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On this page, the software for the IAPWS-IF97 formulation
is described in the two sections
1. Background
2. Software for IAPWS-IF97
1. Background 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)
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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 energy
g(p,T), region 3 by a fundamental equation
for the specific Helmholtz 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 some
other 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:
Thermodynamic properties
The following thermodynamic
properties can be calculated with the corresponding equations
of IAPWS-IF97:
| p |
Pressure |
| T |
Temperature |
| ρ |
Density |
| v |
Volume |
| h |
Enthalpy |
| s |
Entropy |
| cp |
Isobaric heat capacity |
| cv |
Isochoric heat capacity |
| x |
Vapour fraction |
| w |
Speed of sound |
| u |
Internal energy |
| f |
Helmholtz energy, f = u
− Ts |
| g |
Gibbs energy, g = h
− Ts |
| κ |
Isentropic exponent, κ = −
(v/p) (∂p/ ∂v)s |
| α |
Isobaric volume expansion coefficient, α
= v−1 (∂v/∂T)p |
| β |
Isochoric tension coefficient, β
= p−1 (∂p/∂T)v |
| γ |
Isothermal compressibility coefficient,
γ = − v−1
(∂v/∂p)T |
| (∂ρ/∂h)p |
Partial derivative of density with respect
to enthalpy at constant pressure |
| (∂v/∂h)p |
Partial derivative of specific volume with
respect to enthalpy at constant pressure |
| (∂ρ/∂p)h |
Partial derivative of density with respect
to pressure at constant enthalpy |
| (∂v/∂p)h |
Partial derivative of specific volume with
respect to pressure at constant enthalpy |
| (∂h/∂p)T |
Partial derivative of enthalpy with respect
to pressure at constant temperature |
| f* |
Fugacity |
These properties
can be calculated in the whole range of validity of IAPWS-IF97
(see at the beginning of this page).
Transport properties and further
properties
The following transport
properties and further properties can be calculated with the
software:
| η |
Dynamic viscosity |
| ν |
Kinematic viscosity |
| Pr |
Prandtl number |
| λ |
Thermal conductivity |
| e |
Static dielectric constant |
| n |
Refractive index |
| σ |
Surface tension |
The internationally
accepted equations for the calculation of the transport properties
and three further properties, that are not part of IAPWS-IF97,
are compiled and described in [165],
see also www.iapws.org
under “Releases.”
The properties η to n cannot be calculated
in the full range of validity of IAPWS-IF97 because the limited
validity range of the corresponding equations, see [165].
The surface tension σ(T) refers only to
region 4 of IAPWS-IF97.
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 that 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 the function HBPT.
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 package contains an Add-In file that enables the
simple integration of the DLL into Microsoft Excel.
All functions to
be called from the DLL are specified in the file MANUAL.PDF
that is also part of this software.
For regions
1-3 and 5 of the IAPWS-IF97 (homogeneous regions) all
properties listed above (Note the temperature limit for the
properties η to n.) can be calculated
dependend on the following combinations of input variables:
| (p,T) |
(T,h) |
(v,h) |
(h,s) |
| (p,h) |
(T,s) |
(v,s) |
|
| (p,s) |
(T,v) |
|
|
| (p,v) |
|
|
|
The most important
properties can directly be calculated as a function of the
above listed pair of input variables. The calculation of other
properties is possible by combining the corresponding functions
included in the software.
For region 4
of IAPWS-IF97 (saturation state: saturation pressure ps,
saturation temperature Ts, saturated liquid
(' ) and saturated vapour (" )
and within the two-phase region (0 ≤ x ≤1))
the properties in the left column of the following table can
be directly calculated as a function of the given input
variables:
Calculable
properties |
Input values |
| ps |
T |
(T,h) |
(T,s) |
(T,v) |
(v,h) |
(v,s) |
(h,s) |
|
| Ts |
p |
(p,h) |
(p,s) |
(p,v) |
(h,s) |
|
| v |
(p,h) |
(p,s) |
(p,x) |
(T,x) |
(p,x) |
|
| v', v'' |
T |
p |
|
| h |
(p,s) |
(p,v) |
(p,x) |
(T,x) |
|
| h', h'' |
T |
p |
|
| s |
(p,h) |
(p,v) |
(p,x) |
(T,x) |
|
| s',s'' |
T |
p |
|
| x |
(p,h) |
(p,s) |
(p,v) |
|
| cp', cp'' |
T |
p |
|
| cv', cv'' |
T |
p |
|
| w', w'' |
T |
p |
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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.
Contact:
Prof. em. Dr.-Ing.
W. Wagner
Tel. +49 (0)234 32-29033
Fax +49 (0)234 32-14945
wagner@thermo.rub.de
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