Modelica.Media.Water.IF97_Utilities.BaseIF97

Modelica Physical Property Model: the new industrial formulation IAPWS-IF97

Information

Version Info and Revision history

First implemented: July, 2000 by Hubertus Tummescheit for the ThermoFluid Library with help from Jonas Eborn and Falko Jens Wagner
Code reorganization, enhanced documentation, additional functions: December, 2002 by Hubertus Tummescheit and moved to Modelica properties library.

Author: Hubertus Tummescheit,
Modelon AB
Ideon Science Park
SE-22370 Lund, Sweden
email: hubertus@modelon.se

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).

1. Structure and Regions of IAPWS-IF97

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 p_s( 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.

Figure 1: Regions and equations of IAPWS-IF97

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 T_s( 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].

[1]Wagner, W., Kruse, A. Properties of Water and Steam / Zustandsgrößen von Wasser und Wasserdampf / IAPWS-IF97. Springer-Verlag, Berlin, 1998.

[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.

2. Calculable Properties

	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	c_p	J/(kg K)
9	Specific isochoric heat capacity	c_v	J/(kg K)
10	Isentropic exponent, kappa = -(v/p) (dp/dv)_s	kappa (κ)	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 (θ)	1
16	Isobaric volume expansion coefficient, alpha = v^-1 (dv/dT)_p	alpha (α)	1/K
17	Isochoric pressure coefficient, beta = p^-1(dp/dT)_v	beta (β)	1/K
18	Isothermal compressibility, gamma = -v^-1(dv/dp)_T	gamma (γ)	1/Pa
19	Dynamic viscosity	eta (η)	Pa s
20	Kinematic viscosity	nu (ν)	m²/s
21	Thermal conductivity	lambda (λ)	W/(m K)
22	Surface tension	sigma (σ)	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.

Additional functions

Function boundaryvals_p computes the temperature and the specific enthalpy and entropy on both phase boundaries as a function of p
Function boundaryderivs_p is the Modelica derivative function of boundaryvals_p
Function extraDerivs_ph computes all entries to Bridgmans tables for all one-phase regions of IF97 using inputs (p,h). All 336 directional derivatives of the thermodynamic surface can be computed as a ratio of two entries in the return data, see package Common for details.
Function extraDerivs_pT computes all entries to Bridgmans tables for all one-phase regions of IF97 using inputs (p,T).

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

Package Content

Name	Description
IterationData	Constants for iterations internal to some functions
data	Constant IF97 data and region limits
getTstar	Get normalization temperature for region 1, 2 or 5
getpstar	Get normalization pressure for region 1, 2 or 5
critical	Critical point data
triple	Triple point data
Regions	Functions to find the current region for given pairs of input variables
Basic	Base functions as described in IAWPS/IF97
IceBoundaries	The melting line and sublimation line curves from IAPWS
Transport	Transport properties for water according to IAPWS/IF97
Isentropic	Functions for calculating the isentropic enthalpy from pressure p and specific entropy s
Inverses	Efficient inverses for selected pairs of variables
ByRegion	Simple explicit functions for one region only
TwoPhase	Steam properties in the two-phase region and on the phase boundaries
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)

Modelica.Media.Water.IF97_Utilities.BaseIF97.IterationData

Constants for iterations internal to some functions

Information

Extends from Modelica.Icons.Record (Icon for records).

Modelica.Media.Water.IF97_Utilities.BaseIF97.data

Constant IF97 data and region limits

Information

Record description

Constants needed in the international steam properties IF97. SCRIT and HCRIT are calculated from Helmholtz function for region 3.

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: hubertus@modelon.se

Initial version: July 2000
Documentation added: December 2002

Extends from Modelica.Icons.Record (Icon for records).

Modelica.Media.Water.IF97_Utilities.BaseIF97.getTstar

Get normalization temperature for region 1, 2 or 5

Information

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

Inputs

Name	Description
region	IF 97 region

Outputs

Name	Description
Tstar	Normalization temperature [K]

Modelica.Media.Water.IF97_Utilities.BaseIF97.getpstar

Get normalization pressure for region 1, 2 or 5

Information

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

Inputs

Name	Description
region	IF 97 region

Outputs

Name	Description
pstar	Normalization pressure [Pa]

Modelica.Media.Water.IF97_Utilities.BaseIF97.critical

Critical point data

Information

Record description

Critical point data for IF97 steam properties. SCRIT and HCRIT are calculated from Helmholtz function for region 3

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: hubertus@modelon.se

Initial version: July 2000
Documentation added: December 2002

Extends from Modelica.Icons.Record (Icon for records).

Modelica.Media.Water.IF97_Utilities.BaseIF97.triple

Triple point data

Information

Record description

Vapour/liquid/ice triple point data for IF97 steam properties.

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: hubertus@modelon.se

Initial version: July 2000
Documentation added: December 2002

Extends from Modelica.Icons.Record (Icon for records).

Modelica.Media.Water.IF97_Utilities.BaseIF97.extraDerivs_ph

Function to calculate some extra thermophysical properties in regions 1, 2, 3 and 5 as f(p,h)

Information

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

Inputs

Name	Description
p	Pressure [Pa]
h	Specific enthalpy [J/kg]
phase	Phase: 2 for two-phase, 1 for one phase, 0 if unknown

Outputs

Name	Description
dpro	Thermodynamic property collection

Modelica.Media.Water.IF97_Utilities.BaseIF97.extraDerivs_pT

Function to calculate some extra thermophysical properties in regions 1, 2, 3 and 5 as f(p,T)

Information

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

Inputs

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

Outputs

Name	Description
dpro	Thermodynamic property collection

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