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TECHNICAL PAPERS: Thermodynamic Properties

Supplementary Backward Equations T(p,h), v(p,h), and T(p,s), v(p,s) for the Critical and Supercritical Regions (Region 3) of the Industrial Formulation IAPWS-IF97 for Water and Steam

[+] Author and Article Information
H.-J. Kretzschmar1

Department of Technical Thermodynamics,  Zittau/Goerlitz University of Applied Sciences, P.O. Box 1455, D-02754 Zittau, Germanyhj.kretzschmar@hs-zigr.de

J. R. Cooper

Department of Engineering, Queen Mary University of London, Mile End Road, London E1 4NS, UK

A. Dittmann

Department of Technical Thermodynamics,  Technical University of Dresden, Dresden D-01062, Germany

D. G. Friend

Physical and Chemical Properties Division,  National Institute of Standards and Technology, 325 Broadway, Boulder, CO 80305

J. S. Gallagher

Physical and Chemical Properties Division,  National Institute of Standards and Technology, 100 Bureau Drive, Gaithersburg, MD 20899-8380

A. H. Harvey

Physical and Chemical Properties Division,  National Institute of Standards and Technology, 325 Broadway, MS 838.08 Boulder, CO 80305aharvey@boulder.nist.gov

K. Knobloch, I. Stöcker

Department of Technical Thermodynamics,  Zittau/Goerlitz University of Applied Sciences, P.O. Box 1455, D-02754 Zittau, Germany

R. Mareš

Department of Thermodynamics, University of West Bohemia, Univerzitni 8, Plzeň CZ 306 14, Czech Republic

K. Miyagawa

 4-12-11-628 Nishiogu, Arakawa-ku Tokyo 116-0011, Japan

N. Okita

Thermal Plant Systems Project Department,  Toshiba Corporation, 1-1, Shibaura 1-chome Minato-ku, Tokyo 105-8001, Japan

W. Wagner

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

I. Weber

Siemens AG, PG ER4, Freyeslebenstr. 1, D-91058 Erlangen, Germany

1

To whom correspondence should be addressed.

J. Eng. Gas Turbines Power 129(1), 294-303 (Jan 10, 2006) (10 pages) doi:10.1115/1.2181598 History: Received March 17, 2005; Revised January 10, 2006

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.

FIGURES IN THIS ARTICLE
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Copyright © 2007 by American Society of Mechanical Engineers
Topics: Equations
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Figures

Grahic Jump Location
Figure 1

Regions and equations of IAPWS-IF97, IAPWS-IF97-S01, IAPWS-IF97-S04, and the backward equations T303(p,h), v303(p,h), T303(p,s), and v303(p,s) and boundary equations p3sat03(h) and p3sat03(s) of this work

Grahic Jump Location
Figure 2

Numerical consistency relations of the backward functions T(p,h), v(p,h), and T(p,s), v(p,s) with the IAPWS-IF97 basic equation f397(v,T)

Grahic Jump Location
Figure 3

Division of region 3 into subregions 3a and 3b for the backward equations T3(p,h), v3(p,h), T3(p,s), and v3(p,s)

Grahic Jump Location
Figure 4

IAPWS-IF97 region 3 and the boundary equation p3sat(h) in a p-h diagram

Grahic Jump Location
Figure 5

IAPWS-IF97 region 3 and the boundary equation p3sat(s) in a p-s diagram

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