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TECHNICAL PAPERS: Power

The IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam

[+] Author and Article Information
W. Wagner

Ruhr-Universität Bochum, Lehrstuhl für Thermodynamik, D-44780 Bochum, Germany

J. R. Cooper

Queen Mary and Westfield College, Department of Engineering, London, United Kingdom

A. Dittmann

Technishe Universität Dresden, Institut für Thermodynamik und Technische Gebäudeausrüstung, Dresden, Germany

J. Kijima, K. Oguchi, Y. Takaishi, I. Tanishita

Kanagawa Institute of Technology, Faculty of Engineering, Atsugi, Japan

H.-J. Kretzschmar, I. Stöcker

Hochschule Zittau/Görlitz (FH), Fachgebiet Technische Thermodynamik, Zittau, Germany

A. Kruse

Ruhr-Universität Bochum, Lehrstuhl für Thermodynamik, Bochum, Germany

R. Mareš

University of West Bohemia, Department of Thermodynamics, Plzen, Czech Republic

H. Sato

Keio University, Faculty of Science and Technology, Yokohama, Japan

O. Šifner

Academy of Sciences of Czech Republic, Institute of Thermomechanics, Prague, Czech Republic

J. Trübenbach, Th. Willkommen

Technische Universität Dresden, Institut für Thermodynamik und Technische Gebäudeausrüstung, Dresden, Germany

J. Eng. Gas Turbines Power 122(1), 150-184 (Jan 01, 2000) (35 pages) doi:10.1115/1.483186 History:
Copyright © 2000 by ASME
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References

