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NASA NTRS1977

Elastic wave propagation in a highly scattering medium - A diffusion approach

The propagation of elastic waves in the moon, where the first seismograms were characterized by the presence of a long coda attributed to strongly scattered waves, is modeled with the aid of the time-dependent equation of radiative transfer. The average energy density as a function of time and space is described by the diffusion equation with linear dissipation on the assumption that all the energy present has been scattered many times and the time and distance scales of the problem are long compared to the scales of the scattering process. Ultrasonic experiments in the laboratory confirm the applicability of the formalism.

Dainty, A. M.↗

NASA NTRS1979

The thermonuclear-flash model for X-ray burst sources - A new tool for observing neutron stars

The helium-flash model for X-ray burst sources, in which matter is presumed to accrete onto the surface of a neutron star, is discussed. Attention is given to the accretion process, nuclear burning, X-ray emission, and the energy released by convection as well as by radiative diffusion near the surface. The rise times of observed bursts, their spectral evolution, and the properties of the spectrally soft X-ray transients are considered. Problems in interpreting the continuum spectra are discussed, along with problems in the detection and measurement of line features in the spectra. Also considered are the ratio of time-averaged persistent luminosity to time-averaged burst luminosity, peak burst luminosities, and the possibility of detecting binary membership for burst sources.

Joss, P. C.↗

NASA NTRS1980

Observations of diffuse galactic gamma rays

Observations of 35 MeV to several GeV diffuse gamma radiation from the galaxy are available from the SAS-2 and COS-B instruments. This paper gives a brief review of the experimental problem, a discussion of the high-latitude (local) galactic component, and a study of the more distant low-latitude emission from the galactic plane. Finally, the emerging observations in other energy ranges are mentioned.

Simpson, G. A.↗

NASA NTRS1985

Numerical Descriptions of Cosmic-Ray Transport

The behavior of energetic particles in the solar system is described by a well known Fokker-Planck equation. Although analytic methods yield insight into the nature of its solutions, especially in the diffusion regime, calculations that go beyond diffusion are very complicated. The reliability of these calculations is of concern, because numerical methods are notorious for their errors and artifacts. The well known Milne problem of classical transport theory was analyzed with the aid of three different numerical methods. These are: (1) The method of eigenfunctions in which the distribution function is approximated by a sum of eigenfunctions of the scattering operator, (2) Numerical solutions of a finite difference aquation; and (3) Direct simulation of the scattering and streaming of individual particles with the aid of Monte Carlo methods.

Earl, J. A.↗

NASA NTRS1986

Analysis of coaxial spray combustion flames and related numerical issues

An approach to the simulation of strongly coupled multiphase flows in combustion hardware is sketched and its unique requirements highlighted. An example of a successful application to a coaxial injector flame is presented. Furthermore, several numerical issues that tend to interact with the physics of the problem are discussed with special regard to their potential impact on the choices of numerical parameters by the analyst. These include the issues of stability, numerical diffusivity, stiffness, and boundary conditions. The theme of this paper focuses on the intriguing relationships among the grid, the solution algorithm, and the actual physical mechanisms themselves.

Liang, P. Y.↗

NASA NTRS1988

Boundary identification for 2-D parabolic problems arising in thermal testing of materials

Problems on the identification of two-dimensional spatial domains arising in the detection and characterization of structural flaws in materials are considered. For a thermal diffusion system with external boundary input, observations of the temperature on the surface are used in an output least square approach. Parameter estimation techniques based on the method of mappings are discussed, and approximation schemes are developed based on a finite-element Galerkin approach. Theoretical convergence results for computational techniques are given, and the results are applied to the identification of two kinds of boundary shapes.

Banks, H. T.↗

NASA NTRS1989

Electron acceleration by an obliquely propagating electromagnetic wave in the regime of validity of the Fokker-Planck-Kolmogorov approach

The relativistic motion of an ensemble of electrons in an intense monochromatic electromagnetic wave propagating obliquely in a uniform external magnetic field is studied. The problem is formulated from the viewpoint of Hamiltonian theory and the Fokker-Planck-Kolmogorov approach analyzed by Hizanidis (1989), leading to a one-dimensional diffusive acceleration along paths of constant zeroth-order generalized Hamiltonian. For values of the wave amplitude and the propagating angle inside the analytically predicted stochastic region, the numerical results suggest that the diffusion probes proceeds in stages. In the first stage, the electrons are accelerated to relatively high energies by sampling the first few overlapping resonances one by one. During that stage, the ensemble-average square deviation of the variable involved scales quadratically with time. During the second stage, they scale linearly with time. For much longer times, deviation from linear scaling slowly sets in.

