Base functions as described in IAWPS/IF97
Package BaseIF97/Basic computes the fundamental functions for the 5 regions of the steam tables as described in the standards document IF97.pdf. The code of these functions has been generated using Mathematica and the add-on packages "Format" and "Optimize" to generate highly efficient, expression-optimized C-code from a symbolic representation of the thermodynamic functions. The C-code has than been transformed into Modelica code. An important feature of this optimization was to simultaneously optimize the functions and the directional derivatives because they share many common subexpressions.
Equation from:
Extends from Modelica.Icons.FunctionsPackage (Icon for packages containing functions).
Name | Description |
---|---|
g1 | Gibbs function for region 1: g(p,T) |
g2 | Gibbs function for region 2: g(p,T) |
g2metastable | Gibbs function for metastable part of region 2: g(p,T) |
f3 | Helmholtz function for region 3: f(d,T) |
g5 | Base function for region 5: g(p,T) |
gibbs | Gibbs function for region 1, 2 or 5: g(p,T,region) |
g1pitau | Derivative of g w.r.t. pi and tau |
g2pitau | Derivative of g w.r.t. pi and tau |
g5pitau | Derivative of g w.r.t. pi and tau |
f3deltatau | 1st derivatives of f w.r.t. delta and tau |
tph1 | Inverse function for region 1: T(p,h) |
tps1 | Inverse function for region 1: T(p,s) |
tph2 | Reverse function for region 2: T(p,h) |
tps2a | Reverse function for region 2a: T(p,s) |
tps2b | Reverse function for region 2b: T(p,s) |
tps2c | Reverse function for region 2c: T(p,s) |
tps2 | Reverse function for region 2: T(p,s) |
tsat | Region 4 saturation temperature as a function of pressure |
dtsatofp | Derivative of saturation temperature w.r.t. pressure |
tsat_der | Derivative function for tsat |
psat | Region 4 saturation pressure as a function of temperature |
dptofT | Derivative of pressure w.r.t. temperature along the saturation pressure curve |
psat_der | Derivative function for psat |
p1_hs | Pressure as a function of enthalpy and entropy in region 1 |
h2ab_s | Boundary between regions 2a and 2b |
p2a_hs | Pressure as a function of enthalpy and entropy in subregion 2a |
p2b_hs | Pressure as a function of enthalpy and entropy in subregion 2a |
p2c_hs | Pressure as a function of enthalpy and entropy in subregion 2c |
h3ab_p | Region 3 a b boundary for pressure/enthalpy |
T3a_ph | Region 3 a: inverse function T(p,h) |
T3b_ph | Region 3 b: inverse function T(p,h) |
v3a_ph | Region 3 a: inverse function v(p,h) |
v3b_ph | Region 3 b: inverse function v(p,h) |
T3a_ps | Region 3 a: inverse function T(p,s) |
T3b_ps | Region 3 b: inverse function T(p,s) |
v3a_ps | Region 3 a: inverse function v(p,s) |
v3b_ps | Region 3 b: inverse function v(p,s) |
Gibbs function for region 1: g(p,T)
Extends from Modelica.Icons.Function (Icon for functions).
Name | Description |
---|---|
p | Pressure [Pa] |
T | Temperature (K) [K] |
Name | Description |
---|---|
g | Dimensionless Gibbs function and derivatives w.r.t. pi and tau |
Gibbs function for region 2: g(p,T)
Extends from Modelica.Icons.Function (Icon for functions).
Name | Description |
---|---|
p | Pressure [Pa] |
T | Temperature (K) [K] |
checkLimits | Check if inputs p,T are in region of validity |
Name | Description |
---|---|
g | Dimensionless Gibbs function and derivatives w.r.t. pi and tau |
Gibbs function for metastable part of region 2: g(p,T)
Extends from Modelica.Icons.Function (Icon for functions).
Name | Description |
---|---|
p | Pressure [Pa] |
T | Temperature (K) [K] |
Name | Description |
---|---|
g | Dimensionless Gibbs function and derivatives w.r.t. pi and tau |
Helmholtz function for region 3: f(d,T)
Extends from Modelica.Icons.Function (Icon for functions).
