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

2007 ◽  
Vol 129 (4) ◽  
pp. 1125-1137 ◽  
Author(s):  
H.-J. Kretzschmar ◽  
J. R. Cooper ◽  
J. S. Gallagher ◽  
A. H. Harvey ◽  
K. Knobloch ◽  
...  
Keyword(s):  
Thermodynamic Properties ◽  
Steam Turbine ◽  
International Association ◽  
Computing Time ◽  
Phase Region ◽  
Specific Enthalpy ◽  
Two Phase ◽  
Steam Power ◽  
Power Cycles ◽  
Backward Equation

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 Tsat(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 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

2006 ◽  
Vol 129 (1) ◽  
pp. 294-303 ◽  
Author(s):  
H.-J. Kretzschmar ◽  
J. R. Cooper ◽  
A. Dittmann ◽  
D. G. Friend ◽  
J. S. Gallagher ◽  
...  
Keyword(s):  
Thermodynamic Properties ◽  
Specific Volume ◽  
International Association ◽  
Computing Time ◽  
Saturation Pressure ◽  
Two Dimensional ◽  
Steam Power ◽  
Power Cycles ◽  
Computational Speed ◽  
Boundary Equations

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, p3sat(h), and of entropy, p3sat(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 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

2009 ◽  
Vol 131 (4) ◽  
Author(s):  
H.-J. Kretzschmar ◽  
A. H. Harvey ◽  
K. Knobloch ◽  
R. Mareš ◽  
K. Miyagawa ◽  
...  
Keyword(s):  
Thermodynamic Properties ◽  
Critical Point ◽  
International Association ◽  
Computing Time ◽  
Computer Time ◽  
Singular Behavior ◽  
Steam Power ◽  
Power Cycles ◽  
Independent Variables ◽  
Iterative Procedures

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.

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

2004 ◽  
Vol 128 (3) ◽  
pp. 702-713 ◽  
Author(s):  
H.-J. Kretzschmar ◽  
J. R. Cooper ◽  
A. Dittmann ◽  
D. G. Friend ◽  
J. S. Gallagher ◽  
...  
Keyword(s):  
Thermodynamic Properties ◽  
International Association ◽  
Computing Time ◽  
Liquid Region ◽  
Two Dimensional ◽  
Power Cycles ◽  
Enthalpy And Entropy ◽  
Basic Equations ◽  
Time Required ◽  
Fundamental Equations

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.

scholarly journals CO2 power cycle chemistry in the CV Řež experimental loop

2021 ◽  
Vol 61 (4) ◽  
pp. 504-510
Author(s):  
Jan Berka ◽  
Jakub Vojtěch Ballek ◽  
Ladislav Velebil ◽  
Eliška Purkarová ◽  
Alice Vagenknechtová ◽  
...  
Keyword(s):  
Carbon Dioxide ◽  
Steam Turbine ◽  
Control Systems ◽  
Nuclear Power ◽  
Nuclear Reactors ◽  
Gas Purification ◽  
Supercritical State ◽  
Steam Power ◽  
Power Cycles ◽  
Power Cycle

Power cycles using carbon dioxide in a supercritical state (sc-CO2) can be used in both the nuclear and non-nuclear power industry. These systems are characterized by their advantages over steam power cycles, e. g., the sc-CO2 turbine is more compact than the steam turbine with a similar performance. The parameters and lifespan of the system are influenced by the purity of the CO2 in the circuit, especially the admixtures, such as O2, H2O, etc., cause the enhanced structural materials to degrade. Therefore, gas purification and purity control systems for the sc-CO2 power cycles should be proposed and developed. The inspiration for the proposal of these systems could stem from the gas, especially the CO2-cooled nuclear reactors operation. The first information concerning the CO2 and sc-CO2 power cycle chemistry was gathered in the first period of the project and it is summarized in the paper.

scholarly journals COMPARATIVE ANALYSIS OF THE IAPWS-IF97 FORMULATION PERFORMANCE FOR THERMODYNAMIC PROPERTIES OF WATER ON A RANKINE CYCLE

2004 ◽  
Vol 3 (1) ◽  
pp. 52 ◽  
Author(s):  
J. G. Fonseca Jr. ◽  
P. S. Schneider
Keyword(s):  
Comparative Analysis ◽  
Thermodynamic Properties ◽  
General Public ◽  
Constant Pressure ◽  
International Association ◽  
Rankine Cycle ◽  
Specific Enthalpy ◽  
Specific Entropy ◽  
Compressed Liquid ◽  
Computational Implementation

The present paper presents the computational implementation of the industrial formulation of the thermodynamic properties of water at liquid and steam phases, proposed by the International Association for the Properties of Water and Steam, known as IAPWS-IF97. The validity field extends over to temperatures T between 0ºC and 800°C, for pressures p up to 100 MPa. Temperature T, specific volume v, specific enthalpy h, specific entropy s, specific heat at constant pressure cp and constant volume cv, besides saturation pressure ps, are calculated having a pair of known input values (p,T), (p,h) or (p,s). A comparative analysis between the IAPWS-IF97 routines and others, based on foregoing propositions, from an application on Rankine cycle, is made. IAPWS-IF97 has proved to be more precise, mainly because it accounts for the region of compressed liquid, besides requiring less processing time. The development is carried out as FORTRAN90 subroutines and functions and is available for public use according to a General Public License.

