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Computer program for calculating and fitting thermodynamic functions

A computer program is described which (1) calculates thermodynamic functions (heat capacity, enthalpy, entropy, and free energy) for several optional forms of the partition function, (2) fits these functions to empirical equations by means of a least-squares fit, and (3) calculates, as a function of temperture, heats of formation and equilibrium constants. The program provides several methods for calculating ideal gas properties. For monatomic gases, three methods are given which differ in the technique used for truncating the partition function. For diatomic and polyatomic molecules, five methods are given which differ in the corrections to the rigid-rotator harmonic-oscillator approximation. A method for estimating thermodynamic functions for some species is also given.

Mcbride, Bonnie J.↗

A Multiphase Equation of State for Hydrazine and Monomethylhydrazine

The objective of this work was to obtain a validated equation of state for hydrazine and monomethylhydrazine (MMH) and use this equation to calculate thermodynamic properties. The approach was based on using both reliable critical property values and a value of the acentric factor in the Soave Redlich Kwong and the Peng Robinson model equations of state. These equations were validated by comparing calculated molar volumes for phase equilibrium with published experimental values and comparing calculated vapor pressures with published experimental values over the temperature range appropriate for the corresponding state equations. The equation of state giving the best results was used to calculate enthalpy and entropy departure functions and fugacity values. Additional thermodynamic property calculations were performed to produce partial Mollier diagrams and thermodynamic properties containing internal energy, enthalpy, and entropy values for hydrazine and MMH. The analyses of systems in which either adiabatic or near-adiabatic compression of liquid or vapor hydrazine or low velocity detonations occur require a validated equation of state for representing occurring molar volumes and for energy calculations. Other calculations for thermodynamic properties of hydrazine are available, but the values are for a strict ideal gas state. This work characterized destructive events using hydrazine by calculating for isentropic compression temperatures. The final temperatures were calculated and compared using the ideal and real gas fluid equations of state.

Barragan, Michelle↗

Insights on the corrosion thermodynamics of chromium in molten LiF-NaF-KF eutectic salts

The thermodynamic stability of chromium in the Cr 0 , Cr 2+ , and Cr 3+ oxidation states considering various F - ion coordination compounds was investigated in molten LiF–NaF-KF (FLiNaK) eutectic salt. Potential fluoride ion activity (F - and CrF 3 - ) diagrams were constructed to predict the most stable Cr oxidation states as a function of anion activity, solvation state of chromium ions and potential at 600 °C. The Gibbs free energies of these compounds were estimated by utilizing a combined cyclic voltammetry – Nernst theory analysis approach in FLiNaK salt. To verify the constructed diagrams, X-ray diffraction was utilized after exposure of Cr at various applied potentials to determine whether compounds detected in solidified FLiNaK salts agreed with thermodynamic calculations. This work aims to identify key thermodynamic factors that are significant to chromium corrosion for molten salt nuclear reactor applications. The F - stability region spans the entire region where spontaneous corrosion of Cr occurs. Cr may be oxidized to Cr 2+ and Cr 3+ in the presence HF (due to moisture as an impurity) spontaneously except some conditions of p 1/2 H 2 /a HF etc. This situation is not changed qualitatively for various states of solvation between oxidized Cr solute in F - solvent and this aspect is substantially similar for the two cases (pair 1: Cr 0 /CrF 3 - / CrF 6 3- ; pair 2: Cr 0 /CrF 4 2- /CrF 5 2- ) considered in this work.

36 MATERIALS SCIENCE↗

Thermodynamic and transport properties of fluids

Computer program subroutine FLUID calculates thermodynamic and transport properties of pure fluids in liquid, gas, or two-phase (liquid/gas) conditions. Program determines thermodynamic state from assigned values for temperature and density, pressure and density, temperature and pressure, pressure and entropy, or pressure and enthalpy.

