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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.

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NASA NTRS1990

Introduction to Fuzzy Set Theory

An introduction to fuzzy set theory is described. Topics covered include: neural networks and fuzzy systems; the dynamical systems approach to machine intelligence; intelligent behavior as adaptive model-free estimation; fuzziness versus probability; fuzzy sets; the entropy-subsethood theorem; adaptive fuzzy systems for backing up a truck-and-trailer; product-space clustering with differential competitive learning; and adaptive fuzzy system for target tracking.

Kosko, Bart↗
NASA NTRS2007

Nonstandard Analysis and Shock Wave Jump Conditions in a One-Dimensional Compressible Gas

Nonstandard analysis is a relatively new area of mathematics in which infinitesimal numbers can be defined and manipulated rigorously like real numbers. This report presents a fairly comprehensive tutorial on nonstandard analysis for physicists and engineers with many examples applicable to generalized functions. To demonstrate the power of the subject, the problem of shock wave jump conditions is studied for a one-dimensional compressible gas. It is assumed that the shock thickness occurs on an infinitesimal interval and the jump functions in the thermodynamic and fluid dynamic parameters occur smoothly across this interval. To use conservations laws, smooth pre-distributions of the Dirac delta measure are applied whose supports are contained within the shock thickness. Furthermore, smooth pre-distributions of the Heaviside function are applied which vary from zero to one across the shock wave. It is shown that if the equations of motion are expressed in nonconservative form then the relationships between the jump functions for the flow parameters may be found unambiguously. The analysis yields the classical Rankine-Hugoniot jump conditions for an inviscid shock wave. Moreover, non-monotonic entropy jump conditions are obtained for both inviscid and viscous flows. The report shows that products of generalized functions may be defined consistently using nonstandard analysis; however, physically meaningful products of generalized functions must be determined from the physics of the problem and not the mathematical form of the governing equations.

Baty, Roy S.↗
NASA NTRS1994

On the Dynamics of TVD Schemes

The dynamics of a class of TVD schemes for model hyperbolic and parabolic equations is studied numerically using a highly parallel supercomputer (CM-5). The objective is to utilize the highly parallel property of the CM-5 to reveal the reliable time step and entropy parameter ranges, and the degree of compressible flux limiters to avoid slow convergence and the production of nonphysical numerical solutions. We choose to study the nonlinear stability property of TVD schemes numerically since it is otherwise not amenable analytically.

Yee, H. C.↗
NASA NTRS1988

Cosmological quantum chromodynamics, neutron diffusion, and the production of primordial heavy elements

A simple one-dimensional model is used to describe the evolution of neutron density before and during nucleosynthesis in a high-entropy bubble left over from the cosmic quark-hadron phase transition. It is shown why cosmic nucleosynthesis in such a neutron-rich environment produces a surfeit of elements heavier than lithium. Analytical and numerical techniques are used to estimate the abundances of carbon, nitrogen, and heavier elements up to Ne-22. A high-density neutron-rich region produces enough primordial N-14 to be observed in stellar atmospheres. It shown that very heavy elements may be created in a cosmological r-process; the neutron exposure in the neutron-rich regions is large enough for the Ne-22 to trigger a catastrophic r-process runaway in which the quantity of heavy elements doubles in much less than an expansion time due to fission cycling. A primordial abundance of r-process elements is predicted to appear as an excess of rare earth elements in extremely metal-poor stars.

Applegate, J. H.↗
NASA NTRS2002

Diurnal Cycle of Convection in the East Pacific ITCZ during EPIC-2001

During the last three weeks of September 2001, the EPIC-2001 intensive field campaign focused on studies of deep convection in the ITCZ over the Mexican warm pool region (10N, 95W) of the East Pacific. This study focuses on the pronounced observed diurnal cycle of environmental and convective parameters within the experiment domain. Data from three primary sources are examined: the R/V Ronald H. Brown C-band weather radar, 4-hourly soundings from the Brown and the Global Atmospherics, Inc. National Lightning Detection Network (long range product). Satellite data from TRMM, GOES and OV-1 are also used. The domain boundary layer shows a robust daily evolution of moist enthalpy (as reflect by equivalent potential temperature, theta-e, or wet bulb potential temperature, theta-w), with contributions from changes in both dry and moist entropy. Peak theta-w is found after local nightfall; the average diurnal range of theta-w is approximately 1 deg C. A composite diurnal cycle of convective properties was derived from the C-band volume scans, sampled continuously through the experiment at 10 minute updates. Products derived from the volumetric data include a surface PPI, 15 and 30 dBZ echo top height, vertically integrated liquid, and 6 km (mixed phase region) reflectivity CAPPIs. For almost all products, the parameter means showed virtually no diurnal cycle. However, for the upper-level products, the parameter spectra showed a clear peak in the occurrence of deep/vigorous convection (the "tail end of the distribution") between 7-9 UTC (1-3 AM local), while overall frequency of occurrence peaked later, from 12-15 UTC (6-9 AM local). This represents a daily "outbreak" of isolated deep cells a couple of hours after sunset and subsequent growth, organization and decay through the nighttime hours. The coherence of the diurnal cycle of the convective spectrum is impressive given the wide variety of convective organization observed during the experiment, and given the modulation by passage of 3-5 day easterly waves. While earlier satellite OLR composites suggested an offshore coastal migration of storms into the domain at night, examination of the 150 km and 300 km range radar products showed little evidence of such organization; almost all convection developed "in-place" within the analysis domain. Consistent with the diurnal thermodynamic and microphysical evolution, a clear cycle in cloud-to-ground (CG) lightning occurrence was observed. The local CG diurnal cycle is significantly stronger than the satellite-derived tropical ocean diurnal cycle of total (IC+CG) lightning. Flash rates of 3-4 fl/min were often visually observed after nightfall; these are fairly 'healthy' flash rates for tropical ocean storms, and the domain was qualitatively noted to be unusually lightning-productive by the R/V Brown crew (also consistent with satellite-based climatologies).

