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.
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)).
| Name | Description |
|---|---|
AbsolutePressure | Type for absolute pressure with medium specific attributes |
BaseProperties | Base properties of T dependent medium |
Basic … | The most basic version of a record used in several degrees of detail |
beta | Alias for isobaricExpansionCoefficient for user convenience |
Choices … | |
CumulativeExtraProperty | Type for conserved integral of unspecified, mass specific property |
Density | Type for density with medium specific attributes |
density | Return density as a function of the thermodynamic state record |
density_derh_p | Return density derivative w.r.t. specific enthalpy at constant pressure |
density_derp_h | Return density derivative w.r.t. pressure at const specific enthalpy |
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 |
density_phX | Return density from p, h, and X or Xi |
density_psX | Return density from p, s, and X or Xi |
density_pTX | Return density from p, T, and X or Xi |
density_T | Return density as function of temperature |
DerDensityByEnthalpy | Type for partial derivative of density with respect to enthalpy with medium specific attributes |
DerDensityByPressure | Type for partial derivative of density with respect to pressure with medium specific attributes |
DerDensityByTemperature | Type for partial derivative of density with respect to temperature with medium specific attributes |
DerEnthalpyByPressure | Type for partial derivative of enthalpy with respect to pressure with medium specific attributes |
DerTemperatureByPressure | Type for partial derivative of temperature with respect to pressure with medium specific attributes |
DipoleMoment | Type for dipole moment with medium specific attributes |
DynamicViscosity | Type for dynamic viscosity with medium specific attributes |
dynamicViscosity | Return dynamic viscosity as a function of the thermodynamic state record |
EnthalpyFlowRate | Type for enthalpy flow rate with medium specific attributes |
ExtraProperty | Type for unspecified, mass-specific property transported by flow |
ExtraPropertyFlowRate | Type for flow rate of unspecified, mass-specific property |
FixedPhase | Phase of the fluid: 1 for 1-phase, 2 for two-phase, 0 for not known, e.g., interactive use |
FluidConstants | Critical, triple, molecular and other standard data of fluid |
FluidLimits | Validity limits for fluid model |
h_pT | Compute specific enthalpy from pressure and temperature |
h_T | Compute specific enthalpy from temperature |
h_T_der | Compute specific enthalpy from temperature |
heatCapacity_cp | Alias for deprecated name |
heatCapacity_cv | Alias for deprecated name |
IdealGas … | The ideal gas version of a record used in several degrees of detail |
invertTemp | Function to invert temperatures |
isentropicEnthalpy | Return isentropic enthalpy |
IsentropicExponent | Type for isentropic exponent with medium specific attributes |
isentropicExponent | Return isentropic exponent |
IsobaricExpansionCoefficient | Type for isobaric expansion coefficient with medium specific attributes |
isobaricExpansionCoefficient | Return overall the isobaric expansion coefficient beta |
isothermalCompressibility | Return overall the isothermal compressibility factor |
kappa | Alias of isothermalCompressibility for user convenience |
MassFlowRate | Type for mass flow rate with medium specific attributes |
MassFraction | Type for mass fraction with medium specific attributes |
MolarMass | Type for molar mass with medium specific attributes |
molarMass | Return the molar mass of the medium |
MolarVolume | Type for molar volume with medium specific attributes |
MoleFraction | Type for mole fraction with medium specific attributes |
Polynomials_Temp … | Temporary Functions operating on polynomials (including polynomial fitting); only to be used in Modelica.Media.Incompressible.TableBased |
PrandtlNumber | Type for Prandtl number with medium specific attributes |
prandtlNumber | Return the Prandtl number |
pressure | Return pressure as a function of the thermodynamic state record |
s_T | Compute specific entropy |
SaturationProperties | Saturation properties of two phase medium |
setSmoothState | Return thermodynamic state so that it smoothly approximates: if x > 0 then state_a else state_b |
setState_dTX | Returns state record, given pressure and temperature |
setState_ph | Returns state record as function of p and h |
setState_phX | Returns state record, given pressure and specific enthalpy |
setState_ps | Returns state record as function of p and s |
setState_psX | Returns state record, given pressure and specific entropy |
setState_pT | Returns state record as function of p and T |
setState_pTX | Returns state record, given pressure and temperature |
SpecificEnergy | Type for specific energy with medium specific attributes |
SpecificEnthalpy | Type for specific enthalpy with medium specific attributes |
specificEnthalpy | Return specific enthalpy as a function of the thermodynamic state record |
specificEnthalpy_psX | Return specific enthalpy from p, s, and X or Xi |
specificEnthalpy_pTX | Return specific enthalpy from p, T, and X or Xi |
SpecificEntropy | Type for specific entropy with medium specific attributes |
specificEntropy | Return specific entropy as a function of the thermodynamic state record |
specificEntropy_pTX | Return specific enthalpy from p, T, and X or Xi |
specificGibbsEnergy | Return specific Gibbs energy |
SpecificHeatCapacity | Type for specific heat capacity with medium specific attributes |
specificHeatCapacityCp | Specific heat capacity at constant volume (or pressure) of medium |
specificHeatCapacityCv | Specific heat capacity at constant volume (or pressure) of medium |
specificHelmholtzEnergy | Return specific Helmholtz energy |