Fessler, T. E.↗

Air-stable, earth-abundant molten chlorides and corrosion-resistant containment for chemically-robust, high-temperature thermal energy storage for concentrated solar power

A dramatic reduction in man-made CO 2 emissions could be achieved if the cost of electricity generated from concentrated solar power (CSP) plants could become competitive with fossil-fuel-derived electricity. The solar heat-to-electricity conversion efficiency of CSP plants may be significantly increased (and the associated electricity cost decreased) by operating CSP turbines with inlet temperatures ≥750 °C instead of ≤550 °C, and by using thermal energy storage (TES) at ≥750 °C to allow for rapidly dispatchable and/or continuous electricity production. Unfortunately, earth-abundant MgCl 2 -KCl-based liquids currently being considered as low-cost media for large-scale, high-temperature TES are susceptible to oxidation in ambient air, with associated undesired changes in liquid composition and enhanced corrosion of metal alloys in pipes and tanks containing such liquids. In this paper, alternative high-temperature, earth-abundant molten chlorides that are resistant to oxidation in ambient air are identified via thermodynamic calculations. Here, the oxidation resistance, and corrosion-resistant containment, of such molten chlorides at 750 °C are then demonstrated. Such an air-tolerant strategy, involving chemically-robust, low-cost TES media paired with effective containment materials, provides a critical advance towards the higher-temperature operation of, and lower-cost electricity generation from, CSP plants.

14 SOLAR ENERGY↗

High-temperature lean Cu alloys with Cr-to-Nb atomic ratio of 2

Two Cu-Cr-Nb alloys, denoted as alloy 1 (comprising Cu-0.89 at% Cr-0.42 at% Nb) and alloy 2 (comprising Cu-1.84 at% Cr-0.99 at% Nb), were produced through a series of manufacturing processes including vacuum induction melting, melt spinning, consolidation, brazing, and baking, with both alloys aimed at achieving a nominal Cr-to-Nb atomic ratio of 2. Microstructural characterization using transmission electron microscopy and X-ray diffraction identified the cubic C15 Laves-phase Cr 2 Nb as the dominant precipitate in both alloys, cross-validated by thermodynamic calculations and atomistic simulation-based density functional theory (DFT). Besides cubic C15 Cr 2 Nb, hexagonal C14-phase Cr 2 Nb and α-BiF3 cubic structured Cr 3 Nb were also observed in the alloys, including a coherent interface formed between the Cr 3 Nb precipitate and the Cu matrix. The hardness of the alloys increases, and the electrical conductivity decreases with increasing alloying addition content; two practical equations described the trends. Further DFT simulations revealed that the electrical conductivity (conductance) of the Cu/Cr 2 Nb interface is an order of magnitude higher than the intrinsic Cu high-angle grain boundaries.

36 MATERIALS SCIENCE↗

Working Fluid Characterization and Performance Assessment of Subcritical Organic Rankine Cycles Based on the Lee–Kesler Approach for Energy Recovery

Here, a generalized model using the Lee–Kesler approach based on the corresponding states principle is developed to assess the performance of subcritical Organic Rankine Cycles operating with different working fluids. Each fluid is characterized by five parameters: the acentric factor, critical temperature, critical pressure, molar mass, and the ideal-gas ratio of specific heats at the critical temperature. The model was developed using the compressibility factor modified version of the Benedict–Webb–Rubin equation proposed by Lee and Kesler and the enthalpy and entropy functions to calculate thermodynamic state properties. The model was validated by comparing the results calculated with the model and working fluid thermodynamic properties obtained with the CoolProp database. This comparison was conducted for 91 working fluids, obtaining a relative error below 5% for 88 out of the 91 fluids (∼97%). A generalized parametric study was conducted to determine the influence of the pinch point and each fluid parameter on the performance of Organic Rankine Cycle (ORC) systems. It was found that efficiency increases with critical temperature, ideal-gas ratio of specific heats at the critical temperature, and acentric factor, reaching up to 13%. The developed model enables the evaluation of ORC system performance for existing working fluids. It also allows the formulation and evaluation of new fluids to enhance the performance of the ORC while retrieving energy from any kind of source; and likewise, the methodology can be applied to other power generation cycles.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Understanding the deformation behavior of the γ rich transformative Fe 38.5 Mn 20 Co 20 Cr 15 Si 5 Cu 1.5 complex concentrated alloy using in situ synchrotron diffraction

