SEARCH · Engineering Papers

Results for “Diffusion equation”

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.

SourceResearch connectionFrom yearThrough year

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

At least 955 records · Page 53

All sources NASA NTRS DOE OSTI

NASA NTRS1991

Application of a Reynolds Stress turbulence model to a supersonic hydrogen-air diffusion flame

A second-order differential Reynolds Stress turbulence model has been applied to the Favre-averaged Navier-Stokes equations for the study of supersonic flows undergoing hydrogen-air chemical reactions. An assumed Beta Probability Density Function is applied to account for the chemical source terms in the conservation equations. An algebraic Reynolds Flux model is used for the fluctuating density-velocity as well as the species mass fraction-velocity correlations. The variances of temperature and species fluctuations are also modelled using an algebraic flux technique. A seven-species, seven-reaction finite rate chemistry mechanism is used to simulate the combustion processes. The resulting formulation is validated by comparison with experimental data on reacting supersonic axisymmetric jets. Results obtained for specific conditions indicate that the effect of chemical reaction on the turbulence is significant.

Chandrasekhar, R.↗

NASA NTRS1993

Application of a Reynolds stress turbulence model to a supersonic radiating hydrogen-air diffusion flame

A second-order differential Reynolds Stress turbulence model has been applied to the Favre-averaged Navier-Stokes equations for the study of supersonic flows with finite-rate chemistry and radiation. An assumed Beta Probability Density Function is applied to account for the chemical source terms and the radiative flux terms in the conservation equations. A seven-species, seven-reaction finite rate chemistry mechanism is used to simulate the combustion process. The tangent slab approximation is used in radiative flux formulation. A pseudo-gray gas model is used to represent the absorption-emission characteristics of the participating species. The turbulence/radiation interaction is achieved via a new formulation. The resulting formulation is validated by comparison with experimental data on reacting supersonic axisymmetric jets. Results obtained for specific conditions indicate that the effect of chemical reaction on the turbulence is significant. Also, the radiative heat transfer is enhanced by the turbulence.

Chandrasekhar, R.↗

NASA NTRS2024

Detection of Extensive Equatorial Plasma Depletions after the 2022 Tongan Volcanic Eruption from Multiple Geodetic Satellite Ranging Systems

We present a number of unique observations of ionospheric anomalies following the Hunga-Tonga Hunga-Ha'apai (HTHH) volcanic eruption on 15 January 2022. All are based on non-dedicated geodetic satellite systems: Global Positioning System tracking of Low Earth Orbit (LEO) CubeSats, intersatellite tracking between two GRACE Follow-On satellites, satellite radar altimeters to the ocean surface, and Doppler radio beacons from ground stations to LEO geodetic satellites. Their observations revealed the development of anomalously large trough-like plasma depletions, along with plasma bubbles, in the equatorial regions of the Pacific and East Asian sectors. Trough-like plasma depletions appeared to be confined within approximately ±20° magnetic latitude, accompanied by density enhancements just outside this latitude range. These plasma depletions and enhancements were aligned with the magnetic equator and occurred across broad longitudes. They were detected in regions where atmospheric waves from the HTHH eruption passed through around the time of the sunset terminator. We interpret these phenomena in terms of the E dynamo electric fields driven by atmospheric waves from the eruption. The uplift of the ionosphere beyond satellite altitudes, followed by subsequent plasma diffusion to higher latitudes along magnetic field lines, results in the formation of trough-like plasma depletions around the magnetic equator and density enhancement at higher latitudes. The detection of plasma bubbles in the Asian sector during the non-bubble season (January) is likely associated with the uplift of the ionosphere at the sunset terminator.

