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Results for “Equilibrium calculations”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1976

Statistical equilibrium calculations for silicon in early-type model stellar atmospheres

Line profiles of 36 multiplets of silicon (Si) II, III, and IV were computed for a grid of model atmospheres covering the range from 15,000 to 35,000 K in effective temperature and 2.5 to 4.5 in log (gravity). The computations involved simultaneous solution of the steady-state statistical equilibrium equations for the populations and of the equation of radiative transfer in the lines. The variables were linearized, and successive corrections were computed until a minimal accuracy of 1/1000 in the line intensities was reached. The common assumption of local thermodynamic equilibrium (LTE) was dropped. The model atmospheres used also were computed by non-LTE methods. Some effects that were incorporated into the calculations were the depression of the continuum by free electrons, hydrogen and ionized helium line blocking, and auto-ionization and dielectronic recombination, which later were found to be insignificant. Use of radiation damping and detailed electron (quadratic Stark) damping constants had small but significant effects on the strong resonance lines of Si III and IV. For weak and intermediate-strength lines, large differences with respect to LTE computations, the results of which are also presented, were found in line shapes and strengths. For the strong lines the differences are generally small, except for the models at the hot, low-gravity extreme of our range. These computations should be useful in the interpretation of the spectra of stars in the spectral range B0-B5, luminosity classes III, IV, and V.

Kamp, L. W.↗
DOE OSTI2025

Standardising the “Gregory method” for calculating equilibrium climate sensitivity

The equilibrium climate sensitivity (ECS) – the equilibrium global mean temperature response to a doubling of atmospheric CO 2 – is a high-profile metric for quantifying the Earth system's response to human-induced climate change. A widely applied approach to estimating the ECS is the “Gregory method” (Gregory et al., 2004), which uses an ordinary least squares (OLS) regression between the net radiative flux, N, and surface air temperature anomalies, ΔT, from a 150 year experiment in which atmospheric CO 2 concentrations are quadrupled. The ECS is determined by extrapolating the linear fit to N=0, i.e. the ΔT-intercept, indicating the point at which the system is back in equilibrium. This method has been used to compare ECS estimates across the CMIP5 and CMIP6 ensembles and will likely be a key diagnostic for CMIP7. Despite its widespread application, there is little consistency or transparency between studies in how the climate model data is processed prior to the regression, leading to potential discrepancies in ECS estimates. We identify 32 alternative data processing pathways, varying by differences in global mean weighting, net radiative flux variable, anomaly calculation method, and linear regression fit. Using 44 CMIP6 models, we systematically assess the impact of these choices on ECS estimates and calculate uncertainty ranges using two bootstrap approaches. While the inter-model ECS range is insensitive to the data processing pathway, individual outlier models exhibit notable differences. Approximating a model's native grid cell area (if irregular) with cosine of the latitude can decrease the ECS by 11 %, the choice of N-variable can change the ECS by 6 %, and some anomaly calculation methods can introduce spurious temporal correlations in the processed data. Beyond data processing choices, we also evaluate an alternative linear regression method – total least squares (TLS) – which has a more statistically robust basis than OLS. However, for consistency with previous literature, and given TLS may reduce the ECS compared to OLS (by up to 24 %), thereby making a known bias in the Gregory method worse, we do not feel there is sufficient clarity to recommend a transition to TLS in all cases. To improve reproducibility and comparability in future studies, we recommend a standardised Gregory method: weighting the global mean by cell area, using the top of the atmosphere (as opposed to the top of model) N-variable, and calculating anomalies by first applying a rolling average to the preindustrial control timeseries then subtracting from the raw CO 2 quadrupling experiment. This approach accounts for model drift while reducing noise in the data to best meet the pre-conditions of the linear regression. While CMIP6 results of the multi-model mean ECS appear insensitive to these processing choices, similar assumptions may not hold for CMIP7, underscoring the need for standardised data preparation in future climate sensitivity assessments.

Geosciences↗
NASA NTRS1960

An Analytical Investigation of Three General Methods of Calculating Chemical-Equilibrium Compositions

The Brinkley, Huff, and White methods for chemical-equilibrium calculations were modified and extended in order to permit an analytical comparison. The extended forms of these methods permit condensed species as reaction products, include temperature as a variable in the iteration, and permit arbitrary estimates for the variables. It is analytically shown that the three extended methods can be placed in a form that is independent of components. In this form the Brinkley iteration is identical computationally to the White method, while the modified Huff method differs only'slightly from these two. The convergence rates of the modified Brinkley and White methods are identical; and, further, all three methods are guaranteed to converge and will ultimately converge quadratically. It is concluded that no one of the three methods offers any significant computational advantages over the other two.

Zeleznik, Frank J.↗
NASA NTRS1974

Wall pressure spectra calculations for equilibrium boundary layers

Calculation of the flow direction wave-number spectrum of pressure fluctuations on the wall under a turbulent boundary layer. Particular attention is paid to finding the spectral density of the wall pressure fluctuations as a function of the streamwise wave number. For this purpose a five-dimensional integration is employed in which the equilibrium boundary layers are assumed to have velocity profiles given by the law of the wall plus Cole's wake function.

Panton, R. L.↗
NASA NTRS1974

Radiative-dynamical equilibrium states for Jupiter

In order to obtain accurate estimates of the radiative heating that drives motions in Jupiter's atmosphere, previous radiative equilibrium calculations are improved by including the NH3 opacities and updated results for the pressure-induced opacities. These additions increase the radiative lapse rate near the top of the statically unstable region and lead to a fairly constant radiative lapse rate below the tropopause. The radiative-convective equilibrium temperature structure consistent with these changes is calculated, but it differs only slightly from earlier calculations. The radiative equilibrium calculations are used to calculate whether equilibrium states can occur on Jupiter which are similar to the baroclinic instability regimes on the earth and Mars. The results show that Jupiter's dynamical regime cannot be of this kind, except possibly at very high latitudes, and that its regime must be a basically less stable one than this kind.