Boccippio, Dennis J.↗
NASA NTRS2000

On the Spatial Distribution of High Velocity Al-26 Near the Galactic Center

We present results of simulations of the distribution of 1809 keV radiation from the decay of Al-26 in the Galaxy. Recent observations of this emission line using the Gamma Ray Imaging Spectrometer (GRIS) have indicated that the bulk of the AL-26 must have a velocity of approx. 500 km/ s. We have previously shown that a velocity this large could be maintained over the 10(exp 6) year lifetime of the Al-26 if it is trapped in dust grains that are reaccelerated periodically in the ISM. Here we investigate whether a dust grain velocity of approx. 500 km/ s will produce a distribution of 1809 keV emission in latitude that is consistent with the narrow distribution seen by COMPTEL. We find that dust grain velocities in the range 275 - 1000 km/ s are able to reproduce the COMPTEL 1809 keV emission maps reconstructed using the Richardson-Lucy and Maximum Entropy image reconstruction methods while the emission map reconstructed using the Multiresolution Regularized Expectation Maximization algorithm is not well fit by any of our models. The Al-26 production rate that is needed to reproduce the observed 1809 keV intensity yields in a Galactic mass of Al-26 of approx. 1.5 - 2 solar mass which is in good agreement with both other observations and theoretical production rates.

Sturner, Steven J.↗
NASA NTRSDate not supplied

Verification of Viscous Goal-Based Anisotropic Mesh Adaptation

Adaptive unstructured mesh techniques have a limited, but growing impact on production analysis workflows where the control of discretization error is critical to obtaining reliable simulation results. Recent progress has matured a number of independent implementations of flow solvers, anisotropic metric construction methods, and anisotropic mesh adaptation mechanics. A key ingredient for the broader acceptance of unstructured mesh adaptation is the verification of these implementations. Anisotropic metric construction methods are evaluated with analytically defined primal fields and the corresponding entropy variables as adjoint fields. This allows the comparison of different metric formulations and different implementations of the same formulation without the complications of a flow and adjoint solution method. The convergence of the output associated with the entropy variable adjoint is studied for mesh adaptation to these fields and a manufactured solution. Mesh adapted drag output is studied for two simple wings in compressible laminar flow to show fine-mesh convergence of multiple metric construction methods to less than a single drag count. The documentation of these verification exercises helps to prepare these goal-based methods for routine use in more complex simulations for production workflows.

mesh adaptation↗
NASA NTRS1994

The delayed-detonation model of Type Ia supernovae. 2: The detonation phase

The investigation, by use of two-dimensional numerical hydrodynamics simulations, of the 'delayed detonation' mechanism of Khokhlov for the explosion of Type Ia supernovae is continued. Previously we found that the deflagration is insufficient to unbind the star. Expansion shuts off the flame; much of this small production of iron group nuclei occurs at lower densities, which reduces the electron-capture problem. Because the degenerate star has an adiabatic exponent only slightly above 4/3, the energy released by deflagration drives a pulsation of large amplitude. During the first expansion phase, adiabatic cooling shuts off the burning, and a Rayleigh-Taylor instability then gives mixing of high-entropy ashes with low-entropy fuel. During the first contraction phase, compressional heating reignites the material. The burning was allowed to develop into a detonation in these nonspherical models. The detonation grows toward spherical symmetry at late times. At these densities (rho approx. 10(exp 7) to 10(exp 8) g cm(exp -3)), either Ni-56 or nuclei of the Si-Ca group are the dominant products of the burning. The bulk yields are sensitive to the density of the star when the transition to detonation occurs. The relevance of the abundances, velocities, mixing, and total energy release to the theory and interpretation of Type Ia supernovae is discussed.

