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 1,117 records · Page 62

All sources NASA NTRS DOE OSTI

NASA NTRS2017

Evaluation of Full Reynolds Stress Turbulence Models in FUN3D

Full seven-equation Reynolds stress turbulence models are promising tools for today’s aerospace technology challenges. This paper examines two such models for computing challenging turbulent flows including shock-wave boundary layer interactions, separation and mixing layers. The Wilcox and the SSG/LRR full second-moment Reynolds stress models have been implemented into the FUN3D (Fully Unstructured Navier-Stokes Three Dimensional) unstructured Navier-Stokes code and were evaluated for four problems: a transonic two-dimensional diffuser, a supersonic axisymmetric compression corner, a compressible planar shear layer, and a subsonic axisymmetric jet. Simulation results are compared with experimental data and results computed using the more commonly used Spalart-Allmaras (SA) one-equation and the Menter Shear Stress Transport (SST-V) two-equation turbulence models.

reynolds averaging↗

NASA NTRS1973

Analysis of heat transfer for a normally impinging liquid-metal slot jet

A two-dimensional liquid-metal slot jet that is impinging normally against a uniformly heated flat plate is analyzed. The distributions of wall temperature and heat-transfer coefficient are obtained as functions of position along the plate. The liquid-metal assumptions are made that the jet is inviscid and that molecular condition is dominating heat diffusion. The solution is obtained by mapping the jet flow region into a potential plane where it occupies a strip of uniform width. The energy equation is transformed into potential coordinates, and an exact solution obtained in the strip region. Conformal mapping is then used to transform the solution into the physical plane.

Siegel, R.↗

NASA NTRS1973

Ogo 6 measurements of supercooled plasma in the equatorial exosphere.

Plasma measurements performed on Ogo 6 reveal electron and ion temperature values that on occasion appear to be well below the expected neutral gas temperature. The phenomenon is observed only at night above 500 km near the magnetic equator. It is suggested that the expansion cooling of the plasma is accomplished by downward motions of the F region plasma induced by winds or diffusion, by outward E x B drift, or more probably by the upward flow of plasma during interhemisphere transport along magnetic field lines. It is also suggested that preferential cooling of electrons because of their greater thermal conductivity should tend to give ion temperatures greater than electron temperatures during the postsunset cooling of the plasmasphere when photoelectrons are absent.

Hanson, W. B.↗

NASA NTRS1976

The electron Boltzmann equation in a plasma generated by fission fragments

A Boltzmann equation formulation is presented for the determination of the electron distribution function in a plasma generated by fission fragments. The formulation takes into consideration ambipolar diffusion, elastic and inelastic collisions, recombination and ionization, and allows for the fact that the primary electrons are not monoenergetic. Calculations for He in a tube coated with fissionable material show that, over a wide pressure and neutron flux range, the distribution function is non-Maxwellian, but the electrons are essentially thermal. Moreover, about a third of the energy of the primary electrons is transferred into the inelastic levels of He. This fraction of energy transfer is almost independent of pressure and neutron flux but increases sharply in the presence of a sustainer electric field.

Hassan, H. A.↗

NASA NTRS1976

Electron distribution function in a plasma generated by fission fragments

A Boltzmann equation formulation is presented for the determination of the electron distribution function in a plasma generated by fission fragments. The formulation takes into consideration ambipolar diffusion, elastic and inelastic collisions, recombination and ionization, and allows for the fact that the primary electrons are not monoenergetic. Calculations for He in a tube coated with fissionable material shows that, over a wide pressure and neutron flux range, the distribution function is non-Maxwellian, but the electrons are essentially thermal. Moreover, about a third of the energy of the primary electrons is transferred into the inelastic levels of He. This fraction of energy transfer is almost independent of pressure and neutron flux.