Trafton, L. M.↗
NASA NTRS1966

Computer program determines chemical composition of physical system at equilibrium

FORTRAN 4 digital computer program calculates equilibrium composition of complex, multiphase chemical systems. This is a free energy minimization method with solution of the problem reduced to mathematical operations, without concern for the chemistry involved. Also certain thermodynamic properties are determined as byproducts of the main calculations.

Kwong, S. S.↗
NASA NTRS1978

Fractional crystallization of iron meteorites, an experimental study

Measurements of the distribution coefficients of various elements (Ni, Co, P, Pt, Ir, Ge, Cr, and Au) between solid and liquid phases were made for FeNi alloys. A high thermal gradient crystal growing furnace was employed in order to promote plane front solidification, rapid mixing in the liquid and a minimum of diffusion in the solid. Eight measurements of the nickel distribution coefficient gave an average value of 0.91 plus or minus 0.03 and this value was independent of the Ni concentration in the range 5.5 to 8.75 wt. % Ni. Equilibrium distribution coefficients were also calculated by correcting for the diffusion boundary layer present in the liquid. These values are within 20% of the measured distribution coefficient values. Except for Co and Ni, all the measured distribution coefficient values are closer to 1.0 than those calculated by Scott (1972) for the IIIAB irons. Using the experimental values and the calculated equilibrium values for ternary additions to FeNi melts, it appears that fractional crystallization processes will not explain the observed chemical variations in the major iron meteorite groups. Alternative explanations are suggested which also recognize the fact that cooling rates vary widely in several chemical groups.

Goldstein, J. I.↗
NASA NTRS1976

Calculations of the equilibrium photoelectron flux in the thermosphere

Theoretical calculations of the equilibrium photoelectron fluxes in the upper atmosphere are reported. The calculations employ an accurate description of the photoelectron production processes and take explicit account of the discrete nature of the electron energy losses. The neutral atmospheric and ionospheric parameters were obtained from simultaneous measurements by the various instruments of the Atmosphere Explorer-C mission and the solar EUV fluxes measured on the same satellite were used. The photoelectron fluxes are calculated using a recent compilation of photon and electron cross section data. The results are in good agreement with the measured photoelectron fluxes over several orders of magnitude, though there are detailed differences at specific energies that have yet to be resolved.

Victor, G. A.↗
NASA NTRS1971

Solutions for Reacting and Nonreacting Viscous Shock Layers with Multicomponent Diffusion and Mass Injection

Numerical solutions are presented for the viscous shocklayer equations where the chemistry is treated as being either frozen, equilibrium, or nonequilibrium. Also the effects of the diffusion model, surface catalyticity, and mass injection on surface transport and flow parameters are considered. The equilibrium calculations for air species using multicomponent: diffusion provide solutions previously unavailable. The viscous shock-layer equations are solved by using an implicit finite-difference scheme. The flow is treated as a mixture of inert and thermally perfect species. Also the flow is assumed to be in vibrational equilibrium. All calculations are for a 45 deg hyperboloid. The flight conditions are those for various altitudes and velocities in the earth's atmosphere. Data are presented showing the effects of the chemical models; diffusion models; surface catalyticity; and mass injection of air, water, and ablation products on heat transfer; skin friction; shock stand-off distance; wall pressure distribution; and tangential velocity, temperature, and species profiles.

Moss, J. N.↗
NASA NTRS1972

Analytical study of striated nozzle flow with small radius of curvature ratio throats

An analytical method was developed which is capable of estimating the chamber and throat conditions in a nozzle with a low radius of curvature throat. The method was programmed using standard FORTRAN 4 language and includes chemical equilibrium calculation subprograms (modified NASA Lewis program CEC71) as an integral part. The method determines detailed and gross rocket characteristics in the presence of striated flows and gives detailed results for the motor chamber and throat plane with as many as 20 discrete zones. The method employs a simultaneous solution of the mass, momentum, and energy equations and allows propellant types, 0/F ratios, propellant distribution, nozzle geometry, and injection schemes to be varied so to predict spatial velocity, density, pressure, and other thermodynamic variable distributions in the chamber as well as the throat. Results for small radius of curvature have shown good comparison to experimental results. Both gaseous and liquid injection may be considered with frozen or equilibrium flow calculations.

Norton, D. J.↗
NASA NTRS1970

Thermodynamics of the internal combustion engine

The ubiquitous automobile has played both the role of hero and villain during the course of its history. At the present time it is being cast as the villain with increasing frequency because it has been indicted as a major source of air pollution. It is just this characterization that is responsible for our renewed interest in the automobile. When we speak of the automobile as a source of air pollution, we really mean the heart of the automobile, the internal combustion engine. The prototype of the modern internal combustion engine was first successfully operated by Nicholas August Otto in 1876. In spite of its long history, the internal combustion engine is still poorly understood in terms of the details of the physical processes that take place during its operations. The internal combustion engine operates on what is known as the Otto cycle, and Otto cycle calculations have been with us for many years. The emphasis in earlier calculations was usually on the performance rather than on the pollution aspects. Performance characteristics can often be estimated reasonably accurately even with a considerable degree of simplification. We are interested in the pollution aspects of the internal combustion engine, and therefore the calculations must be performed with more care. Our extensive experience with equilibrium calculations places us in a position to carry out such careful calculations. We have just recently begun such an analysis, and its objective is the prediction of exhaust gas properties. I will describe our progress by first reviewing the Otto cycle, and then I will illustrate the effect of various assumptions on the calculated results.

Frank J. Zeleznik↗