Pressure and Density Series Equations of State for Steam as Derived from the Haar–Gallagher–Kell Formulation

TLDR

The authors develop two power‑series equations of state for steam properties derived from the HGK84 formulation. These equations are expressed as power series in pressure and density, enabling efficient numerical evaluation. The resulting equations achieve high accuracy in the equilibrium region, accurately extrapolate into the metastable vapor–spinodal region, and provide efficient, high‑accuracy calculations for small to moderate deviations from ideal gas, with conversion tables for coefficients up to the tenth term.

Abstract

Two equations of state for the properties of steam, which are in the form of power series in pressure and density, are developed from the HGK84 formulation. These equations are of high accuracy in the equilibrium region where extensive measurements exist. They also accurately represent the extrapolated data in the metastable region between the vapor saturation and spinodal lines. The accuracy of the representations as a function of the number of terms of the series is presented. Their greatest utility is their use for high accuracy calculations that involve small to moderate departures from ideal-gas behavior. Conversion relationships for the second through the tenth coefficients of the pressure and density series, which apply to the corresponding virial coefficients, are presented. The pressure and density expansions are advantageous for efficient numerical calculations of water vapor properties in the equilibrium and metastable regions.