Hassan, H. A.↗

NASA NTRS1981

On the origin of the MeV energy nucleon flux associated with CIRs

Measurements of recurrent enhancements of interplanetary nucleon flux in the MeV energy range are presented and interpreted. The features recur at the solar rotation period in association with stream-stream plasma interaction regions corotating with the sun. At distances from the sun less than 1 AU, the maximum intensities of the hydrogen and helium components increase with increasing distance between 300%/AU and 600%/AU. A model is proposed which predicts the acceleration of nuclei from keV plasma energies to MeV energies by means of transit time damping of magnetosonic waves as solar wind plasma flows from the sun. Numerical solutions of the transport equation are derived to demonstrate that the model does not reproduce radial variations of hydrogen and helium fluxes, and estimates are made of the radial diffusive mean free path. Finally, the observations are found to be consistent with nucleon acceleration at the CIR shocks beyond 1 AU with subsequent diffusion toward the sun.

Christon, S. P.↗

NASA NTRS1986

Effects of three-dimensional heliospheric structures on cosmic-ray modulation

The theory of cosmic-ray transport in the heliosphere contains four distinct physical processes - diffusion, convection, adiabatic cooling, and drifts. The last of these has only recently been evaluated. Extrapolation of present understanding of the regions near the heliospheric equator to high heliographic latitudes leads to the conclusion that particle drift in the large-scale magnetic field plays an important role in cosmic-ray modulation. The large-scale, three-dimensional structure of the interplanetary magnetic field is therefore very important in understanding cosmic rays. Several key observed modulation effects are summarized, each of which is a natural consequence of drift, but which requires special assumptions if drift plays no role. It is concluded that particle drifts play an important and possibly dominant role in transport in the heliosphere.

Jokipii, J. R.↗

NASA NTRS1988

A multidimensional model for aerosols - Description of computational analogs

The numerical algorithms used to simulate the advection, diffusion, sedimentation, coagulation, and condensational growth of atmospheric aerosols are described. The model can be used in one, two, or three spatial dimensions. The continuity equation in a generalized horizontal and vertical coordinate system is developed, which allows the model to be quickly adapted to a wide variety of dynamical models of global or regional scale. Algorithms are developed to treat the various physical processes, and the results of simulations are presented, which show the strengths and weaknesses of these algorithms. Although the emphasis is on the modeling of aerosols, the work is also applicable to the simulations of the transport of gases.

Toon, O. B.↗

NASA NTRS1990

Theory of Influence of a Low-Volatility, Soluble Impurity on Spherically-Symmetric Combustion of Fuel Droplets

Analyses are given for the evolution of liquid-phase mass fraction profiles and temperature during combustion of fuel droplets composed of binary miscible mixtures of low-volatility and high-volatility constituents, with small initial mass fractions of the low-volatility material, or slow introduction of low-volatility material into the liquid phase by absorption from the gas phase. The gas phase is assumed to remain quasi-steady and the liquid temperature spatially uniform. The ratio of the liquid-phase diffusion coefficient to the initial burning-rate constant is treated as a small parameter. Asymptotic analyses in this parameter are developed, and the conservation equations are integrated numerically in obtaining descriptions of the combustion history. It is shown that at the surface of the droplet a boundary layer arises in which the mass fraction of the low-volatility component increases with time. The results are used to explain qualitatively some observed conditions of flame contraction and liquid disruption in droplet combustion.

Shaw, B. D.↗

NASA NTRS1990

Influence of convection on microstructure

In eutectic growth, as the solid phases grow they reject atoms to the liquid. This results in a variation of melt composition along the solid/liquid interface. In the past, mass transfer in eutectic solidification, in the absence of convection, was considered to be governed only by the diffusion induced by compositional gradients. However, mass transfer can also be generated by a temperature gradient. This is called thermotransport, thermomigration, thermal diffusion or the Soret effect. A theoretical model of the influence of the Soret effect on the growth of eutectic alloys is presented. A differential equation describing the compositional field near the interface during unidirectional solidification of a binary eutectic alloy was formulated by including the contributions of both compositional and thermal gradients in the liquid. A steady-state solution of the differential equation was obtained by applying appropriate boundary conditions and accounting for heat flow in the melt. Following that, the average interfacial composition was converted to a variation of undercooling at the interface, and consequently to microstructural parameters. The results obtained show that thermotransport can, under certain circumstances, be a parameter of paramount importance.

