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WOLFRAM SYSTEM MODELER

PartialLinearFluid

Generic pure liquid model with constant cp, compressibility and thermal expansion coefficients

Package Contents

	ThermodynamicState A selection of variables that uniquely defines the thermodynamic state
	BaseProperties Base properties of medium
	setState_pTX Set the thermodynamic state record from p and T (X not needed)
	setState_phX Set the thermodynamic state record from p and h (X not needed)
	setState_psX Set the thermodynamic state record from p and s (X not needed)
	setState_dTX Set the thermodynamic state record from d and T (X not needed)
	setSmoothState Return thermodynamic state so that it smoothly approximates: if x > 0 then state_a else state_b
	pressure Return the pressure from the thermodynamic state
	temperature Return the temperature from the thermodynamic state
	density Return the density from the thermodynamic state
	specificEnthalpy Return the specific enthalpy from the thermodynamic state
	specificEntropy Return the specific entropy from the thermodynamic state
	specificInternalEnergy Return the specific internal energy from the thermodynamic state
	specificGibbsEnergy Return specific Gibbs energy from the thermodynamic state
	specificHelmholtzEnergy Return specific Helmholtz energy from the thermodynamic state
	velocityOfSound Return velocity of sound from the thermodynamic state
	isentropicExponent Return isentropic exponent from the thermodynamic state
	isentropicEnthalpy Return isentropic enthalpy
	specificHeatCapacityCp Return specific heat capacity at constant volume
	specificHeatCapacityCv Return specific heat capacity at constant volume from the thermodynamic state
	isothermalCompressibility Return the isothermal compressibility kappa
	isobaricExpansionCoefficient Return the isobaric expansion coefficient
	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 Returns the partial derivative of density with respect to mass fractions at constant pressure and temperature
	molarMass Return molar mass
	T_ph Return temperature from pressure and specific enthalpy
	T_ps Return temperature from pressure and specific entropy

Package Constants (28)

ThermoStates	Value: Modelica.Media.Interfaces.Choices.IndependentVariables.pTX Type: IndependentVariables Description: Enumeration type for independent variables
mediumName	Value: "unusablePartialMedium" Type: String Description: Name of the medium
substanceNames	Value: {mediumName} Type: String[:] Description: Names of the mixture substances. Set substanceNames={mediumName} if only one substance.
extraPropertiesNames	Value: fill("", 0) Type: String[:] Description: Names of the additional (extra) transported properties. Set extraPropertiesNames=fill("",0) if unused
singleState	Value: false Type: Boolean Description: = true, if u and d are not a function of pressure
reducedX	Value: true Type: Boolean Description: = true if medium contains the equation sum(X) = 1.0; set reducedX=true if only one substance (see docu for details)
fixedX	Value: true Type: Boolean Description: = true if medium contains the equation X = reference_X
reference_p	Value: 101325 Type: AbsolutePressure (Pa) Description: Reference pressure of Medium: default 1 atmosphere
reference_T	Value: 298.15 Type: Temperature (K) Description: Reference temperature of Medium: default 25 deg Celsius
reference_X	Value: fill(1 / nX, nX) Type: MassFraction[nX] (kg/kg) Description: Default mass fractions of medium
p_default	Value: 101325 Type: AbsolutePressure (Pa) Description: Default value for pressure of medium (for initialization)
T_default	Value: Modelica.Units.Conversions.from_degC(20) Type: Temperature (K) Description: Default value for temperature of medium (for initialization)
h_default	Value: specificEnthalpy_pTX(p_default, T_default, X_default) Type: SpecificEnthalpy (J/kg) Description: Default value for specific enthalpy of medium (for initialization)
X_default	Value: reference_X Type: MassFraction[nX] (kg/kg) Description: Default value for mass fractions of medium (for initialization)
C_default	Value: fill(0, nC) Type: ExtraProperty[nC] Description: Default value for trace substances of medium (for initialization)
nS	Value: size(substanceNames, 1) Type: Integer Description: Number of substances
nX	Value: nS Type: Integer Description: Number of mass fractions
nXi	Value: if fixedX then 0 else if reducedX then nS - 1 else nS Type: Integer Description: Number of structurally independent mass fractions (see docu for details)
nC	Value: size(extraPropertiesNames, 1) Type: Integer Description: Number of extra (outside of standard mass-balance) transported properties
C_nominal	Value: 1.0e-6 * ones(nC) Type: Real[nC] Description: Default for the nominal values for the extra properties
cp_const	Value: Type: SpecificHeatCapacity (J/(kg⋅K)) Description: Specific heat capacity at constant pressure
beta_const	Value: Type: IsobaricExpansionCoefficient (1/K) Description: Thermal expansion coefficient at constant pressure
kappa_const	Value: Type: IsothermalCompressibility (1/Pa) Description: Isothermal compressibility
MM_const	Value: Type: MolarMass (kg/mol) Description: Molar mass
reference_d	Value: Type: Density (kg/m³) Description: Density in reference conditions
reference_h	Value: Type: SpecificEnthalpy (J/kg) Description: Specific enthalpy in reference conditions
reference_s	Value: Type: SpecificEntropy (J/(kg⋅K)) Description: Specific entropy in reference conditions
constantJacobian	Value: Type: Boolean Description: If true, entries in thermodynamic Jacobian are constant, taken at reference conditions

