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Results for “equilibrium modeling”

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NASA NTRSDate not supplied

Study of Graphite Ablation at Arc-Jet Conditions using Finite-Rate and Equilibrium Chemistry Models

Moving at hypersonic speeds through the atmosphere generates immense amount of heat that triggers thermo-chemical non-equilibrium effects in the flow approaching the vehicle and leads to surface chemical reactions that cause ablation and consume the material mass. This complex behavior and interaction of the aerothermal environment with a graphite surface is com- putationally modeled in the present work using a fully-coupled simulation between flow solver CHAMPS NBS-Cart and material response solver KATS-MR. In this study, we account for the thermo-chemical non-equilibrium effects occurring in the flow and use an 11-species air-carbon re- action model to simulate the ablation of the material. The reactions at the surface such oxidation, nitridation and recombination are modeled with a newly developed air-carbon reaction model. The coupled simulation is applied to study two experimental cases performed at IHF arc-jet facility at NASA Ames research center. The obtained results are compared against the measured data of surface recession, as well as surface and in-depth temperatures. Additionally, uncoupled sim- ulations, performed with equilibrium chemistry at the wall, point out the substantial differences between the coupled and uncoupled solutions, leading to higher deviation of the predicted temper- atures. Overall, we show excellent agreement between the coupled simulation predictions and the experimental data in all measured quantities.

EDL↗

NASA NTRS1991

Discharge rate of cryogens in microgravity - What ground based experimentation cannot resolve

The discharge of cryogenic vapor and liquid from tanks to a vacuum is examined and the effects of the mass quality, length/diameter ratio, supply tank transient and gravitational environment are discussed. Existing model results and normal gravity experiments are presented which indicate that the homogeneous equilibrium model provides an accurate description of two-phase critical flow for a number of conditions likely to be encountered in practical microgravity systems. Nonequilibrium effects are shown to produce flow rates greater than homogeneous equilibrium model predictions for long tubes with low inlet pressure and short tubes with high inlet pressure.

Purwin, T. P.↗

NASA NTRS1977

Prediction of hydrodynamics and chemistry of confined turbulent methane-air flames with attention to formation of oxides of nitrogen

A formulation of the governing partial differential equations for fluid flow and reacting chemical species in a tubular combustor is presented. A numerical procedure for the solution of the governing differential equations is described, and models for chemical equilibrium and chemical kinetics calculations are presented. The chemical equilibrium model is used to characterize the hydrocarbon reactions. The chemical kinetics model is used to predict the concentrations of the oxides of nitrogen. The combustor consists of a cylindrical duct of varying cross sections with concentric streams of gaseous fuel and air entering the duct at one end. Four sample cases with specified inlet and boundary conditions are considered, and the results are discussed

Elghobashi, S.↗

NASA NTRS1993

Computational analysis of Variable Thrust Engine (VTE) performance

The Variable Thrust Engine (VTE) of the Orbital Maneuvering Vehicle (OMV) uses a hypergolic propellant combination of Monomethyl Hydrazine (MMH) and Nitrogen Tetroxide (NTO) as fuel and oxidizer, respectively. The performance of the VTE depends on a number of complex interacting phenomena such as atomization, spray dynamics, vaporization, turbulent mixing, convective/radiative heat transfer, and hypergolic combustion. This study involved the development of a comprehensive numerical methodology to facilitate detailed analysis of the VTE. An existing Computational Fluid Dynamics (CFD) code was extensively modified to include the following models: a two-liquid, two-phase Eulerian-Lagrangian spray model; a chemical equilibrium model; and a discrete ordinate radiation heat transfer model. The modified code was used to conduct a series of simulations to assess the effects of various physical phenomena and boundary conditions on the VTE performance. The details of the models and the results of the simulations are presented.

