Ingo Weber

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

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, P 3sat (h), and of entropy, p 3Sat (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.

The IAPWS industrial formulation for the thermodynamic properties of seawater

AbstractIn 2008, the International Association for the Properties of Water and Steam (IAPWS) adopted a standard formulation for the thermodynamic properties of seawater as a sum of contributions to the Gibbs free energy from pure water and from dissolved sea salt. For pure water, the IAPWS formulation for general and scientific use (IAPWS-95) was used. However, for industrial uses such as desalination and seawater power-plant cooling, it is likely to be more convenient to use the computationally simpler IAPWS formulation for industrial use (IAPWS-IF97), which is standard in the steam power industry. This paper documents this approach and gives formulas for calculating thermodynamic properties of seawater and steam (volume, enthalpy, isobaric heat capacity, etc.). The calculation of colligative properties (such as boiling and freezing points and osmotic pressure) is also described, as is the calculation of properties of two-phase states such as brine-vapor and brine-ice (sea ice). The computing speeds for ...

Supplementary Backward Equations v(p,T) for the Critical and Supercritical Regions (Region 3) of the IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam

When steam power cycles are modeled, thermodynamic properties as functions of pressure and temperature are required in the critical and supercritical regions (region 3 of IAPWS-IF97). With IAPWS-IF97, such calculations require cumbersome iterative calculations, because temperature and volume are the independent variables in the formulation for this region. In order to reduce the computing time, the International Association for the Properties of Water and Steam (IAPWS) adopted a set of backward equations for volume as a function of pressure and temperature in region 3. The necessary numerical consistency is achieved by dividing the region into 20 subregions, plus auxiliary subregions near the critical point in which the consistency requirements are relaxed due to the singular behavior at the critical point. In this work, we provide complete documentation of these equations, along with a discussion of their numerical consistency and the savings in computer time. The numerical consistency of these equations should be sufficient for most applications in heat-cycle, boiler, and steam-turbine calculations; if even higher consistency is required, the equations may be used to generate guesses for iterative procedures.