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Wagner, W., and Kruse, A., 1998, “Properties of Water and Steam/Zustandsgrößn von Wasser und Wasserdampf/IAPWS-IF97,” Springer-Verlag, Berlin, Heidelberg.
1999 JSME Steam Tables Based on IAPWS-IF97, 1999, The Japan Society of Mechanical Engineers, Tokyo.
Parry, W. T., Bellows, J. C., Gallagher, J. S., and Harvey, A. H., 2000, “ASME International Steam Tables for Industrial Use,” ASME Press, New York.
International Association for the Properties of Water and Steam, 1997, “IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam,” IAPWS Release, IAPWS Secretariat.6
Setzmann,  U., and Wagner,  W., 1989, “A New Method for Optimizing the Structure of Thermodynamic Correlation Equations,” Int. J. Thermophys., 10, pp. 1103–1126.
Preston-Thomas,  H., 1990, “The International Temperature Scale of 1990 (ITS-90),” Metrologia, 27, pp. 3–10.
International Association for the Properties of Water and Steam, 1996, “IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use,” IAPWS Release, IAPWS Secretariat.5
Wagner, W., and Pruß, A., 1999, “The IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use,” to be submitted to J. Phys. Chem. Ref. Data.
International Association for the Properties of Water and Steam, 1994, “Skeleton Tables 1985 for the Thermodynamic Properties of Ordinary Water Substance,” IAPWS Release, IAPWS Secretariat; also in: White, Jr., H. J., Sengers, J. V., Neumann, D. B., and Bellows, J. C., eds., 1995, “Physical Chemistry of Aqueous Systems: Meeting the Needs of Industry,” Proceedings of the 12th International Conference on the Properties of Water and Steam, Begell House, New York, pp. A13–A32.
International Formulation Committee of ICPS, 1965, “Minutes of the Meeting of the International Formulation Committee of ICPS,” Prague.
Cohen, E. R., and Taylor, B. N., 1986, “The 1986 Adjustment of the Fundamental Physical Constants,” CODATA Bulletin, No. 63, Committee on Data for Science and Technology, Int. Council of Scientific Unions, Pergamon Press, Oxford.
Audi,  G., and Wapstra,  A. H., 1993, “The 1993 Atomic Mass Evaluation. (I) Atomic Mass Table,” Nucl. Phys., A565, pp. 1–65.
1991, “Isotopic Compositions of the Elements 1989,” Commission on Atomic Weights and Isotopic Abundances. Subcommittee for Isotopic Abundance Measurements, Pure Appl. Chem., 63, pp. 991–1002.
International Association for the Properties of Water and Steam, 1995, “Release on The Values of Temperature, Pressure and Density of Ordinary and Heavy Water Substances at Their Respective Critical Points,” IAPWS Secretariat; also in: White, Jr., H. J., Sengers, J. V., Neumann, D. B., and Bellows, J. C., eds., 1995, “Physical Chemistry of Aqueous Systems: Meeting the Needs of Industry,” Proceedings of the 12th International Conference on the Properties of Water and Steam, Begell House, New York, pp. A101–A102.
Guildner,  L. A., Johnson,  D. P., and Jones,  F. E., 1976, “Vapor Pressure of Water at Its Triple Point,” J. Res. Natl. Bur. Stand., Sect. A, 80A, pp. 505–521.
Setzmann,  U., and Wagner,  W., 1991, “A New Equation of State and Tables of Thermodynamic Properties for Methane Covering the Range from the Melting Line to 625 K at Pressures up to 1000 MPa,” J. Phys. Chem. Ref. Data, 20, pp. 1061–1155.
Span,  R., and Wagner,  W., 1996, “A New Equation of State for Carbon Dioxide Covering the Fluid Region from the Triple-Point Temperature to 1100 K at Pressures up to 800 MPa,” J. Phys. Chem. Ref. Data, 25, pp. 1509–1596.
Kruse, A., and Wagner, W., 1998, “Neue Zustandsgleichungen für industrielle Anwendungen im technisch relevanten Zustandsgebiet von Wasser,” Fortschr.-Ber. VDI. Reihe 6, Nr. 393, VDI-Verlag, Düsseldorf.
Wagner, W., 1974, “Eine Mathematisch Statistische Methode zum Aufstellen Thermodynamischer Gleichungen—gezeigt am Beispiel der Dampfdruckkurve reiner fluider Stoffe,” Fortscher.-Ber, VDI-Z, Reihe 3, Nr. 39, VDI-Verlag, Düsseldorf.
Kretzschmar, H.-J., Stöcker, I., Klinger, J., and Dittmann, A., 2000, “Calculation of Thermodynamic Derivatives of Water and Steam Using the New Industrial Formulation IAPWS-IF97,” Proceedings of the 13th International Conference on the Properties of Water and Steam, P. Tremaine, P. G. Hill, D. Irish, and P. V. Balakrishnan, eds., NRC Press, Ottawa.
International Association for the Properties of Water and Steam, 1994, “Release on the Pressure along the Melting and the Sublimation Curves of Ordinary Water Substance,” in Wagner,  W., Saul,  A., and Pruß,  A., 1994, J. Phys. Chem. Ref. Data, 23, pp. 515–527: also in White, Jr., H. J., Sengers, J. V., Neumann, D. B., and Bellows, J. C., eds., 1995, “Physical Chemistry of Aqueous Systems: Meeting the Needs of Industry,” Proceedings of the 12th International Conference on the Properties of Water and Steam, Begell House, New York, pp. A9–A12.
Miyagawa, K., Spencer, R. C., McClintock, R. B., Bradly, H. W., Kodl, I., Perstrup, C., Parry, W. T., Rukes, B., Scala, M., and Smith, P. F., 1997, “Acceptance Test Report of Proposal of a New Industrial Formulation of IAPWS,” report, IAPWS Task Group NIF Evaluation.5
Kretzschmar, H.-J., Oguchi, K., and Willkommen, Th., 2000, “Numerically Consistent Equations for Vapor Pressure ps(T) and Saturation Temperature Ts(p) of Ordinary Water Substance,” to be submitted to Int. J. Thermophys.
Willkommen, Th., Kretzschmar, H.-J., and Dittmann, A., 1995, “An Algorithm for Setting Up Numerically Consistent Forward and Backward Equations for Process Modelling,” in White, Jr., H. J., Sengers, J. V., Neumann, D. B., Bellows, J. C., eds., “Physical Chemistry of Aqueous Systems: Meeting the Needs of Industry,” Proceedings of the 12th International Conference on the Properties of Water and Steam, Begell House, New York, pp. 194–201.
Zschunke,  T., Kretzschmar,  H.-J., and Dittmann,  A., 1991, “Erstellung von konsistenten Zustandsgleichungen mit simultaner gleichmäßiger Approximation,” Brennstoff-Wärme-Kraft, 43, pp. 567–570.
Mareš,  R., and Sifner,  O., 1996, “Equation of State for Superheated Steam in the Range from 800 to 2000°C and Pressures up to 10 MPa,” Acta Tech. CSAV, 41, pp. 647–652.
Cooper,  J. R., 1982, “Representation of the Ideal-Gas Thermodynamic Properties of Water,” Int. J. Thermophys., 3, pp. 35–43.
Trübenbach, J., 1999, “Ein Algorithmus zur Aufstellung rechenzeitoptimierter Gleichungen für thermodynamische Zustandsgrößen,” Fortscher.-Ber. VDI, Reihe 6, 417 , VDI-Verlag, Düsseldorf.
Willkommen, Th., 1996, “Ein Algorithmus zur Aufstellung numerisch konsistenter Gleichungen für die in Prozeßmodellierungen benötigten thermodynamihen Umkehrfunktionen,” dissertation, Technische Universität Dresden, Fakultät Maschinenwesen, Dresden.
Smukala, J., 1995, “Entwicklung eines Verfahrens zur Berücksichtigung der numerischen Konsistenz bei der Aufstellung von Zustandsgleichungen in Form von Vorwärts- und Rückwärtsgleichungen,” Diplomarbeit, Lehrstuhl für Thermodynamik, Ruhr-Universität Bochum, Bochum.
McClintock, R. B., and Silvestri, G. J., 1968, Formulations and Iterative Procedures for the Calculation of Properties of Steam, ASME, New York.

