Critical, triple, molecular and other standard data of fluid
Return thermodynamic state so that it smoothly approximates: if x > 0 then state_a else state_b
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.Icons.Function (Icon for functions).
Type | Name | Default | 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) |
Return the Prandtl number
Extends from Modelica.Icons.Function (Icon for functions).
Type | Name | Default | Description |
---|---|---|---|
ThermodynamicState | state | Thermodynamic state record |
Type | Name | Description |
---|---|---|
PrandtlNumber | Pr | Prandtl number [1] |
Alias for deprecated name
Type | Name | Default | Description |
---|---|---|---|
ThermodynamicState | state | Thermodynamic state record |
Type | Name | Description |
---|---|---|
SpecificHeatCapacity | cp | Specific heat capacity at constant pressure [J/(kg.K)] |
Alias for deprecated name
Type | Name | Default | Description |
---|---|---|---|
ThermodynamicState | state | Thermodynamic state record |
Type | Name | Description |
---|---|---|
SpecificHeatCapacity | cv | Specific heat capacity at constant volume [J/(kg.K)] |
Return isentropic exponent
Extends from Modelica.Icons.Function (Icon for functions).
Type | Name | Default | Description |
---|---|---|---|
ThermodynamicState | state | Thermodynamic state record |
Type | Name | Description |
---|---|---|
IsentropicExponent | gamma | Isentropic exponent [1] |
Return velocity of sound
Extends from Modelica.Icons.Function (Icon for functions).
Type | Name | Default | Description |
---|---|---|---|
ThermodynamicState | state | Thermodynamic state record |
Type | Name | Description |
---|---|---|
VelocityOfSound | a | Velocity of sound [m/s] |
Alias for isobaricExpansionCoefficient for user convenience
Type | Name | Default | Description |
---|---|---|---|
ThermodynamicState | state | Thermodynamic state record |
Type | Name | Description |
---|---|---|
IsobaricExpansionCoefficient | beta | Isobaric expansion coefficient [1/K] |
Alias of isothermalCompressibility for user convenience
Type | Name | Default | Description |
---|---|---|---|
ThermodynamicState | state | Thermodynamic state record |
Type | Name | Description |
---|---|---|
IsothermalCompressibility | kappa | Isothermal compressibility [1/Pa] |
Return density derivative w.r.t. pressure at const specific enthalpy
Extends from Modelica.Icons.Function (Icon for functions).
Type | Name | Default | Description |
---|---|---|---|
ThermodynamicState | state | Thermodynamic state record |
Type | Name | Description |
---|---|---|
DerDensityByPressure | ddph | Density derivative w.r.t. pressure [s2/m2] |
Return density derivative w.r.t. specific enthalpy at constant pressure
Extends from Modelica.Icons.Function (Icon for functions).
Type | Name | Default | Description |
---|---|---|---|
ThermodynamicState | state | Thermodynamic state record |
Type | Name | Description |
---|---|---|
DerDensityByEnthalpy | ddhp | Density derivative w.r.t. specific enthalpy [kg.s2/m5] |
Return specific enthalpy from p, T, and X or Xi
Extends from Modelica.Icons.Function (Icon for functions).
Type | Name | Default | Description |
---|---|---|---|
AbsolutePressure | p | Pressure [Pa] | |
Temperature | T | Temperature [K] | |
MassFraction | X[:] | reference_X | Mass fractions [kg/kg] |
Type | Name | Description |
---|---|---|
SpecificEntropy | s | Specific entropy [J/(kg.K)] |
Return density from p, T, and X or Xi
Extends from Modelica.Icons.Function (Icon for functions).
Type | Name | Default | Description |
---|---|---|---|
AbsolutePressure | p | Pressure [Pa] | |
Temperature | T | Temperature [K] | |
MassFraction | X[:] | Mass fractions [kg/kg] |
Type | Name | Description |
---|---|---|
Density | d | Density [kg/m3] |
Return density from p, h, and X or Xi
Extends from Modelica.Icons.Function (Icon for functions).
Type | Name | Default | Description |
---|---|---|---|
AbsolutePressure | p | Pressure [Pa] | |
SpecificEnthalpy | h | Specific enthalpy [J/kg] | |
MassFraction | X[:] | reference_X | Mass fractions [kg/kg] |
Type | Name | Description |
---|---|---|
Density | d | Density [kg/m3] |
Return temperature from p,s, and X or Xi
Extends from Modelica.Icons.Function (Icon for functions).
Type | Name | Default | Description |
---|---|---|---|
AbsolutePressure | p | Pressure [Pa] | |
SpecificEntropy | s | Specific entropy [J/(kg.K)] | |
MassFraction | X[:] | reference_X | Mass fractions [kg/kg] |
Type | Name | Description |
---|---|---|
Temperature | T | Temperature [K] |
Return density from p, s, and X or Xi
Extends from Modelica.Icons.Function (Icon for functions).
Type | Name | Default | Description |
---|---|---|---|
AbsolutePressure | p | Pressure [Pa] | |
SpecificEntropy | s | Specific entropy [J/(kg.K)] | |
MassFraction | X[:] | reference_X | Mass fractions [kg/kg] |
Type | Name | Description |
---|---|---|
Density | d | Density [kg/m3] |
Return specific enthalpy from p, s, and X or Xi
Extends from Modelica.Icons.Function (Icon for functions).
