Generic pure liquid model with constant cp, compressibility and thermal expansion coefficients
Information
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: [email protected]
and
Hubertus Tummescheit
Modelon AB
Ideon Science Park
SE-22730 Lund, Sweden
email: [email protected]
Extends from Interfaces.PartialPureSubstance (Base class for pure substances of one chemical substance).
Package Content
| 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 selection of variables that uniquely defines the thermodynamic state
Information
Extends from Modelica.Icons.Record (Icon for records).
Base properties of medium
Information
Extends from .
Parameters
| Name | Description |
|---|
| Advanced |
| preferredMediumStates | = true if StateSelect.prefer shall be used for the independent property variables of the medium |
Set the thermodynamic state record from p and T (X not needed)
Information
Extends from (Return thermodynamic state as function of p, T and composition X or Xi).
Inputs
Outputs
| Name | Description |
|---|
| state | Thermodynamic state record |
Set the thermodynamic state record from p and h (X not needed)
Information
Extends from (Return thermodynamic state as function of p, h and composition X or Xi).
Inputs
Outputs
| Name | Description |
|---|
| state | Thermodynamic state record |
Set the thermodynamic state record from p and s (X not needed)
Information
Extends from (Return thermodynamic state as function of p, s and composition X or Xi).
Inputs
Outputs
| Name | Description |
|---|
| state | Thermodynamic state record |
Set the thermodynamic state record from d and T (X not needed)
Information
Extends from (Return thermodynamic state as function of d, T and composition X or Xi).
Inputs
Outputs
| Name | Description |
|---|
| state | Thermodynamic state record |
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).
Inputs
Outputs
| Name | Description |
|---|
| state | Smooth thermodynamic state for all x (continuous and differentiable) |
Return the pressure from the thermodynamic state
Information
Extends from (Return pressure).
Inputs
Outputs
| Name | Description |
|---|
| p | Pressure [Pa] |
Return the temperature from the thermodynamic state
Information
Extends from (Return temperature).
Inputs
Outputs
| Name | Description |
|---|
| T | Temperature [K] |
Return the density from the thermodynamic state
Information
Extends from (Return density).
Inputs
Outputs
| Name | Description |
|---|
| d | Density [kg/m3] |
Return the specific enthalpy from the thermodynamic state
Information
Extends from (Return specific enthalpy).
Inputs
Outputs
| Name | Description |
|---|
| h | Specific enthalpy [J/kg] |
Return the specific entropy from the thermodynamic state
Information
Extends from (Return specific entropy).
Inputs
Outputs
| Name | Description |
|---|
| s | Specific entropy [J/(kg.K)] |
Return the specific internal energy from the thermodynamic state
Information
Extends from (Return specific internal energy).
Inputs
Outputs
| Name | Description |
|---|
| u | Specific internal energy [J/kg] |
Return specific Gibbs energy from the thermodynamic state
Information
Extends from Modelica.Icons.Function (Icon for functions), (Return specific Gibbs energy).
Inputs
Outputs
| Name | Description |
|---|
| g | Specific Gibbs energy [J/kg] |
Return specific Helmholtz energy from the thermodynamic state
Information
Extends from Modelica.Icons.Function (Icon for functions), (Return specific Helmholtz energy).
Inputs
Outputs
| Name | Description |
|---|
| f | Specific Helmholtz energy [J/kg] |
Return velocity of sound from the thermodynamic state
Information
Extends from Modelica.Icons.Function (Icon for functions), (Return velocity of sound).
Inputs
Outputs
| Name | Description |
|---|
| a | Velocity of sound [m/s] |
Return isentropic exponent from the thermodynamic state
Information
Extends from Modelica.Icons.Function (Icon for functions), (Return isentropic exponent).
Inputs
Outputs
| Name | Description |
|---|
| gamma | Isentropic exponent [1] |
Return isentropic enthalpy
Information
A minor approximation is used: the reference density is used instead of the real
one, which would require a numeric solution.
Extends from (Return isentropic enthalpy).
Inputs
Outputs
| Name | Description |
|---|
| h_is | Isentropic enthalpy [J/kg] |
Return specific heat capacity at constant volume
Information
Extends from (Return specific heat capacity at constant pressure).
Inputs
Outputs
| Name | Description |
|---|
| cp | Specific heat capacity at constant pressure [J/(kg.K)] |
Return specific heat capacity at constant volume from the thermodynamic state
Information
Extends from (Return specific heat capacity at constant volume).
Inputs
Outputs
| Name | Description |
|---|
| cv | Specific heat capacity at constant volume [J/(kg.K)] |
Return the isothermal compressibility kappa
Information
Extends from (Return overall the isothermal compressibility factor).
Inputs
Outputs
| Name | Description |
|---|
| kappa | Isothermal compressibility [1/Pa] |
Return the isobaric expansion coefficient
Information
Extends from (Return overall the isobaric expansion coefficient beta).
Inputs
Outputs
| Name | Description |
|---|
| beta | Isobaric expansion coefficient [1/K] |
Return density derivative w.r.t. pressure at const specific enthalpy
Information
Extends from (Return density derivative w.r.t. pressure at const specific enthalpy).
Inputs
Outputs
| Name | Description |
|---|
| ddph | Density derivative w.r.t. pressure [s2/m2] |
Return density derivative w.r.t. specific enthalpy at constant pressure
Information
Extends from (Return density derivative w.r.t. specific enthalpy at constant pressure).
Inputs
Outputs
| Name | Description |
|---|
| ddhp | Density derivative w.r.t. specific enthalpy [kg.s2/m5] |
Return density derivative w.r.t. pressure at const temperature
Information
Extends from (Return density derivative w.r.t. pressure at const temperature).
Inputs
Outputs
| Name | Description |
|---|
| ddpT | Density derivative w.r.t. pressure [s2/m2] |
Return density derivative w.r.t. temperature at constant pressure
Information
Extends from (Return density derivative w.r.t. temperature at constant pressure).
Inputs
Outputs
| Name | Description |
|---|
| ddTp | Density derivative w.r.t. temperature [kg/(m3.K)] |
Returns the partial derivative of density with respect to mass fractions at constant pressure and temperature
Information
Extends from (Return density derivative w.r.t. mass fraction).
Inputs
Outputs
| Name | Description |
|---|
| dddX[nX] | Derivative of density w.r.t. mass fraction [kg/m3] |
Return molar mass
Information
Extends from (Return the molar mass of the medium).
Inputs
Outputs
| Name | Description |
|---|
| MM | Mixture molar mass [kg/mol] |
Return temperature from pressure and specific enthalpy
Information
Extends from Modelica.Icons.Function (Icon for functions).
Inputs
Outputs
| Name | Description |
|---|
| T | Temperature [K] |
Return temperature from pressure and specific entropy
Information
Extends from Modelica.Icons.Function (Icon for functions).
Inputs
Outputs
| Name | Description |
|---|
| T | Temperature [K] |
Automatically generated Tue Apr 05 09:36:54 2016.
Modelica.Media.Interfaces.PartialLinearFluid.ThermodynamicState
Modelica.Media.Interfaces.PartialLinearFluid.BaseProperties
Modelica.Media.Interfaces.PartialLinearFluid.setState_pTX
Modelica.Media.Interfaces.PartialLinearFluid.specificGibbsEnergy
Modelica.Media.Interfaces.PartialLinearFluid.isentropicEnthalpy