Wilcox, William R.↗

NASA NTRS1992

Computer Program For Variable-Conductance Heat Pipes

VCHPDA provides accurate mathematical models of transient as well as steady-state performance of variable-conductance heat pipes over wide range of operating conditions. Applies to heat pipes with either cold, wicked or hot, nonwicked gas reservoirs and uses ideal-gas law and "flat-front" (negligible vapor diffusion) gas theory. Calculates length of gas-blocked region and temperature of vapor in active portion of heat pipe by solving set of nonlinear equations for conservation of energy and mass. Written in FORTRAN 77.

Antoniuk, D.↗

NASA NTRS1992

Radiative shocks and hydrogen molecules in pregalactic gas - The effects of postshock radiation

Previous calculations of radiative shocks in pregalactic gas are generalized and substantially improved. The hydrodynamical conservations are solved, along with the rate equations for nonequilibrium ionization, recombination, and molecule formation, and the equation of radiative transfer, for steady-state shocks in a gas of primordial compositions. This calculation self-consistently includes the effects of the diffuse postshock emission as well as a possible external radiation flux on the postshock flow and the preshock ionization levels. A previous result is confirmed that the shocked gas cools faster than it can recombine and, as a result, is able to form an H2 concentration as high as 0.003 via the formation of H(-) and H2(+) intermediaries due to the enhanced nonequilibrium ionization fraction at 10,000 K. It is shown that, as the level of the external radiation flux is increased, the formation of and cooling by H2 molecules can be inhibited and delayed. The detailed radiation spectra and ionizing photon number fluxes emergent from these shocks are presented.

Kang, Hyesung↗

NASA NTRS1991

The computation of standard solar models

Procedures for calculating standard solar models with the usual simplifying approximations of spherical symmetry, no mixing except in the surface convection zone, no mass loss or gain during the solar lifetime, and no separation of elements by diffusion are described. The standard network of nuclear reactions among the light elements is discussed including rates, energy production and abundance changes. Several of the equation of state and opacity formulations required for the basic equations of mass, momentum and energy conservation are presented. The usual mixing-length convection theory is used for these results. Numerical procedures for calculating the solar evolution, and current evolution and oscillation frequency results for the present sun by some recent authors are given.

Ulrich, Roger K.↗

NASA NTRS2003

Theory of Transport of Long Polymer Molecules through Carbon Nanotube Channels

A theory of transport of long chain polymer molecules through carbon nanotube (CNT) channels is developed using Fokker-Planck equation and direct molecular dynamics (MD) simulations. The mean transport or translocation time tau is found to depend on the chemical potential energy, entropy and diffusion coefficient. A power law dependence tau approx. N(sup 2)is found where N is number of monomers in a molecule. For 10(exp 5)-unit long polyethylene molecules, tau is estimated to be approx. 1micro-s. The diffusion coefficient of long polymer molecules inside CNTs, like that of short ones, are found to be few orders of magnitude larger than in ordinary silicate based zeolite systems.