Sentinel-3B↗

NASA NTRS1972

Solar flare particle propagation: Comparision of a new analytic solution with spacecraft measurements

An analytic solution was obtained to the complete Fokker-Planck equation for solar flare particle propagation including the effects of convection, energy-change, corotation, and diffusion. It is assumed that the particles are injected impulsively at a single point in space, and that a boundary exists beyond which the particles are free to escape. Several solar flare particle events were observed with solar and galactic cosmic ray experiment aboard OGO 6. Detailed comparisons of the predictions of the solution with observations of 1 to 70 MeV protons show that the model adequately describes both the rise and decay times. The solution also yields a time evolution for the vector anisotropy which agrees well with reported observations.

Lupton, J. E.↗

NASA NTRS1972

Oxygen and hydrogen ion densities above Millstone Hill.

Measurements of the vertical flux of oxygen ions, when combined with simultaneous measurements of electron density and of electron and ion temperatures, present a unique opportunity to examine conditions in the topside ionosphere. The measured fluxes and densities may be used directly to evaluate terms in the O+ continuity equation without requiring any assumptions to be made about neutral winds, electric fields, or the ambipolar diffusion coefficient. From observations at Millstone Hill we have, in this way, derived the rate of loss of O+ in the charge-exchange reaction with hydrogen, the rate of photoionization of atomic oxygen, and the rate of loss of O+ in reactions with N2 and O2. In combination with laboratory and theoretical results, these rates can be interpreted to yield number densities of the corresponding neutral species. When the measured fluxes are examined for consistency with measured density gradients and temperature profiles, we find clear evidence of wind-induced or electrodynamic vertical drifts larger than 60 m/sec.

Schunk, R. W.↗

NASA NTRS1974

Scattering and absorption from poly-dispersed aerosols

Results from numerical computations of the diffuse sky radiances and degree of polarization are given. These results were obtained by solving the equation of radiative transfer in the formulation of Eschelbach. In these computations, multiple scattering and absorption by aerosol particles were considered. In addition, results from experimental measurements of the complex refractive index of aerosol samples at different relative humidities are presented. From the radiation flux divergences which were computed based on the determined properties of atmospheric aerosol particles, atmospheric heating rates were derived which were found to be comparable to the heating rates by water vapor.

Bullrich, K.↗

NASA NTRS1976

Aerodynamic design guidelines and computer program for estimation of subsonic wind tunnel performance

General guidelines are given for the design of diffusers, contractions, corners, and the inlets and exits of non-return tunnels. A system of equations, reflecting the current technology, has been compiled and assembled into a computer program (a user's manual for this program is included) for determining the total pressure losses. The formulation presented is applicable to compressible flow through most closed- or open-throat, single-, double-, or non-return wind tunnels. A comparison of estimated performance with that actually achieved by several existing facilities produced generally good agreement.

Eckert, W. T.↗

NASA NTRS1978

A self-consistent model of a corotating Jovian magnetosphere

In the rotation-dominated model of the Jovian magnetosphere, proposed in the present paper, the plasma current distribution is dynamically consistent with the magnetic field. The model is constructed under the assumptions of an ionospheric plasma source without pitch angle scattering; loss-free radiation transport through flux tube interchange diffusion; and a static balance between centrifugal force and magnetic stress. Using these assumptions, a dynamic equation is derived for a self-consistent field configuration having a single adjustable parameter that is related to the plasma source strength. The equation is solved by an iterative technique. The self-consistent field resembles a radially distorted dipole field, rather than the flat magnetodisk configuration inferred from Pioneer data. The implication is that such a magnetodisk field would require an equatorial plasma source rather than a source at the feet of the field lines.

Carbary, J. F.↗

NASA NTRS1979

Numerical solution of compressible viscous flows

The presented review is concerned with the problem of calculating compressible viscous flows. Basic numerical considerations and problems associated with calculating viscous flows are examined and current numerical approaches toward the solution of the Navier-Stokes equations are discussed. It is pointed out that the numerical solution of the full time-dependent equations for turbulent flow is not practical with present computers. Therefore, turbulence effects must be accounted for by modeling. Developments related to turbulence modeling are described. In connection with a discussion of numerical methods for solving viscous flow equations, attention is given to numerical domains of dependence of typical explicit and implicit methods, the diffusion problem, the convection-diffusion problem, and the split-hybrid method.