scholarly journals COMPARATIVE ANALYSIS OF THE IAPWS-IF97 FORMULATION PERFORMANCE FOR THERMODYNAMIC PROPERTIES OF WATER ON A RANKINE CYCLE

2004 ◽  
Vol 3 (1) ◽  
Author(s):  
J. G. Fonseca Jr. ◽  
P. S. Schneider
Keyword(s):  
Comparative Analysis ◽  
Thermodynamic Properties ◽  
Constant Pressure ◽  
International Association ◽  
Saturation Pressure ◽  
Rankine Cycle ◽  
Specific Enthalpy ◽  
Specific Entropy ◽  
Compressed Liquid ◽  
Computational Implementation

The present paper presents the computational implementation of the industrial formulation of the thermodynamic properties of water at liquid and steam phases, proposed by the International Association for the Properties of Water and Steam, known as IAPWS-IF97. The validity field extends over to temperatures T between 0ºC and 800°C, for pressures p up to 100 MPa. Temperature T, specific volume v, specific enthalpy h, specific entropy s, specific heat at constant pressure cp and constant volume cv, besides saturation pressure ps, are calculated having a pair of known input values (p,T), (p,h) or (p,s). A comparative analysis between the IAPWS-IF97 routines and others, based on foregoing propositions, from an application on Rankine cycle, is made. IAPWS-IF97 has proved to be more precise, mainly because it accounts for the region of compressed liquid, besides requiring less processing time. The development is carried out as FORTRAN90 subroutines and functions and is available for public use according to a General Public License.

THE EFFECT OF TEMPERATURE GLIDE OF R407C REFRIGERANT ON THE POWER OF EVAPORATOR IN AIR REFRIGERATORS / WPŁYW POŚLIZGU TEMPERATURY CZYNNIKA CHŁODNICZEGO R407C NA MOC PAROWNIKA CHŁODZIARKI POWIETRZA

2013 ◽  
Vol 58 (4) ◽  
pp. 1333-1346
Author(s):  
Bernard Nowak ◽  
Piotr Życzkowski
Keyword(s):  
Initial Temperature ◽  
Saturated Vapor ◽  
Thermal Power ◽  
Phase Region ◽  
Effect Of Temperature ◽  
Specific Enthalpy ◽  
Evaporation Process ◽  
Vapor Quality ◽  
Two Phase ◽  
Air Compression

Abstract The article discusses the effect of the phenomenon of temperature glide of zeotropic refrigerants on thermal power of an evaporator in an air compression refrigerator. Zeotropic mixtures are subject to phase transitions, the process of which significantly differs from that of homogeneous refrigerants. In contrast to homogeneous refrigerants, where boiling and condensing processes take place at a constant temperature, for the zeotropic mixtures it is essential to know the vapor quality to unambiguously determine the temperature at which the evaporation process is initiated. The R407C refrigerant serves as an example to describe the method of determining the initial temperature of the evaporation process taking into account the effect of temperature glide. The developed formula (7) has been based on a proven linear course of isobars in the two-phase region (Fig. 5) and thus determining a polynomial describing their angle of inclination (8). In addition, temperature calculation formulas (9) and specific enthalpy (10) of dry saturated vapor of the R407C refrigerant have been presented as well. This approach allows to determine the temperature of the R407C refrigerant at the inlet to the evaporator without the required knowledge of its vapor quality. The previously used simplified methods for determining the temperature of a refrigerant at the inlet to the evaporator result in considerable deviations in calculated power of the evaporator compared with its actual value. The presented calculation example involving mine air compression refrigerator of TS-450P type shows that relative deviations of the evaporator thermal power may even exceed 20%. This example compares two simplified methods for determining zeotropic evaporating temperature of a refrigerant used in comparative calculations of refrigerants with the method presented in this article.

A Laser-Based Technique for Particle Sizing to Study Two-Phase Expansion in Turbines

1991 ◽  
Vol 113 (3) ◽  
pp. 211-218 ◽  
Author(s):  
D. Yogi Goswami ◽  
S. Hingorani ◽  
Greg Mines
Keyword(s):  
Scattering Theory ◽  
Rayleigh Scattering ◽  
Scattered Light ◽  
Incident Radiation ◽  
Phase Region ◽  
Particle Sizing ◽  
Scattered Intensity ◽  
Small Particles ◽  
Two Phase ◽  
Power Cycles

Efficiency of binary power cycles can be improved by expanding the hydrocarbon working fluids through two-phase region in a turbine and exiting at saturated or superheated condition. This improvement can be achieved if there is no condensation during the expansion or if there is condensation, the droplet size is extremely small. In order to verify this, a particle sizing technique for extremely small particles in flow is needed. In this study, a laser-based technique is developed by which it is possible to detect particles as small at ten angstroms in size. The basis of the technique is that particles of size less than one third of the wavelength of the incident radiation will scatter according to Rayleigh scattering theory. According to this theory, the intensity of the scattered light will be the same in the forward as well as in the backward directions. Therefore, measurement of the scattered intensity at two or three different angles will confirm the presence of Rayleigh scattering. The size of the particles can, then, be calculated from the measured scattered intensity according to the Rayleigh scattering equation.

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