Modelica.Media.Water.IF97_Utilities.BaseIF97.Basic

Base functions as described in IAWPS/IF97

Information

Package description

Package BaseIF97/Basic computes the 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.

Package contents

Function g1 computes the dimensionless Gibbs function for region 1 and all derivatives up to order 2 w.r.t. pi and tau. Inputs: p and T.
Function g2 computes the dimensionless Gibbs function for region 2 and all derivatives up to order 2 w.r.t. pi and tau. Inputs: p and T.
Function g2metastable computes the dimensionless Gibbs function for metastable vapour (adjacent to region 2 but 2-phase at equilibrium) and all derivatives up to order 2 w.r.t. pi and tau. Inputs: p and T.
Function f3 computes the dimensionless Helmholtz function for region 3 and all derivatives up to order 2 w.r.t. delta and tau. Inputs: d and T.
Function g5computes the dimensionless Gibbs function for region 5 and all derivatives up to order 2 w.r.t. pi and tau. Inputs: p and T.
Function tph1 computes the inverse function T(p,h) in region 1.
Function tph2 computes the inverse function T(p,h) in region 2.
Function tps2a computes the inverse function T(p,s) in region 2a.
Function tps2b computes the inverse function T(p,s) in region 2b.
Function tps2c computes the inverse function T(p,s) in region 2c.
Function tps2 computes the inverse function T(p,s) in region 2.
Function tsat computes the saturation temperature as a function of pressure.
Function dtsatofp computes the derivative of the saturation temperature w.r.t. pressure as a function of pressure.
Function tsat_der computes the Modelica derivative function of tsat.
Function psat computes the saturation pressure as a function of temperature.
Function dptofT computes the derivative of the saturation pressure w.r.t. temperature as a function of temperature.
Function psat_der computes the Modelica derivative function of psat.

Version Info and Revision history

First implemented: July, 2000 by Hubertus Tummescheit

Author: Hubertus Tummescheit,
Modelon AB
Ideon Science Park
SE-22370 Lund, Sweden
email: [email protected]

Initial version: July 2000
Documentation added: December 2002

Equation from:

[1] The international Association for the Properties of Water and Steam
Vejle, Denmark
August 2003
Supplementary Release on Backward Equations for the Functions T(p,h), v(p,h) and T(p,s),
v(p,s) for Region 3 of the IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of
Water and Steam

Extends from Modelica.Icons.Package (Icon for standard packages).

Package Content

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)

Modelica.Media.Water.IF97_Utilities.BaseIF97.Basic.g1

Gibbs function for region 1: g(p,T)

Information

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Name	Description
p	Pressure [Pa]
T	Temperature (K) [K]

Outputs

Name	Description
g	Dimensionless Gibbs function and derivatives w.r.t. pi and tau

Modelica.Media.Water.IF97_Utilities.BaseIF97.Basic.g2

Gibbs function for region 2: g(p,T)

Information

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Name	Description
p	Pressure [Pa]
T	Temperature (K) [K]

Outputs

Name	Description
g	Dimensionless Gibbs function and derivatives w.r.t. pi and tau

Modelica.Media.Water.IF97_Utilities.BaseIF97.Basic.g2metastable

Gibbs function for metastable part of region 2: g(p,T)

Information

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Name	Description
p	Pressure [Pa]
T	Temperature (K) [K]

Outputs

Name	Description
g	Dimensionless Gibbs function and derivatives w.r.t. pi and tau

Modelica.Media.Water.IF97_Utilities.BaseIF97.Basic.f3

Helmholtz function for region 3: f(d,T)

Information

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Name	Description
d	Density [kg/m3]
T	Temperature (K) [K]

Outputs

Name	Description
f	Dimensionless Helmholtz function and derivatives w.r.t. delta and tau

Modelica.Media.Water.IF97_Utilities.BaseIF97.Basic.g5

Base function for region 5: g(p,T)

Information

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Name	Description
p	Pressure [Pa]
T	Temperature (K) [K]

Outputs

Name	Description
g	Dimensionless Gibbs function and derivatives w.r.t. pi and tau

Modelica.Media.Water.IF97_Utilities.BaseIF97.Basic.gibbs

Gibbs function for region 1, 2 or 5: g(p,T,region)

Information

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Name	Description
p	Pressure [Pa]
T	Temperature (K) [K]
region	IF97 region, 1, 2 or 5

Outputs

Name	Description
g	Dimensionless Gibbs function

Modelica.Media.Water.IF97_Utilities.BaseIF97.Basic.g1pitau

Derivative of g w.r.t. pi and tau

Information

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Name	Description
p	Pressure [Pa]
T	Temperature (K) [K]

