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At least 325 records · Page 18
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Bond Dissociation Energies in Heavy Element Chalcogen and Halogen Small Molecules

Thermodynamic properties including bond dissociation energies, heats of formation, and gas phase acidities for the hydrides and dimers of chalcogens and halogens: H 2 Y, HX, Y 2 and X 2 for Y = Se, Te, At and X = Br, I, and At have been predicted using the Feller-Peterson-Dixon composite correlated molecular orbital theory approach. A full 4-component CCSD(T) approach was used to calculate the spin-orbit effects on thermodynamic properties, except for Se 2 where the AoC-DHF value was used due to strong multireference effects in Se 2 for the SO calculations. The calculated results show that the At 2 bond dissociation energy is quite small, 19.5 kcal/mol, with much of the low bond energy due to spin orbit effects. H 2 Po is not predicted to be stable to dehydrogenation to Po + H 2 in terms of the free energy at 298 K. In the gas phase, HAt is predicted to be a stronger acid than H 2 SO 4 . Here, the current results provide insights into potential difficulties in the actual experimental observation of such species for heavy elements.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Development and Validation of Physics-Based Sub-Models of High-Pressure Supercritical Fuel Injection at Diesel Conditions Insert

The project sought to develop and validate accurate, physics-based, numerical submodels and implement them in computational fluid dynamics (CFD) software codes to enable accurate predictions of diesel sprays at pressures higher than the current systems. The combined experimental-computational effort has four main objectives: (1) acquire spatially and temporally resolved scalar measurements of fuel-oxidizer mixing in the near field of the fuel jet, (2) develop software modules to calculate thermo-physical properties of diesel surrogates and their mixtures with oxidizer of interest in real-gas operating regime, (3) integrate the real-fluid model into a commercial and an open-source CFD code to simulate fuel-air mixing in high-pressure diesel sprays, and (4) assess the robustness, accuracy, and uncertainty of the integrated CFD solvers in computing diesel sprays. Project accomplishments are consistent with the original goals of the project. Although we acquired spatially and temporally resolved scalar measurements, they were limited to refractive index difference and not to thermodynamic properties such as temperature and equivalence ratio. However, we successfully developed the theoretical background needed to acquire such measurements at diesel conditions and demonstrated the capability of the RSD for scalar measurements in a canonical turbulent jet flow replicating features of the diesel jet. Additional work will be needed to implement these procedures at high-pressure, high-temperature engine-like conditions of the CPFR. Mainly, we did not anticipate the need to find the liquid boundary and its statistical features or the state relationships between refractive index and thermodynamic properties, assuming the widely known Dale-Gladstone equation would suffice. Still, efforts devoted to these tasks were essential to fulfil the goals of the project and serves as the foundation on which many of the conclusions and key contributions of this project are based. Further assessment and application of the developed CFD codes is recommended to fully realize the benefits of this research.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2022

Analysis of Intermediates and Products from the Dehydrogenation of Mg(BH 4 ) 2

The thermodynamic properties of key compounds, Mg(B 3 H 8 ) 2 , MgB 2 H 6 , MgB 10 H 10 , Mg(B 11 H 14 ) 2 , Mg 3 (B 3 H 6 ) 2 , and MgB 12 H 12 , proposed to be formed in the release of hydrogen from magnesium borohydride Mg(BH 4 ) 2 and uptake of hydrogen by MgB 2 , have been investigated using solid–state density functional theory (DFT) calculations. Further, more accurate treatment of cell–size effects to the entropies were also investigated, in order to improve the accuracy of the thermodynamic properties of complex borohydrides. We find that the zero–point energy corrections can lower the electronic energies of reaction by 20–30 kJ/(mol H 2 ) for these intermediates, while adding the thermal and entropy contributions results in the total decrease up to ~50 kJ/(mol H 2 ). Although our treatment lowers the calculated formation energy of Mg(B 3 H 8 ) 2 , it is still too high to explain the experimental observation of B 3 H 8 – . We discuss possible reasons for this disparity and propose that the formation of B 3 H 8 – and H – in a disordered amorphous phase has a large energy difference compared to the phase–separated Mg(B 3 H 8 ) 2 and MgH 2 considered in calculations. Comparison of the experimental and NMR chemical shifts calculated within a DFT approach for known species Mg(BH 4 ) 2 , Mg(B 3 H 8 ) 2 , Mg(B 11 H 14 ) 2 , MgB 10 H 10 and MgB 12 H 12 provides validation for predicting the chemical shifts of the other compounds which are yet to be confirmed experimentally. These include MgB 2 H 6 and the proposed tri–anion species Mg 3 (B 3 H 6 ) 2 that both have favorable thermodynamics for reversible hydrogen storage in Mg(BH 4 ) 2 without the formation of MgH 2 as a co–product which could phase–separate and inhibit rehydrogenation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Overcoming significant challenges in extracting off-stoichiometric thermodynamics using the compound energy formalism through complementary use of experimental and first principles data: A case study of Ba 1-x Sr x FeO 3-δ

