Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “equilibrium”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
NASA NTRS1988

On the prediction of equilibrium states in homogeneous turbulence

A comparison of several commonly used turbulence models (including the Kappa-epsilon and two second-order closures) is made for the test problem of homogeneous turbulent shear flow in a rotating frame. The time evolution of the turbulent kinetic energy and dissipation rate is calculated for a variety of models and comparisons are made with previously published experiments and numerical simulations. Particular emphasis is placed on examining the ability of each model to accurately predict equilibrium states for a range of the parameter Omega/S (the ratio of the rotation rate to the shear rate). It is found that none of the commonly used second-order closure models yield substantially improved predictions for the time evolution of the turbulent kinetic energy and dissipation rate over the somewhat defective results obtained from the simpler Kappa-epsilon model for the turbulent flow regime. There is also a problem with the equilibrium states predicted by the various models. For example, the Kappa-epsilon model erroneously yields equilibrium states that are independent of Omega/S while the Launder, Reece, and Rodi model predicts a flow relaminarization when Omega/S is greater than 0.39 - a result which is contrary to numerical simulations and linear spectral analysis which indicate flow instability for at least the range 0 less than or = Omega/S less than or = 0.5. The physical implications of the results obtained from the various turbulence models considered here are discussed in detail along with proposals to remedy the deficiencies based on a dynamical systems approach.

Speziale, C. G.↗
NASA NTRS1990

Liquid-Vapor Equilibrium of Multicomponent Cryogenic Systems

Liquid-vapor and solid-vapor equilibria at low to moderate pressures and low temperatures are important in many solar system environments, including the surface and clouds of Titan, the clouds of Uranus and Neptune, and the surfaces of Mars and Triton. The familiar cases of ideal behavior are limiting cases of a general thermodynamic representation for the vapor pressure of each component in a homogeneous multicomponent system. The fundamental connections of laboratory measurements to thermodynamic models are through the Gibbs-Duhem relation and the Gibbs-Helmholtz relation. Using laboratory measurements of the total pressure, temperature, and compositions of the liquid and vapor phases at equilibrium, the values of these parameters can be determined. The resulting model for vapor-liquid equilibrium can then conveniently and accurately be used to calculate pressures, compositions, condensation altitudes, and their dependencies on changing climatic conditions. A specific system being investigated is CH4-C2H6-N2, at conditions relevant to Titan's surface and atmosphere. Discussed are: the modeling of existing data on CH4-N2, with applications to the composition of Titan's condensate clouds; some new measurements on the CH4-C2H6 binary, using a high-precision static/volumetric system, and on the C2H6-N2 binary, using the volumetric system and a sensitive cryogenic flow calorimeter; and describe a new cryogenic phase-equilibrium vessel with which we are beginning a detailed, systematic study of the three constituent binaries and the ternary CH4-C2H6-N2 system at temperatures ranging from 80 to 105 K and pressures from 0.1 to 7 bar.

Thompson, W. Reid↗
NASA NTRS1989

Force-free magnetic fields - Is there a 'loss of equilibrium'?

This paper examines concept in solar physics that is known as loss of equilibrium in which a sequence of force-free magnetic fields, said to represent a possible quasi-static evolution of solar magnetic fields, reaches a critical configuration beyond which no acceptable solution of the prescribed form exists. This concept is used to explain eruptive phenomena ranging from solar flares to coronal mass ejections. Certain sequences of force-free configurations are discussed that exhibit a loss of equilibrium, and it is argued that the concept is devoid of physical significance since each sequence is defined a way that does not represent an acceptable thought experiment. For example, the sequence may be defined in terms of a global constraint on the boundary conditions, or the evolution of the sequence may require the creation of mgnetic flux that is not connected to the photosphere and is not present in the original configuration. The global constraints typically occur in using the so-called generating function method. An acceptance thought experiment is proposed to specify the field configuration in terms of photospheric boundary conditions comprising the normal component of the field and the field-line connectivity. Consider a magnetic-field sequence that, when described in terms of a generating function, exhibits a loss of equilibrium and show that, when one instead defines the sequence in terms of the corresponding boundary conditions, the sequence is well behaved.

