Abstract

In modeling advanced steam power cycles, thermodynamic properties as functions of pressure and enthalpy (p,h) or pressure and entropy (p,s) are required in the critical and supercritical regions (region 3 of IAPWS-IF97). With IAPWS-IF97, these calculations require cumbersome two-dimensional iteration of temperature T and specific volume v from (p,h) or (p,s). While these calculations in region 3 are not frequently required, the computing time can be significant. Therefore, the International Association for the Properties of Water and Steam (IAPWS) adopted backward equations for T(p,h), v(p,h), T(p,s), and v(p,s) in region 3, along with boundary equations for the saturation pressure as a function of enthalpy, p3sat(h), and of entropy, p3sat(s). Using the new equations, two-dimensional iteration can be avoided. The numerical consistency of temperature and specific volume obtained in this way is sufficient for most uses. This paper summarizes the need and the requirements for these equations and gives complete numerical information. In addition, numerical consistency and computational speed are discussed.

1.
International Association for the Properties of Water and Steam
, 1997, “
Release on the IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam
,” IAPWS Release,
IAPWS Secretariat
, available at www.iapws.org
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.
,
Tanishita
,
I.
,
Trübenbach
,
J.
, and
Willkommen
,
Th.
, 2000, “
The IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam
,”
J. Eng. Gas Turbines Power
0742-4795,
122
, pp.
150
182
.
3.
International Association for the Properties of Water and Steam
, 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
,” IAPWS Release,
IAPWS Secretariat
, available at www.iapws.org
4.
Kretzschmar
,
H.-J.
,
Cooper
,
J. R.
,
Dittmann
,
A.
,
Friend
,
D. G.
,
Gallagher
,
J. S.
,
Knobloch
,
K.
,
Mareš
,
R.
,
Miyagawa
,
K.
,
Stöcker
,
I.
,
Trübenbach
,
J.
,
Wagner
,
W.
, and
Willkommen
,
Th.
, “
Supplementary Backward Equations for Pressure as a Function of Enthalpy and Entropy p(h,s) to the Industrial Formulation IAPWS-IF97 for Water and Steam
,”
J. Eng. Gas Turbines Power
0742-4795, in press.
5.
International Association for the Properties of Water and Steam
, 2004, “
Revised 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
,” IAPWS Release,
IAPWS Secretariat
, available at www.iapws.org
6.
International Association for the Properties of Water and Steam
, 2004, “
Supplementary Release on Backward Equations p(h,s) for Region 3, Equations as a Function of h and s for the Region Boundaries, and an Equation Tsat(h,s) for Region 4 of the IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam
,” IAPWS Release,
IAPWS Secretariat
, available at www.iapws.org
7.
Kretzschmar
,
H.-J.
, and
Knobloch
,
K.
, 2005, “
Supplementary Backward Equations for the Industrial Formulation IAPWS-IF97 of Water and Steam for Fast Calculations of Heat Cycles, Boilers, and Steam Turbines
,” in
M.
Nakahara
et al.
, eds.,
Water, Steam and Aqueous Solutions for Electric Power: Advances in Science and Technology
,
Proceedings of the 14th International Conference on the Properties of Water and Steam
,
Maruzen Co., Ltd.
,
Kyoto, Japan
, pp.
34
45
.
8.
Kretzschmar
,
H.-J.
, 2001, “
Specifications for the Supplementary Backward Equations T(p,h) and T(p,s) in Region 3 of IAPWS-IF97
,”
B.
Dooley
, ed.,
Minutes of the Meetings of the Executive Committee of the International Association for the Properties of Water and Steam
, Gaithersburg 2001,
IAPWS Secretariat
,
Palo Alto, CA
, p.
6
and Attachment 7-Item #6.
9.
Rukes
,
B.
, 1994, “
Specifications for Numerical Consistency
,”
B.
Dooley
, ed.,
Minutes of the Meetings of the Executive Committee of the International Association for the Properties of Water and Steam
, Orlando, 1994,
IAPWS Secretariat
,
Palo Alto, CA
, pp.
31
33
.
10.
Kretzschmar
,
H.-J.