Arnett, David↗
NASA NTRS2016

Towards an Entropy Stable Spectral Element Framework for Computational Fluid Dynamics

Entropy stable (SS) discontinuous spectral collocation formulations of any order are developed for the compressible Navier-Stokes equations on hexahedral elements. Recent progress on two complementary efforts is presented. The first effort is a generalization of previous SS spectral collocation work to extend the applicable set of points from tensor product, Legendre-Gauss-Lobatto (LGL) to tensor product Legendre-Gauss (LG) points. The LG and LGL point formulations are compared on a series of test problems. Although being more costly to implement, it is shown that the LG operators are significantly more accurate on comparable grids. Both the LGL and LG operators are of comparable efficiency and robustness, as is demonstrated using test problems for which conventional FEM techniques suffer instability. The second effort generalizes previous SS work to include the possibility of p-refinement at non-conforming interfaces. A generalization of existing entropy stability machinery is developed to accommodate the nuances of fully multi-dimensional summation-by-parts (SBP) operators. The entropy stability of the compressible Euler equations on non-conforming interfaces is demonstrated using the newly developed LG operators and multi-dimensional interface interpolation operators.

Carpenter, Mark H.↗
NASA NTRS1994

The r-process and neutrino-heated supernova ejecta

As a neutron star is formed by the collapse of the iron core of a massive star, its Kelvin-Helmholtz evolution is characterized by the release of gravitational binding energy as neutrinos. The interaction of these neutrinos with heated material above the neutron star generates a hot bubble in an atmosphere that is nearly in hydrostatic equilibrium and heated, after approximately 10 s, to an entropy of S/N(sub AS)k greater than or approximately = 400. The neutron-to-proton ratio for material moving outward through this bubble is set by the balance between neutrino and antineutrino capture on nucleons. Because the electron antineutrino spectrum at this time is hotter than the electron neutrino spectrum, the bubble is neutron-rich (0.38 less than or approximately = Y(sub e) less than or approximately = 0.47). Previous work using a schematic model has shown that these conditions are well suited to the production of heavy elements by the r-process. In this paper we have advanced the numerical modeling of a 20 solar mass 'delayed' supernova explosion to the point that we can follow the detailed evolution of material moving through the bubble at the late times appropiate to r-process nucleosynthesis. The supernova model predicts a final kinetic energy for the ejecta of 1.5 x 10(exp 51) ergs and leaves behind a remnant with a baryon mass of 1.50 solar mass (and a gravitational mass of 1.445 solar mass). We follow the thermodynamic and compositional evolution of 40 trajectories in rho(t), T(t), Y(sub e)(t) for a logarithmic grid of mass elements for the last approximately = 0.03 solar mass to be ejected by the proto-neutron star down to the last less than 10(exp -6) solar mass of material expelled at up to approximately = 18 s after core collapse. We find that an excellent fit to the solar r-process abundance distribution is obtained with no adjustable parameters in the nucleosynthesis calculations. Moreover, the abundances are produced in the quantities required to account for the present Galactic abundances. However, at earlier times, this one-dimensional model ejects too much material with entropies S/N(sub A)k approximately 50 and Y(sub e) approximately 0.46. This leads to an acceptable over production of N = 50 nuclei, particularly Sr-88, Y-89, and Zr-90, relative to their solar abundances. We speculate on various means to avoid the early overproduction and/or ejection of N = 50 isotonic nuclei while still producing and ejecting the correct amount of r-process material.

Woosley, S. E.↗
NASA NTRS1959

A General Method for Automatic Computation of Equilibrium Compositions and Theoretical Rocket Performance of Propellants

A general computer program for chemical equilibrium and rocket performance calculations was written for the IBM 650 computer with 2000 words of drum storage, 60 words of high-speed core storage, indexing registers, and floating point attachments. The program is capable of carrying out combustion and isentropic expansion calculations on a chemical system that may include as many as 10 different chemical elements, 30 reaction products, and 25 pressure ratios. In addition to the equilibrium composition, temperature, and pressure, the program calculates specific impulse, specific impulse in vacuum, characteristic velocity, thrust coefficient, area ratio, molecular weight, Mach number, specific heat, isentropic exponent, enthalpy, entropy, and several thermodynamic first derivatives.

Gordon, Sanford↗
NASA NTRS1988

Extrema principles of entrophy production and energy dissipation in fluid mechanics

A survey is presented of several extrema principles of energy dissipation as applied to problems in fluid mechanics. An exact equation is derived for the dissipation function of a homogeneous, isotropic, Newtonian fluid, with terms associated with irreversible compression or expansion, wave radiation, and the square of the vorticity. By using entropy extrema principles, simple flows such as the incompressible channel flow and the cylindrical vortex are identified as minimal dissipative distributions. The principal notions of stability of parallel shear flows appears to be associated with a maximum dissipation condition. These different conditions are consistent with Prigogine's classification of thermodynamic states into categories of equilibrium, linear nonequilibrium, and nonlinear nonequilibrium thermodynamics; vortices and acoustic waves appear as examples of dissipative structures. The measurements of a typical periodic shear flow, the rectangular wall jet, show that direct measurements of the dissipative terms are possible.