Giridharan, M. G.↗

NASA NTRS1979

Two-phase choked flow of cryogenic fluids in converging-diverging nozzles

Data are presented for the two phase choked flow of three cryogenic fluids - nitrogen, methane, and hydrogen - in four converging-diverging nozzles. The data cover a range of inlet stagnation conditions, all single phase, from well below to well above the thermodynamic critical conditions. In almost all cases the nozzle throat conditions were two phase. The results indicate that the choked flow rates were not very sensitive to nozzle geometry. However, the axial pressure profiles, especially the throat pressure and the point of vaporization, were very sensitive to both nozzle geometry and operating conditions. A modified Henry-Fauske model correlated all the choked flow rate data to within + or - 10 percent. Neither the equilibrium model nor the Henry-Fauske model predicted throat pressures well over the whole range of data. Above the thermodynamic critical temperature the homogeneous equilibrium model was preferred for both flow rate and pressure ratio. The data of the three fluids could be normalized by the principle of corresponding states.

Simoneau, R. J.↗

NASA NTRS1974

On the distribution of He+ in the plasmasphere from observations of resonantly scattered He II 304-A radiation

The intensity of the He II 304-A radiation in the night sky was measured from a sounding rocket launched from White Sands Missile Range on June 9, 1972. The data obtained on this flight are compared with predictions of theoretical models of the He(+) altitude distribution within the plasmasphere. The observations are not consistent with an isothermal equilibrium model of the helium ion in the plasmasphere, confirming earlier results. The data are best fit by a diffussive equilibrium model of exospheric He(+) having a plasma temperature gradient of 0.5 K per km and a number density at 1600 km of 200,000 He(+) ions per cu cm. In this model the ion densities are calculated without allowance for thermal diffusion. A similar model that allows for thermal diffusion and that has a He(+) number density at 1600 km of 1500 per cu cm and a temperature gradient of 1.2 K per km yields a less satisfactory fit to the observations but is more consistent with in situ satellite observations.

Paresce, F.↗

NASA NTRS2013

Modelling of Equilibrium Between Mantle and Core: Refractory, Volatile, and Highly Siderophile Elements

Siderophile elements have been used to constrain conditions of core formation and differentiation for the Earth, Mars and other differentiated bodies [1]. Recent models for the Earth have concluded that the mantle and core did not fully equilibrate and the siderophile element contents of the mantle can only be explained under conditions where the oxygen fugacity changes from low to high during accretion and the mantle and core do not fully equilibrate [2,3]. However these conclusions go against several physical and chemical constraints. First, calculations suggest that even with the composition of accreting material changing from reduced to oxidized over time, the fO2 defined by metal-silicate equilibrium does not change substantially, only by approximately 1 logfO2 unit [4]. An increase of more than 2 logfO2 units in mantle oxidation are required in models of [2,3]. Secondly, calculations also show that metallic impacting material will become deformed and sheared during accretion to a large body, such that it becomes emulsified to a fine scale that allows equilibrium at nearly all conditions except for possibly the length scale for giant impacts [5] (contrary to conclusions of [6]). Using new data for D(Mo) metal/silicate at high pressures, together with updated partitioning expressions for many other elements, we will show that metal-silicate equilibrium across a long span of Earth s accretion history may explain the concentrations of many siderophile elements in Earth's mantle. The modeling includes refractory elements Ni, Co, Mo, and W, as well as highly siderophile elements Au, Pd and Pt, and volatile elements Cd, In, Bi, Sb, Ge and As.

Righter, K.↗

NASA NTRS1993

Ellipsoidal figures of equilibrium - Compressible models

The results of Chandrasekhar (1969) are generalized to polytropes, using a formalism based on ellipsoidal energy variational principle to construct approximate stellar equilibrium solutions and study their stability. After reviewing the energy variational method and describing the approach, several equivalent stability conditions are established and secular vs. dynamical instabilities are discussed. Then, the equilibrium structure equations are derived for isolated, rotating polytropes, and axisymmetric configurations (compressible Maclaurin spheroids) are considered. Particular attention is given to triaxial configurations, either in a state of uniform rotation (generalizing the classical Jacobi ellipsoids) or with internal fluid motions of uniform vorticity (the compressible analogues of Riemann-S ellipsoids) and to the stability of these single star configurations. The compressible generalizations of the Roche and Roche-Riemann problems for a polytrope in orbit about a point-mass companion are solved, and the generalized Darwin problem for two identical polytropes in a binary is considered.

