Radim Mareš

The IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam

In the 1960’s an industrial formulation for the thermodynamic properties of water and steam was developed called “The 1967 IFC Formulation for Industrial Use” (IFC-67) [1]. Since 1967 IFC-67 has been formally recognized to calculate thermodynamic properties of water and steam for any official use such as performance guarantee calculations of power cycles. In addition to this, IFC-67 has been used for innumerable other industrial applications. However, during the last few years a number of weaknesses of IFC-67 have appeared. This fact and the progress that has been achieved in mathematical methods to develop accurate equations of state led to the development of a new industrial formulation in an international research project initiated and coordinated by the International Association for the Properties of Water and Steam (IAPWS).

New International Formulation for the Viscosity of H2O

The International Association for the Properties of Water and Steam (IAPWS) encouraged an extensive research effort to update the IAPS Formulation 1985 for the Viscosity of Ordinary Water Substance, leading to the adoption of a Release on the IAPWS Formulation 2008 for the Viscosity of Ordinary Water Substance. This manuscript describes the development and evaluation of the 2008 formulation, which provides a correlating equation for the viscosity of water for fluid states up to 1173K and 1000MPa with uncertainties from less than 1% to 7% depending on the state point.

Surface Tension of Supercooled Water: No Inflection Point down to −25 °C

A dramatic increase in the surface tension of water with decreasing temperature in the supercooled liquid region has appeared as one of the many anomalies of water. This claimed anomaly characterized by the second inflection point at about +1.5 °C was observed in older surface tension data and was partially supported by some molecular simulations and theoretical considerations. In this study, two independent sets of experimental data for the surface tension of water in the temperature range between +33 and -25 °C are reported. The two data sets are mutually consistent, and they lie on a line smoothly extrapolating from the stable region. No second inflection point and no other anomalies in the course of the surface tension were observed. The new data lies very close to the extrapolated IAPWS correlation for the surface tension of ordinary water, which hence can be recommended for use, e.g., in atmospheric modeling.

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.

Supplementary Backward Equations for Pressure as a Function of Enthalpy and Entropy p(h,s) to the Industrial Formulation IAPWS-IF97 for Water and Steam

In modeling steam power cycles, thermodynamic properties as functions of the variables enthalpy and entropy are required in the liquid and the vapor regions. It is difficult to perform these calculations with IAPWS-IF97, because they require two-dimensional iterations calculated from the IAPWS-IF97 fundamental equations. While these calculations are not frequently required, 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 pressure as a function of enthalpy and entropy p(h,s) as a supplement to the IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam (IAPWS-IF97) in 2001. These p(h,s) equations are valid in the liquid region 1 and the vapor region 2. With pressure p, temperature T(h,s) can be calculated from the IAPWS-IF97 backward equations T(p,h). By using the p(h,s) equations, the two dimensional iterations of the IAPWS-IF97 basic equations can be avoided. The numerical consistency of pressure and temperature obtained in this way is sufficient for most heat cycle calculations. This paper summarizes the need and the requirements for the p(h,s) equations and gives complete numerical information about the equations. Moreover, the achieved quality of the equations and their use in the calculation of the backward function T(h,s) is presented. The three aspects, numerical consistency with the IAPWS-IF97 basic equations, consistency along subregion boundaries, and computational speed important for industrial use are discussed.

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

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 T sat (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.

Mean-field equation of state of supercooled water and vapor pressure approximations

An equation of state for supercooled water in the mean-field approximation is presented in the paper. The model describes experimental data in the supercooled region and satisfies a condition that for very low temperatures heat capacity of liquid water is close to the heat capacity of ice. The equation is used to calculate vapor pressure data at ambient pressure in the temperature interval from 123 K to 273 K. Based on the data, two very simple formulas for vapor pressure below 230 K and above 230 K are calculated.

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.

New Equation for Vapor Pressures of Difluoromethane (HFC-32)

Critically evaluated experimental vapor-pressure data sets supplemented with calculated data for low-temperature region were used in the development of vapor-pressure equations. The optimum number of terms, coefficients, and exponents of the Wagner-type equation were derived by means of the Setzmann–Wagner program OPTIM based on the combination of the stepwise regression analysis and evolutionary optimization method. Equations were checked by the reduced enthalpy of vaporization criterion derived from the Clausius–Clapeyron equation and specific volume of ideal gas. An equation developed using 261 experimental data points and low-temperature data calculated by Lüddecke and Magee gives an RMS deviation of 0.102%; a second equation based on the same experimental data and low-temperature data calculated by Tillner-Roth gives an RMS deviation of 0.101% from experimental points. The triple-point pressure extrapolated to the measured temperature Ttp = 136.34 K is discussed. Comparisons with vapor pressure equations by Outcalt and McLinden, Duarte-Garza and Magee. and Kubota et al. are also given.