In situ tensile testing coupled with synchrotron x-ray diffraction was used to study the deformation behavior of metastability-engineered Fe 38.5 Mn 20 Co 20 Cr 15 Si 5 Cu 1.5 complex concentrated alloy. Monitoring the evolution of phase fraction and strain hardening response allowed the determination of true critical stress for the onset of the transformation-induced plasticity (TRIP) to be ∼375 MPa, preceded by slip starting at ∼255 MPa. In situ EBSD was used to validate the critical stress for transformation at the microstructure level and observe slip traces to confirm prior slip activity before the transformation. Further, a modeling framework based on stacking fault energy (SFE) was developed to predict the critical stress for transformation. Modeling suggested the SFE of the alloy to fall nearly 15 mJ/m 2 , which agrees well with SFE values calculated using synchrotron peak shifting (12 mJ/m 2 ) and thermodynamic calculation (11 mJ/m 2 ). As a result of γ-fcc to ε-hcp phase transformation, new {0002} ε planes emerged parallel to unaligned {111} γ planes with the tensile loading following S-N orientation relationship. Such selective emergence of new diffraction rings corresponding to ε phase is understood based on the reorientation of γ crystals with reference to tensile axis. In conclusion, this approach can be extended to effectively design alloys based on critical stress required for activating different deformation mechanisms to further push the limits of the strength-ductility envelope.

Complex concentrated alloy↗

FLUID: A numerical interpolation procedure for obtaining thermodynamic and transport properties of fluids

A computer program subroutine, FLUID, was developed to calculate thermodynamic and transport properties of pure fluid substances. It provides for determining the thermodynamic state from assigned values for temperature-density, pressure-density, temperature-pressure, pressure-entropy, or pressure-enthalpy. Liquid or two-phase (liquid-gas) conditions are considered as well as the gas phase. A van der Waals model is used to obtain approximate state values; these values are then corrected for real gas effects by model-correction factors obtained from tables based on experimental data. Saturation conditions, specific heat, entropy, and enthalpy data are included in the tables for each gas. Since these tables are external to the FLUID subroutine itself, FLUID can implement any gas for which a set of tables has been generated. (A setup phase is used to establish pointers dynamically to the tables for a specific gas.) Data-table preparation is described. FLUID is available in both SFTRAN and FORTRAN

Fessler, T. E.↗

Thermodynamics of hydrogen-helium mixtures at high pressure and finite temperature

A technique is reviewed for calculating thermodynamic quantities for mixtures of light elements at high pressure, in the metallic state. Ensemble averages are calculated with Monte Carlo techniques and periodic boundary conditions. Interparticle potentials are assumed to be coulombic, screened by the electrons in dielectric function theory. This method is quantitatively accurate for alloys at pressures above about 10 Mbar. An alloy of equal parts hydrogen and helium by mass appears to remain liquid and mixed for temperatures above about 3000 K, at pressures of about 15 Mbar. The additive volume law is satisfied to within about 10%, but the Gruneisen equation of state gives poor results. A calculation at 1300 K shows evidence of a hydrogen-helium phase separation.

Hubbard, W. B.↗

Correlations for determining thermodynamic properties of hydrogen-helium gas mixtures at temperatures from 7,000 to 35,000 K

Simple relations for determining the enthalpy and temperature of hydrogen-helium gas mixtures were developed for hydrogen volumetric compositions from 1.0 to 0.7. These relations are expressed as a function of pressure and density and are valid for a range of temperatures from 7,000 to 35,000 K and pressures from 0.10 to 3.14 MPa. The proportionality constant and exponents in the correlation equations were determined for each gas composition by applying a linear least squares curve fit to a large number of thermodynamic calculations obtained from a detailed computer code. Although these simple relations yielded thermodynamic properties suitable for many engineering applications, their accuracy was improved significantly by evaluating the proportionality constants at postshock conditions and correlating these values as a function of the gas composition and the product of freestream velocity and shock angle. The resulting equations for the proportionality constants in terms of velocity and gas composition and the corresponding simple realtions for enthalpy and temperature were incorporated into a flow field computational scheme. Comparison was good between the thermodynamic properties determined from these relations and those obtained by using a detailed computer code to determine the properties. Thus, an appreciable savings in computer time was realized with no significant loss in accuracy.

Zoby, E. V.↗