Lai, Dong↗

NASA NTRS1993

Particle motion in x-dependent Harris-like magnetotail models

The dynamics of charged particles in x-dependent magnetotail models is examined, where x is along the sun-earth direction. An earlier paper showed that particle motion in a class of x-dependent Harris-like equilibrium models can be significantly different from the motion in x-independent magnetotail field models. In the present paper, it is shown that this Harris-like equilibrium models have 'bulb-shaped' field lines and that this property leads to the reported differences. Furthermore, it is shown that the scale length of variation of the Harris-like models in the x direction, L(x), is comparable to the typical excursion distance, Delta, of particles in the x direction and to rho(n) which is the gyroradius based on the magnetic field component B(n) normal to the plane of the current sheet. It is argued that neither bulb-shaped field lines nor scale lengths L(x) comparable to Delta or rho(n) apply to the earth's magnetotail. It is suggested that a key criterion for applicability of x-dependent models to the terrestrial magnetotail is Delta, rho(n) much less than L(x).

Burkhart, Grant R.↗

NASA NTRS1985

Consequences of hot gas in the broad line region of active galactic nuclei

Models for hot gas in the broad line region of active galactic nuclei are discussed. The results of the two phase equilibrium models for confinement of broad line clouds by Compton heated gas are used to show that high luminosity quasars are expected to show Fe XXVI L alpha line absorption which will be observed with spectrometers such as those planned for the future X-ray spectroscopy experiments. Two phase equilibrium models also predict that the gas in the broad line clouds and the confining medium may be Compton thick. It is shown that the combined effects of Comptonization and photoabsorption can suppress both the broad emission lines and X-rays in the Einstein and HEAO-1 energy bands. The observed properties of such Compton thick active galaxies are expected to be similar to those of Seyfert 2 nuclei. The implications for polarization and variability are also discussed.

Kallman, T.↗

NASA NTRS1985

Consequences of hot gas in the broad-line region of active galactic nuclei

Kallman, T.↗

NASA NTRS1993

Equilibrium Slab Models of Lyman-Alpha Clouds

We model the L(sub y(alpha)) clouds as slabs of hydrogen with an ionizing extragalactic radiation field incident from both sides. In general, the equilibrium configuration of a slab at redshift z approx. less than 5 is determined by a balance of the gas pressure, gravity (including the effects of a dark matter halo), and the pressure exerted by the inter-galactic medium, P(sub ext). These models have been used to make predictions of the number of slabs as a function of the neutral hydrogen column density, N(sub H). A break in the curve is predicted at the transition between regimes where gravity and pressure are the dominant confining forces, with a less rapid decrease at larger N(sub H). The transition from optically thin to optically thick slabs leads to a gap in the distribution, whose location is governed largely by the spectrum of ionizing radiation. There are certain parallels between lines of sight through the outer HI disk of spiral galaxy with increasing radius, and the progression from damped, to Lyman limit, to forest clouds. We discuss briefly the possibility that at least some of the observed low z forest clouds may be a separate population, associated with galaxies, as suggested by the observations of Bahcall et al. This population could dominate the forest at present if the dark matter attached to galaxies should lead to gravity confinement for this disk population, while the isolated clouds remain pressure confined. The formalism developed in this paper will allow a more detailed study. We also discuss a more general parameter study of the equilibrium configuration of slabs, including mock gravity and L(sub y(alpha)) photon trapping.

Charlton, Jane C.↗

NASA NTRS1984

Solar Inverse Theory

Helioseismological inversion, as with the inversion of any other data, is divided into three phases. The first is the solution of the so-called forward problem: namely, the calculation of the eigenfrequencies of a theoretical equilibrium state. The second is an attempt to understand the results, either empirically by determining how those frequencies vary as chosen parameters defining the equilibrium model are varied, or analytically from asymptotic expansions in limiting cases of high order or degree. The third phase is to pose and solve an inverse problem, which seeks to find a plausible equilibrium model of the Sun whose eigenfrequencies are consistent with observation. The three phases are briefly discussed in this review, and the third, which is not yet widely used in helioseismology, is illustrated with some selected inversions of artificial solar data.