Figures

Grahic Jump Location
Regions and equations of IFC-67. The boundary between regions 2 and 3 is described by the L-function.
Grahic Jump Location
Regions and equations of IAPWS-IF97. The boundary between regions 2 and 3 is described by the B23-equation, see section 5.3
Grahic Jump Location
(a) Percentage deviations of the specific volumes v calculated from Eq. (15) and IFC-67, respectively, from values vIAPWS-95 calculated from IAPWS-95 89. (b) Relative deviations in ppm of the specific volumes v calculated from Eq. (15) and IFC-67, respectively, from values vIAPWS-95 calculated from IAPWS-95 89; Δv=(v−vIAPWS-95)/v.
Grahic Jump Location
Absolute deviations of the specific enthalpies h calculated from Eq. (15) and IFC-67, respectively, from values hIAPWS-95 calculated from IAPWS-95 89; see the spread pressure scale up to p=10 MPa in the first deviation diagram for 273.15 K.
Grahic Jump Location
Percentage deviations of the specific isobaric heat capacities cp calculated from Eq. (15) and IFC-67, respectively, from values cp,IAPWS-95 calculated from IAPWS-95 89
Grahic Jump Location
Percentage deviations of the speeds of sound w calculated from Eq. (15) and IFC-67, respectively, from values wIAPWS-95 calculated from IAPWS-95 89
Grahic Jump Location
Percentage deviations of the specific isobaric heat capacities in the ideal-gas state cpo calculated from Eq. (20) from values cp,IAPWS-95o calculated from IAPWS-95 89; Δcpo=((cpo/R)−(cpo/R)IAPWS-95)/(cpo/R)
Grahic Jump Location
Percentage deviations of the specific volumes v calculated from Eq. (19) and IFC-67, respectively, from values vIAPWS-95 calculated from IAPWS-95 89
Grahic Jump Location
Absolute deviations of the specific enthalpies h calculated from Eq. (19) and IFC-67, respectively, from values hIAPWS-95 calculated from IAPWS-95 89
Grahic Jump Location
Percentage deviations of the specific isobaric heat capacities cp calculated from Eq. (19) and IFC-67, respectively, from values cp,IAPWS-95 calculated from IAPWS-95 89
Grahic Jump Location
Percentage deviations of the speeds of sound w calculated from Eq. (19) and IFC-67, respectively, from values wIAPWS-95 calculated from IAPWS-95 89
Grahic Jump Location
Percentage deviations of the values of v,cp, and w and absolute deviations of h values calculated from Eq. (19) and IFC-67, respectively, from the corresponding values calculated from IAPWS-95 89 along the boundary between regions 2 and 3 defined by the B23-equation: Δv=(v−vIAPWS-95)/v;Δcp=(cp−cp,IAPWS-95)/cp;Δh=h−hIAPWS-95;Δw=(w−wIAPWS-95)/W.
Grahic Jump Location
Mollier h-s diagram for the metastable-vapor region with isotherms calculated from the equations given above
Grahic Jump Location
(a) Percentage deviations of the specific volumes v calculated from Eq. (25) and IFC-67, respectively, from values vIAPWS-95-95 calculated from IAPWS-95 89. (b) Percentage deviations of the specific volumes v calculated from Eq. (25) and IFC-67, respectively, from values vIAPWS-95-95 calculated from IAPWS-95 89; spread pressure scale for the enlarged critical region.
Grahic Jump Location
Absolute deviations of the specific enthalpies h calculated from Eq. (25) and IFC-67, respectively, from values hIAPWS-95-95 calculated from IAPWS-95 89
Grahic Jump Location
(a) Percentage deviations of the specific isobaric heat capacities cp calculated from Eq. (25) and IFC-67, respectively, from values cp,IAPWS-95-95 calculated from IAPWS-95 89. (b) Percentage deviations of the specific isobaric heat capacities cp calculated from Eq. (25) and IFC-67, respectively, from values cp,IAPWS-95-95 calculated from IAPWS-95 89; spread pressure scale for the enlarged critical region.
Grahic Jump Location
Percentage deviations of the speeds of sound w calculated from Eq. (25) and IFC-67, respectively, from values wIAPWS-95-95 calculated from IAPWS-95 89
Grahic Jump Location