The compound energy formalism (CEF) is a powerful framework to describe the thermodynamics of metal oxides as a function of off-stoichiometry, temperature, and composition. The thermodynamic properties are crucial materials design attributes in metal oxide-based oxygen-exchange chemical processes. Despite the richness of information an accurate CEF model provides, a method to determine a unique and accurate fit for oxygen exchange materials remains elusive. This contribution details a method for fitting the CEF model that overcomes the current fitting challenges through three innovations: 1) the combination of density functional theory calculations with experimental data decorrelates excess terms and delineates the enthalpic/entropic contributions to the Gibbs free energy; 2) a systematic determination of the important CEF model terms, removing thermodynamic predetermining human intervention; 3) a self-consistent solution of the starting oxygen offstoichiometry (δ 0 ) of thermogravimetric measurements. Thus, our method enables the reliable extraction of off-stoichiometric metal oxide thermodynamic properties and facilitates rapid materials compositional screening, and reliable process design of systems dependent on off-stoichiometric redox-active metal oxides. We apply this method to a Ba x Sr 1-x FeO 3-δ test case. We find by systematically examining the performance of the CEF model fit with and without each innovation that all three innovations are necessary for an accurate fit. We determined that reduction enthalpy is higher and more sensitive to off-stoichiometry when the Sr fraction is large (139.5 and 185.3 kJ/mol O 2 for SrFeO 3 at δ = 0 and δ = 0.5, respectively vs. nearly constant 83 kJ/mol O 2 for BaFeO 3 ). However, the reduction entropy is mostly insensitive to Sr fraction, but highly dependent on δ suggesting larger contributions in the non-configurational entropy parameters.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1973

Ablation of ATJ Graphite at High Temperatures

Results of an extensive experimental program on the ablation of ATJ graphite in air at surface pressures of 0.3 to 4.4 atm and surface temperatures of 2570 to 4030 K are presented. The measured mass-loss rates are correlated with surface temperature, pressure, and effective nose radius. The results are compared with several equilibrium thermochemical ablation theories which differ basically in the chemical species that are considered and in the thermodynamic properties assigned to these species. All the theories predict about the same mass-loss rate in the diffusion-controlled oxidation regime and are in good agreement with the experimental results. At higher temperatures, however, the experimental and theoretical results do not agree. At temperatures above 3700 K, the experimental mass-loss rate becomes independent of pressure and an exponential function of temperature. A comparison of the high-temperature results with the theories indicates that all the theories, except the one based on the thermodynamic properties from the JANAF tables, are invalid because they overpredict the mass-loss rate. On the other hand, the theory based on the JANAF properties underpredicts the measured mass-loss rate by a factor of three at 4000 K. At least a portion of this difference between experiment and theory is attributed to particulate mass loss which is visually observed.