Outputs

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

Modelica.Media.Water.IF97_Utilities.BaseIF97.Basic.g2pitau

Derivative of g w.r.t. pi and tau

Information

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Name	Description
p	Pressure [Pa]
T	Temperature (K) [K]

Outputs

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

Modelica.Media.Water.IF97_Utilities.BaseIF97.Basic.g5pitau

Derivative of g w.r.t. pi and tau

Information

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Name	Description
p	Pressure [Pa]
T	Temperature (K) [K]

Outputs

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

Modelica.Media.Water.IF97_Utilities.BaseIF97.Basic.f3deltatau

1st derivatives of f w.r.t. delta and tau

Information

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Name	Description
d	Density [kg/m3]
T	Temperature (K) [K]

Outputs

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

Modelica.Media.Water.IF97_Utilities.BaseIF97.Basic.tph1

Inverse function for region 1: T(p,h)

Information

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Name	Description
p	Pressure [Pa]
h	Specific enthalpy [J/kg]

Outputs

Name	Description
T	Temperature (K) [K]

Modelica.Media.Water.IF97_Utilities.BaseIF97.Basic.tps1

Inverse function for region 1: T(p,s)

Information

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Name	Description
p	Pressure [Pa]
s	Specific entropy [J/(kg.K)]

Outputs

Name	Description
T	Temperature (K) [K]

Modelica.Media.Water.IF97_Utilities.BaseIF97.Basic.tph2

Reverse function for region 2: T(p,h)

Information

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Name	Description
p	Pressure [Pa]
h	Specific enthalpy [J/kg]

Outputs

Name	Description
T	Temperature (K) [K]

Modelica.Media.Water.IF97_Utilities.BaseIF97.Basic.tps2a

Reverse function for region 2a: T(p,s)

Information

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Name	Description
p	Pressure [Pa]
s	Specific entropy [J/(kg.K)]

Outputs

Name	Description
T	Temperature (K) [K]

Modelica.Media.Water.IF97_Utilities.BaseIF97.Basic.tps2b

Reverse function for region 2b: T(p,s)

Information

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Name	Description
p	Pressure [Pa]
s	Specific entropy [J/(kg.K)]

Outputs

Name	Description
T	Temperature (K) [K]

Modelica.Media.Water.IF97_Utilities.BaseIF97.Basic.tps2c

Reverse function for region 2c: T(p,s)

Information

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Name	Description
p	Pressure [Pa]
s	Specific entropy [J/(kg.K)]

Outputs

Name	Description
T	Temperature (K) [K]

Modelica.Media.Water.IF97_Utilities.BaseIF97.Basic.tps2

Reverse function for region 2: T(p,s)

Information

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Name	Description
p	Pressure [Pa]
s	Specific entropy [J/(kg.K)]

Outputs

Name	Description
T	Temperature (K) [K]

Modelica.Media.Water.IF97_Utilities.BaseIF97.Basic.tsat

Region 4 saturation temperature as a function of pressure

Information

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Name	Description
p	Pressure [Pa]

Outputs

Name	Description
t_sat	Temperature [K]

Modelica.Media.Water.IF97_Utilities.BaseIF97.Basic.dtsatofp

Derivative of saturation temperature w.r.t. pressure

Information

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Name	Description
p	Pressure [Pa]

Outputs

Name	Description
dtsat	Derivative of T w.r.t. p [K/Pa]

Modelica.Media.Water.IF97_Utilities.BaseIF97.Basic.tsat_der

Derivative function for tsat

Information

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Name	Description
p	Pressure [Pa]
der_p	Pressure derivative [Pa/s]

Outputs

Name	Description
der_tsat	Temperature derivative [K/s]

Modelica.Media.Water.IF97_Utilities.BaseIF97.Basic.psat

Region 4 saturation pressure as a function of temperature

Information

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Name	Description
T	Temperature (K) [K]

Outputs

Name	Description
p_sat	Pressure [Pa]

Modelica.Media.Water.IF97_Utilities.BaseIF97.Basic.dptofT

Derivative of pressure w.r.t. temperature along the saturation pressure curve

Information

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Name	Description
T	Temperature (K) [K]

Outputs

Name	Description
dpt	Temperature derivative of pressure [Pa/K]

Modelica.Media.Water.IF97_Utilities.BaseIF97.Basic.psat_der

Derivative function for psat

Information

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Name	Description
T	Temperature (K) [K]
der_T	Temperature derivative [K/s]

Outputs

Name	Description
der_psat	Pressure [Pa/s]

Modelica.Media.Water.IF97_Utilities.BaseIF97.Basic.p1_hs

Pressure as a function of enthalpy and entropy in region 1

Information

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).