Wei, Chenyu↗

NASA NTRS2005

Linear Stability Analysis of Gravitational Effects on a Low-Density Gas Jet Injected into a High-Density Medium

Lawson, Anthony L.↗

NASA NTRS2001

Instability Analysis of a Low-Density Gas Jet Injected into a High-Density Gas

The objective of this study was to determine the effects of buoyancy on the absolute instability of low-density gas jets injected into high-density gas mediums. Most of the existing analyses of low-density gas jets injected into a high-density ambient have been carried out neglecting effects of gravity. In order to investigate the influence of gravity on the near-injector development of the flow, a linear temporal stability analysis and a spatio-temporal stability analysis of a low-density round jet injected into a high-density ambient gas were performed. The flow was assumed to be isothermal and locally parallel; viscous and diffusive effects were ignored. The variables were represented as the sum of the mean value and a normal-mode small disturbance. An ordinary differential equation governing the amplitude of the pressure disturbance was derived. The velocity and density profiles in the shear layer, and the Froude number (signifying the effects of gravity) were the three important parameters in this equation. Together with the boundary conditions, an eigenvalue problem was formulated. Assuming that the velocity and density profiles in the shear layer to be represented by hyperbolic tangent functions, the eigenvalue problem was solved for various values of Froude number. The temporal growth rates and the phase velocity of the disturbances were obtained. It was found that the presence of variable density within the shear layer resulted in an increase in the temporal amplification rate of the disturbances and an increase in the range of unstable frequencies, accompanied by a reduction in the phase velocities of the disturbances. Also, the temporal growth rates of the disturbances were increased as the Froude number was reduced (i.e. gravitational effects increased), indicating the destabilizing role played by gravity. The spatio-temporal stability analysis was performed to determine the nature of the absolute instability of the jet. The roles of the density ratio, Froude number, Schmidt number, and the lateral shift between the density and velocity profiles on the jet s absolute instability were determined. Comparisons of the results with previous experimental studies show good agreement when the effects of these variables are combined together. Thus, the combination of these variables determines how absolutely unstable the jet will be. Experiments were carried out to observe the qualitative differences between a round low-density gas jet injected into a high-density gas (helium jet injected into air) and a round constant density jet (air jet injected into air). Flow visualizations and velocity measurements in the near-injector region of the helium jet show more mixing and spreading of the helium jet than the air jet. The vortex structures develop and contribute to the jet spreading causing the helium jet to oscillate.

Lawson, Anthony Layiwola↗

NASA NTRS2002

Linear Temporal Stability Analysis of a Low-Density Round Gas Jet Injected into a High-Density Gas

It has been observed in previous experimental studies that round helium jets injected into air display a repetitive structure for a long distance, somewhat similar to the buoyancy-induced flickering observed in diffusion flames. In order to investigate the influence of gravity on the near-injector development of the flow, a linear temporal stability analysis of a round helium jet injected into air was performed. The flow was assumed to be isothermal and locally parallel; viscous and diffusive effects were ignored. The variables were represented as the sum of the mean value and a normal-mode small disturbance. An ordinary differential equation governing the amplitude of the pressure disturbance was derived. The velocity and density profiles in the shear layer, and the Froude number (signifying the effects of gravity) were the three important parameters in this equation. Together with the boundary conditions, an eigenvalue problem was formulated. Assuming that the velocity and density profiles in the shear layer to be represented by hyperbolic tangent functions, the eigenvalue problem was solved for various values of Froude number. The temporal growth rates and the phase velocity of the disturbances were obtained. The temporal growth rates of the disturbances increased as the Froude number was reduced (i.e. gravitational effects increased), indicating the destabilizing role played by gravity.

Lawson, Anthony L.↗

NASA NTRS1975

Diffusion in liquid metal systems

Physical properties of twenty liquid metals are reported; some of the data on such liquid metal properties as density, electrical resistivity, thermal conductivity, and heat capacity are summarized in graphical form. Data on laboratory handling and safety procedure are summarized for each metal; heat-transfer-correlations for liquid metals under various conditions of laminar and turbulent flow are included. Where sufficient data were available, temperature equations of properties were obtained by the method of least-squares fit. All values of properties given are valid in the given liquid phase ranges only. Additional tabular data on some 40 metals are reported in the appendix. Included is a brief description of experiments that were performed to investigate diffusion in liquid indium-gallium systems.

Ukanwa, A. O.↗