SpecificInternalEnergy | Type for specific internal energy with medium specific attributes |
specificInternalEnergy | Return specific internal energy as a function of the thermodynamic state record |
SurfaceTension | Type for surface tension with medium specific attributes |
T_ph | Compute temperature from pressure and specific enthalpy |
T_ps | Compute temperature from pressure and specific enthalpy |
Temperature | Type for temperature with medium specific attributes |
temperature | Return temperature as a function of the thermodynamic state record |
temperature_phX | Return temperature from p, h, and X or Xi |
temperature_psX | Return temperature from p,s, and X or Xi |
ThermalConductivity | Type for thermal conductivity with medium specific attributes |
thermalConductivity | Return thermal conductivity as a function of the thermodynamic state record |
ThermodynamicState | |
TwoPhase … | The two phase fluid version of a record used in several degrees of detail |
VelocityOfSound | Type for velocity of sound with medium specific attributes |
velocityOfSound | Return velocity of sound |
| Type | Name | Value | Description |
|---|---|---|---|
ExtraProperty | C_default[nC] | fill(0, nC) | Default value for trace substances of medium (for initialization) |
Real | C_nominal[nC] | 1e-6 * ones(nC) | Default for the nominal values for the extra properties |
Boolean | densityOfT | 1 < size(tableDensity, 1) | True if density is a function of temperature |
Boolean | enthalpyOfT | true | True if enthalpy is approximated as a function of T only, (p-dependence neglected) |
String | extraPropertiesNames[:] | fill("", 0) | Names of the additional (extra) transported properties. Set extraPropertiesNames=fill("",0) if unused |
final Boolean | fixedX | true | = true if medium contains the equation X = reference_X |
SpecificEnthalpy | h0 | 0 | Reference enthalpy at T0, reference_p |
SpecificEnthalpy | h_default | specificEnthalpy_pTX(p_default, T_default, X_default) | Default value for specific enthalpy of medium (for initialization) |
Boolean | hasDensity | not size(tableDensity, 1) == 0 | True if table tableDensity is present |
Boolean | hasHeatCapacity | not size(tableHeatCapacity, 1) == 0 | True if table tableHeatCapacity is present |
Boolean | hasVaporPressure | not size(tableVaporPressure, 1) == 0 | True if table tableVaporPressure is present |
Boolean | hasViscosity | not size(tableViscosity, 1) == 0 | True if table tableViscosity is present |
final Real | invTK[neta] | if 0 < size(tableViscosity, 1) then if TinK then 1 ./ tableViscosity[:,1] else 1 ./ Cv.from_degC(tableViscosity[:,1]) else fill(0, neta) | |
String | mediumName | "tableMedium" | Name of the medium |
MolarMass | MM_const | 0.1 | Molar mass |
final Integer | nC | size(extraPropertiesNames, 1) | Number of extra (outside of standard mass-balance) transported properties |
Integer | neta | size(tableViscosity, 1) | Number of data points for viscosity |
Integer | npol | 2 | Degree of polynomial used for fitting |
Integer | npolConductivity | npol | Degree of polynomial used for fitting lambda(T) |
Integer | npolDensity | npol | Degree of polynomial used for fitting rho(T) |
Integer | npolHeatCapacity | npol | Degree of polynomial used for fitting Cp(T) |
Integer | npolVaporPressure | npol | Degree of polynomial used for fitting pVap(T) |
Integer | npolViscosity | npol | Degree of polynomial used for fitting eta(T) |
final Integer | nS | size(substanceNames, 1) | Number of substances |
Integer | nX | nS | Number of mass fractions |
Integer | nXi | if fixedX then 0 else if reducedX then nS - 1 else nS | Number of structurally independent mass fractions (see docu for details) |
AbsolutePressure | p_default | 101325 | Default value for pressure of medium (for initialization) |
final Real | poly_Cp[:] | if hasHeatCapacity then Poly.fitting(tableHeatCapacity[:,1], tableHeatCapacity[:,2], npolHeatCapacity) else zeros(npolHeatCapacity + 1) | |
final Real | poly_eta[:] | if hasViscosity then Poly.fitting(invTK, Math.log(tableViscosity[:,2]), npolViscosity) else zeros(npolViscosity + 1) | |
final Real | poly_lam[:] | if 0 < size(tableConductivity, 1) then Poly.fitting(tableConductivity[:,1], tableConductivity[:,2], npolConductivity) else zeros(npolConductivity + 1) | |
final Real | poly_pVap[:] | if hasVaporPressure then Poly.fitting(tableVaporPressure[:,1], tableVaporPressure[:,2], npolVaporPressure) else zeros(npolVaporPressure + 1) | |
final Real | poly_rho[:] | if hasDensity then Poly.fitting(tableDensity[:,1], tableDensity[:,2], npolDensity) else zeros(npolDensity + 1) | |
final Boolean | reducedX | true | = true if medium contains the equation sum(X) = 1.0; set reducedX=true if only one substance (see docu for details) |
AbsolutePressure | reference_p | 101300 | Reference pressure of Medium: default 1 atmosphere |
Temperature | reference_T | 298.15 | Reference temperature of Medium: default 25 deg Celsius |
MassFraction | reference_X[nX] | fill(nX ^ (-1), nX) | Default mass fractions of medium |
SpecificEntropy | s0 | 0 | Reference entropy at T0, reference_p |
Boolean | singleState | true | = true, if u and d are not a function of pressure |
String | substanceNames[:] | {mediumName} | Names of the mixture substances. Set substanceNames={mediumName} if only one substance. |
Temperature | T0 | 273.15 | Reference Temperature |
Temperature | T_default | Modelica.SIunits.Conversions.from_degC(20) | Default value for temperature of medium (for initialization) |
IndependentVariables | ThermoStates | if enthalpyOfT then Modelica.Media.Interfaces.Choices.IndependentVariables.T else Modelica.Media.Interfaces.Choices.IndependentVariables.pT | Enumeration type for independent variables |
MassFraction | X_default[nX] | reference_X | Default value for mass fractions of medium (for initialization) |
Extends from Modelica.SIunits.AbsolutePressure.
