Kiyoshi Miyagawa

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.

New International Formulation for the Thermal Conductivity 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 Thermal Conductivity of Ordinary Water Substance, leading to the adoption of a Release on the IAPWS Formulation 2011 for the Thermal Conductivity of Ordinary Water Substance. This paper describes the development and evaluation of the 2011 formulation, which provides a correlating equation for the thermal conductivity of water for fluid states from the melting temperature up to 1173 K and 1000 MPa with uncertainties from less than 1% to 6%, depending on the state point.

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.

Supplementary Backward Equations for the Industrial Formulation IAPWS-IF97 of Water and Steam for Fast Calculations of Heat Cycles, Boilers, and Steam Turbines

In 1997, the International Association for the Properties of Water and Steam (IAPWS) adopted the “IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam” (IAPWS-IF97) [1, 2]. The IAPWS-IF97 contains fundamental equations g(p, T) for liquid region 1, vapor region 2 and high-temperature region 5, a fundamental equation f(v, T) for the critical and supercritical regions (region 3) and an equation pair for saturation pressure psat (T) and for saturation temperature Tsat (p); see Fig. 1. Using the fundamental equations, all thermodynamic properties can be calculated from a given pressure and temperature in regions 1, 2, 5, or from a given specific volume and temperature in region 3. In addition, the IAPWS-IF97 contains “backward” equations for the most used implicit functions T(p, h) and T(p, s) in regions 1 and 2 for fast calculations in thermodynamic process modeling. Further dependencies must be calculated iteratively from the fundamental equations. Thus, one- and two-dimensional iterations are necessary for determining certain thermodynamic properties in process modeling. Over the past 6 years, IAPWS has established a task group and developed further backward equations for water and steam supplementing the IAPWS Industrial Formulation 1997. First, backward equations p(h, s) for the liquid and vapor regions were developed and adopted as a supplementary release by IAPWS in 2001 (IAPWS-IF97-S01) [3, 4]; see Fig. 1. An international survey of the power industry revealed that backward equations in the critical and supercritical regions were also required in process modeling. Thus the backward equations T(p, h), v(p, h), T(p, s), and v(p, s) were developed for region 3 and adopted as a supplementary release in 2003 and revised in 2004 (IAPWS-IF97-S03rev) [5, 6]. Backward equations p(h, s) developed for the critical and supercritical regions were then adopted by IAPWS in 2004 (IAPWS-IF97-S04) [7, 8]. This supplementary release also contains a backward equation for the saturation temperature Tsat (h, s) in the part of the two-phase region important for steam-turbine calculations. Finally, backward equations v(p, T) for the critical and supercritical regions (region 3) were published in a supplementary release in 2005 (IAPWS-IF97-S05) [9, 10]; see Fig. 1. In order to determine whether a given state point is located in one of the single-phase regions or in the two-phase region, iterations are necessary for the backward functions of the given properties (p, h), (p, s) or (h, s). To avoid these iterations, special region-boundary equations were developed and adopted as a part of the supplementary releases IAPWS-IF97-03rev and IAPWS-IF97-S04. In conclusion, using the equations of IAPWS-IF97, the supplementary backward equations, and the region-boundary equations, all thermodynamic properties can be calculated without iteration from the input variables (p, t), (p, h), (p, s) and (h, s) in the entire range of validity of IAPWS-IF97, including determination of the region (except for the high-temperature region 5). The numerical consistencies of the backward and region-boundary equations are sufficient for most heat-cycle, boiler, and steam-turbine calculations. For users not satisfied with the numerical consistency, the equations are still recommended for generating good starting points for an iterative process. The supplementary backward equations and the region-boundary equations presented will significantly reduce the computing time for calculating the properties of water and steam [11]. All new backward equations and their use are described comprehensively in [12].Copyright

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.