Hizanidis, Kyriakos↗

NASA NTRS1988

The Galerkin/least-squares method for advective-diffusive equations

Galerkin/least-squares finite-element methods are presented for advective-diffusive equations. Galerkin/least-squares represents a conceptual simplification of streamline-upwind Petrov-Galerkin methods, and is in fact applicable to a wide variety of other problem types. A convergence analysis and error estimates are presented. Some numerical results for compressible Navier-Stokes flows are presented.

Hughes, T. J. R.↗

NASA NTRS1989

Boundary estimation problems arising in thermal tomography

Problems on the identification of two-dimensional spatial domains arising in the detection and characterization of structural flaws in materials are considered. For a thermal diffusion system with external boundary input, observations of the temperature on the surface are used in a output least squares approach. Parameter estimation techniques based on the method of mappings are discussed and approximation schemes are developed based on a finite element Galerkin approach. Theoretical convergence results for computational techniques are given and the results are applied to experimental data for the identification of flaws in the thermal testing of materials.

Banks, H. T.↗

NASA NTRS1997

The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems

In this paper, we study the Local Discontinuous Galerkin methods for nonlinear, time-dependent convection-diffusion systems. These methods are an extension of the Runge-Kutta Discontinuous Galerkin methods for purely hyperbolic systems to convection-diffusion systems and share with those methods their high parallelizability, their high-order formal accuracy, and their easy handling of complicated geometries, for convection dominated problems. It is proven that for scalar equations, the Local Discontinuous Galerkin methods are L(sup 2)-stable in the nonlinear case. Moreover, in the linear case, it is shown that if polynomials of degree k are used, the methods are k-th order accurate for general triangulations; although this order of convergence is suboptimal, it is sharp for the LDG methods. Preliminary numerical examples displaying the performance of the method are shown.

Cockburn, Bernardo↗

NASA NTRS2010

Meridional Distribution of CH3C2H and C4H2 in Saturn's Stratosphere from CIRS/Cassini Limb and Nadir Observations

Limb and nadir spectra acquired by Cassini/CIRS (Composite InfraRed Spectrometer) are analyzed in order to derive, for the first time, the meridional variations of diacetylene (C4H2) and methylacetylene (CH3C2H) mixing ratios in Saturn's stratosphere, from 5 hPa up to 0.05 hPa and 80 deg S to 45 deg N. We find that the C4H2 and CH3C2H meridional distributions mimic that of acetylene (C2H2), exhibiting small-scale variations that are not present in photochemical model predictions. The most striking feature of the meridional distribution of both molecules is an asymmetry between mid-southern and mid-northern latitudes. The mid-southern latitudes are found depleted in hydrocarbons relative to their northern counterparts. In contrast, photochemical models predict similar abundances at north and south mid-latitudes. We favor a dynamical explanation for this asymmetry, with upwelling in the south and downwelling in the north, the latter coinciding with the region undergoing ring shadowing. The depletion in hydrocarbons at mid-southern latitudes could also result from chemical reactions with oxygen-bearing molecules. Poleward of 60 deg S, at 0.1 and 0.05 hPa, we find that the CH3C2H and C4H2 abundances increase dramatically. This behavior is in sharp contradiction with photochemical model predictions, which exhibit a strong decrease towards the south pole. Several processes could explain our observations, such as subsidence, a large vertical eddy diffusion coefficient at high altitudes, auroral chemistry that enhances CH3C2H and C4H2 production, or shielding from photolysis by aerosols or molecules produced from auroral chemistry. However, problems remain with all these hypotheses, including the lack of similar behavior at lower altitudes. Our derived mean mixing ratios at 0.5 hPa of (2.4 +/- 0.3) 10(exp -10) for C4H2 and of (1.1 +/- 0.3) 10(exp -9) for CH3C2H are compatible with the analysis of global-average ISO observations performed by Moses et al. Finally, we provide values for the ratios [CH3C2H]/[C2H2] and [C4H2]/[C2H2] that can constrain the coupled chemistry of these hydrocarbons.