| Name | Value |
|---|---|
quantity | "Pressure" |
unit | "Pa" |
displayUnit | "bar" |
min | 0 |
max | 1e+8 |
start | 100000 |
nominal | 100000 |
Extends from Modelica.SIunits.Density.
| Name | Value |
|---|---|
quantity | "Density" |
unit | "kg/m3" |
displayUnit | "g/cm3" |
min | 0 |
max | 100000 |
start | 1 |
nominal | 1 |
Extends from Modelica.SIunits.DynamicViscosity.
| Name | Value |
|---|---|
quantity | "DynamicViscosity" |
unit | "Pa.s" |
min | 0 |
max | 1e+8 |
start | 0.001 |
nominal | 0.001 |
Extends from Modelica.SIunits.EnthalpyFlowRate.
| Name | Value |
|---|---|
quantity | "EnthalpyFlowRate" |
unit | "W" |
min | -1e+8 |
max | 1e+8 |
start | 0. |
nominal | 1000 |
Extends from Real.
| Name | Value |
|---|---|
quantity | "MassFraction" |
unit | "kg/kg" |
min | 0 |
max | 1 |
start | 0. |
nominal | 0.1 |
Extends from Real.
| Name | Value |
|---|---|
quantity | "MoleFraction" |
unit | "mol/mol" |
min | 0 |
max | 1 |
start | 0. |
nominal | 0.1 |
Extends from Modelica.SIunits.MolarMass.
| Name | Value |
|---|---|
quantity | "MolarMass" |
unit | "kg/mol" |
min | 0.001 |
max | 0.25 |
start | 0. |
nominal | 0.032 |
Extends from Modelica.SIunits.MolarVolume.
| Name | Value |
|---|---|
quantity | "MolarVolume" |
unit | "m3/mol" |
min | 1e-6 |
max | 1000000 |
start | 0. |
nominal | 1 |
Extends from Modelica.SIunits.RatioOfSpecificHeatCapacities.
| Name | Value |
|---|---|
quantity | "RatioOfSpecificHeatCapacities" |
unit | "1" |
min | 1 |
max | 500000 |
start | 1.2 |
nominal | 1.2 |
Extends from Modelica.SIunits.SpecificEnergy.
| Name | Value |
|---|---|
quantity | "SpecificEnergy" |
unit | "J/kg" |
min | -1e+8 |
max | 1e+8 |
start | 0. |
nominal | 1000000 |
Extends from Modelica.Media.Incompressible.TableBased.SpecificEnergy (Type for specific energy with medium specific attributes).
| Name | Value |
|---|---|
quantity | "SpecificEnergy" |
unit | "J/kg" |
min | -1e+8 |
max | 1e+8 |
start | 0. |
nominal | 1000000 |
Extends from Modelica.SIunits.SpecificEnthalpy.
| Name | Value |
|---|---|
quantity | "SpecificEnergy" |
unit | "J/kg" |
min | -1e+10 |
max | 1e+10 |
start | 0. |
nominal | 1000000 |
Extends from Modelica.SIunits.SpecificEntropy.
| Name | Value |
|---|---|
quantity | "SpecificEntropy" |
unit | "J/(kg.K)" |
min | -1e+7 |
max | 1e+7 |
start | 0. |
nominal | 1000 |
Extends from Modelica.SIunits.SpecificHeatCapacity.
| Name | Value |
|---|---|
quantity | "SpecificHeatCapacity" |
unit | "J/(kg.K)" |
min | 0 |
max | 1e+7 |
start | 1000 |
nominal | 1000 |
Extends from Modelica.SIunits.SurfaceTension.
| Name | Value |
|---|---|
quantity | "SurfaceTension" |
unit | "N/m" |
min | -Modelica.Constants.inf |
max | Modelica.Constants.inf |
start | 0. |
Extends from Modelica.SIunits.Temperature.
| Name | Value |
|---|---|
quantity | "ThermodynamicTemperature" |
unit | "K" |
displayUnit | "degC" |
min | T_min |
max | T_max |
start | 288.15 |
nominal | 300 |
Extends from Modelica.SIunits.ThermalConductivity.