Thermochemical ablation↗
DOE OSTI2020

Electronic Structures and Magnetism of Zr-, Th-, and U-based Metal-Organic Frameworks (MOFs) by Density Functional Theory

Metal-organic frameworks (MOFs) have recently gained wide interest as candidate materials for nuclear waste immobilization. While the fundamental thermodynamic properties, such as the substitution energies determine the favorability of radionuclide sequestration by utilization of a MOF matrix, the studies of MOF electronic structure reveal the role of d-, and/or f-electrons on changes in physical properties of actinide-containing materials. We use density functional theory (DFT) calculations to investigate the electronic structures of Zr-, Th-, and U-MOFs, including their electronic band structures and, where appropriate, their magnetic properties. We employ various DFT methods including DFT+U, collinear spin-polarization, spin-orbit coupling, and different flavors of exchange-correlation functionals to assess the robustness to the specific exchange-correlation functional. Unlike the Zr-, and Th-MOFs, the U-MOF is found to be sensitive to electron localization and spin; hence we explore the magnetic structure of the U-MOF in further detail.

Metal-Organic Framework, MOF, Actinides, DFT↗
NASA NTRS1973

An equation of state for oxygen and nitrogen

Recent measurements of the thermodynamic properties of oxygen and nitrogen have been used to develop a single equation of state for both fluids; with appropriate coefficients, the equation describes the pressure-density-temperature surface for each fluid within the estimated experimental uncertainty of the data. The formulation uses least squares curve fitting of the equation of state to the available experimental data (including pressure-density-temperature data, saturation data, and measured isochoric heat capacities). New vapor pressure equations and equations for the ideal gas heat capacities of oxygen and nitrogen are included for use in calculation of derived thermodynamic properties.

Jacobsen, R. T.↗
NASA NTRS2003

Modeling, Simulation and Control of a Propellant Mixer

This paper addresses some modeling and control issues for a mixing chamber used in rocket engine testing at NASA Stennis Space Center. The mixer must combine high pressure liquid hydrogen (LH2) and gaseous hydrogen (GH2) to produce and output flow that meets certain thermodynamic properties before it is fed into a test article. More precisely, this paper considers that the quantities to be tracked and/or regulated are mixer internal pressure, exit mass flow, and exit temperature. The available control inputs are given by three value positions, namely those of the GH2, LH2 and exit valves. The mixer is modelled by a system of two nonlinear ordinary differential equations having density and internal energy as states. The model must be simple enough to lend itself to subsequent feedback controller design, yet its accuracy must be tested against real data. For this reason, the model includes function calls to thermodynamic property data. Some structural properties of the resulting model that pertain to controller design, such as controllability and uniqueness of the equilibrium point are shown to hold. Validation of the model against real data is also provided. As a first control approach, a small-signal (linear) model is developed based on the nonlinear model and simulated as well. Pulse disturbances are introduced to the valve positions and the quality of the linear model is ascertained by comparing its behavior against the nonlinear model simulations. Valve control strategies that simulate an operator-in-the-loop scenario are then explored demonstrating the need for automatic feedback control. Classical optimal single-output and multi-output Proportional/Integral controllers are designed based on the linear model and applied to the nonlinear model with excellent results to track simultaneous, constant setpoint changes in desired exit flow, exit temperature, and mixer pressure, as well as to reject unmeasurable but bounded additive step perturbations in the valve positions. A feedback linearization controller is designed and used to achieve tracking and regulation of the outputs over an extended range of the variables of interest.

Richter, Hanz↗
NASA NTRS2003

Modeling and Validation of a Propellant Mixer for Controller Design

A mixing chamber used in rocket engine testing at the NASA Stennis Space Center is modelled by a system of two nonlinear ordinary differential equations. The mixer is used to condition the thermodynamic properties of cryogenic liquid propellant by controlled injection of the same substance in the gaseous phase. The three inputs of the mixer are the positions of the valves regulating the liquid and gas flows at the inlets, and the position of the exit valve regulating the flow of conditioned propellant. Mixer operation during a test requires the regulation of its internal pressure, exit mass flow, and exit temperature. A mathematical model is developed to facilitate subsequent controller designs. The model must be simple enough to lend itself to subsequent feedback controller design, yet its accuracy must be tested against real data. For this reason, the model includes function calls to thermodynamic property data. Some structural properties of the resulting model that pertain to controller design, such as uniqueness of the equilibrium point, feedback linearizability and local stability are shown to hold under conditions having direct physical interpretation. The existence of fixed valve positions that attain a desired operating condition is also shown. Validation of the model against real data is likewise provided.