Maccormack, R. W.↗

NASA NTRS1982

ADI on staggered mesh - A method for the calculation of compressible convection

An alternating direction implicit (ADI) method has been applied to a staggered grid for the computation of convection in a highly stratified fluid. Since artificial viscosity is not needed, subtle effects like the onset of convection can be studied. These computations compare well with the 2-D results by Graham (1975) and also agree with standard Boussinesq results when taken to that limit. Good efficiency has been achieved with a time step hundreds of times larger than the stability limit imposed by the explicit treatment of diffusion and the Courant number is not restricted to be below 1. The Navier-Stokes equation contains cross spatial derivatives which are treated explicitly in most ADI schemes. The destabilizing effect of such a practice on a 2-D model system with second-order spatial derivative terms only was analyzed and found to be not excessive.

Chan, K. L.↗

NASA NTRS1990

Ozone measurements from the NOAA-9 and the Nimbus-7 satellites - Implications of short and long term variabilities

An overview of the measurements of total ozone and ozone profiles by the SBUV/2 instrument on the NOAA-9 spacecraft relative to similar measurements from the solar backscatter ultraviolet (SBUV) and TOMS instruments on Nimbus-7 is presented. During the three-year period from March 14, 1985 to February 28, 1988, when these data sets overlap, it is shown that there have been significant changes in the calibrations of the three instruments that may be attributed to diffuser plate degradation (for SBUV/TOMS) and to the drift of the NOAA-9 orbit to later equator crossing times (for SBUV/2). Though these instrument characteristic changes have effected the absolute values of the trends derived from the three instruments, their geophysical characteristics and response to short-term variations are accurate and correlate well among the three instruments. It is seen that the total column ozone measured by the three instruments shows good agreement with respect to its day-to-day, seasonal, and latitudinal variabilities.

Chandra, S.↗

NASA NTRS1993

The reionization of the universe: The feedback of galaxy formation on the intergalactic medium

The thermal and ionization evolution of a uniform intergalactic medium (IGM) composed of H and He, undergoing reionization, including the mean effect of gas clumps embedded in a smoothly distributed ambient gas were calculated. The rate equations for ionization and recombination were solved together with the equations of energy conservation, including the effects of cosmological expansion, radiative and Compton cooling, and the diffuse flux emitted by the gas, and radiative transfer. The contribution to the continuum opacity of the universe due to the observed quasar absorption line clouds (QALC'S) were included. A variety of sources of photoionization, including quasars and primeval galaxies, as well as the possibility that hydrodynamical processes deposit thermal energy in the IGM were considered. Applications of these calculations including the evolution of the Ly-alpha forest clouds are described. A self-consistent treatment of the thermal and ionization history of the intergalactic medium (IGM) must take account of the growth of structure in the universe, since the mean density of the IGM corresponds primarily to the time-varying uncollapsed fraction of the baryon-electron component of the matter, and the collapsed fraction, in turn, can have a feedback effect on this uncollapsed fraction by releasing ionizing radiation and thermal energy and by contributing to the opacity of the universe. The coupled evolution of the IGM and the emerging structure with a special focus on the reionization of the IGM, which is believed to have been completed by some redshift z is approximately greater than 4, as inferred from the absence of the Gunn-Peterson effect in the spectra of high z quasars, are studied. The results and implications of detailed, numerical calculations of the thermal and ionization balance and radiative transfer in a uniform IGM of H and He, including the mean effect of an evolving distribution of gas clumps embedded in a smoothly distributed ambient gas is described.