Name | Description |
---|---|
d | Density [kg/m3] |
T | Temperature (K) [K] |
Name | Description |
---|---|
f | Dimensionless Helmholtz function and derivatives w.r.t. delta and tau |
Base function for region 5: g(p,T)
Extends from Modelica.Icons.Function (Icon for functions).
Name | Description |
---|---|
p | Pressure [Pa] |
T | Temperature (K) [K] |
Name | Description |
---|---|
g | Dimensionless Gibbs function and derivatives w.r.t. pi and tau |
Gibbs function for region 1, 2 or 5: g(p,T,region)
Extends from Modelica.Icons.Function (Icon for functions).
Name | Description |
---|---|
p | Pressure [Pa] |
T | Temperature (K) [K] |
region | IF97 region, 1, 2 or 5 |
Name | Description |
---|---|
g | Dimensionless Gibbs function |
Derivative of g w.r.t. pi and tau
Extends from Modelica.Icons.Function (Icon for functions).
Name | Description |
---|---|
p | Pressure [Pa] |
T | Temperature (K) [K] |
Name | Description |
---|---|
pi | Dimensionless pressure |
tau | Dimensionless temperature |
gpi | Dimensionless derivative of Gibbs function w.r.t. pi |
gtau | Dimensionless derivative of Gibbs function w.r.t. tau |
Derivative of g w.r.t. pi and tau
Extends from Modelica.Icons.Function (Icon for functions).
Name | Description |
---|---|
p | Pressure [Pa] |
T | Temperature (K) [K] |
Name | Description |
---|---|
pi | Dimensionless pressure |
tau | Dimensionless temperature |
gpi | Dimensionless derivative of Gibbs function w.r.t. pi |
gtau | Dimensionless derivative of Gibbs function w.r.t. tau |
Derivative of g w.r.t. pi and tau
Extends from Modelica.Icons.Function (Icon for functions).
Name | Description |
---|---|
p | Pressure [Pa] |
T | Temperature (K) [K] |
Name | Description |
---|---|
pi | Dimensionless pressure |
tau | Dimensionless temperature |
gpi | Dimensionless derivative of Gibbs function w.r.t. pi |
gtau | Dimensionless derivative of Gibbs function w.r.t. tau |
1st derivatives of f w.r.t. delta and tau
Extends from Modelica.Icons.Function (Icon for functions).
Name | Description |
---|---|
d | Density [kg/m3] |
T | Temperature (K) [K] |
Name | Description |
---|---|
delta | Dimensionless density |
tau | Dimensionless temperature |
fdelta | Dimensionless derivative of Helmholtz function w.r.t. delta |
ftau | Dimensionless derivative of Helmholtz function w.r.t. tau |
Inverse function for region 1: T(p,h)
Extends from Modelica.Icons.Function (Icon for functions).
Name | Description |
---|---|
p | Pressure [Pa] |
h | Specific enthalpy [J/kg] |
Name | Description |
---|---|
T | Temperature (K) [K] |
Inverse function for region 1: T(p,s)
Extends from Modelica.Icons.Function (Icon for functions).
Name | Description |
---|---|
p | Pressure [Pa] |
s | Specific entropy [J/(kg.K)] |
Name | Description |
---|---|
T | Temperature (K) [K] |
Reverse function for region 2: T(p,h)
Extends from Modelica.Icons.Function (Icon for functions).
Name | Description |
---|---|
p | Pressure [Pa] |
h | Specific enthalpy [J/kg] |
Name | Description |
---|---|
T | Temperature (K) [K] |
Reverse function for region 2a: T(p,s)
Extends from Modelica.Icons.Function (Icon for functions).
Name | Description |
---|---|
p | Pressure [Pa] |
s | Specific entropy [J/(kg.K)] |
Name | Description |
---|---|
T | Temperature (K) [K] |
Reverse function for region 2b: T(p,s)
Extends from Modelica.Icons.Function (Icon for functions).
