## Software for the Industrial Formulation IAPWS-IF97 for Water and Steam

Information about the several Windows operating systems and Excel versions as well as about 64 Bit DLLs and .Net DLLs are given at the end of this software description.

The Industrial Formulation IAPWS-IF97 consists of a set of equations for different regions, which covers the following range of validity:

0 °C ≤ t ≤ 800 °C,   p ≤ 1000 bar (100 MPa)

800 °C < t ≤ 2000 °C,   p ≤ 500 bar (50 MPa) Structure and regions of IAPWS-IF97.

The figure above shows the five regions into which the entire range of validity of IAPWS-IF97 is divided. Regions 1 and 2 are both 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(ρ,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 five equations, shown in rectangular boxes in the figure, form the so called basic equations.

In addition to these basic equations, so-called backward equations are provided for regions 1 to 4. These backward equations were developed in the following combinations of variables: For regions 1 and 2 as equations of the form T(p,h), T(p,s), and p(h,s), for region 3 as equations of the form T(p,h), v(p,h), T(p,s), v(p,s), p(h,s) and v(p,T). The backward equation for the entire region 4 is a saturation-temperature equation Ts(p), and for the technically most important part of region 4 (s ≥ s’’ (623.15 K)), there is a saturation-temperature equation of the form Ts(h,s). In the figure above, in addition to the (framed) basic equations, all of these types of backward equations (marked in grey) are assigned to the corresponding region of IAPWS-IF97.

With these backward equations, properties dependent on the input quantities (p,h), (p,s), (h,s), in region 3 also on the input quantities (p,T), are calculable without iterations, and thus very fast.

Further details of IAPWS-IF97 see here.

Furthermore, the book

Wagner, W., Kretzschmar, H.-J. International Steam Tables - Properties of Water and Steam Based on the Industrial Formulation IAPWS-IF97. Springer-Verlag (Berlin), 2008

comprehensively describes IAPWS-IF97. This book also contains the IAPWS equations for the most important transport properties and some other properties, and two wall charts, a Mollier h,s diagram and a T,s diagram. For more details (contents, sample pages, etc.) see here.

2. Software for IAPWS-IF97

On the basis of IAPWS-IF97, including all of the backward equations as well as the IAPWS equations for the transport properties and three further properties, there is a software package for the calculation of more than 25 properties. This software was especially established regarding an optimal programming to achieve short computing times.

When applying the software, it is not necessary to know which region of IAPWS-IF97 the property to be calculated belongs to. Based on the given input quantities, the software automatically determines which equation of IAPWS-IF97 has to be applied.

With our software package, the following thermodynamic properties, transport properties and three further properties of water and steam can be calculated:

## 2.1 Thermodynamic properties

Based on the corresponding equations of IAPWS-IF97 the thermodynamic properties listed in Table 1 can be calculated with the software:

Table 1. Calculable thermodynamic properties

 Symbol       Property

 p Pressure T Temperature v Specific volume ρ Density h Specific enthalpy s Specific entropy cp Specific isobaric heat capacity u Specific internal energy cv Specific isochoric heat capacity x Vapour fraction w Speed of sound g Specific Gibbs free energy g = h − Ts f Specific Helmholtz free energy f = u − Ts z Compression factor f* Fugacity αv Isobaric cubic expansion coefficient,  αv = v− 1 (∂v/∂T)p αp Relative pressure coefficient,  α = v−1 (∂v/∂T)p βp Isothermal stress coefficient,  β = p−1 (∂p/∂T)v κ Isentropic exponent,  κ = − (v/p) (∂p/ ∂v)s κT Isothermal compressibility,  κT = –v- 1 (∂v/∂p)T µ Joule‑Thomson coefficient,  µ = (∂T/∂p)h (∂v/∂p)h Partial derivative (∂ρ/∂p)h Partial derivative (∂v/∂h)p Partial derivative (∂ρ/∂h)p Partial derivative (∂h/∂p)T Partial derivative x Vapour fraction ________________________________________________________

All these properties can be calculated in the entire range of validity of IAPWS-IF97, see Sec. 1. Concerning region 4 (two-phase region), the properties ν, ρ, h, s, u, f, g and x can also be calculated within the two-phase region. The other properties can only be calculated on the phase boundaries (saturated-liquid line and saturated-vapour line) because they are not defined within the two-phase region.

2.2 Transport properties and further properties

The software allows the calculation of transport properties, dielectric constant, refractive index, and surface tension listed in Table 2.

Table 2. Calculable transport and further properties

 Symbol Property η Dynamic viscosity v Kinematic viscosity, v = η / ρ λ Thermal conductivity Pr Prandtl number, Pr = η  cp/ λ a Thermal diffusivity, a = λ /(ρcp) ε Relative static dielectric constant n Refractive index σ Surface tension

_____________________________________________________

The internationally agreed equations for calculating these properties, which do not belong to IAPWS-IF97, are described in Ref.  and in the corresponding IAPWS Releases, see www.iapws.org. It should be noted that these equations are functions of temperature and density (not pressure). This fact has consequences for the necessity of iterations. The surface tension is a function of temperature only. Except for the dielectric constant ε, all the other properties can be calculated in the entire range of validity of IAPWS-IF97, see Sec. 1.

