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Publication Citation: Supplemental backward equations T(pkh), v(p,h), and T(p,s), v(p,s) for the critical and supercritical regions (region 3) of the industrial formulation

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Author(s): H J. Kretzchmar; J R. Cooper; A Dittmann; Daniel G. Friend; J S. Gallagher; Allan H. Harvey; K Knobloch; Radim Mares; Kiyoshi Miyagawa; N Okita; I. Stocker; W Wagner; I Weber;
Title: Supplemental backward equations T(pkh), v(p,h), and T(p,s), v(p,s) for the critical and supercritical regions (region 3) of the industrial formulation
Published: January 07, 2009
Abstract: In modeling steam power cycles, thermodynamic properties as functions of the variables ( ), p h or ( ), p s are required in the critical and supercritical regions (region 3 of IAPWSIF97). It is difficult to perform these calculations with IAPWS-IF97, because they require two-dimensional iterations calculated from the IAPWS-IF97 fundamental equation. While these calculations are not frequently required in region 3, the relatively large computing time required for two-dimensional iteration can be significant in process modeling. Therefore, the International Association for the Properties of Water and Steam (IAPWS) adopted backward equations for temperature and specific volume as functions of pressure and enthalpy ( ), T p h, ( ) , v p h and also as functions of pressure and entropy ( ), T p s, ( ), v p s as a supplement to the IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam (IAPWS-IF97) in 2003. These backward equations were issued as "Supplementary Release on Backward Equation! 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". By using the new backward equations, two-dimensional iterations of the IAPWS-IF97 basic equation can be avoided. The numerical consistencies of temperature and specific volume obtained in this way are sufficient for most calculations for heat cycles, boiler, and turbines. In addition, the paper provides equations for the saturation pressure as a function of enthalpy ( ) 3sat p h and as a function of entropy ( 3sat p s for the saturated liquid and saturated vapor boundaries of region 3. Using these equations, it may be determined without iteration whether a state point is located in the single-phase region or in the two-phase region. This paper summarizes the need and the requirements for the equation and gives complete numerical information. In addition, the numerical consistency with the IAPWS-IF97 basic equation, consistency along subregion boundaries, and computational speed are discussed.
Citation: Journal of Engineering for Gas Turbines and Power-Transactions of the ASME
Volume: 129
Pages: pp. 294 - 303
Keywords: calculation;steam;thermodynamic properties;water
Research Areas: Thermophysics
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