| Name | Value |
|---|---|
quantity | "ThermalConductivity" |
unit | "W/(m.K)" |
min | 0 |
max | 500 |
start | 1 |
nominal | 1 |
Extends from Modelica.SIunits.PrandtlNumber.
| Name | Value |
|---|---|
quantity | "PrandtlNumber" |
unit | "1" |
min | 0.001 |
max | 100000 |
start | 0. |
nominal | 1 |
Extends from Modelica.SIunits.Velocity.
| Name | Value |
|---|---|
quantity | "Velocity" |
unit | "m/s" |
min | 0 |
max | 100000 |
start | 1000 |
nominal | 1000 |
Extends from Real.
| Name | Value |
|---|---|
min | 0 |
max | Modelica.Constants.inf |
start | 1 |
Extends from Real.
| Name | Value |
|---|---|
min | 0 |
max | Modelica.Constants.inf |
start | 1 |
Extends from Real.
| Name | Value |
|---|---|
unit | "kg/s" |
min | -Modelica.Constants.inf |
max | Modelica.Constants.inf |
start | 0. |
Extends from Real.
| Name | Value |
|---|---|
unit | "1/K" |
min | 0 |
max | 1e+8 |
start | 0. |
Extends from Real.
| Name | Value |
|---|---|
quantity | "ElectricDipoleMoment" |
unit | "debye" |
min | 0 |
max | 2 |
start | 0. |
Extends from Modelica.SIunits.DerDensityByPressure.
| Name | Value |
|---|---|
unit | "s2/m2" |
min | -Modelica.Constants.inf |
max | Modelica.Constants.inf |
start | 0. |
Extends from Modelica.SIunits.DerDensityByEnthalpy.
| Name | Value |
|---|---|
unit | "kg.s2/m5" |
min | -Modelica.Constants.inf |
max | Modelica.Constants.inf |
start | 0. |
Extends from Modelica.SIunits.DerEnthalpyByPressure.
| Name | Value |
|---|---|
unit | "J.m.s2/kg2" |
min | -Modelica.Constants.inf |
max | Modelica.Constants.inf |
start | 0. |
Extends from Modelica.SIunits.DerDensityByTemperature.
| Name | Value |
|---|---|
unit | "kg/(m3.K)" |
min | -Modelica.Constants.inf |
max | Modelica.Constants.inf |
start | 0. |
Extends from Real.
| Name | Value |
|---|---|
unit | "K/Pa" |
min | -Modelica.Constants.inf |
max | Modelica.Constants.inf |
start | 0. |
This icon is indicates a record.
Extends from Modelica.Icons.Record (Icon for records).
| Type | Name | Description |
|---|---|---|
AbsolutePressure | psat | Saturation pressure |
Temperature | Tsat | Saturation temperature |
The minimum pressure mostly applies to the liquid state only. The minimum density is also arbitrary, but is reasonable for technical applications to limit iterations in non-linear systems. The limits in enthalpy and entropy are used as safeguards in inverse iterations.
Extends from Modelica.Icons.Record (Icon for records).
| Type | Name | Description |
|---|---|---|
Temperature | TMIN | Minimum temperature |
Temperature | TMAX | Maximum temperature |
Density | DMIN | Minimum density |
Density | DMAX | Maximum density |
AbsolutePressure | PMIN | Minimum pressure |
AbsolutePressure | PMAX | Maximum pressure |
SpecificEnthalpy | HMIN | Minimum enthalpy |
SpecificEnthalpy | HMAX | Maximum enthalpy |
SpecificEntropy | SMIN | Minimum entropy |
SpecificEntropy | SMAX | Maximum entropy |
Extends from Integer.
| Name | Value |
|---|---|
min | 0 |
max | 2 |
start | 0 |
This icon is indicates a record.
Extends from Modelica.Media.Interfaces.Types.Basic.FluidConstants (Critical, triple, molecular and other standard data of fluid).
| Type | Name | Description |
|---|---|---|
String | iupacName | Complete IUPAC name (or common name, if non-existent) |
String | casRegistryNumber | Chemical abstracts sequencing number (if it exists) |
String | chemicalFormula | Chemical formula, (brutto, nomenclature according to Hill |
String | structureFormula | Chemical structure formula |
MolarMass | molarMass | Molar mass |
This icon is indicates a record.
Extends from Modelica.Media.Incompressible.Common.BaseProps_Tpoly (Fluid state record).
| Type | Name | Description |
|---|---|---|
Temperature | T | Temperature |
Pressure | p | Pressure |
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 Modelica.Media.Interfaces.PartialMedium.BaseProperties (Base properties (p, d, T, h, u, R, MM and, if applicable, X and Xi) of a medium).
| Type | Name | Default | Description |
|---|---|---|---|
Boolean | preferredMediumStates | false | = true if StateSelect.prefer shall be used for the independent property variables of the medium |
final Boolean | standardOrderComponents | true | If true, and reducedX = true, the last element of X will be computed from the other ones |
Temperature | T_start | 298.15 | Initial temperature |
| Type | Name | Description |
|---|---|---|
input InputAbsolutePressure | p | Absolute pressure of medium |
input InputMassFraction | Xi[nXi] | Structurally independent mass fractions |
input InputSpecificEnthalpy | h | Specific enthalpy of medium |
This icon indicates Modelica functions.
