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TECHNICAL PAPERS: Thermodynamic Properties

# Supplementary Backward Equations $p(h,s)$ for the Critical and Supercritical Regions (Region 3), and Equations for the Two-Phase Region and Region Boundaries of the IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam

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

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, London, UK

J. S. Gallagher

Physical and Chemical Properties Division, National Institute of Standards and Technology, Gaithersburg, MD

A. H. Harvey

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

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, Plzeň, Czech Republic

K. Miyagawa

Tokyo, Japan

N. Okita

Thermal Plant Systems Project Department, Toshiba Corporation, Yokohama, Japan

R. Span, W. Wagner

Department of Thermodynamics, Ruhr-University of Bochum, Bochum, Germany

I. Weber

Power Generation, Siemens AG, Erlangen, Germany

The alternative use of the IAPWS-IF97-S03rev backward equation $T303(p,s)$ leads to worse numerical consistency.

The alternative use of the IAPWS-IF97-S03rev backward equation $v303(p,h)$ leads to worse numerical consistency.

The alternative use of the IAPWS-IF97-S03 backward equation $T303(p,s)$ leads to worse numerical consistency.

The alternative use of the IAPWS-IF97-S03 backward equation $v303(p,h)$ leads to worse numerical consistency.

The alternative calculation of the temperature on the saturated-liquid line using the IAPWS-IF97 saturation-temperature equation $Tsat97(p101(h1′(s),s))$ or $Tsat97(p3a(h3a′(s),s))$ leads to worse numerical consistency.

The alternative calculation of the temperature on the saturated-vapor line using the saturation-temperature equation $Tsat97(p201(h2ab″(s),s))$, $Tsat97(p201(h2c3b″(s),s))$ or $Tsat97(p3b(h2c3b″(s),s))$ of IAPWS-IF97 leads to worse numerical consistency.

The calculation of the vapor fraction from the saturated-liquid entropy $s′$ and the saturated-vapor entropy $s″$ leads to worse numerical consistency.

J. Eng. Gas Turbines Power 129(4), 1125-1137 (Jan 16, 2007) (13 pages) doi:10.1115/1.2719267 History: Received October 18, 2006; Revised January 16, 2007

## Abstract

When steam power cycles are modeled, thermodynamic properties as functions of enthalpy and entropy 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 specific enthalpy $h$ and specific entropy $s$. While these calculations 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 $p(h,s)$ in region 3. For calculating properties as a function of $h$ and $s$ in the part of the two-phase region that is important for steam-turbine calculations, a backward equation $Tsat(h,s)$ is provided. In order to avoid time-consuming iteration in determining the region for given values of $h$ and $s$, equations for the region boundaries were developed. The numerical consistency of the equations documented here is sufficient for most applications in heat-cycle, boiler, and steam-turbine calculations.

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Copyright © 2007 by American Society of Mechanical Engineers
Topics: Equations
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## Figures

Figure 1

Regions and equations of IAPWS-IF97, IAPWS-IF97-S01, IAPWS-IF97-S03rev, IAPWS-IF97-S05 and the backward equations p304(h,s) and Tsat04(h,s) of this work

Figure 2

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

Figure 3

Regions of IAPWS-IF97 and boundary equations h1′(s), h3a′(s), h2ab″(s), h2c3b″(s), hB13(s), and TB23(h,s) of this work

Figure 4

Illustration of the B23-equation pB2397(T) of IAPWS-IF97 and the range of validity of the boundary equation TB23(h,s) in a h-s diagram

Figure 5

Illustration of the B23-equation pB2397(T) of IAPWS-IF97 and the range of validity of the boundary equation TB23(h,s) in a p-T diagram

Figure 6

Regions and subregions of IAPWS-IF97 and the backward equation Tsat(h,s) of this work

## Errata

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