Richter, Hanz↗
DOE OSTI2023

Automated reaction kinetics and network exploration (Arkane): A statistical mechanics, thermodynamics, transition state theory, and master equation software

The open-source statistical mechanics software described here, Arkane–Automated Reaction Kinetics and Network Exploration–facilitates computations of thermodynamic properties of chemical species, high-pressure limit reaction rate coefficients, and pressure-dependent rate coefficient over multi-well molecular potential energy surfaces (PES) including the effects of collisional energy transfer on phenomenological kinetics. Arkane can use estimates to fill in information for molecules or reactions where quantum chemistry information is missing. The software solves the internal energy master equation for complex unimolecular reaction systems. Inputs to the software include converged electronic structure computations performed by the user using a variety of supported software packages (Gaussian, Molpro, Orca, TeraChem, Q-Chem, Psi4). The software outputs high-pressure limit rate coefficients and pressure-dependent phenomenological rate coefficients, as well as computed thermodynamic properties (enthalpy, entropy, and constant pressure heat capacity) with added energy corrections. Some of the key features of Arkane include treatment of 1D, 2D or ND hindered internal rotation modes, treatment of free internal rotation modes, quantum tunneling effect consideration, transition state theory (TST) and Rice-Ramsperger-Kassel-Marcus (RRKM) rate coefficient computations, master equation solution with four implemented methods, inverse-Laplace transform of high-pressure limit rate coefficients into the energy domain, energy corrections based on bond-additivity or isodesmic reactions, automated and efficient PES exploration, and PES sensitivity analysis. The present work describes the design of Arkane, how it should be used, and refers to the theory that it employs. Arkane is distributed via the RMG-Py software suite (https://github.com/ReactionMechanismGenerator/RMG-Py).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2004

Chemical Reaction and Flow Modeling in Fullerene and Nanotube Production

The development of processes to produce fullerenes and carbon nanotubes has largely been empirical. Fullerenes were first discovered in the soot produced by laser ablation of graphite [1]and then in the soot of electric arc evaporated carbon. Techniques and conditions for producing larger and larger quantities of fullerenes depended mainly on trial and error empirical variations of these processes, with attempts to scale them up by using larger electrodes and targets and higher power. Various concepts of how fullerenes and carbon nanotubes were formed were put forth, but very little was done based on chemical kinetics of the reactions. This was mainly due to the complex mixture of species and complex nature of conditions in the reactors. Temperatures in the reactors varied from several thousand degrees Kelvin down to near room temperature. There are hundreds of species possible, ranging from atomic carbon to large clusters of carbonaceous soot, and metallic catalyst atoms to metal clusters, to complexes of metals and carbon. Most of the chemical kinetics of the reactions and the thermodynamic properties of clusters and complexes have only been approximated. In addition, flow conditions in the reactors are transient or unsteady, and three dimensional, with steep spatial gradients of temperature and species concentrations. All these factors make computational simulations of reactors very complex and challenging. This article addresses the development of the chemical reaction involved in fullerene production and extends this to production of carbon nanotubes by the laser ablation/oven process and by the electric arc evaporation process. In addition, the high-pressure carbon monoxide (HiPco) process is discussed. The article is in several parts. The first one addresses the thermochemical aspects of modeling; and considers the development of chemical rate equations, estimates of reaction rates, and thermodynamic properties where they are available. The second part addresses modeling of the arc process for fullerene and carbon nanotube production using O-D, 1-D and 2-D fluid flow models. The third part addresses simulations of the pulsed laser ablation process using time-dependent techniques in 2-D, and a steady state 2-D simulation of a continuous laser ablation process. The fourth part addresses steady state modeling in O-D and 2-D of the HiPco process. In each of the simulations, there is a variety of simplifications that are made that enable one to concentrate on one aspect or another of the process. There are simplifications that can be made to the chemical reaction models , e.g. reduction in number of species by lumping some of them together in a representative species. Other simulations are carried out by eliminating the chemistry altogether in order to concentrate on the fluid dynamics. When solving problems with a large number of species in more than one spatial dimension, it is almost imperative that the problem be decoupled by solving for the fluid dynamics to find the fluid motion and temperature history of "particles" of fluid moving through a reactor. Then one can solve the chemical rate equations with complex chemistry following the temperature and pressure history. One difficulty is that often mixing with an ambient gas is involved. Therefore, one needs to take dilution and mixing into account. This changes the ratio of carbon species to background gas. Commercially available codes may have no provision for including dilution as part of the input. One must the write special solvers for including dilution in decoupled problems. The article addresses both ful1erene production and single-walled carbon nanotube (SWNT) production. There are at least two schemes or concepts of SWNT growth. This article will only address growth in the gas phase by carbon and catalyst cluster growth and SW T formation by the addition of carbon. There are other models that conceive of SWNT growth as a phase separation process from clusters me up carbon and metal catalyst, with the carbon precipitating from the cluster as it cools. We will not deal with that concept in this article. Further research is needed to determine the rates at which these composite clusters form, evaporate, and segregate.