,
Stöcker
,
I.
,
Klinger
,
J.
, and
Dittmann
,
A.
, 2000, “
Calculation of Thermodynamic Derivatives for Water and Steam Using the New Industrial Formulation IAPWS-IF97
,”
P. R.
Tremaine
et al.
, eds.,
Steam, Water and Hydrothermal Systems: Physics and Chemistry Meeting the Needs of Industry
,
Proceedings of the 13th International Conference on the Properties of Water and Steam
,
NRC Press
,
Ottawa
, pp.
238
247
.
11.
Rukes
,
B.
, and
Wagner
,
W.
, 1991, “
Final Set of Specifications for the New Industrial Formulation
,”
B.
Dooley
, ed.,
Minutes of the Meetings of the Executive Committee of the International Association for the Properties of Water and Steam
, Tokyo 1991,
IAPWS Secretariat
,
Palo Alto, CA
, pp.
78
82
.
12.
Kruse
,
A.
, and
Wagner
,
W.
, 1998, “
Neue Zustandsgleichungen für industrielle Anwendungen im technisch relevanten Zustandsgebiet von Wasser (New Equations of State for Water for Industrial Use)
,”
Fortschr.-Ber. VDI, Reihe 6
, Nr. 393,
VDI-Verlag
,
Düsseldorf
.
13.
Trübenbach
,
J.
, 1999, “
Ein Algorithmus zur Aufstellung rechenzeitoptimierter Gleichungen für thermodynamische Zustandsgrößen (An Algorithm for Developing Equations of State Optimized Regarding Their Computing Time Consumption)
,”
Fortschr.-Ber. VDI, Reihe 6
, Nr. 417,
VDI-Verlag
,
Düsseldorf
.
14.
Willkommen
,
Th.
,
Kretzschmar
,
H.-J.
, and
Dittmann
,
A.
, 1995, “
An Algorithm for Setting up Numerically Consistent Forward and Backward Equations for Process Modelling
,” in
H. J.
White
et al.
, eds.,
Physical Chemistry of Aqueous Systems
,
Proceedings of the 12th International Conference on the Properties of Water and Steam
,
Begell House
,
New York
, pp.
194
201
.
15.
Willkommen
,
Th.
, 1995, “
Ein Algorithmus zur Aufstellung numerisch konsistenter Gleichungen für die in Prozessmodellierungen benötigten thermodynamischen Umkehrfunktionen (An Algorithm for Developing Numerically Consistent Backward Equations for Use in Process Modeling)
,” Dissertation, Faculty of Mechanical Engineering, Technical University of Dresden, Dresden.
16.
Kretzschmar
,
H.-J.
, 1990, “
Zur Aufbereitung und Darbietung thermophysikalischer Stoffdaten für die Energietechnik (The Preparation and Processing of Thermophysical Properties for Power Engineering)
,” Habilitation, Faculty of Mechanical Engineering, Technical University of Dresden, Dresden.
17.
Wagner
,
W.
, 1974, “
Eine mathematisch statistische Methode zum Aufstellen thermodynamischer Gleichungen—gezeigt am Beispiel der Dampfdruckkurve reiner fluider Stoffe (A Mathematical Statistical Method for Developing Equations of State—Demonstration With the Vapor Pressure Curves of Pure Fluids)
,”
Fortschr.-Ber. VDI, Reihe 3
, Nr. 39,
VDI-Verlag
,
Düsseldorf
.
18.
Setzmann
,
W.
, and
Wagner
,
W.
, 1989, “
A New Method for Optimizing the Structure of Thermodynamic Correlation Equations
,”
Int. J. Thermophys.
0195-928X,
10
, pp.
1103
1126
.
19.
Knobloch
,
K.
, “
Gleichungen für thermodynamische Umkehrfunktionen von Wasser und Wasserdampf im kritischen und überkritischen Zustandsgebiet für energietechnische Prozessberechnungen (Equations for Thermodynamic Backward Functions of Water in the Critical and Supercritical Regions for Power Cycle Calculations)
,”
Fortschr.-Ber. VDI, Reihe 6
, in preparation.
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