Extends from Modelica.Media.Interfaces.PartialMedium.setState_pTX (Return thermodynamic state as function of p, T and composition X or Xi).
| Type | Name | Description |
|---|---|---|
AbsolutePressure | p | Pressure |
Temperature | T | Temperature |
MassFraction | X[:] | Mass fractions |
| Type | Name | Description |
|---|---|---|
ThermodynamicState | state | Thermodynamic state record |
This icon indicates Modelica functions.
Extends from Modelica.Media.Interfaces.PartialMedium.setState_phX (Return thermodynamic state as function of p, h and composition X or Xi).
| Type | Name | Description |
|---|---|---|
AbsolutePressure | p | Pressure |
SpecificEnthalpy | h | Specific enthalpy |
MassFraction | X[:] | Mass fractions |
| Type | Name | Description |
|---|---|---|
ThermodynamicState | state | Thermodynamic state record |
This icon indicates Modelica functions.
Extends from Modelica.Media.Interfaces.PartialMedium.setState_psX (Return thermodynamic state as function of p, s and composition X or Xi).
| Type | Name | Description |
|---|---|---|
AbsolutePressure | p | Pressure |
SpecificEntropy | s | Specific entropy |
MassFraction | X[:] | Mass fractions |
| Type | Name | Description |
|---|---|---|
ThermodynamicState | state | Thermodynamic state record |
This icon indicates Modelica functions.
Extends from Modelica.Media.Interfaces.PartialMedium.setState_dTX (Return thermodynamic state as function of d, T and composition X or Xi).
| Type | Name | Description |
|---|---|---|
Density | d | Density |
Temperature | T | Temperature |
MassFraction | X[:] | Mass fractions |
| Type | Name | Description |
|---|---|---|
ThermodynamicState | state | Thermodynamic state record |
This function is used to approximate the equation
state = if x > 0 then state_a else state_b;
by a smooth characteristic, so that the expression is continuous and differentiable:
state := smooth(1, if x > x_small then state_a else
if x < -x_small then state_b else f(state_a, state_b));
This is performed by applying function Media.Common.smoothStep(..) on every element of the thermodynamic state record.
If mass fractions X[:] are approximated with this function then this can be performed for all nX mass fractions, instead of applying it for nX-1 mass fractions and computing the last one by the mass fraction constraint sum(X)=1. The reason is that the approximating function has the property that sum(state.X) = 1, provided sum(state_a.X) = sum(state_b.X) = 1. This can be shown by evaluating the approximating function in the abs(x) < x_small region (otherwise state.X is either state_a.X or state_b.X):
X[1] = smoothStep(x, X_a[1] , X_b[1] , x_small);
X[2] = smoothStep(x, X_a[2] , X_b[2] , x_small);
...
X[nX] = smoothStep(x, X_a[nX], X_b[nX], x_small);
or
X[1] = c*(X_a[1] - X_b[1]) + (X_a[1] + X_b[1])/2
X[2] = c*(X_a[2] - X_b[2]) + (X_a[2] + X_b[2])/2;
...
X[nX] = c*(X_a[nX] - X_b[nX]) + (X_a[nX] + X_b[nX])/2;
c = (x/x_small)*((x/x_small)^2 - 3)/4
Summing all mass fractions together results in
sum(X) = c*(sum(X_a) - sum(X_b)) + (sum(X_a) + sum(X_b))/2
= c*(1 - 1) + (1 + 1)/2
= 1
Extends from Modelica.Media.Interfaces.PartialMedium.setSmoothState (Return thermodynamic state so that it smoothly approximates: if x > 0 then state_a else state_b).
| Type | Name | Description |
|---|---|---|
Real | x | m_flow or dp |
ThermodynamicState | state_a | Thermodynamic state if x > 0 |
ThermodynamicState | state_b | Thermodynamic state if x < 0 |
Real | x_small | Smooth transition in the region -x_small < x < x_small |
| Type | Name | Description |
|---|---|---|
ThermodynamicState | state | Smooth thermodynamic state for all x (continuous and differentiable) |
This icon indicates Modelica functions.
Extends from Modelica.Media.Interfaces.PartialMedium.dynamicViscosity (Return dynamic viscosity).
| Type | Name | Description |
|---|---|---|
ThermodynamicState | state | Thermodynamic state record |
| Type | Name | Description |
|---|---|---|
DynamicViscosity | eta | Dynamic viscosity |
This icon indicates Modelica functions.
Extends from Modelica.Media.Interfaces.PartialMedium.thermalConductivity (Return thermal conductivity).
| Type | Name | Description |
|---|---|---|
ThermodynamicState | state | Thermodynamic state record |
| Type | Name | Description |
|---|---|---|
ThermalConductivity | lambda | Thermal conductivity |
This icon indicates Modelica functions.
Extends from Modelica.Icons.Function (Icon for functions).
| Type | Name | Description |
|---|---|---|
ThermodynamicState | state | Thermodynamic state record |
| Type | Name | Description |
|---|---|---|
PrandtlNumber | Pr | Prandtl number |
This icon indicates Modelica functions.
