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
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.
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:
| Name | Description |
|---|
| cp_const | Specific heat capacity at constant pressure |
| beta_const | Thermal expansion coefficient at constant pressure |
| kappa_const | Isothermal compressibility |
| MM_const | Molar mass |
| reference_d | Density in reference conditions |
| reference_h | Specific enthalpy in reference conditions |
| reference_s | Specific entropy in reference conditions |
| constantJacobian | If true, entries in thermodynamic Jacobian are constant, taken at reference conditions |
 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 |
| 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 |
 FluidConstants
| Critical, triple, molecular and other standard data of fluid |
 dynamicViscosity
| Return dynamic viscosity |
| thermalConductivity
| Return thermal conductivity |
| prandtlNumber
| Return the Prandtl number |
 heatCapacity_cp
| Alias for deprecated name |
| heatCapacity_cv
| Alias for deprecated name |
| beta
| Alias for isobaricExpansionCoefficient for user convenience |
| kappa
| Alias of isothermalCompressibility for user convenience |
| 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 |
A minor approximation is used: the reference density is used instead of the real
one, which would require a numeric solution.
Modelica.Media.Interfaces.PartialLinearFluid.ThermodynamicState
Modelica.Media.Interfaces.PartialLinearFluid.BaseProperties
Modelica.Media.Interfaces.PartialLinearFluid.setState_pTX