Scott, Carl D.↗
DOE OSTI2023

High-Temperature Thermodynamics of Uranium from Ab Initio Modeling

We present high-temperature thermodynamic properties for uranium in its γ phase (γ-U) from first-principles, relativistic, and anharmonic theory. The results are compared to CALPHAD modeling. The ab initio electronic structure is obtained from density-functional theory (DFT) that includes spin–orbit coupling and an added self-consistent orbital-polarization (OP) mechanism for more accurate treatment of magnetism. The first-principles method is coupled to a lattice dynamics scheme that is used to model anharmonic lattice vibrations, namely, Self-Consistent Ab Initio Lattice Dynamics (SCAILD). The methodology can be summarized in the acronym DFT + OP + SCAILD. Upon thermal expansion, γ-U develops non-negligible magnetic moments that are included for the first time in thermodynamic theory. The all-electron DFT approach is shown to model γ-U better than the commonly used pseudopotential method. In addition to CALPHAD, DFT + OP + SCAILD thermodynamic properties are compared with other ab initio and semiempirical modeling and experiments. Our first-principles approach produces Gibbs free energy that is essentially identical to CALPHAD. The DFT + OP + SCAILD heat capacity is close to CALPHAD and most experimental data and is predicted to have a significant thermal dependence due to the electronic contribution.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS2009

Frozen Chemistry Effects on Nozzle Performance Simulations

Simulations of exhaust nozzle flows are typically conducted assuming the gas is calorically perfect, and typically modeled as air. However the gas inside a real nozzle is generally composed of combustion products whose thermodynamic properties may differ. In this study, the effect of gas model assumption on exhaust nozzle simulations is examined. The three methods considered model the nozzle exhaust gas as calorically perfect air, a calorically perfect exhaust gas mixture, and a frozen exhaust gas mixture. In the latter case the individual non-reacting species are tracked and modeled as a gas which is only thermally perfect. Performance parameters such as mass flow rate, gross thrust, and thrust coefficient are compared as are mean flow and turbulence profiles in the jet plume region. Nozzles which operate at low temperatures or have low subsonic exit Mach numbers experience relatively minor temperature variations inside the nozzle, and may be modeled as a calorically perfect gas. In those which operate at the opposite extreme conditions, variations in the thermodynamic properties can lead to different expansion behavior within the nozzle. Modeling these cases as a perfect exhaust gas flow rather than air captures much of the flow features of the frozen chemistry simulations. Use of the exhaust gas reduces the nozzle mass flow rate, but has little effect on the gross thrust. When reporting nozzle thrust coefficient results, however, it is important to use the appropriate gas model assumptions to compute the ideal exit velocity. Otherwise the values obtained may be an overly optimistic estimate of nozzle performance.