Name | Description |
---|---|
p | Pressure [Pa] |
s | Specific entropy [J/(kg.K)] |
Name | Description |
---|---|
T | Temperature (K) [K] |
Reverse function for region 2c: T(p,s)
Extends from Modelica.Icons.Function (Icon for functions).
Name | Description |
---|---|
p | Pressure [Pa] |
s | Specific entropy [J/(kg.K)] |
Name | Description |
---|---|
T | Temperature (K) [K] |
Reverse function for region 2: T(p,s)
Extends from Modelica.Icons.Function (Icon for functions).
Name | Description |
---|---|
p | Pressure [Pa] |
s | Specific entropy [J/(kg.K)] |
Name | Description |
---|---|
T | Temperature (K) [K] |
Region 4 saturation temperature as a function of pressure
Extends from Modelica.Icons.Function (Icon for functions).
Name | Description |
---|---|
p | Pressure [Pa] |
Name | Description |
---|---|
t_sat | Temperature [K] |
Derivative of saturation temperature w.r.t. pressure
Extends from Modelica.Icons.Function (Icon for functions).
Name | Description |
---|---|
p | Pressure [Pa] |
Name | Description |
---|---|
dtsat | Derivative of T w.r.t. p [K/Pa] |
Derivative function for tsat
Extends from Modelica.Icons.Function (Icon for functions).
Name | Description |
---|---|
p | Pressure [Pa] |
der_p | Pressure derivative [Pa/s] |
Name | Description |
---|---|
der_tsat | Temperature derivative [K/s] |
Region 4 saturation pressure as a function of temperature
Extends from Modelica.Icons.Function (Icon for functions).
Name | Description |
---|---|
T | Temperature (K) [K] |
Name | Description |
---|---|
p_sat | Pressure [Pa] |
Derivative of pressure w.r.t. temperature along the saturation pressure curve
Extends from Modelica.Icons.Function (Icon for functions).
Name | Description |
---|---|
T | Temperature (K) [K] |
Name | Description |
---|---|
dpt | Temperature derivative of pressure [Pa/K] |
Derivative function for psat
Extends from Modelica.Icons.Function (Icon for functions).
Name | Description |
---|---|
T | Temperature (K) [K] |
der_T | Temperature derivative [K/s] |
Name | Description |
---|---|
der_psat | Pressure [Pa/s] |
Pressure as a function of enthalpy and entropy in region 1
Equation number 1 from:
The International Association for the Properties of Water and Steam
Gaithersburg, Maryland, USA
September 2001
Supplementary Release on Backward Equations for Pressure as a
Function of Enthalpy and Entropy p(h,s) to the IAPWS Industrial
Formulation 1997 for the Thermodynamic Properties of Water and Steam
Extends from Modelica.Icons.Function (Icon for functions).
Name | Description |
---|---|
h | Specific enthalpy [J/kg] |
s | Specific entropy [J/(kg.K)] |
Name | Description |
---|---|
p | Pressure [Pa] |
Boundary between regions 2a and 2b
Equation number 2 from:
The International Association for the Properties of Water and Steam
Gaithersburg, Maryland, USA
September 2001
Supplementary Release on Backward Equations for Pressure as a
Function of Enthalpy and Entropy p(h,s) to the IAPWS Industrial
Formulation 1997 for the Thermodynamic Properties of Water and Steam
Extends from Modelica.Icons.Function (Icon for functions).
Name | Description |
---|---|
s | Entropy [J/(kg.K)] |
Name | Description |
---|---|
h | Enthalpy [J/kg] |
Pressure as a function of enthalpy and entropy in subregion 2a
Equation number 3 from:
The International Association for the Properties of Water and Steam
Gaithersburg, Maryland, USA
September 2001
Supplementary Release on Backward Equations for Pressure as a
Function of Enthalpy and Entropy p(h,s) to the IAPWS Industrial
Formulation 1997 for the Thermodynamic Properties of Water and Steam
Extends from Modelica.Icons.Function (Icon for functions).
