Package Modelica.Media.Water.IF97_Utilities.BaseIF97Modelica Physical Property Model: the new industrial formulation IAPWS-IF97
Package Modelica.Media.Water.IF97_Utilities.BaseIF97
In September 1997, the International Association for the Properties of Water and Steam (IAPWS) adopted a new formulation for the thermodynamic properties of water and steam for industrial use. This new industrial standard is called "IAPWS Industrial Formulation for the Thermodynamic Properties of Water and Steam" (IAPWS-IF97). The formulation IAPWS-IF97 replaces the previous industrial standard IFC-67.
Based on this new formulation, a new steam table, titled "Properties of Water and Steam" by W. Wagner and A. Kruse, was published by the Springer-Verlag, Berlin - New-York - Tokyo in April 1998. This steam table, ref. [1] is bilingual (English / German) and contains a complete description of the equations of IAPWS-IF97. This reference is the authoritative source of information for this implementation. A mostly identical version has been published by the International Association for the Properties of Water and Steam (IAPWS) with permission granted to re-publish the information if credit is given to IAPWS. This document is distributed with this library as IF97.pdf. In addition, the equations published by IAPWS for the transport properties dynamic viscosity (standards document: visc.pdf) and thermal conductivity (standards document: thcond.pdf) and equations for the surface tension (standards document: surf.pdf) are also implemented in this library and included for reference.
The functions in BaseIF97.mo are low level functions which should only be used in those exceptions when the standard user level functions in Water.mo do not contain the wanted properties.
Based on IAPWS-IF97, Modelica functions are available for calculating the most common thermophysical properties (thermodynamic and transport properties). The implementation requires part of the common medium property infrastructure of the Modelica.Thermal.Properties library in the file Common.mo. There are a few extensions from the version of IF97 as documented in IF97.pdf in order to improve performance for dynamic simulations. Input variables for calculating the properties are only implemented for a limited number of variable pairs which make sense as dynamic states: (p,h), (p,T), (p,s) and (d,T).
The IAPWS Industrial Formulation 1997 consists of a set of equations for different regions which cover the following range of validity:
| 273,15 K < T < 1073,15 K | p < 100 MPa |
| 1073,15 K < T < 2273,15 K | p < 10 MPa |
Figure 1 shows the 5 regions into which the entire range of validity of IAPWS-IF97 is divided. The boundaries of the regions can be directly taken from Fig. 1 except for the boundary between regions 2 and 3; this boundary, which corresponds approximately to the isentropic line s = 5.047 kJ kg -1K-1, is defined by a corresponding auxiliary equation. Both regions 1 and 2 are individually covered by a fundamental equation for the specific Gibbs free energy g( p,T ), region 3 by a fundamental equation for the specific Helmholtz free energy f ( r,T ), and the saturation curve, corresponding to region 4, by a saturation-pressure equation ps( T ). The high-temperature region 5 is also covered by a g( p,T ) equation. These 5 equations, shown in rectangular boxes in Fig. 1, form the so-called basic equations.
|
In addition to these basic equations, so-called backward equations are provided for regions 1, 2, and 4 in form of T( p,h ) and T( p,s ) for regions 1 and 2, and Ts( p ) for region 4. These backward equations, marked in grey in Fig. 1, were developed in such a way that they are numerically very consistent with the corresponding basic equation. Thus, properties as functions of p,h and of p,s for regions 1 and 2, and of p for region 4 can be calculated without any iteration. As a result of this special concept for the development of the new industrial standard IAPWS-IF97, the most important properties can be calculated extremely quickly. All Modelica functions are optimized with regard to short computing times.
The complete description of the individual equations of the new industrial formulation IAPWS-IF97 is given in IF97.pdf. Comprehensive information on IAPWS-IF97 (requirements, concept, accuracy, consistency along region boundaries, and the increase of computing speed in comparison with IFC-67, etc.) can be taken from IF97.pdf or [2].