Yoder, Dennis A.↗
DOE OSTI2021

Dynamics of disordered mechanical systems with large connectivity, free probability theory, and quasi-Hermitian random matrices

Disordered mechanical systems with high connectivity represent a limit opposite to the more familiar case of disordered crystals. Individual ions in a crystal are subjected essentially to nearest-neighbor interactions. In contrast, the systems studied in this paper have all their degrees of freedom coupled to each other. Thus, the problem of linearized small oscillations of such systems involves two full positive-definite and non-commuting matrices, as opposed to the sparse matrices associated with disordered crystals. Consequently, the familiar methods for determining the averaged vibrational spectra of disordered crystals, introduced many years ago by Dyson and Schmidt, are inapplicable for highly connected disordered systems. In this paper we apply random matrix theory (RMT) to calculate the averaged vibrational spectra of such systems, in the limit of infinitely large system size. At the heart of our analysis lies a calculation of the average spectrum of the product of two positive definite random matrices by means of free probability theory techniques. We also show that this problem is intimately related with quasi-hermitian random matrix theory (QHRMT), which means that the ‘hamiltonian’ matrix is hermitian with respect to a non-trivial metric. This extends ordinary hermitian matrices, for which the metric is simply the unit matrix. The analytical results we obtain for the spectrum agree well with our numerical results. The latter also exhibit oscillations at the high-frequency band edge, which fit well the Airy kernel pattern. We also compute inverse participation ratios of the corresponding amplitude eigenvectors and demonstrate that they are all extended, in contrast with conventional disordered crystals. Finally, we compute the thermodynamic properties of the system from its spectrum of vibrations. In addition to matrix model analysis, we also study the vibrational spectra of various multi-segmented disordered pendula, as concrete realizations of highly connected mechanical systems. A universal feature of the density of vibration modes, common to both pendula and the matrix model, is that it tends to a non-zero constant at vanishing frequency.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Synthesis, characterization, and thermodynamic study of selected K-based zeolites

Potassium-rich zeolites often occur in cementitious systems, as K{sup +} is widespread in various cementitious materials, such as Portland, blended and alkali-activated cements. The knowledge of their stability and of thermodynamic models for solid solutions with Na{sup +} and Ca{sup 2+} are critical to understand long-term development and durability in such cements. Completing previous studies on Na- and Ca-based zeolites, the current work aims to determine the thermodynamic data of 14 types of K-based zeolites, which could possibly form in cementitious systems. The zeolites were synthesized hydrothermally, exchanged with K{sup +}, and characterized thoroughly with respect to framework structures, elemental compositions, water contents, and bond variations. Their thermodynamic properties were derived from the experimental solubility data, which allowed establishing predominance diagrams in the K{sub 2}O-SiO{sub 2}-Al{sub 2}O{sub 3}-H{sub 2}O system. The K-based zeolites typically showed the lowest solubility between 0 and 100 °C, with the notable exception of Ca-gismondine and two Na-based zeolites: natrolite and Na-mordenite.

36 MATERIALS SCIENCE↗
NASA NTRS1993

Coefficients for calculating thermodynamic and transport properties of individual species

Libraries of thermodynamic data and transport properties are given for individual species in the form of least-squares coefficients. Values of C(sup 0)(sub p)(T), H(sup 0)(T), and S(sup 0)(T) are available for 1130 solid, liquid, and gaseous species. Viscosity and thermal conductivity data are given for 155 gases. The original C(sup 0)(sub p)(T) values were fit to a fourth-order polynomial with integration constants for H(sup 0)(T) and S(sup 0)(T). For each species the integration constant for H(sup 0)(T) includes the heat of formation. Transport properties have a different functional form. The temperature range for most of the data is 300 to 5000 K, although some of the newer thermodynamic data have a range of 200 to 6000 K. Because the species are mainly possible products of reaction, the data are useful for chemical equilibrium and kinetics computer codes. Much of the data has been distributed for several years with the NASA Lewis equilibrium program CET89. The thermodynamic properties of the reference elements were updated along with about 175 species that involve the elements carbon, hydrogen, oxygen, and nitrogen. These sets of data will be distributed with the NASA Lewis personal computer program for calculating chemical equilibria, CETPC.