Klimchuk, J. A.↗
NASA NTRS1989

Ionization and thermal equilibrium models for O star winds based on time-independent radiation-driven wind theory

Ab initio ionization and thermal equilibrium models are calculated for the winds of O stars using the results of steady state radiation-driven wind theory to determine the input parameters. Self-consistent methods are used for the roles of H, He, and the most abundant heavy elements in both the statistical and the thermal equilibrium. The model grid was chosen to encompass all O spectral subtypes and the full range of luminosity classes. Results of earlier modeling of O star winds by Klein and Castor (1978) are reproduced and used to motivate improvements in the treatment of the hydrogen equilibrium. The wind temperature profile is revealed to be sensitive to gross changes in the heavy element abundances, but insensitive to other factors considered such as the mass-loss rate and velocity law. The reduced wind temperatures obtained in observing the luminosity dependence of the Si IV lambda 1397 wind absorption profile are shown to eliminate any prospect of explaining the observed O VI lambda 1036 line profiles in terms of time-independent radiation-driven wind theory.

Drew, J. E.↗
NASA NTRS1990

Linear tearing modes of a forced current-sheet equilibrium

Linear tearing modes are studied in a nearly singular forced current-sheet equilibrium, such as could result from global magnetic forces in the solar corona. Growth rates for the tearing modes, determined by solving the linearized reduced MHD (Strauss) equations numerically, were found to scale as (gamma)tau(d) = about S exp 4/5 k(y) exp 4/5, where S is the Lundquist number, k(y) is the wavenumber, and tau(d) is the classical resistive diffusion time. This scaling is in agreement with predictions from analytical theory. Because of the faster S scaling of these modes compared to the tearing modes of a diffuse current-sheet equilibrium, the modes have much higher growth rates (by a factor of about 10,000) for coronal values of S (about 10 to the 12th). For coronal parameters, the growth times of these new modes are estimated to be on the order of several hours to days, as compared to growth times of months to years for the tearing modes in a diffuse current-shear equilibrium. The growth times are comparable to reconnection times scales required in models of coronal heating by magnetic field dissipation.

Liewer, Paulett C.↗
NASA NTRS1990

Evaluation of equilibrium turbulence for a naturally developing hypersonic boundary layer at nonadiabatic wall conditions

Experimental data for defining test conditions necessary for a naturally developing hypersonic equilibrium turbulent boundary layer are presented. The tests were conducted at nominal boundary-layer edge Mach number of 6.2 and 5.0; the adiabatic wall to actual wall temperature ratio was 5.4. The data indicate that a momentum thickness Reynold number of at least 4000 is required for an equilibrium turbulent boundary layer. Based on the above results, a test envelope defining equilibrium flow conditions for an eight-foot high-temperature tunnel in terms of the basic facility operating conditions is given for a Mach-7 nozzle configuration. Representative experimental results for two-dimensional and three-dimensional test articles are assessed, including results of complete and partial adaptation and of residual-interference calculations.

Albertson, Cindy W.↗
NASA NTRS1990

Particle orbits in two-dimensional equilibrium models for the magnetotail

Assuming that there exist an equilibrium state for the magnetotail, particle orbits are investigated in two-dimensional kinetic equilibrium models for the magnetotail. Particle orbits in the equilibrium field are compared with those calculated earlier with one-dimensional models, where the main component of the magnetic field (Bx) was approximated as either a hyperbolic tangent or a linear function of z with the normal field (Bz) assumed to be a constant. It was found that the particle orbits calculated with the two types of models are significantly different, mainly due to the neglect of the variation of Bx with x in the one-dimensional fields.