Extends from Modelica.Media.Interfaces.PartialMedium.pressure (Return pressure).
| Type | Name | Description |
|---|---|---|
ThermodynamicState | state | Thermodynamic state record |
| Type | Name | Description |
|---|---|---|
AbsolutePressure | p | Pressure |
This icon indicates Modelica functions.
Extends from Modelica.Media.Interfaces.PartialMedium.temperature (Return temperature).
| Type | Name | Description |
|---|---|---|
ThermodynamicState | state | Thermodynamic state record |
| Type | Name | Description |
|---|---|---|
Temperature | T | Temperature |
This icon indicates Modelica functions.
Extends from Modelica.Media.Interfaces.PartialMedium.density (Return density).
| Type | Name | Description |
|---|---|---|
ThermodynamicState | state | Thermodynamic state record |
| Type | Name | Description |
|---|---|---|
Density | d | Density |
This icon indicates Modelica functions.
Extends from Modelica.Media.Interfaces.PartialMedium.specificEnthalpy (Return specific enthalpy).
| Type | Name | Description |
|---|---|---|
ThermodynamicState | state | Thermodynamic state record |
| Type | Name | Description |
|---|---|---|
SpecificEnthalpy | h | Specific enthalpy |
This icon indicates Modelica functions.
Extends from Modelica.Media.Interfaces.PartialMedium.specificInternalEnergy (Return specific internal energy).
| Type | Name | Description |
|---|---|---|
ThermodynamicState | state | Thermodynamic state record |
| Type | Name | Description |
|---|---|---|
SpecificEnergy | u | Specific internal energy |
This icon indicates Modelica functions.
Extends from Modelica.Media.Interfaces.PartialMedium.specificEntropy (Return specific entropy).
| Type | Name | Description |
|---|---|---|
ThermodynamicState | state | Thermodynamic state record |
| Type | Name | Description |
|---|---|---|
SpecificEntropy | s | Specific entropy |
This icon indicates Modelica functions.
Extends from Modelica.Icons.Function (Icon for functions).
| Type | Name | Description |
|---|---|---|
ThermodynamicState | state | Thermodynamic state record |
| Type | Name | Description |
|---|---|---|
SpecificEnergy | g | Specific Gibbs energy |
This icon indicates Modelica functions.
Extends from Modelica.Icons.Function (Icon for functions).
| Type | Name | Description |
|---|---|---|
ThermodynamicState | state | Thermodynamic state record |
| Type | Name | Description |
|---|---|---|
SpecificEnergy | f | Specific Helmholtz energy |
This icon indicates Modelica functions.
Extends from Modelica.Media.Interfaces.PartialMedium.specificHeatCapacityCp (Return specific heat capacity at constant pressure).
| Type | Name | Description |
|---|---|---|
ThermodynamicState | state | Thermodynamic state record |
| Type | Name | Description |
|---|---|---|
SpecificHeatCapacity | cp | Specific heat capacity at constant pressure |
This icon indicates Modelica functions.
Extends from Modelica.Media.Incompressible.TableBased.specificHeatCapacityCp (Specific heat capacity at constant volume (or pressure) of medium).
| Type | Name | Description |
|---|---|---|
ThermodynamicState | state | Thermodynamic state record |
| Type | Name | Description |
|---|---|---|
SpecificHeatCapacity | cp | Specific heat capacity at constant pressure |
This icon indicates Modelica functions.
Extends from Modelica.Media.Interfaces.PartialMedium.specificHeatCapacityCv (Return specific heat capacity at constant volume).
| Type | Name | Description |
|---|---|---|
ThermodynamicState | state | Thermodynamic state record |
| Type | Name | Description |
|---|---|---|
SpecificHeatCapacity | cv | Specific heat capacity at constant volume |
This icon indicates Modelica functions.
Extends from Modelica.Media.Incompressible.TableBased.specificHeatCapacityCv (Specific heat capacity at constant volume (or pressure) of medium).
| Type | Name | Description |
|---|---|---|
ThermodynamicState | state | Thermodynamic state record |
| Type | Name | Description |
|---|---|---|
SpecificHeatCapacity | cv | Specific heat capacity at constant volume |
This icon indicates Modelica functions.
Extends from Modelica.Icons.Function (Icon for functions).
| Type | Name | Description |
|---|---|---|
ThermodynamicState | state | Thermodynamic state record |
| Type | Name | Description |
|---|---|---|
IsentropicExponent | gamma | Isentropic exponent |
This function computes an isentropic state transformation:
Extends from Modelica.Icons.Function (Icon for functions).
| Type | Name | Description |
|---|---|---|
AbsolutePressure | p_downstream | Downstream pressure |
ThermodynamicState | refState | Reference state for entropy |
| Type | Name | Description |
|---|---|---|
SpecificEnthalpy | h_is | Isentropic enthalpy |
This icon indicates Modelica functions.
Extends from Modelica.Icons.Function (Icon for functions).
| Type | Name | Description |
|---|---|---|
ThermodynamicState | state | Thermodynamic state record |
| Type | Name | Description |
|---|---|---|
VelocityOfSound | a | Velocity of sound |
beta is defined as 1/v * der(v,T), with v = 1/d, at constant pressure p.