Type | Name | Default | Description |
---|---|---|---|
AbsolutePressure | p | Pressure [Pa] | |
SpecificEntropy | s | Specific entropy [J/(kg.K)] | |
MassFraction | X[:] | reference_X | Mass fractions [kg/kg] |
Type | Name | Description |
---|---|---|
SpecificEnthalpy | h | Specific enthalpy [J/kg] |
Return thermodynamic state as function of p, s and composition X or Xi
Extends from Modelica.Icons.Function (Icon for functions).
Type | Name | Default | Description |
---|---|---|---|
AbsolutePressure | p | Pressure [Pa] | |
SpecificEntropy | s | Specific entropy [J/(kg.K)] | |
MassFraction | X[:] | reference_X | Mass fractions [kg/kg] |
Type | Name | Description |
---|---|---|
ThermodynamicState | state | Thermodynamic state record |
Return isentropic enthalpy
This function computes an isentropic state transformation:
Extends from Modelica.Icons.Function (Icon for functions).
Type | Name | Default | Description |
---|---|---|---|
AbsolutePressure | p_downstream | Downstream pressure [Pa] | |
ThermodynamicState | refState | Reference state for entropy |
Type | Name | Description |
---|---|---|
SpecificEnthalpy | h_is | Isentropic enthalpy [J/kg] |
Return overall the isobaric expansion coefficient beta
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 | Default | Description |
---|---|---|---|
ThermodynamicState | state | Thermodynamic state record |
Type | Name | Description |
---|---|---|
IsobaricExpansionCoefficient | beta | Isobaric expansion coefficient [1/K] |
Return overall the isothermal compressibility factor
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 | Default | Description |
---|---|---|---|
ThermodynamicState | state | Thermodynamic state record |
Type | Name | Description |
---|---|---|
IsothermalCompressibility | kappa | Isothermal compressibility [1/Pa] |
Return density derivative w.r.t. pressure at const temperature
Extends from Modelica.Icons.Function (Icon for functions).
Type | Name | Default | Description |
---|---|---|---|
ThermodynamicState | state | Thermodynamic state record |
Type | Name | Description |
---|---|---|
DerDensityByPressure | ddpT | Density derivative w.r.t. pressure [s2/m2] |
Return density derivative w.r.t. temperature at constant pressure
Extends from Modelica.Icons.Function (Icon for functions).
Type | Name | Default | Description |
---|---|---|---|
ThermodynamicState | state | Thermodynamic state record |
Type | Name | Description |
---|---|---|
DerDensityByTemperature | ddTp | Density derivative w.r.t. temperature [kg/(m3.K)] |
Return density derivative w.r.t. mass fraction
Extends from Modelica.Icons.Function (Icon for functions).
Type | Name | Default | Description |
---|---|---|---|
ThermodynamicState | state | Thermodynamic state record |
Type | Name | Description |
---|---|---|
Density | dddX[nX] | Derivative of density w.r.t. mass fraction [kg/m3] |
Return the molar mass of the medium
Extends from Modelica.Icons.Function (Icon for functions).
Type | Name | Default | Description |
---|---|---|---|
ThermodynamicState | state | Thermodynamic state record |
Type | Name | Description |
---|---|---|
MolarMass | MM | Mixture molar mass [kg/mol] |
Return specific enthalpy from p, T, and X or Xi
Extends from Modelica.Icons.Function (Icon for functions).
Type | Name | Default | Description |
---|---|---|---|
AbsolutePressure | p | Pressure [Pa] | |
Temperature | T | Temperature [K] | |
MassFraction | X[:] | reference_X | Mass fractions [kg/kg] |
Type | Name | Description |
---|---|---|
SpecificEnthalpy | h | Specific enthalpy [J/kg] |
Return temperature from p, h, and X or Xi
Extends from Modelica.Icons.Function (Icon for functions).
Type | Name | Default | Description |
---|---|---|---|
AbsolutePressure | p | Pressure [Pa] | |
SpecificEnthalpy | h | Specific enthalpy [J/kg] | |
MassFraction | X[:] | reference_X | Mass fractions [kg/kg] |
Type | Name | Description |
---|---|---|
Temperature | T | Temperature [K] |
Return specific entropy
Extends from Modelica.Icons.Function (Icon for functions).
Type | Name | Default | Description |
---|---|---|---|
ThermodynamicState | state | Thermodynamic state record |
Type | Name | Description |
---|---|---|
SpecificEntropy | s | Specific entropy [J/(kg.K)] |
Return specific Gibbs energy
Extends from Modelica.Icons.Function (Icon for functions).
Type | Name | Default | Description |
---|---|---|---|
ThermodynamicState | state | Thermodynamic state record |
Type | Name | Description |
---|---|---|
SpecificEnergy | g | Specific Gibbs energy [J/kg] |
Return specific Helmholtz energy
Extends from Modelica.Icons.Function (Icon for functions).
Type | Name | Default | Description |
---|---|---|---|
ThermodynamicState | state | Thermodynamic state record |
Type | Name | Description |
---|---|---|
SpecificEnergy | f | Specific Helmholtz energy [J/kg] |
Return specific internal energy
Extends from Modelica.Icons.Function (Icon for functions).
Type | Name | Default | Description |
---|---|---|---|
ThermodynamicState | state | Thermodynamic state record |
Type | Name | Description |
---|---|---|
SpecificEnergy | u | Specific internal energy [J/kg] |