Behavior of Eq. (25) in the vapor-liquid two-phase region of region 3
Grahic Jump Location
Percentage deviations of the values of v,cp, and w and absolute deviations of h values calculated from Eq. (29) from the corresponding values calculated from IAPWS-95 89; Δv=(v−vIAPWS-95)/v;Δcp=(cp−cp,IAPWS-95)/cp;Δh=h−hIAPWS-95;Δw=(w−wIAPWS-95)/w.
Grahic Jump Location
Inconsistencies Δv,Δh,Δcp,Δw,Δs, and Δg along the boundary between regions 1 and 3 (left column) and the boundary between regions 2 and 3 (right column) when calculating the properties without an index from the corresponding g equation (Eq. (15) for region 1 and Eq. (19) for region 2) and the properties with the index f from the f equation for region 3, Eq. (25). For the calculations with IFC-67 its corresponding g and f equations were used, see text: Δv=(v−vf)/v;Δcp=(cp−cp,f)/cp;Δs=s−sf;Δh=h−hf;Δw=(w−wf)/w;Δg=g−gf.
Grahic Jump Location
Percentage deviations of the saturation pressure ps calculated from Eq. (28) and IFC-67, respectively, from values ps,IAPWS-95-95 calculated from IAPWS-95 89
Grahic Jump Location
Absolute deviations of temperatures T calculated from Eq. (49) for subregion 2(a), Eq. (50) for subregion 2(b), and Eq. (51) for subregion 2(c) from values TEq. (19) calculated from Eq. (19) for given values of p and s
Grahic Jump Location
Uncertainties in specific volume, Δv, estimated for the corresponding equations of IAPWS-IF97. In the enlarged critical region (triangle), the uncertainty is given as percentage uncertainty in pressure, Δp. This region is bordered by the two isochores 0.0019 m3 kg−1 and 0.0069 m3 kg−1 and by the 30 MPa isobar. The positions of the lines separating the uncertainty regions are approximate.
Grahic Jump Location
Uncertainties in specific isobaric heat capacity, Δcp, estimated for the corresponding equations of IAPWS-IF97. For the definition of the triangle around the critical point, see Fig. 29. The positions of the lines separating the uncertainty regions are approximate.
Grahic Jump Location
Uncertainties in speed of sound, Δw, estimated for the corresponding equations of IAPWS-IF97. For the definition of the triangle around the critical point, see Fig. 29. The positions of the lines separating the uncertainty regions are approximate.
Grahic Jump Location
Uncertainties in saturation pressure, Δps, estimated for the saturation-pressure equation, Eq. (28)
Grahic Jump Location
Inconsistencies Δps along region 4 (saturation curve) when calculating the saturation pressures as ps values from Eq. (15) together with Eq. (19) and from Eq. (25), respectively, and as values ps,Eq. (28) directly from the saturation-pressure equation, Eq. (28): Δps=(ps−ps,Eq. (28))/ps
Grahic Jump Location
Inconsistencies Δv,Δs, and Δcp caused by two different ways of determining the needed saturation pressures ps. For vEq. (28),sEq. (28), and cp,Eq. (28) the ps values were directly calculated from Eq. (28) and for v,s, and cp the ps values were determined from Eqs. (15) and (19) and from Eq. (19), respectively, via the phase-equilibrium condition: Δv=(vEq. (28)−v)/v,Δs=sEq. (28)−s,Δcp=(cp,Eq. (28)−cp)/cp
Grahic Jump Location
Absolute deviations of temperatures TEq. (37) calculated from Eq. (37) from values TEq. (15) calculated from Eq. (15) from values of p and h
Grahic Jump Location
Absolute deviations of temperatures TEq. (39) calculated from Eq. (39) from values TEq. (15) calculated from Eq. (15) for given values of p and s
Grahic Jump Location
Division of region 2 of IAPWS-IF97 into the three subregions 2(a), 2(b), and 2(c) for the backward equations T(p,h) and T(p,s)
Grahic Jump Location
Absolute deviations of temperatures T calculated from Eq. (43) for subregion 2(a), Eq. (44) for subregion 2(b), and Eq. (45) for subregion 2(c) from values TEq. (19) calculated from Eq. (19) for given values of p and h

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