Karimabadi, H.↗
NASA NTRS1992

Conservative-variable average states for equilibrium gas multi-dimensional fluxes

Modern split component evaluations of the flux vector Jacobians are thoroughly analyzed for equilibrium-gas average-state determinations. It is shown that all such derivations satisfy a fundamental eigenvalue consistency theorem. A conservative-variable average state is then developed for arbitrary equilibrium-gas equations of state and curvilinear-coordinate fluxes. Original expressions for eigenvalues, sound speed, Mach number, and eigenvectors are then determined for a general average Jacobian, and it is shown that the average eigenvalues, Mach number, and eigenvectors may not coincide with their classical pointwise counterparts. A general equilibrium-gas equation of state is then discussed for conservative-variable computational fluid dynamics (CFD) Euler formulations. The associated derivations lead to unique compatibility relations that constrain the pressure Jacobian derivatives. Thereafter, alternative forms for the pressure variation and average sound speed are developed in terms of two average pressure Jacobian derivatives. Significantly, no additional degree of freedom exists in the determination of these two average partial derivatives of pressure. Therefore, they are simultaneously computed exactly without any auxiliary relation, hence without any geometric solution projection or arbitrary scale factors. Several alternative formulations are then compared and key differences highlighted with emphasis on the determination of the pressure variation and average sound speed. The relevant underlying assumptions are identified, including some subtle approximations that are inherently employed in published average-state procedures. Finally, a representative test case is discussed for which an intrinsically exact average state is determined. This exact state is then compared with the predictions of recent methods, and their inherent approximations are appropriately quantified.

Iannelli, G. S.↗
NASA NTRS1990

Computer program to solve two-dimensional shock-wave interference problems with an equilibrium chemically reacting air model

The computer program EASI, an acronym for Equilibrium Air Shock Interference, was developed to calculate the inviscid flowfield, the maximum surface pressure, and the maximum heat flux produced by six shock wave interference patterns on a 2-D, cylindrical configuration. Thermodynamic properties of the inviscid flowfield are determined using either an 11-specie, 7-reaction equilibrium chemically reacting air model or a calorically perfect air model. The inviscid flowfield is solved using the integral form of the conservation equations. Surface heating calculations at the impingement point for the equilibrium chemically reacting air model use variable transport properties and specific heat. However, for the calorically perfect air model, heating rate calculations use a constant Prandtl number. Sample calculations of the six shock wave interference patterns, a listing of the computer program, and flowcharts of the programming logic are included.

Glass, Christopher E.↗
NASA NTRS1992

Resonant behaviour of MHD waves on magnetic flux tubes. III - Effect of equilibrium flow

The Hollweg et al. (1990) analysis of MHD surface waves in a stationary equilibrium is extended. The conservation laws and jump conditions at Alfven and slow resonance points obtained by Sakurai et al. (1990) are generalized to include an equilibrium flow, and the assumption that the Eulerian perturbation of total pressure is constant is recovered as the special case of the conservation law for an equilibrium with straight magnetic field lines and flow along the magnetic field lines. It is shown that the conclusions formulated by Hollweg et al. are still valid for the straight cylindrical case. The effect of curvature is examined.

Goossens, Marcel↗
NASA NTRS1992

Geometrically thin, hot accretion disks - Topology of the thermal equilibrium curves

All the possible thermal equilibrium states of geometrically thin alpha-disks around stellar-mass black holes are presented. A (vertically) one-zone disk model is employed and it is assumed that a main energy source is viscous heating of protons and that cooling is due to bremsstrahlung and Compton scattering. There exist various branches of the thermal equilibrium solution, depending on whether disks are effectively optically thick or thin, radiation pressure-dominated or gas pressure-dominated, composed of one-temperature plasmas or of two-temperature plasmas, and with high concentration of e(+)e(-) pairs or without pairs. The thermal equilibrium curves at high temperatures (greater than or approximately equal to 10 exp 8 K) are substantially modified by the presence of e(+)e(-) pairs. The thermal stability of these branches are examined.

Kusunose, Masaaki↗
NASA NTRS1992

Vapor-liquid equilibrium thermodynamics of N2 + CH4 - Model and Titan applications

A thermodynamic model is presented for vapor-liquid equilibrium in the N2 + CH4 system, which is implicated in calculations of the Titan tropospheric clouds' vapor-liquid equilibrium thermodynamics. This model imposes constraints on the consistency of experimental equilibrium data, and embodies temperature effects by encompassing enthalpy data; it readily calculates the saturation criteria, condensate composition, and latent heat for a given pressure-temperature profile of the Titan atmosphere. The N2 content of condensate is about half of that computed from Raoult's law, and about 30 percent greater than that computed from Henry's law.