Extends from Modelica.Icons.Function (Icon for functions).
| Type | Name | Description |
|---|---|---|
ThermodynamicState | state | Thermodynamic state record |
| Type | Name | Description |
|---|---|---|
IsobaricExpansionCoefficient | beta | Isobaric expansion coefficient |
beta is defined as 1/v * der(v,T), with v = 1/d, at constant pressure p.
Extends from Modelica.Media.Incompressible.TableBased.isobaricExpansionCoefficient (Return overall the isobaric expansion coefficient beta).
| Type | Name | Description |
|---|---|---|
ThermodynamicState | state | Thermodynamic state record |
| Type | Name | Description |
|---|---|---|
IsobaricExpansionCoefficient | beta | Isobaric expansion coefficient |
kappa is defined as - 1/v * der(v,p), with v = 1/d at constant temperature T.
Extends from Modelica.Icons.Function (Icon for functions).
| Type | Name | Description |
|---|---|---|
ThermodynamicState | state | Thermodynamic state record |
| Type | Name | Description |
|---|---|---|
IsothermalCompressibility | kappa | Isothermal compressibility |
kappa is defined as - 1/v * der(v,p), with v = 1/d at constant temperature T.
Extends from Modelica.Media.Incompressible.TableBased.isothermalCompressibility (Return overall the isothermal compressibility factor).
| Type | Name | Description |
|---|---|---|
ThermodynamicState | state | Thermodynamic state record |
| Type | Name | Description |
|---|---|---|
IsothermalCompressibility | kappa | Isothermal compressibility |
This icon indicates Modelica functions.
Extends from Modelica.Icons.Function (Icon for functions).
| Type | Name | Description |
|---|---|---|
ThermodynamicState | state | Thermodynamic state record |
| Type | Name | Description |
|---|---|---|
DerDensityByPressure | ddph | Density derivative w.r.t. pressure |
This icon indicates Modelica functions.
Extends from Modelica.Icons.Function (Icon for functions).
| Type | Name | Description |
|---|---|---|
ThermodynamicState | state | Thermodynamic state record |
| Type | Name | Description |
|---|---|---|
DerDensityByEnthalpy | ddhp | Density derivative w.r.t. specific enthalpy |
This icon indicates Modelica functions.
Extends from Modelica.Icons.Function (Icon for functions).
| Type | Name | Description |
|---|---|---|
ThermodynamicState | state | Thermodynamic state record |
| Type | Name | Description |
|---|---|---|
DerDensityByPressure | ddpT | Density derivative w.r.t. pressure |
This icon indicates Modelica functions.
Extends from Modelica.Icons.Function (Icon for functions).
| Type | Name | Description |
|---|---|---|
ThermodynamicState | state | Thermodynamic state record |
| Type | Name | Description |
|---|---|---|
DerDensityByTemperature | ddTp | Density derivative w.r.t. temperature |
This icon indicates Modelica functions.
Extends from Modelica.Icons.Function (Icon for functions).
| Type | Name | Description |
|---|---|---|
ThermodynamicState | state | Thermodynamic state record |
| Type | Name | Description |
|---|---|---|
Density | dddX[nX] | Derivative of density w.r.t. mass fraction |
This icon indicates Modelica functions.
Extends from Modelica.Icons.Function (Icon for functions).
| Type | Name | Description |
|---|---|---|
ThermodynamicState | state | Thermodynamic state record |
| Type | Name | Description |
|---|---|---|
MolarMass | MM | Mixture molar mass |
This icon indicates Modelica functions.
Extends from Modelica.Icons.Function (Icon for functions).
| Type | Name | Description |
|---|---|---|
AbsolutePressure | p | Pressure |
Temperature | T | Temperature |
MassFraction | X[:] | Mass fractions |
| Type | Name | Description |
|---|---|---|
SpecificEnthalpy | h | Specific enthalpy |
This icon indicates Modelica functions.
Extends from Modelica.Icons.Function (Icon for functions).
| Type | Name | Description |
|---|---|---|
AbsolutePressure | p | Pressure |
Temperature | T | Temperature |
MassFraction | X[:] | Mass fractions |
| Type | Name | Description |
|---|---|---|
SpecificEntropy | s | Specific entropy |
This icon indicates Modelica functions.
Extends from Modelica.Icons.Function (Icon for functions).
| Type | Name | Description |
|---|---|---|
AbsolutePressure | p | Pressure |
Temperature | T | Temperature |
MassFraction | X[:] | Mass fractions |
| Type | Name | Description |
|---|---|---|
Density | d | Density |
This icon indicates Modelica functions.
Extends from Modelica.Icons.Function (Icon for functions).
| Type | Name | Description |
|---|---|---|
AbsolutePressure | p | Pressure |
SpecificEnthalpy | h | Specific enthalpy |
MassFraction | X[:] | Mass fractions |
| Type | Name | Description |
|---|---|---|
Temperature | T | Temperature |
This icon indicates Modelica functions.