The range of validity of the equation for ε is limited to 873.15 K, but the equation can be reasonably extrapolated up to 1073.15 K. The surface tension σ(T) refers only to the two-phase region, region 4.

2.3 Combinations of input variables for calculating the several properties

2.3.1 Regions 1-5

For regions 1-3 and 5 (single-phase regions) and region 4 (two-phase region), all properties listed in Tables 1 and 2 can be calculated as a function of the pairs of input variables shown in Table 3. For region 5, properties for input variables other than (p,T) are calculated via iterations only; there are no backward equations. Properties in region 4 cannot be calculated for the combination (p,T) as input variables, because p and T are not independent of each other in this region.

 Table 3. Possible combinations of input variables for calculations in regions 1 to 5; for region 4, (p,T) cannot be used
 (p,T) (T,h) (ν,h) (h,s) (p,h) (T,s) (ν,s) (p,s) (T,ν) (p,ν) (T,ρ)

The most important properties can directly be calculated from the functions in the software for the pairs of input variables listed in Table 3. The calculation of further properties as functions of all the pairs of input variables is possible by corresponding combinations of functions in the software.

2.3.2 Calculations for region 4
(two-phase region) only
For region 4 [saturation pressure psat , saturation temperature Tsat, saturated-liquid line [('), x = 0, bubble line], saturated-vapour line [("), x = 1, dew line], two-phase region (0 < x < 1)], the properties in the left column of Table 4 can be calculated from the functions given in the software for all listed input variables.

 Table 4. Calculable properties for the entire region 4 (saturated-liquid line, saturated-vapour line and within the two-phase region) from the corresponding functions listed in the software
 Calculable properties Input variables1 Explanations psat T, h, s, ρ, x 1In addition to the input variables given here, the properties can also be calculated using the corresponding input variables listed in Table 3 [except for the combination (p,T)]; the belonging functions are given in the software. The software finds out if the state point is in region 4. Tsat p, h, s, ρ v, h, s (T,x), (p,x) ν, f, g (T,x), (p,x) x (p,h), (p,s), (p,v)

Those properties listed in Tables 1 and 2 that are not given in the left column of Table 4 cannot be calculated within the two-phase region (0 < x < 1) but only on the saturated-liquid and saturated-vapour line; these properties are not defined within the two-phase region.

2.4 Dynamic Link Library for user-specific calculations

For the integration of IAPWS-IF97 into user specific applications, the software contains a Dynamic Link Library (DLL). This DLL contains numerous functions thath enable the calculation of all properties listed above dependend on all combinations of input variables listed below. The user can choose between the calculation of properties with the backward equations of IAPWS-IF97 or with iterations using only the basic equations. The calls of the functions of the DLL are made via simple names of functions that are based on the property to be calculated and the selected input variables. For example, the enthalpy h for given values of temperature T and pressure p is calculated from function HBPT.

The software allows the selection whether the backward equations should be used or only basic equations with iterations if iterations are necessary for the calculation of the corresponding property.

The software contains a .LIB file that allows the integration of the DLL into user specific Fortran programs, C programs, and Visual Basic.

In addition, the software contains an Add-In file that allows a simple integration of the DLL into Microsoft Excel. In this way, the considered properties can directly be calculated from within an Excel spreadsheet by calling the name of the corresponding function with the required input values.

As an example, the following screenshot shows the results of the calculation of all the properties for T = 300 K and p = 1 MPa. For T = 300 K, all properties on the saturated-liquid line and saturated-vapour line were calculated as well. For the vapour fraction x = 0.5, all properties that are defined within the two-phase region are also calculated. All these properties were calculated at once. This Excel spreadsheet contains all the functions that are provided by the software. Of course, a user-specific Excel spreadsheet can be designed. Example screenshot of calculations with the software package IAPWS-IF97 from within a Microsoft Excel spreadsheet.

All functions that can be called from the DLL are specified in the file MANUAL.PDF that is also part of this software.

The DLL and the die Excel-files .xla, .xlam, .xls, xlsm are configurated in such a way that they can be used under the several Windows operating systems [Windows 2000 to XP (32 Bit), Windows 7 and 8
(32 Bit/64 Bit)] and under the several Excel versions [2003 to 2013 (32 Bit)].

The IAPWS-IF97 software is now available as a 64-Bit version, which can be, under the 64-Bit operating systems of Windows XP to Windows 2010 and the supplied 64-bit Excel Add-ins, incorporated into the 64-Bit versions of Excel 2010-2016. Using the supplied LIB file, the software can also be integrated into other 64-Bit applications (e.g. Matlab).

.Net DLLs are also available.

The software is not free of charge.

Contact:

Prof. em. Dr.-Ing. W. Wagner
Tel. +49 (0)234 32-29033
Fax +49 (0)234 32-14945
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