Name | Description |
---|---|
h | Specific enthalpy [J/kg] |
s | Specific entropy [J/(kg.K)] |
Name | Description |
---|---|
p | Pressure [Pa] |
Pressure as a function of enthalpy and entropy in subregion 2a
Equation number 4 from:
The International Association for the Properties of Water and Steam
Gaithersburg, Maryland, USA
September 2001
Supplementary Release on Backward Equations for Pressure as a
Function of Enthalpy and Entropy p(h,s) to the IAPWS Industrial
Formulation 1997 for the Thermodynamic Properties of Water and Steam
Extends from Modelica.Icons.Function (Icon for functions).
Name | Description |
---|---|
h | Specific enthalpy [J/kg] |
s | Specific entropy [J/(kg.K)] |
Name | Description |
---|---|
p | Pressure [Pa] |
Pressure as a function of enthalpy and entropy in subregion 2c
Equation number 5 from:
The International Association for the Properties of Water and Steam
Gaithersburg, Maryland, USA
September 2001
Supplementary Release on Backward Equations for Pressure as a
Function of Enthalpy and Entropy p(h,s) to the IAPWS Industrial
Formulation 1997 for the Thermodynamic Properties of Water and Steam
Extends from Modelica.Icons.Function (Icon for functions).
Name | Description |
---|---|
h | Specific enthalpy [J/kg] |
s | Specific entropy [J/(kg.K)] |
Name | Description |
---|---|
p | Pressure [Pa] |
Region 3 a b boundary for pressure/enthalpy
Equation number 1 from:
Extends from Modelica.Icons.Function (Icon for functions).
Name | Description |
---|---|
p | Pressure [Pa] |
Name | Description |
---|---|
h | Enthalpy [J/kg] |
Region 3 a: inverse function T(p,h)
Equation number 2 from:
Extends from Modelica.Icons.Function (Icon for functions).
Name | Description |
---|---|
p | Pressure [Pa] |
h | Specific enthalpy [J/kg] |
Name | Description |
---|---|
T | Temperature [K] |
Region 3 b: inverse function T(p,h)
Equation number 3 from:
Extends from Modelica.Icons.Function (Icon for functions).
Name | Description |
---|---|
p | Pressure [Pa] |
h | Specific enthalpy [J/kg] |
Name | Description |
---|---|
T | Temperature [K] |
Region 3 a: inverse function v(p,h)
Equation number 4 from:
Extends from Modelica.Icons.Function (Icon for functions).
Name | Description |
---|---|
p | Pressure [Pa] |
h | Specific enthalpy [J/kg] |
Name | Description |
---|---|
v | Specific volume [m3/kg] |
Region 3 b: inverse function v(p,h)
Equation number 5 from:
Extends from Modelica.Icons.Function (Icon for functions).
Name | Description |
---|---|
p | Pressure [Pa] |
h | Specific enthalpy [J/kg] |
Name | Description |
---|---|
v | Specific volume [m3/kg] |
Region 3 a: inverse function T(p,s)
Equation number 6 from:
Extends from Modelica.Icons.Function (Icon for functions).
Name | Description |
---|---|
p | Pressure [Pa] |
s | Specific entropy [J/(kg.K)] |
Name | Description |
---|---|
T | Temperature [K] |
Region 3 b: inverse function T(p,s)
Equation number 7 from:
Extends from Modelica.Icons.Function (Icon for functions).
Name | Description |
---|---|
p | Pressure [Pa] |
s | Specific entropy [J/(kg.K)] |
Name | Description |
---|---|
T | Temperature [K] |
Region 3 a: inverse function v(p,s)
Equation number 8 from:
Extends from Modelica.Icons.Function (Icon for functions).
Name | Description |
---|---|
p | Pressure [Pa] |
s | Specific entropy [J/(kg.K)] |
Name | Description |
---|---|
v | Specific volume [m3/kg] |
Region 3 b: inverse function v(p,s)
Equation number 9 from:
Extends from Modelica.Icons.Function (Icon for functions).
Name | Description |
---|---|
p | Pressure [Pa] |
s | Specific entropy [J/(kg.K)] |
Name | Description |
---|---|
v | Specific volume [m3/kg] |