WOLFRAM SYSTEMMODELER

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.SIunits.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

  1. the density (reference_d),
  2. the specific enthalpy (reference_h),
  3. 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