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At least 1,315 records · Page 73
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NASA NTRS1990

Mathematical theory of a relaxed design problem in structural optimization

Various attempts have been made to construct a rigorous mathematical theory of optimization for size, shape, and topology (i.e. layout) of an elastic structure. If these are represented by a finite number of parametric functions, as Armand described, it is possible to construct an existence theory of the optimum design using compactness argument in a finite dimensional design space or a closed admissible set of a finite dimensional design space. However, if the admissible design set is a subset of non-reflexive Banach space such as L(sup infinity)(Omega), construction of the existence theory of the optimum design becomes suddenly difficult and requires to extend (i.e. generalize) the design problem to much more wider class of design that is compatible to mechanics of structures in the sense of variational principle. Starting from the study by Cheng and Olhoff, Lurie, Cherkaev, and Fedorov introduced a new concept of convergence of design variables in a generalized sense and construct the 'G-Closure' theory of an extended (relaxed) optimum design problem. A similar attempt, but independent in large extent, can also be found in Kohn and Strang in which the shape and topology optimization problem is relaxed to allow to use of perforated composites rather than restricting it to usual solid structures. An identical idea is also stated in Murat and Tartar using the notion of the homogenization theory. That is, introducing possibility of micro-scale perforation together with the theory of homogenization, the optimum design problem is relaxed to construct its mathematical theory. It is also noted that this type of relaxed design problem is perfectly matched to the variational principle in structural mechanics.

Kikuchi, Noboru↗
NASA NTRS1993

Psychophysiological measures of cognitive workload in laboratory and flight

Psychophysiological data have been recorded during different levels of cognitive workload in laboratory and flight settings. Cardiac, eye blink, and brain data have shown meaningful changes as a function of the levels of mental workload. Increased cognitive workload is generally associated with increased heart rates, decreased blink rates and eye closures, and decreased evoked potential amplitudes. However, comparisons of laboratory and flight data show that direct transference of laboratory findings to the flight environment is not possible in many cases. While the laboratory data are valuable, a data base from flight is required so that 'real world' data can be properly interpreted.

Wilson, Glenn F.↗
NASA NTRS1993

Stable isotope analyses of the peralkaline volcanics Gregory Rift Valley, Kenya

Delta O-18 analyses of the Naivasha rhyolites, basalts, Menengai trachytes and the Yatta phonolite are presented together with D/H analyses of the Naivasha rhyolites. Delta O-18 results vary from 5.7 to 8.9 per mill which is within the reported range of delta O-18 analyses for continental volcanics. Closure temperatures calulated from the basalts and rhyolites show equilibration to be at magmatic temperatures. D/H values range from -40 to -148 per mill indicating that the rhyolites have undergone large scale degasssing.

Black, S.↗
NASA NTRS1993

Ar-39 - Ar-40 ages of acapulcoites and lodranites: Evidence for early parent body heating

New age dating of acapulcoites (Acapulco, Monument Draw) and lodranites (Gibson) allow us to reconstruct the history of their parent body in a chronological framework. These meteorites originated on a common parent body -4.55 Ga ago. Non-collisional heating caused partial melting, with lodranites having been heated slightly higher than acapulcoites. This parent body cooled to the Ar closure temperature at -4.51 Ga for acapulcoites and -4.48 Ga for lodranites. The difference in ages is consistent with the higher temperature and longer cooling time for lodranites. Cooling probably occurred at a few to tens of deg C/Ma, with slower cooling rates at lower temperatures.