Extends from Modelica.Icons.Function (Icon for functions).
| Type | Name | Description |
|---|---|---|
AbsolutePressure | p | Pressure |
SpecificEnthalpy | h | Specific enthalpy |
MassFraction | X[:] | Mass fractions |
| Type | Name | Description |
|---|---|---|
Density | d | Density |
This icon indicates Modelica functions.
Extends from Modelica.Icons.Function (Icon for functions).
| Type | Name | Description |
|---|---|---|
AbsolutePressure | p | Pressure |
SpecificEntropy | s | Specific entropy |
MassFraction | X[:] | Mass fractions |
| Type | Name | Description |
|---|---|---|
Temperature | T | Temperature |
This icon indicates Modelica functions.
Extends from Modelica.Icons.Function (Icon for functions).
| Type | Name | Description |
|---|---|---|
AbsolutePressure | p | Pressure |
SpecificEntropy | s | Specific entropy |
MassFraction | X[:] | Mass fractions |
| Type | Name | Description |
|---|---|---|
Density | d | Density |
This icon indicates Modelica functions.
Extends from Modelica.Icons.Function (Icon for functions).
| Type | Name | Description |
|---|---|---|
AbsolutePressure | p | Pressure |
SpecificEntropy | s | Specific entropy |
MassFraction | X[:] | Mass fractions |
| Type | Name | Description |
|---|---|---|
SpecificEnthalpy | h | Specific enthalpy |
Extends from Modelica.SIunits.MassFlowRate.
| Name | Value |
|---|---|
quantity | "MassFlowRate." + mediumName |
unit | "kg/s" |
min | -100000 |
max | 100000 |
start | 0. |
This icon indicates Modelica functions.
Extends from Modelica.Icons.Function (Icon for functions).
| Type | Name | Description |
|---|---|---|
Real | table[:] | Table temperature data |
Boolean | Tink | Flag for Celsius or Kelvin |
| Type | Name | Description |
|---|---|---|
Real | invTable[size(table, 1)] | Inverted temperatures |
This icon indicates Modelica functions.
Extends from Modelica.Icons.Function (Icon for functions).
| Type | Name | Description |
|---|---|---|
AbsolutePressure | p | Pressure |
Temperature | T | Temperature |
| Type | Name | Description |
|---|---|---|
ThermodynamicState | state | Thermodynamic state |
This icon indicates Modelica functions.
Extends from Modelica.Icons.Function (Icon for functions).
| Type | Name | Description |
|---|---|---|
AbsolutePressure | p | Pressure |
SpecificEnthalpy | h | Specific enthalpy |
| Type | Name | Description |
|---|---|---|
ThermodynamicState | state | Thermodynamic state |
This icon indicates Modelica functions.
Extends from Modelica.Icons.Function (Icon for functions).
| Type | Name | Description |
|---|---|---|
AbsolutePressure | p | Pressure |
SpecificEntropy | s | Specific entropy |
| Type | Name | Description |
|---|---|---|
ThermodynamicState | state | Thermodynamic state |
This icon indicates Modelica functions.
Extends from Modelica.Icons.Function (Icon for functions).
| Type | Name | Description |
|---|---|---|
Temperature | T | Temperature |
| Type | Name | Description |
|---|---|---|
SpecificEntropy | s | Specific entropy |
This icon indicates Modelica functions.
Extends from Modelica.Icons.Function (Icon for functions).
| Type | Name | Description |
|---|---|---|
Temperature | T | Temperature |
| Type | Name | Description |
|---|---|---|
SpecificEnthalpy | h | Specific enthalpy at p, T |
This icon indicates Modelica functions.
Extends from Modelica.Icons.Function (Icon for functions).
| Type | Name | Description |
|---|---|---|
Temperature | T | Temperature |
Real | dT | Temperature derivative |
| Type | Name | Description |
|---|---|---|
Real | dh | Derivative of Specific enthalpy at T |
This icon indicates Modelica functions.
Extends from Modelica.Icons.Function (Icon for functions).
| Type | Name | Description |
|---|---|---|
Pressure | p | Pressure |
Temperature | T | Temperature |
Boolean | densityOfT | Include or neglect density derivative dependence of enthalpy |
| Type | Name | Description |
|---|---|---|
SpecificEnthalpy | h | Specific enthalpy at p, T |
This icon indicates Modelica functions.
Extends from Modelica.Icons.Function (Icon for functions).
| Type | Name | Description |
|---|---|---|
Temperature | T | Temperature |
| Type | Name | Description |
|---|---|---|
Density | d | Density |
This icon indicates Modelica functions.
Extends from Modelica.Icons.Function (Icon for functions).
| Type | Name | Description |
|---|---|---|
AbsolutePressure | p | Pressure |
SpecificEnthalpy | h | Specific enthalpy |
| Type | Name | Description |
|---|---|---|
Temperature | T | Temperature |
This icon indicates Modelica functions.
Extends from Modelica.Icons.Function (Icon for functions).
| Type | Name | Description |
|---|---|---|
AbsolutePressure | p | Pressure |
SpecificEntropy | s | Specific entropy |
| Type | Name | Description |
|---|---|---|
Temperature | T | Temperature |
Generated 2018-12-12 12:14:18 EST by MapleSim.