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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

Figures

Grahic Jump Location
Regions and equations of IFC-67. The boundary between regions 2 and 3 is described by the L-function.
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Regions and equations of IAPWS-IF97. The boundary between regions 2 and 3 is described by the B23-equation, see section 5.3
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(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.
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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.
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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
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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
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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)
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Percentage deviations of the specific volumes v calculated from Eq. (19) and IFC-67, respectively, from values vIAPWS-95 calculated from IAPWS-95 89
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Absolute deviations of the specific enthalpies h calculated from Eq. (19) and IFC-67, respectively, from values hIAPWS-95 calculated from IAPWS-95 89
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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
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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
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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.
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Mollier h-s diagram for the metastable-vapor region with isotherms calculated from the equations given above
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(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.
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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
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(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.
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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
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Behavior of Eq. (25) in the vapor-liquid two-phase region of region 3
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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
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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.
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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.
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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
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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
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Absolute deviations of temperatures TEq. (37) calculated from Eq. (37) from values TEq. (15) calculated from Eq. (15) from values of p and h
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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
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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)
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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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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
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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.
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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.
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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.
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Uncertainties in saturation pressure, Δps, estimated for the saturation-pressure equation, Eq. (28)

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