Guerlet, Sandrine↗

NASA NTRS1960

Comparison of Turbulent Heat-Transfer Results for Uniform Wall Heat Flux and Uniform Wall Temperature

The purpose of this note is to examine in a more precise way how the Nusselt numbers for turbulent heat transfer in both the fully developed and thermal entrance regions of a circular tube are affected by two different wall boundary conditions. The comparisons are made for: (a) Uniform wall temperature (UWT); and (b) uniform wall heat flux (UHF). Several papers which have been concerned with the turbulent thermal entrance region problem are given. 1 Although these analyses have all utilized an eigenvalue formulation for the thermal entrance region there were differences in the choices of eddy diffusivity expressions, velocity distributions, and methods for carrying out the numerical solutions. These differences were also found in the fully developed analyses. Hence when making a comparison of the analytical results for uniform wall temperature and uniform wall heat flux, it was not known if differences in the Nusselt numbers could be wholly attributed to the difference in wall boundary conditions, since all the analytical results were not obtained in a consistent way. To have results which could be directly compared, computations were carried out for the uniform wall temperature case, using the same eddy diffusivity, velocity distribution, and digital computer program employed for uniform wall heat flux. In addition, the previous work was extended to a lower Reynolds number range so that comparisons could be made over a wide range of both Reynolds and Prandtl numbers.

Siegel, R.↗

NASA NTRSDate not supplied

The Calculation of Diffusion Properties for Open Shell Molecules

- Navier-Stokes requires as input various collision integrals for gases - Diffusion, - Viscosity - Thermal conductivity - Thermal diffusion ... - Levin, Stallcop and Partridge state-of-the-art - Non-Relativistic Born-Oppenheimer Approximation (freeze nuclei first, let them move second) - Solve electron problem: Compute realistic Potential Curves (PC) from first principles, - Solve nuclei problem: Compute scattering properties for each PC using sophisticated semi-classical method - Compute cross sections - Compute appropriate thermal collision integrals

STMD↗

NASA NTRS2010

Ocean Turbulence, III: New GISS Vertical Mixing Scheme

We have found a new way to express the solutions of the RSM (Reynolds Stress Model) equations that allows us to present the turbulent diffusivities for heat, salt and momentum in a way that is considerably simpler and thus easier to implement than in previous work. The RSM provides the dimensionless mixing efficiencies Gamma-alpha (alpha stands for heat, salt and momentum). However, to compute the diffusivities, one needs additional information, specifically, the dissipation Epsilon. Since a dynamic equation for the latter that includes the physical processes relevant to the ocean is still not available, one must resort to different sources of information outside the RSM to obtain a complete Mixing Scheme usable in OGCMs. As for the RSM results, we show that the Gamma-alpha s are functions of both Ri and Rq (Richardson number and density ratio representing double diffusion, DD); the Gamma-alpha are different for heat, salt and momentum; in the case of heat, the traditional value Gamma-h = 0.2 is valid only in the presence of strong shear (when DD is inoperative) while when shear subsides, NATRE data show that Gamma-h can be three times as large, a result that we reproduce. The salt Gamma-s is given in terms of Gamma-h. The momentum Gamma-m has thus far been guessed with different prescriptions while the RSM provides a well defined expression for Gamma-m(Ri,R-rho). Having tested Gamma-h, we then test the momentum Gamma-m by showing that the turbulent Prandtl number Gamma-m/Gamma-h vs. Ri reproduces the available data quite well. As for the dissipation epsilon, we use different representations, one for the mixed layer (ML), one for the thermocline and one for the ocean;s bottom. For the ML, we adopt a procedure analogous to the one successfully used in PB (planetary boundary layer) studies; for the thermocline, we employ an expression for the variable epsilon/N(exp 2) from studies of the internal gravity waves spectra which includes a latitude dependence; for the ocean bottom, we adopt the enhanced bottom diffusivity expression used by previous authors but with a state of the art internal tidal energy formulation and replace the fixed Gamma-alpha = 0.2 with the RSM result that brings into the problem the Ri, R-rho dependence of the Gamma-alpha; the unresolved bottom drag, which has thus far been either ignored or modeled with heuristic relations, is modeled using a formalism we previously developed and tested in PBL studies. We carried out several tests without an OGCM. Prandtl and flux Richardson numbers vs. Ri. The RSM model reproduces both types of data satisfactorily. DD and Mixing efficiency Gamma-h(Ri,Rq). The RSM model reproduces well the NATRE data. Bimodal epsilon-distribution. NATRE data show that epsilon (Ri < 1) approximately equals 10epsilon(Ri > 1), which our model reproduces. Heat to salt flux ratio. In the Ri much greater than 1 regime, the RSM predictions reproduce the data satisfactorily. NATRE mass diffusivity. The z-profile of the mass diffusivity reproduces well the measurements at NATRE. The local form of the mixing scheme is algebraic with one cubic equation to solve.