[2] Wagner, W., Cooper, J. R., Dittmann, A., Kijima, J., Kretzschmar, H.-J., Kruse, A., Mareš R., Oguchi, K., Sato, H., Stöcker, I., Šifner, O., Takaishi, Y., Tanishita, I., Trübenbach, J., and Willkommen, Th. The IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam. ASME Journal of Engineering for Gas Turbines and Power 122 (2000), 150 - 182.
| Common name |
Abbreviation |
Unit |
|
| 1 |
Pressure | p |
Pa |
| 2 |
Temperature | T |
K |
| 3 |
Density | d |
kg/m3 |
| 4 |
Specific volume | v |
m3/kg |
| 5 |
Specific enthalpy | h |
J/kg |
| 6 |
Specific entropy | s |
J/(kg K) |
| 7 |
Specific internal energy |
u |
J/kg |
| 8 |
Specific isobaric heat capacity | cp |
J/(kg K) |
| 9 |
Specific isochoric heat capacity | cv |
J/(kg K) |
| 10 |
Isentropic exponent, kappa=-(v/p) (dp/dv)s | kappa (k) |
1 |
| 11 |
Speed of sound |
a |
m/s |
| 12 |
Dryness fraction |
x |
kg/kg |
| 13 |
Specific Helmholtz free energy, f = u - Ts | f |
J/kg |
| 14 |
Specific Gibbs free energy, g = h - Ts | g |
J/kg |
| 15 |
Isenthalpic exponent, theta = -(v/p)(dp/dv)h | theta (q) |
1 |
| 16 |
Isobaric volume expansion coefficient, alpha = v-1 (dv/dT)p | alpha (a) |
1/K |
| 17 |
Isochoric pressure coefficient, beta = p-1(dp/dT)v | beta (b) |
1/K |
| 18 |
Isothermal compressibility, gamma = -v-1(dv/dp)T | gamma (g) |
1/Pa |
| 19 |
Dynamic viscosity | eta (h) |
Pa s |
| 20 |
Kinematic viscosity | nu (n) |
m2/s |
| 21 |
Thermal conductivity | lambda (l) |
W/(m K) |
| 22 |
Surface tension | sigma (s) |
N/m |
The properties 1-11 are calculated by default with the functions for dynamic simulation, 2 of these variables are the dynamic states and are the inputs to calculate all other properties. In addition to these properties of general interest, the entries to the thermodynamic Jacobian matrix which render the mass- and energy balances explicit in the input variables to the property calculation are also calculated. For an explanatory example using pressure and specific enthalpy as states, see the Examples sub-package.
The high-level calls to steam properties are grouped into records comprising both the properties of general interest and the entries to the thermodynamic Jacobian. If additional properties are needed the low level functions in BaseIF97 provide more choice.
Extends from Modelica.Icons.Package (Icon for standard packages).
| Name | Description |
|---|---|
Basic … | Base functions as described in IAWPS/IF97 |
ByRegion … | Simple explicit functions for one region only |
critical | Critical point data |
data | Constant IF97 data and region limits |
extraDerivs_ph | Function to calculate some extra thermophysical properties in regions 1, 2, 3 and 5 as f(p,h) |
extraDerivs_pT | Function to calculate some extra thermophysical properties in regions 1, 2, 3 and 5 as f(p,T) |
getpstar | Get normalization pressure for region 1, 2 or 5 |
getTstar | Get normalization temperature for region 1, 2 or 5 |
IceBoundaries … | The melting line and sublimation line curves from IAPWS |
Inverses … | Efficient inverses for selected pairs of variables |
Isentropic … | Functions for calculating the isentropic enthalpy from pressure p and specific entropy s |
IterationData | Constants for iterations internal to some functions |
Regions … | Functions to find the current region for given pairs of input variables |
Transport … | Transport properties for water according to IAPWS/IF97 |
triple | Triple point data |
TwoPhase … | Steam properties in the two-phase region and on the phase boundaries |
Record Modelica.Media.Water.IF97_Utilities.BaseIF97.IterationData
This icon is indicates a record.
Extends from Modelica.Icons.Record (Icon for records).
| Type | Name | Description |
|---|---|---|
constant Integer | IMAX | Maximum number of iterations for inverse functions |
constant Real | DELP | Maximum iteration error in pressure, Pa |
constant Real | DELS | Maximum iteration error in specific entropy, J/{kg.K} |
constant Real | DELH | Maximum iteration error in specific enthalpy, J/kg |
constant Real | DELD | Maximum iteration error in density, kg/m^3 |
Record Modelica.Media.Water.IF97_Utilities.BaseIF97.data
Constants needed in the international steam properties IF97. SCRIT and HCRIT are calculated from Helmholtz function for region 3.
