Modelica.Media.Interfaces.Choices.IndependentVariables.pT	Enumeration type for independent variables
mediumName="tableMedium"	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	= 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=1.013e5	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)
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
ThermodynamicState	Minimal variable set that is available as input argument to every medium function
prandtlNumber	Return the Prandtl number
specificGibbsEnergy	Return specific Gibbs energy
specificHelmholtzEnergy	Return specific Helmholtz energy
heatCapacity_cp	Alias for deprecated name
heatCapacity_cv	Alias for deprecated name
isentropicExponent	Return isentropic exponent
isentropicEnthalpy	Return isentropic enthalpy
velocityOfSound	Return velocity of sound
isobaricExpansionCoefficient	Return overall the isobaric expansion coefficient beta
beta	Alias for isobaricExpansionCoefficient for user convenience
isothermalCompressibility	Return overall the isothermal compressibility factor
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
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
molarMass	Return the molar mass of the medium
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

Modelica.Media.Incompressible.TableBased.invertTemp

Function to invert temperatures

Information

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

Inputs

Outputs

Modelica.Media.Incompressible.TableBased.BaseProperties

Base properties of T dependent medium

Information

Note that the inner energy neglects the pressure dependence, which is only true for an incompressible medium with d = constant. The neglected term is p-reference_p)/rho*(T/rho)*(partial rho /partial T). This is very small for liquids due to proportionality to 1/d^2, but can be problematic for gases that are modeled incompressible.

It should be noted that incompressible media only have 1 state per control volume (usually T), but have both T and p as inputs for fully correct properties. The error of using only T-dependent properties is small, therefore a Boolean flag enthalpyOfT exists. If it is true, the enumeration Choices.independentVariables is set to Choices.independentVariables.T otherwise it is set to Choices.independentVariables.pT.

Enthalpy is never a function of T only (h = h(T) + (p-reference_p)/d), but the error is also small and non-linear systems can be avoided. In particular, non-linear systems are small and local as opposed to large and over all volumes.

Entropy is calculated as

  s = s0 + integral(Cp(T)/T,dt)

which is only exactly true for a fluid with constant density d=d0.

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

Parameters

Modelica.Media.Incompressible.TableBased.setState_pTX

Returns state record, given pressure and temperature

Information

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

Inputs

Outputs

Modelica.Media.Incompressible.TableBased.setState_dTX

Returns state record, given pressure and temperature

Information

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

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Outputs

Modelica.Media.Incompressible.TableBased.setState_pT

Returns state record as function of p and T

Information

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

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Outputs

Modelica.Media.Incompressible.TableBased.setState_phX

Returns state record, given pressure and specific enthalpy

Information

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

Inputs

Outputs

Modelica.Media.Incompressible.TableBased.setState_ph

Returns state record as function of p and h

Information

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

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Outputs

Modelica.Media.Incompressible.TableBased.setState_psX

Returns state record, given pressure and specific entropy

Information

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

Inputs

Outputs

Modelica.Media.Incompressible.TableBased.setState_ps

Returns state record as function of p and s

Information

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

Inputs

Outputs

Modelica.Media.Incompressible.TableBased.setSmoothState

Return thermodynamic state so that it smoothly approximates: if x > 0 then state_a else state_b

Information

Extends from (Return thermodynamic state so that it smoothly approximates: if x > 0 then state_a else state_b).

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Outputs

Modelica.Media.Incompressible.TableBased.specificHeatCapacityCv

Specific heat capacity at constant volume (or pressure) of medium

Information

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

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Outputs

Modelica.Media.Incompressible.TableBased.specificHeatCapacityCp

Specific heat capacity at constant volume (or pressure) of medium

Information

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

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Outputs

Modelica.Media.Incompressible.TableBased.dynamicViscosity

Return dynamic viscosity as a function of the thermodynamic state record

Information

Extends from (Return dynamic viscosity).

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Outputs

Modelica.Media.Incompressible.TableBased.thermalConductivity

Return thermal conductivity as a function of the thermodynamic state record

Information

Extends from (Return thermal conductivity).

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Outputs

Modelica.Media.Incompressible.TableBased.s_T

Compute specific entropy

Information

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

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Outputs

Modelica.Media.Incompressible.TableBased.specificEntropy

Return specific entropy as a function of the thermodynamic state record

Information

Extends from (Return specific entropy).

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Outputs

Modelica.Media.Incompressible.TableBased.h_T

Compute specific enthalpy from temperature

Information

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

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Outputs

Modelica.Media.Incompressible.TableBased.h_T_der

Compute specific enthalpy from temperature

Information

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

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Outputs

Modelica.Media.Incompressible.TableBased.h_pT

Compute specific enthalpy from pressure and temperature

Information

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

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Outputs

Modelica.Media.Incompressible.TableBased.density_T

Return density as function of temperature

Information

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

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Outputs

Modelica.Media.Incompressible.TableBased.temperature

Return temperature as a function of the thermodynamic state record

Information

Extends from (Return temperature).

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Outputs

Modelica.Media.Incompressible.TableBased.pressure

Return pressure as a function of the thermodynamic state record

Information

Extends from (Return pressure).

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Outputs

Modelica.Media.Incompressible.TableBased.density

Return density as a function of the thermodynamic state record

Information

Extends from (Return density).

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Outputs

Modelica.Media.Incompressible.TableBased.specificEnthalpy

Return specific enthalpy as a function of the thermodynamic state record

Information

Extends from (Return specific enthalpy).

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Outputs

Modelica.Media.Incompressible.TableBased.specificInternalEnergy

Return specific internal energy as a function of the thermodynamic state record

Information

Extends from (Return specific internal energy).

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Outputs

Modelica.Media.Incompressible.TableBased.T_ph

Compute temperature from pressure and specific enthalpy

Information

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

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Outputs

Modelica.Media.Incompressible.TableBased.T_ps

Compute temperature from pressure and specific enthalpy

Information

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

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Outputs