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H.-J. Kretzschmar

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Proceedings Papers

*Proc. ASME*. IMECE2007, Volume 6: Energy Systems: Analysis, Thermodynamics and Sustainability, 481-482, November 11–15, 2007

Paper No: IMECE2007-41987

Abstract

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 p sat (T) and for saturation temperature T sat (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 T sat (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].

Proceedings Papers

*Proc. ASME*. IMECE2007, Volume 6: Energy Systems: Analysis, Thermodynamics and Sustainability, 483, November 11–15, 2007

Paper No: IMECE2007-42033

Abstract

The program libraries developed for calculating the thermophysical properties of working fluids can be used by engineers who routinely calculate heat cycles, steam or gas turbines, boilers, heat pumps, or other thermal or refrigeration processes. Thermodynamic properties, transport properties, derivatives, and inverse functions can be calculated. Today gas turbines are being developed for higher and higher temperatures and pressures. However, the calculation of the combustion gas as an ideal gas mixture will be inaccurate at high pressures. For this reason, a property library has been developed for humid combustion gases calculated as an ideal mixture of real fluids. The advanced adiabatic compressed air energy storage technology requires very accurate algorithms for the thermodynamic and transport properties of humid air at low temperatures and high pressures. At these parameters, humid air cannot be calculated as an ideal gas mixture. For this reason, a property library with real gas algorithms has been developed. The following properly libraries will be presented: LibHuGas for humid combustion gas mixtures at high pressures calculated as an ideal mixture of real fluids. The library also includes mixtures of steam and carbon dioxide. The dissociation at high temperatures, the poynting effect, and the condensation of water are considered as well. LibHuAir for humid air at high pressures calculated as an ideal mixture of the real fluids dry air, steam and water or ice. The dissociation at high temperatures and the poynting effect are taken into consideration. LibAmWa for mixtures of ammonia and water in the Kalina cycle and in absorption refrigeration processes. LibWaLi for mixtures of water and lithium bromide in absorption refrigeration processes. LibldGas for combustion gas mixtures calculated as an ideal mixture of ideal gases using the VDI-Guideline 4670. LibIdAir for humid air calculated as an ideal mixture of the ideal gases dry air and steam using the VDI-Guideline 4670. LibIdGasMix for 25 ideal gases and their mixtures. LibIF97 for water and steam calculated from the Industrial Formulation IAPWS-IF97 and all new backward equations of the four supplementary releases adopted by IAPWS between 2001 and 2005. LibCO2 for carbon dioxide. LibNH3 for ammonia. LibR134a for the refrigerant R134a. LibPropane for propane. LibButane_Iso and LibButane_n for Iso- and n-butane. LibHe for helium. LibH2 for hydrogen. The libraries contain the most accurate algorithms for thermodynamic and transport properties. The following software solutions will also be presented: - DLLs for Windows ® applications. - Add-In FluidEXL for Excel ® . - Add-On FluidLAB for MATLAB ® . - Add-On FluidMAT for Mathcad ® . - Properly libraries for HP, TI, and Casio pocket calculators. Student versions of all programs are available.

Journal Articles

H.-J. Kretzschmar, A. H. Harvey, K. Knobloch, R. Mareš, K. Miyagawa, N. Okita, R. Span, I. Stöcker, W. Wagner, I. Weber

Article Type: Research Papers

*. July 2009, 131(4): 043101.*

*J. Eng. Gas Turbines Power*Published Online: April 13, 2009

Abstract

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.

Journal Articles

H.-J. Kretzschmar, J. R. Cooper, J. S. Gallagher, A. H. Harvey, K. Knobloch, R. Mareš, K. Miyagawa, N. Okita, R. Span, I. Stöcker, W. Wagner, I. Weber

Article Type: Technical Papers

*. October 2007, 129(4): 1125–1137.*

*J. Eng. Gas Turbines Power*Published Online: January 16, 2007

Abstract

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.

Journal Articles

H.-J. Kretzschmar, J. R. Cooper, A. Dittmann, D. G. Friend, J. S. Gallagher, A. H. Harvey, K. Knobloch, R. Mareš, K. Miyagawa, N. Okita, I. Stöcker, W. Wagner, I. Weber

Article Type: Technical Papers

*. January 2007, 129(1): 294–303.*

*J. Eng. Gas Turbines Power*Published Online: January 10, 2006

Abstract

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

Journal Articles

H.-J. Kretzschmar, J. R. Cooper, A. Dittmann, D. G. Friend, J. S. Gallagher, K. Knobloch, R. Mareš, K. Miyagawa, I. Stöcker, J. Trübenbach, W. Wagner, Th. Willkommen

Article Type: Technical Papers

*. July 2006, 128(3): 702–713.*

*J. Eng. Gas Turbines Power*Published Online: June 22, 2004

Abstract

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.

Journal Articles

W. Wagner, J. R. Cooper, A. Dittmann, J. Kijima, H.-J. Kretzschmar, A. Kruse, R. Maresˇ, K. Oguchi, H. Sato, I. Sto¨cker, O. Sˇifner, Y. Takaishi, I. Tanishita, J. Tru¨benbach, Th. Willkommen

Article Type: Technical Papers

*. January 2000, 122(1): 150–184.*

*J. Eng. Gas Turbines Power*Published Online: January 1, 2000

Abstract

In 1997, the International Association for the Properties of Water and Steam (IAPWS) adopted a new formulation for the thermodynamic properties of water and steam for industrial use. This new formulation, called IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam (IAPWS-IF97), replaces the previous industrial formulation, IFC-67, that had formed the basis for power-plant calculations and other applications in energy engineering since the late 1960’s. IAPWS-IF97 improves significantly both the accuracy and the speed of the calculation of the thermodynamic properties compared with IFC-67. The differences between IAPWS-IF97 and IFC-67 will require many users, particularly boiler and turbine manufacturers, to modify design and application codes. This paper summarizes the need and the requirements for such a new industrial formulation and gives the entire numerical information about the individual equations of IAPWS-IF97. Moreover, the scientific basis for the development of the equations is summarized and the achieved quality of IAPWS-IF97 is presented regarding the three criterions accuracy, consistency along region boundaries, and computation speed. For comparison, corresponding results for the previous standard IFC-67 are also presented. [S0742-4795(00)02201-8]