Inputs

Name	Description
h	Specific enthalpy [J/kg]
s	Specific entropy [J/(kg.K)]

Outputs

Name	Description
p	Pressure [Pa]

Modelica.Media.Water.IF97_Utilities.BaseIF97.Basic.h2ab_s

Boundary between regions 2a and 2b

Information

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).

Inputs

Name	Description
s	Entropy [J/(kg.K)]

Outputs

Name	Description
h	Enthalpy [J/kg]

Modelica.Media.Water.IF97_Utilities.BaseIF97.Basic.p2a_hs

Pressure as a function of enthalpy and entropy in subregion 2a

Information

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).

Inputs

Name	Description
h	Specific enthalpy [J/kg]
s	Specific entropy [J/(kg.K)]

Outputs

Name	Description
p	Pressure [Pa]

Modelica.Media.Water.IF97_Utilities.BaseIF97.Basic.p2b_hs

Pressure as a function of enthalpy and entropy in subregion 2a

Information

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).

Inputs

Name	Description
h	Specific enthalpy [J/kg]
s	Specific entropy [J/(kg.K)]

Outputs

Name	Description
p	Pressure [Pa]

Modelica.Media.Water.IF97_Utilities.BaseIF97.Basic.p2c_hs

Pressure as a function of enthalpy and entropy in subregion 2c

Information

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).

Inputs

Name	Description
h	Specific enthalpy [J/kg]
s	Specific entropy [J/(kg.K)]

Outputs

Name	Description
p	Pressure [Pa]

Modelica.Media.Water.IF97_Utilities.BaseIF97.Basic.h3ab_p

Region 3 a b boundary for pressure/enthalpy

Information

Equation number 1 from:

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Name	Description
p	Pressure [Pa]

Outputs

Name	Description
h	Enthalpy [J/kg]

Modelica.Media.Water.IF97_Utilities.BaseIF97.Basic.T3a_ph

Region 3 a: inverse function T(p,h)

Information

Equation number 2 from:

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Name	Description
p	Pressure [Pa]
h	Specific enthalpy [J/kg]

Outputs

Name	Description
T	Temperature [K]

Modelica.Media.Water.IF97_Utilities.BaseIF97.Basic.T3b_ph

Region 3 b: inverse function T(p,h)

Information

Equation number 3 from:

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Name	Description
p	Pressure [Pa]
h	Specific enthalpy [J/kg]

Outputs

Name	Description
T	Temperature [K]

Modelica.Media.Water.IF97_Utilities.BaseIF97.Basic.v3a_ph

Region 3 a: inverse function v(p,h)

Information

Equation number 4 from:

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Name	Description
p	Pressure [Pa]
h	Specific enthalpy [J/kg]

Outputs

Name	Description
v	Specific volume [m3/kg]

Modelica.Media.Water.IF97_Utilities.BaseIF97.Basic.v3b_ph

Region 3 b: inverse function v(p,h)

Information

Equation number 5 from:

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Name	Description
p	Pressure [Pa]
h	Specific enthalpy [J/kg]

Outputs

Name	Description
v	Specific volume [m3/kg]

Modelica.Media.Water.IF97_Utilities.BaseIF97.Basic.T3a_ps

Region 3 a: inverse function T(p,s)

Information

Equation number 6 from:

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Name	Description
p	Pressure [Pa]
s	Specific entropy [J/(kg.K)]

Outputs

Name	Description
T	Temperature [K]

Modelica.Media.Water.IF97_Utilities.BaseIF97.Basic.T3b_ps

Region 3 b: inverse function T(p,s)

Information

Equation number 7 from:

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Name	Description
p	Pressure [Pa]
s	Specific entropy [J/(kg.K)]

Outputs

Name	Description
T	Temperature [K]

Modelica.Media.Water.IF97_Utilities.BaseIF97.Basic.v3a_ps

Region 3 a: inverse function v(p,s)

Information

Equation number 8 from:

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Name	Description
p	Pressure [Pa]
s	Specific entropy [J/(kg.K)]

Outputs

Name	Description
v	Specific volume [m3/kg]

Modelica.Media.Water.IF97_Utilities.BaseIF97.Basic.v3b_ps

Region 3 b: inverse function v(p,s)

Information

Equation number 9 from:

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Name	Description
p	Pressure [Pa]
s	Specific entropy [J/(kg.K)]

Outputs

Name	Description
v	Specific volume [m3/kg]

Automatically generated Tue Apr 05 09:37:02 2016.