Canuto, V. M.↗

NASA NTRS1993

Effects of Buoyancy on Laminar, Transitional, and Turbulent Gas Jet Diffusion Flames

Gas jet diffusion flames have been a subject of research for many years. However, a better understanding of the physical and chemical phenomena occurring in these flames is still needed, and, while the effects of gravity on the burning process have been observed, the basic mechanisms responsible for these changes have yet to be determined. The fundamental mechanisms that control the combustion process are in general coupled and quite complicated. These include mixing, radiation, kinetics, soot formation and disposition, inertia, diffusion, and viscous effects. In order to understand the mechanisms controlling a fire, laboratory-scale laminar and turbulent gas-jet diffusion flames have been extensively studied, which have provided important information in relation to the physico-chemical processes occurring in flames. However, turbulent flames are not fully understood and their understanding requires more fundamental studies of laminar diffusion flames in which the interplay of transport phenomena and chemical kinetics is more tractable. But even this basic, relatively simple flame is not completely characterized in relation to soot formation, radiation, diffusion, and kinetics. Therefore, gaining an understanding of laminar flames is essential to the understanding of turbulent flames, and particularly fires, in which the same basic phenomena occur. In order to improve and verify the theoretical models essential to the interpretation of data, the complexity and degree of coupling of the controlling mechanisms must be reduced. If gravity is isolated, the complication of buoyancy-induced convection would be removed from the problem. In addition, buoyant convection in normal gravity masks the effects of other controlling parameters on the flame. Therefore, the combination of normal-gravity and microgravity data would provide the information, both theoretical and experimental, to improve our understanding of diffusion flames in general, and the effects of gravity on the burning process in particular.

Bahadori, M. Yousef↗

NASA NTRS1973

Analysis of gas flow through a multilayer insulation system.

A theoretical investigation of gas flow inside a multilayer insulation system has been made for the case of the broadside pumping process. A set of simultaneous first-order differential equations for the temperature and pressure of the gas mixture was obtained by considering the diffusion mechanism of the gas molecules through the perforations on the insulation layers. A modified Runge-Kutta method was used for numerical experiment. The numerical stability problem was investigated. It has been shown that when the relaxation time is small compared with the time period over which the gas properties change appreciably, the set of differential equations can be replaced by a set of algebraic equations for solution. Numerical examples were given and comparison with experimental data was made.

Lin, J. T.↗

NASA NTRS1973

Thermal engineering research

Shih, C. C.↗

NASA NTRS1976

Design, development, and test of a laser velocimeter for high speed turbomachinery

The paper describes the design, development, and test of a laser Doppler velocimeter (LDV) to map the velocity fields in a small, high speed, 8:1 pressure ratio, 0.91 kg/s (2 lbm/s), centrifugal compressor. This instrument is being used as a diagnostic tool for the study of the basic fluid dynamics of the inducer, impeller and the diffuser regions of high pressure ratio, small, centrifugal compressors. The LDV instrumentation has been optimized to permit the measurement of instantaneous velocities up to approximately 500 m/s, measured in absolute coordinates, within a rotating compressor impeller. Velocities of the same magnitude can also be measured in the two-dimensional radial plane of the diffuser. It is shown that LDV can make nondisturbing gas velocity measurements and surmount the difficulties found in applying other types of aerodynamic instrumentation to this measurement problem.

Runstadler, P. W., Jr.↗