Radiative-convective equilibrium calculations for a two-layer Mars atmosphere
Radiative-convective equilibrium calculations for two-layer Martian atmosphere
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Radiative-convective equilibrium calculations for two-layer Martian atmosphere
Several sets of ionization equilibrium calculations exist for use in interpreting X-ray and EUV spectra of astrophysical plasmas. In particular, the calculations of Jordan (1969, 1970), Jacobs et al. (1977, 1978) and Summers (1974) are well known. The temperatures of maximum fractional abundance calculated by Summers for the more highly ionized and heavier elements such as iron are about a factor of two higher than the temperatures calculated by Jordan and Jacobs et al. By the use of recently obtained X-ray spectra of solar flares, it is shown that the temperatures calculated by Summers (1974) for iron are incorrect. The temperatures calculated by Jordan or Jacobs et al. should be used until further improvements become available.
Comparison of chemical equilibrium formulations and thermodynamic derivative computations for gases
A vectorized code, EQUIL, was developed for calculating the equilibrium chemistry of a reacting gas mixture on the Control Data STAR-100 computer. The code provides species mole fractions, mass fractions, and thermodynamic and transport properties of the mixture for given temperature, pressure, and elemental mass fractions. The code is set up for the electrons H, He, C, O, N system of elements. In all, 24 chemical species are included.
Non-Maxwellian electron velocity distribution functions, previously computed for Dupree's model of the solar transition region are used to calculate ionization rates for ions of carbon, nitrogen, and oxygen. Ionization equilibrium populations for these ions are then computed and compared with similar calculations assuming Maxwellian distribution functions for the electrons. The results show that the ion populations change (compared to the values computed with a Maxwellian) in some cases by several orders of magnitude depending on the ion and its temperature of formation.
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.
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.
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The properties of the flat spin mode of a general aviation configuration have been studied through analysis of rotary balance data, numerical simulation, and analytical study of the equilibrium state. The equilibrium state is predicted well from rotary balance data. The variations of yawing moment and pitching moment as functions of sideslip have been shown to be of great importance in obtaining accurate modeling. These dependencies are not presently available with sufficient accuracy from previous tests or theories. The stability of the flat spin mode has been examined extensively using numerical linearization, classical perturbation methods, and reduced order modeling. The stability exhibited by the time histories and the eigenvalue analyses is shown to be strongly dependent on certain static cross derivatives and more so on the dynamic derivatives. Explicit stability criteria are obtained from the reduced order models.
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The vibrational and rotational excitation of the CO molecule in cometary comae were investigated using a model which includes IR vibrational pumping by the solar flux, vibrational and rotational radiative decay, and collisional coupling among rotational states. Steady state was not assumed in solving the rate equations. The evolution of a shell of CO gas was monitored as it expanded from the nucleus into the outer coma. Collisional effects were treated using a kinetic temperature profile derived from theoretical work on the coma energy balance. The kinetic temperature was assumed to be extremely cold in the inner coma; this has significant consequences for the CO excitation. If optical depth effects are ignored, only low J transitions will be significantly excited in comets observed at high spatial resolution. Ground-based observations of CO co-vibrational and rotational transitions will be extremely difficult due to lack of sensitivity and/or terrestrial absorption. However, CO should be detectable from a large comet with favorable observing geometry if the CO is a parent molecule present at the 10% level (or greater) relative to H2O. Observations using cooled, spaceborne instruments should be capable of detecting CO emission from even moderately bright comets.
Plasma equilibrium calculations and thermophysical properties of Jupiter
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.
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.
This paper treats the accurate and efficient calculation of thermodynamic properties of arbitrary gas mixtures for equilibrium flow computations. New improvements in the Stupochenko-Jaffe model for the calculation of thermodynamic properties of diatomic molecules are presented. A unified formulation of equilibrium calculations for gas mixtures in terms of irreversible entropy is given. Using a highly accurate thermo-chemical data base, a new, efficient and vectorizable search algorithm is used to construct piecewise interpolation procedures with generate accurate thermodynamic variable and their derivatives required by modern computational algorithms. Results are presented for equilibrium air, and compared with those given by the Srinivasan program.
Computer programs for calculating equilibrium states in reflected shock plasmas
Boltzmann distribution mechanics for digital calculations on equilibrium thermodynamic properties of air
In the foreseeable future, an expedition may be undertaken to explore the planet Mars. Some of the power source options being considered for such a mission are photovoltaics, regenerative fuel cells and nuclear reactors. In addition to electrical power requirements, environmental conditions en route to Mars, in the planetary orbit and on the Martian surface must be simulated and studied in order to anticipate and solve potential problems. Space power systems components such as photovoltaic arrays, radiators, and solar concentrators may be vulnerable to degradation in the Martian environment. Natural characteristics of Mars which may pose a threat to surface power systems include high velocity winds, dust, ultraviolet radiation, large daily variation in temperature, reaction to components of the soil, atmosphere and atmospheric condensates as well as synergistic combinations. Most of the current knowledge of the characteristics of the Martian atmosphere and soil composition was obtained from the Viking 1 and 2 missions in 1976. A theoretical study is presented which was used to assess the effects of the Martian atmospheric conditions on the power systems components. A computer program written at NASA-Lewis for combustion research that uses a free energy minimization technique was used to calculate chemical equilibrium for assigned thermodynamic states of temperature and pressure. The power system component materials selected for this study include: silicon dioxide, silicon, carbon, copper, and titanium. Combinations of environments and materials considered include: (1) Mars atmosphere with power surface material, (2) Mars atmosphere and dust component with power surface material, and (3) Mars atmosphere and hydrogen peroxide or superoxide or superoxide with power system material. The chemical equilibrium calculations were performed at a composition ratio (oxidant to reactant) of 100. The temperature for the silicon dioxide material and silicon, which simulate photovoltaic cells, were 300 and 400 K; for carbon, copper and titanium, which simulate radiator surfaces, 300, 500, and 1000 K. All of the systems were evaluated at pressures of 700, 800, and 900 Pa, which stimulate the Martian atmosphere.