Mcbride, Bonnie J.↗
DOE OSTI2019

H2OI95: A Stand-Alone Fortran Code for Evaluating the IAPWS-95 Equation-of-State Model for Water

H2OI95 is a stand-alone Fortran code for evaluating the IAPWS-95 equation-of-state model (Wagner and Pruss, 2002) for the thermodynamic properties of water. It further evaluates the corresponding thermochemical properties of water consistent with the CODATA recommendations (Cox et al., 1989). The IAPWS-95 model is based on a model equation for the dimensionless Helmholtz energy for which the primary variables are the inverse reduced temperature and reduced density. Here is the absolute temperature (K), is density (kg/m3), and the subscript refers to the critical point of water (647.096 K and 22.064 MPa pressure in this model, for which is 322 kg/m3). The code solves four basic types of problems, distinguished by the specified inputs: 1, Temperature (K) and density (kg/m3) or reduced density 2. Temperature (K) and pressure (MPa). 3. Temperature (K) on the saturation (liquid-vapor equilibrium) curve 4. Pressure (MPa) on the saturation curve Each type of problem is run using a corresponding input (text) file. All but the first type of problem require iteration. For example, to solve for desired temperature and pressure, the reduced density must be adjusted to give the desired pressure. Iteration is accomplished using the Newton-Raphson method, though the secant method is also used in solving the fourth type of problem. H2OI95 has been used to conduct numerical studies of convergence and the problem of multiple numerical solutions, only some of which correspond to valid results. Obtaining valid results depends mainly on appropriate choice of starting values. The default values in H2OI95 appear to consistently lead to generally desired results. With modification (not addressed here), H2OI95 can be used to support SUPCRT92 (Johnson et al., 1992) and similar codes that compute chemical thermodynamic properties of species and reactions over a wide range of temperature and pressure (273.16-1273K and 0-1000 MPa).

Wolery, ThomasJ.↗
DOE OSTI2020

H2OI95: A Stand-Alone Fortran Code for Evaluating the IAPWS-95 Equation-of-State Model for Water (Rev. 1)

H2OI95 is a stand-alone Fortran code for evaluating the IAPWS-95 equation-of-state model for the thermodynamic properties of water. It also evaluates the corresponding thermochemical properties of water consistent with the CODATA recommendations. The IAPWS-95 model is based on a model equation for the dimensionless Helmholtz energy for which the primary variables are the inverse reduced temperature (τ = T cr /T ) and reduced density (δ = ρ/ρ cr ). Here T is the absolute temperature (K), ρ is density (kg/m³), and the subscript “ cr ” refers to the critical point of water (647.096 K and 22.064 MPa pressure in this model, for which ρ cr is 322 kg/m³). The code solves four basic types of problems, distinguished by the specified inputs: 1. Temperature (K) and density (ρ kg/m³) or reduced density (δ) 2. Temperature (K) and pressure (MPa). 3. Temperature (K) on the saturation (liquid-vapor equilibrium) curve 4. Pressure (MPa) on the saturation curve. Each type of problem is run using a corresponding input (text) file. All but the first type of problem require iteration. For example, to solve for desired temperature and pressure, the reduced density must be adjusted to give the desired pressure. Iteration is accomplished using the Newton-Raphson method, though the secant method is also used in solving the fourth type of problem. For the last three types of problems, H2OI95 has been used to conduct numerical studies of convergence and the problem of multiple numerical solutions, some of which are not physically valid. Obtaining valid results depends mainly on appropriate choice of starting values for the density. The default values used in H2OI95 appear to consistently lead to generally desired results. With modification (not addressed here), H2OI95 can be used to support SUPCRT92 and similar codes that compute chemical thermodynamic properties of species and reactions over a wide range of temperature and pressure (273.16-1273K and 0-1000 MPa). Version 1.1 of this software calculates an extended set of water properties, including some derivable solely from IAPWS-95, such as the isobaric thermal expansivity and the isothermal compressibility, and still other properties based on supplementary models sanctioned by IAPWS, including the dynamic viscosity, thermal conductivity, surface tension, and static dielectric constant, and various other properties (notably Debye-Hückel parameters) derivable from the dielectric constant and its partial derivatives with respect to temperature and pressure. A coding error in Version 1.0 was identified while testing the implementation of the viscosity model. This error is described in Appendix C. It mainly affects calculation of “higher order” properties such as compressibility and heat capacity near the critical point.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