Gough, D.↗

NASA NTRS1977

Combustion of hydrogen injected into a supersonic airstream (the SHIP computer program)

The mathematical and physical basis of the SHIP computer program which embodies a finite-difference, implicit numerical procedure for the computation of hydrogen injected into a supersonic airstream at an angle ranging from normal to parallel to the airstream main flow direction is described. The physical hypotheses built into the program include: a two-equation turbulence model, and a chemical equilibrium model for the hydrogen-oxygen reaction. Typical results for equilibrium combustion are presented and exhibit qualitatively plausible behavior. The computer time required for a given case is approximately 1 minute on a CDC 7600 machine. A discussion of the assumption of parabolic flow in the injection region is given which suggests that improvement in calculation in this region could be obtained by use of the partially parabolic procedure of Pratap and Spalding. It is concluded that the technique described herein provides the basis for an efficient and reliable means for predicting the effects of hydrogen injection into supersonic airstreams and of its subsequent combustion.

Markatos, N. C.↗

NASA NTRS1990

Calculation of infrared limb emission by ozone in the terrestrial middle atmosphere. I - Source functions. II - Emission calculations

The departure from LTE in the vibration-rotation bands of ozone in the middle atmosphere is analyzed using two statistical equilibrium models: the energy gap model and the simplified single model. The diurnal variations in the fundamental band source functions nu(1) and nu(3) is determined by the diurnal change in the rate of ozone photolysis by the solar radiation. Source functions are presented for the vibration-rotation bands of ozone that emit in the 9-11-micron spectral interval, over an altitude range of 1-110 km. Results are also reported of the evaluation of the radiative transfer equation incorporating these source functions and energy level populations. Using the results of the two statistical equilibrium models, calculations are carried out of the spectrally integrated limb radiance for the limb viewing geometry for daytime conditions. Results indicate that the interpretation of the measurements of spectrally integrated limb radiance from ozone will be greatly complicated by the breakdown of LTE in the vibration-rotational bands of ozone.

Mlynczak, Martin G.↗

NASA NTRS1978

Prediction of hydrodynamics and chemistry of confined turbulent methane-air frames in a two concentric tube combustor

A formulation of the governing partial differential equations for fluid flow and reacting chemical species in a two-concentric-tube combustor is presented. A numerical procedure for the solution of the governing differential equations is described and models for chemical-equilibrium and chemical-kinetics calculations are presented. The chemical-equilibrium model is used to characterize the hydrocarbon reactions. The chemical-kinetics model is used to predict the concentrations of the oxides of nitrogen. The combustor considered consists of two coaxial ducts. Concentric streams of gaseous fuel and air enter the inlet duct at one end; the flow then reverses and flows out through the outer duct. Two sample cases with specified inlet and boundary conditions are considered and the results are discussed.

Markatos, N. C.↗

NASA NTRS1980

Equilibrium geochemical modeling of a seasonal thermal energy storage aquifer field test

A geochemical mathematical modeling study designed to investigate the well plugging problems encountered at the Auburn University experimental field tests is summarized. The results, primarily of qualitative interest, include: (1) loss of injectivity was probably due to a combination of native particulate plugging and clay swelling and dispersion; (2) fluid-fluid incompatibilities, hydrothermal reactions, and oxidation reactions were of insignificant magnitude or too slow to have contributed markedly to the plugging; and (3) the potential for and contributions from temperature-induced dissolved gas solubility reductions, capillary boundary layer viscosity increases, and microstructural deformation cannot be deconvolved from the available data.

Stottlemyre, J. S.↗

NASA NTRS1988

The Milankovitch theory and climate sensitivity. I - Equilibrium climate model solutions for the present surface conditions. II - Interaction between the Northern Hemisphere ice sheets and the climate system

A seasonal climate model was developed to test the climate sensitivity and, in particular, the Milankovitch (1941) theory. Four climate model versions were implemented to investigate the range of uncertainty in the parameterizations of three basic feedback mechanisms: the ice albedo-temperature, the outgoing long-wave radiation-temperature, and the eddy transport-meridional temperature gradient. It was found that the differences between the simulation of the present climate by the four versions were generally small, especially for annually averaged results. The climate model was also used to study the effect of growing/shrinking of a continental ice sheet, bedrock sinking/uplifting, and sea level changes on the climate system, taking also into account the feedback effects on the climate of the building of the ice caps.

Neeman, Binyamin U.↗