Extends from Modelica.Icons.Record (Icon for records).
| Type | Name | Description |
|---|---|---|
constant SpecificHeatCapacity | RH2O | Specific gas constant of water vapour |
constant MolarMass | MH2O | Molar weight of water |
constant Temperature | TSTAR1 | Normalization temperature for region 1 IF97 |
constant Pressure | PSTAR1 | Normalization pressure for region 1 IF97 |
constant Temperature | TSTAR2 | Normalization temperature for region 2 IF97 |
constant Pressure | PSTAR2 | Normalization pressure for region 2 IF97 |
constant Temperature | TSTAR5 | Normalization temperature for region 5 IF97 |
constant Pressure | PSTAR5 | Normalization pressure for region 5 IF97 |
constant SpecificEnthalpy | HSTAR1 | Normalization specific enthalpy for region 1 IF97 |
constant Real | IPSTAR | Normalization pressure for inverse function in region 2 IF97 |
constant Real | IHSTAR | Normalization specific enthalpy for inverse function in region 2 IF97 |
constant Temperature | TLIMIT1 | Temperature limit between regions 1 and 3 |
constant Temperature | TLIMIT2 | Temperature limit between regions 2 and 5 |
constant Temperature | TLIMIT5 | Upper temperature limit of 5 |
constant Pressure | PLIMIT1 | Upper pressure limit for regions 1, 2 and 3 |
constant Pressure | PLIMIT4A | Pressure limit between regions 1 and 2, important for two-phase (region 4) |
constant Pressure | PLIMIT5 | Upper limit of valid pressure in region 5 |
constant Pressure | PCRIT | The critical pressure |
constant Temperature | TCRIT | The critical temperature |
constant Density | DCRIT | The critical density |
constant SpecificEntropy | SCRIT | The calculated specific entropy at the critical point |
constant SpecificEnthalpy | HCRIT | The calculated specific enthalpy at the critical point |
constant Real | n[5] | Polynomial coefficients for boundary between regions 2 and 3 |
Function Modelica.Media.Water.IF97_Utilities.BaseIF97.getTstar
This icon indicates Modelica functions.
Extends from Modelica.Icons.Function (Icon for functions).
| Type | Name | Description |
|---|---|---|
Integer | region | IF 97 region |
| Type | Name | Description |
|---|---|---|
Temperature | Tstar | Normalization temperature |
Function Modelica.Media.Water.IF97_Utilities.BaseIF97.getpstar
This icon indicates Modelica functions.
Extends from Modelica.Icons.Function (Icon for functions).
| Type | Name | Description |
|---|---|---|
Integer | region | IF 97 region |
| Type | Name | Description |
|---|---|---|
Pressure | pstar | Normalization pressure |
Record Modelica.Media.Water.IF97_Utilities.BaseIF97.critical
Critical point data for IF97 steam properties. SCRIT and HCRIT are calculated from Helmholtz function for region 3
Extends from Modelica.Icons.Record (Icon for records).
| Type | Name | Description |
|---|---|---|
constant Pressure | PCRIT | The critical pressure |
constant Temperature | TCRIT | The critical temperature |
constant Density | DCRIT | The critical density |
constant SpecificEnthalpy | HCRIT | The calculated specific enthalpy at the critical point |
constant SpecificEntropy | SCRIT | The calculated specific entropy at the critical point |
Record Modelica.Media.Water.IF97_Utilities.BaseIF97.triple
Vapour/liquid/ice triple point data for IF97 steam properties.
Extends from Modelica.Icons.Record (Icon for records).
| Type | Name | Description |
|---|---|---|
constant Temperature | Ttriple | The triple point temperature |
constant Pressure | ptriple | The triple point pressure |
constant Density | dltriple | The triple point liquid density |
constant Density | dvtriple | The triple point vapour density |
Function Modelica.Media.Water.IF97_Utilities.BaseIF97.extraDerivs_ph
This icon indicates Modelica functions.
Extends from Modelica.Icons.Function (Icon for functions).
| Type | Name | Description |
|---|---|---|
Pressure | p | Pressure |
SpecificEnthalpy | h | Specific enthalpy |
Integer | phase | Phase: 2 for two-phase, 1 for one phase, 0 if unknown |
| Type | Name | Description |
|---|---|---|
ExtraDerivatives | dpro | Thermodynamic property collection |
Function Modelica.Media.Water.IF97_Utilities.BaseIF97.extraDerivs_pT
This icon indicates Modelica functions.
Extends from Modelica.Icons.Function (Icon for functions).
| Type | Name | Description |
|---|---|---|
Pressure | p | Pressure |
Temperature | T | Temperature |
| Type | Name | Description |
|---|---|---|
ExtraDerivatives | dpro | Thermodynamic property collection |