Horne, W. Clifton↗
NASA NTRS1975

Thermochemical production of hydrogen via multistage water splitting processes

This paper presents and reviews the fundamental thermodynamic principles underlying thermochemical water splitting processes. The overall system is considered first and the temperature limitation in process thermal efficiency is developed. The relationship to an ideal water electrolysis cell is described and the nature of efficient multistage reaction processes is discussed. The importance of the reaction entropy change and the relation of the reaction free energy change to the work of separation is described. A procedure for analyzing thermochemical water splitting processes is presented and its use to calculate individual stage efficiency is demonstrated. A number of processes are used to illustrate the concepts and procedures.

Funk, J. E.↗
NASA NTRS1991

Data compression: The end-to-end information systems perspective for NASA space science missions

The unique characteristics of compressed data have important implications to the design of space science data systems, science applications, and data compression techniques. The sequential nature or data dependence between each of the sample values within a block of compressed data introduces an error multiplication or propagation factor which compounds the effects of communication errors. The data communication characteristics of the onboard data acquisition, storage, and telecommunication channels may influence the size of the compressed blocks and the frequency of included re-initialization points. The organization of the compressed data are continually changing depending on the entropy of the input data. This also results in a variable output rate from the instrument which may require buffering to interface with the spacecraft data system. On the ground, there exist key tradeoff issues associated with the distribution and management of the science data products when data compression techniques are applied in order to alleviate the constraints imposed by ground communication bandwidth and data storage capacity.

Tai, Wallace↗
NASA NTRS1975

Theoretical study of production of unique glasses in space

The potential of producing the glassy form of selected materials in the weightless, containerless nature of space processing is examined through the development of kinetic relationships describing nucleation and crystallization phenomena. Transformation kinetics are applied to a well-characterized system (SiO2), an excellent glass former (B2O3), and a poor glass former (Al2O3) by conventional earth processing methods. Viscosity and entropy of fusion are shown to be the primary materials parameters controlling the glass forming tendency. For multicomponent systems diffusion-controlled kinetics and heterogeneous nucleation effects are considered. An analytical empirical approach is used to analyze the mullite system. Results are consistent with experimentally observed data and indicate the promise of mullite as a future space processing candidate.

Larsen, D. C.↗
NASA NTRS1984

Application of maximum entropy optimal projection design synthesis to the NASA Spacecraft Control Laboratory Experiment (SCOLE)

The scope of this study covered steady-state, continuous-time vibration control under disturbances applied to the Space Shuttle and continuous-time models of actuators, sensors, and disturbances. Focus was on a clear illustration of the methodology, therefore sensor/actuator dynamics were initially ignored, and a finite element model of the NASA Spacecraft Control Laboratory Experiment (SCOLE) was conducted, including products of inertia and offset of reflector CM from the mast tip.

Hyland, Dave↗
NASA NTRS1978

Computer program for obtaining thermodynamic and transport properties of air and products of combustion of ASTM-A-1 fuel and air

A computer program for determining desired thermodynamic and transport property values by means of a three-dimensional (pressure, fuel-air ratio, and either enthalpy or temperature) interpolation routine was developed. The program calculates temperature (or enthalpy), molecular weight, viscosity, specific heat at constant pressure, thermal conductivity, isentropic exponent (equal to the specific heat ratio at conditions where gases do not react), Prandtl number, and entropy for air and a combustion gas mixture of ASTM-A-1 fuel and air over fuel-air ratios from zero to stoichiometric, pressures from 1 to 40 atm, and temperatures from 250 to 2800 K.

Hippensteele, S. A.↗
NASA NTRS1995

Stealth Plumes on Io

We suggest that Io's eruptive activity may include a class of previously undetected SO2 geysers. The thermodynamic models for the eruptive plumes discovered by Voyager 'involve low to moderate entropy SO2 eruptions. The resulting plumes are a mixture of solid and gas which emerge from the vent and follow essentially ballistic trajectories. We show that intrusion of silicate magma into buried SO2 deposits can create the required conditions for high entropy eruptions which proceed entirely in the vapor phase. These purely gaseous plumes would have been invisible to Voyager's instruments. Hence, we call them "stealth" plumes. Such eruptions could explain the "patchy" SO2 atmosphere inferred from recent UV and micro-wave spectral observations. The magma intrusion rate required to support the required gas production for these plumes is a negligible fraction of estimated global magma intrusion rates.

Johnson, T. V.↗