Thompson, W. R.↗
NASA NTRS1993

Radiative interactions in molecular gases under local and nonlocal thermodynamic equilibrium conditions

Basic formulations, analyses, and numerical procedures are presented to investigate radiative heat interactions in diatomic and polyatomic gases under local and nonlocal thermodynamic equilibrium conditions. Essential governing equations are presented for both gray and nongray gases. Information is provided on absorption models, relaxation times, and transfer equations. Radiative flux equations are developed which are applicable under local and nonlocal thermodynamic equilibrium conditions. The problem is solved for fully developed laminar incompressible flows between two parallel plates under the boundary condition of a uniform surface heat flux. For specific applications, three diatomic and three polyatomic gases are considered. The results are obtained numerically by employing the method of variation of parameters. The results are compared under local and nonlocal thermodynamic equilibrium conditions at different temperature and pressure conditions. Both gray and nongray studies are conducted extensively for all molecular gases considered. The particular gases selected for this investigation are CO, NO, OH, CO2, H2O, and CH4. The temperature and pressure range considered are 300-2000 K and 0.1-10 atmosphere, respectively. In general, results demonstrate that the gray gas approximation overestimates the effect of radiative interaction for all conditions. The conditions of NLTE, however, result in underestimation of radiative interactions. The method developed for this study can be extended to solve complex problems of radiative heat transfer involving nonequilibrium phenomena.

Tiwari, S. N.↗
NASA NTRS1992

Radiative equilibrium in rapidly expanding shells

The equation of radiative equilibrium for rapidly expanding spherical shells including the special relativistic terms is discussed, and a temperature-correction procedure for the solution of this equation is given. The temperature-correction scheme combines a partial linearization approach with the approximate Lambda-operator iteration method. For some test problems, the temperature structures of atmospheres in radiative equilibrium in the Lagrangian frame are calculated. The effects of the velocity field on the temperature stratification and the luminosity are also discussed. We find that the temperature structure of a moving photosphere in radiative equilibrium in the Lagrangian frame differs significantly from that of a static photosphere and that, at least, all first-order terms, in particular the advection and aberration terms, have to be included consistently both in the radiative transfer and the energy equation in studies of supernovae atmospheres and other high-speed radiating flows.

Hauschildt, P. H.↗
NASA NTRS1992

Viscous equilibrium computations using program LAURA

Modifications have been made to the Langley Aerothermodynamic Upwind Relaxation Algorithm (LAURA) that enable it to compute viscous airflows under the assumption of thermal and chemical equilibrium. Equilibrium thermodynamic and transport property information are input to the code via curve fits. The periodic updating of this information enables the equilibrium algorithm to perform at a computational rate that is only a small percentage larger than the rate associated with the perfect-gas algorithm. Presented in this article are the results of the initial validation of the modified code. Solutions for surface pressure and heating are presented for the flow over slender and blunt cones at realistic reentry conditions. LAURA solutions are compared with those produced by a viscous shock-layer method, and, for one case considered, with heat transfer data from a flight experiment. For both pressure and heating, the agreement is good. In general, differences in pressure of a few percent were noted, while differences in heating rates were in the 5-10 percent range.

Greene, Francis A.↗
NASA NTRS1993

An experimental study of trace element partitioning between olivine, orthopyroxene and melt in chondrules - Equilibrium values and kinetic effects

Mineral/melt partition coefficients were measured using an ion microprobe for 32 elements in orthopyroxene and olivine in equilibrium and dynamic crystallization experiments on compositions corresponding to chondrules. The mineral/melt partition coefficients calculated from the measured concentrations for both olivine and orthopyroxene show very little change between equilibrium experiments and dynamic experiments with cooling rates of up to 100 C/h. The results provide a self-consistent set of partition coefficients that can be used in thermodynamic models of equilibrium and kinetic partitioning between olivine, orthopyroxene, and melt. These data can be used in models of partial melting and crystal fractionation in olivine- and orthopyroxene-rich systems, such as chondrules. The results may also be applicable to mantle peridotites, komatiitic and picritic lavas, and ultramafic intrusions.