Shapiro, Paul R.↗

NASA NTRS1993

Centrifugally driven winds from protostellar disks. I - Wind model and thermal structure

The thermal structure of a wind that is centrifugally driven from the surface of a protostellar disk is studied. A generalized version of the Blandford and Payne self-similar wind model is introduced, and the temperature and ionization distributions in the outflow are investigated. For the evolution of atomic winds, the heat equation and the rate equations that describe the ionization and excitation state of hydrogen are solved self-consistently. Ambipolar diffusion is found to be a robust mechanism for heating the gas. In the more powerful outflows, molecular hydrogen is collisionally dissociated close to the disk surface, and hydrogen is mainly atomic within a few astronomical units from the central source. It is also demonstrated that these outflows have enough momentum to lift dust grains from the disk surface.

Safier, Pedro N.↗

NASA NTRS1993

Morphological instability in epitaxially strained dislocation-free solid films - Linear stability theory

The morphological instability of a growing epitaxially strained dislocation-free solid film is analyzed. An evolution equation for the film surface is derived in the dilute limit of vacancies based on surface diffusion driven by a stress-dependent chemical potential. From the time-dependent linear stability problem the conditions for which a growing film is unstable are determined. It is found that the instability is driven by the lattice mismatch between the film and the substrate; however, low temperatures as well as elastically stiff substrates are stabilizing influences. The results also reveal that the critical film thickness for instability depends on the growth rate of the film itself. Detailed comparison with experimental observations indicates that the instability described exhibits many of the observed features of the onset of the 'island instability'.

Spencer, B. J.↗

NASA NTRS1993

Segmented multigrid domain decomposition solutions for three dimensional viscous recirculating flows

A segmented multigrid domain decomposition strategy is combined with a pressure-based form of flux-vector discretization for 3D incompressible and compressible viscous flow applications. A pressure-based form of flux-vector splitting is applied to the Navier-Stokes (NS) equations, which are represented by an implicit lowest-order reduced NS system and a purely diffusive higher-order deferred corrector. A trapezoidal or boxlike form of discretization insures that all mass conservation properties are satisfied at interfacial and outflow boundaries, even for this primitive-variable nonstaggered grid computation. Improvements in gridding strategy are presented by allowing for disjoint subdomains that provide optimal resolution of disparate flow features.

Srinivasan, Kumar↗

NASA NTRS1951

Method of successive approximations for the solution of certain problems in aerodynamics

A method of successive approximations for the solution of problems in the fields of diffusion, boundary-layer flow, and heat-transfer is illustrated by solving problems in each of these fields. In most of the examples, the approximate solutions are compared with known accurate solutions and the agreement is shown to be good.

FLOW, TURBULENT - DIFFUSION↗

NASA NTRS1994

An analytic solution of the radiative transfer equation for a gray scattering atmosphere in motion

We provide a formal analytic solution of the radiative transfer equation for a gray moving atmosphere in a plane parallel geometry. A formal solution in the diffusion and the free-streaming limit is also provided in the case of a spherically extended atmosphere. The formal solutions are written explicitly for scattering atmospheres in which the density and the velocity fields are given by a power law. A self-consistent temperature profile accurate to O(Beta = v/c) is provided for the case in which the absorption or the scattering are temperature independent. The gray extinction temperature profile is considerably simplified in the case of a scattering atmosphere. Steady state flow and homologous expansion are special cases that are considered in detail.

Pistinner, Shlomi↗

NASA NTRS1993

Trace elements in migrating high-temperature fluids: Effects of diffusive exchange with the adjoining solid

Trace element concentrations and isotopic ratios are frequently used to study the behavior of high-temperature fluids in both metamorphic and igneous systems. Many theoretical formulations of the effects of fluid migration on trace elements have assumed instantaneous reequilibration between the migrating fluid and the solid material through which it is passing. This paper investigates the additional effects which arise when equilibration is not instantaneous due to a limited rate of diffusion in the solid, using an analytical steady state solution to a set of partial differential equations describing the exchange of trace elements between the fluid and the solid during the migration of the fluid.

Kenyon, Patricia M.↗