Information

This information is part of the Modelica Standard Library maintained by the Modelica Association.

Linear Compressibility Fluid Model

This linear compressibility fluid model is based on the assumptions that:

The specific heat capacity at constant pressure (cp) is constant
The isobaric expansion coefficient (beta) is constant
The isothermal compressibility (kappa) is constant
Pressure and temperature are used as states
The influence of density on specific enthalpy (h), entropy (s), inner energy (u) and heat capacity (cv) at constant volume is neglected.

That means that the density is a linear function in temperature and in pressure. In order to define the complete model, a number of constant reference values are needed which are computed at the reference values of the states pressure p and temperature T. The model can be interpreted as a linearization of a full non-linear fluid model (but it is not linear in all thermodynamic coordinates). Reference values are needed for

the density (reference_d),
the specific enthalpy (reference_h),
the specific entropy (reference_s).

Apart from that, a user needs to define the molar mass, MM_const. Note that it is possible to define a fluid by computing the reference values from a full non-linear fluid model by computing the package constants using the standard functions defined in a fluid package (see example in liquids package).

In order to avoid numerical inversion of the temperature in the T_ph and T_ps functions, the density is always taken to be the reference density in the computation of h, s, u and cv. For liquids (and this model is intended only for liquids) the relative error of doing so is 1e-3 to 1e-4 at most. The model would be more "correct" based on the other assumptions, if occurrences of reference_d in the computations of h,s,u and cv would be replaced by a call to density(state). That would require a numerical solution for T_ps, while T_ph can be solved symbolically from a quadratic function. Errors from this approximation are small because liquid density varies little.

Efficiency considerations

One of the main reasons to use a simple, linear fluid model is to achieve high performance in simulations. There are a number of possible compromises and possibilities to improve performance. Some of them can be influenced by a flag. The following rules where used in this model:

All forward evaluations (using the ThermodynamicState record as input) are exactly following the assumptions above.
If the flag constantJacobian is set to true in the package, all functions that typically appear in thermodynamic Jacobians (specificHeatCapacityCv, density_derp_h, density_derh_p, density_derp_T, density_derT_p) are evaluated at reference conditions (that means using the reference density) instead of the density of the current pressure and temperature. This makes it possible to evaluate the thermodynamic Jacobian at compile time.
For inverse functions using other inputs than the states (e.g pressure p and specific enthalpy h), the inversion is using the reference state whenever that is necessary to achieve a symbolic inversion.
If constantJacobian is set to false, the above list of functions is computed exactly according to the above list of assumptions

Authors:: Francesco Casella
Dipartimento di Elettronica e Informazione
Politecnico di Milano
Via Ponzio 34/5
I-20133 Milano, Italy
email: casella@elet.polimi.it
and
Hubertus Tummescheit
Modelon AB
Ideon Science Park
SE-22730 Lund, Sweden
email: Hubertus.Tummescheit@Modelon.se

Wolfram Language

In[1]:=

SystemModel["Modelica.Media.Interfaces.PartialLinearFluid"]

Out[1]:=

Extended by (2)

LinearColdWater

Modelica.Media.CompressibleLiquids

Cold water model with linear compressibility

LinearWater_pT

Modelica.Media.CompressibleLiquids.Common

Base class for liquid, linear compressibility water models