Kennedy, A. K.↗
NASA NTRS1994

The tropical water and energy cycles in a cumulus ensemble model. Part 1: Equilibrium climate

A cumulus ensemble model is used to study the tropical water and energy cycles and their role in the climate system. The model includes cloud dynamics, radiative processes, and microphysics that incorporate all important production and conversion processes among water vapor and five species of hydrometeors. Radiative transfer in clouds is parameterized based on cloud contents and size distributions of each bulk hydrometeor. Several model integrations have been carried out under a variety of imposed boundary and large-scale conditions. In Part 1 of this paper, the primary focus is on the water and heat budgets of the control experiment, which is designed to simulate the convective - radiative equilibrium response of the model to an imposed vertical velocity and a fixed sea surface temperature at 28 C. The simulated atmosphere is conditionally unstable below the freezing level and close to neutral above the freezing level. The equilibrium water budget shows that the total moisture source, M(sub s), which is contributed by surface evaporation (0.24 M(sub s)) and the large-scale advection (0.76 M(sub s)), all converts to mean surface precipitation bar-P(sub s). Most of M(sub s) is transported verticaly in convective regions where much of the condensate is generated and falls to surface (0.68 bar-P(sub s)). The remaining condensate detrains at a rate of 0.48 bar-P(sub s) and constitutes 65% of the source for stratiform clouds above the melting level. The upper-level stratiform cloud dissipates into clear environment at a rate of 0.14 bar-P(sub s), which is a significant moisture source comparable to the detrained water vapor (0.15 bar-P(sub s)) to the upper troposphere from convective clouds. In the lower troposphere, stratiform clouds evaporate at a rate of 0.41 bar-P(sub s), which is a more dominant moisture source than surface evaporation (0.22 bar-P(sub s)). The precipitation falling to the surface in the stratiform region is about 0.32 bar-P(sub s). The associated latent heating in the water cycle is the dominant source in the heat budget that generates a net upward motion in convective regions, upper stratiform regions (above the freezing level), and a downward motion in the lower stratiform regions. The budgets reveal a cycle of water and energy resulted from radiation-dynamic-convection interactions that maintain equilibrium of the atmosphere.

Sui, C. H.↗
NASA NTRS1994

Rapid computation of spectrally integrated non-local thermodynamic equilibrium limb emission

The interpretation of infrared radiance measurements made by satellite-borne limb-scanning broadband radiometers requires accurate and computationally fast techniques with which to evaluate the equation of radiative transfer. This requirement is made even more stringent when analyzing measurements of non-local thermodynamic equilibrium (non-LTE) emission from the terrestrial mesosphere and lower thermosphere. In principle, line-by-line calculations which explicitly account for the departure from thermodynamic equilibrium in both the source functions and the transmittances are necessary. In this paper we extend the emissivity growth approximation (EGA) technique developed for local thermodynamic equilibrium (LTE) limb radiance for the molecular oxygen dayglow (1.27 micrometers and 762 nm), ozone and carbon dioxide in the 9- to 11-micrometer spectral interval, carbon monoxide (4.6 micrometers), nitric oxide (5.3 micrometers), and the carbon dioxide bands (15 micrometers) are presented. Using the non-LTE form of the EGA, the spectrally integrated limb emission is calculated for 35 tangent heights in the mesosphere and lower thermosphere (a total of 1200 atmospheric layers) with line-by-line accuracy in approximately 0.35 s of CPU time on readily available desktop computer hardware, while the corresponding line-by-line calculations may require several minutes. The non-LTE EGA technique will allow kinetic temperature and minor constituend retrieval algorithms to readily include non-LTE efects limited only by the a priori knowledge of the departure from LTE in the observed bands.

Mlynczak, Martin G.↗