Bogard, D. D.↗
NASA NTRS1993

Micro-zoning in minerals of a Landes silicate inclusion

There is an increasing number of meteorites with chondritic bulk composition but completely different textures than the conventional chondrite groups. Winonaites, Acapulcoites and silicate inclusions in IAB-iron meteorites have in common coarse grain size, highly equilibrated mineralogy with frequent 120 deg triple junctions and they record a significantly lower degree of oxidation than ordinary chondrites. They all have equilibration temperatures, based on Ca-exchange among pyroxenes, of around 900 to 1100 deg C. However, on cooling disequilibrium features may develop: (1) Olivine in IAB-inclusions has lower Fa-content than equilibrium Fs-content of pyroxenes requires; (2) CaO-zoning in olivine was established at temperatures of around 500 deg C, several hundred degrees below pyroxene equilibration temperatures. Obviously, olivine responded faster to changes in fO2 (Fa in olivine) and temperature (Ca-zoning) than pyroxenes. Differences in diffusion coefficients can readily explain the observed trends. Here we report on much more subtle zoning features in pyroxenes. TEM-observations reveal large compositional gradients in Ca, Na, Cr, Ti and Fe within the first micrometer of cpx and opx crystals. In summary, the data reflect the complicated subsolidus history of a chondritic mineral assemblage that was in thermodynamic equilibrium at about 900 deg C and cooled slowly from this temperature whereby oxidation reactions and different closure temperatures for various minerals and elements played an important role. The oxidation of P dissolved in metal and formation of phosphate, which is thermodynamically stable at low temperatures, is suggested to be responsible for most of the observed zoning.

Eisenhour, D. D.↗
NASA NTRS1993

Progress in modeling hypersonic turbulent boundary layers

A good knowledge of the turbulence structure, wall heat transfer, and friction in turbulent boundary layers (TBL) at high speeds is required for the design of hypersonic air breathing airplanes and reentry space vehicles. This work reports on recent progress in the modeling of high speed TBL flows. The specific research goal described here is the development of a second order closure model for zero pressure gradient TBL's for the range of Mach numbers up to hypersonic speeds with arbitrary wall cooling requirements.

Zeman, Otto↗
NASA NTRS1993

An investigation of small scales of turbulence in a boundary layer at high Reynolds numbers

The assumption that turbulence at large wave-numbers is isotropic and has universal spectral characteristics which are independent of the flow geometry, at least for high Reynolds numbers, has been a cornerstone of closure theories as well as of the most promising recent development in the effort to predict turbulent flows, viz. large eddy simulations. This hypothesis was first advanced by Kolmogorov based on the supposition that turbulent kinetic energy cascades down the scales (up the wave-numbers) of turbulence and that, if the number of these cascade steps is sufficiently large (i.e. the wave-number range is large), then the effects of anisotropies at the large scales are lost in the energy transfer process. Experimental attempts were repeatedly made to verify this fundamental assumption. However, Van Atta has recently suggested that an examination of the scalar and velocity gradient fields is necessary to definitively verify this hypothesis or prove it to be unfounded. Of course, this must be carried out in a flow with a sufficiently high Reynolds number to provide the necessary separation of scales in order unambiguously to provide the possibility of local isotropy at large wave-numbers. An opportunity to use our 12-sensor hot-wire probe to address this issue directly was made available at the 80'x120' wind tunnel at the NASA Ames Research Center, which is normally used for full-scale aircraft tests. An initial report on this high Reynolds number experiment and progress toward its evaluation is presented.

Wallace, James M.↗
NASA NTRS1993

The helical decomposition and the instability assumption

Direct numerical simulations show that the triadic transfer function T(k,p,q) peaks sharply when q (or p) is much smaller than k. The triadic transfer function T(k,p,q) gives the rate of energy input into wave number k from all interactions with modes of wave number p and q, where k, p, q form a triangle. This observation was thought to suggest that energy is cascaded downscale through non-local interactions with local transfer and that there was a strong connection between large and small scales. Both suggestions were in contradiction with the classical Kolmogorov picture of the energy cascade. The helical decomposition was found useful in distinguishing between kinematically independent interactions. That analysis has gone beyond the question of non-local interaction with local transfer. In particular, an assumption about the statistical direction of triadic energy transfer in any kinematically independent interaction was introduced (the instability assumption). That assumption is not necessary for the conclusions about non-local interactions with local transfer recalled above. In the case of turbulence under rapid rotation, the instability assumption leads to the prediction that energy is transferred in spectral space from the poles of the rotation axis toward the equator. The instability assumption is thought to be of general validity for any type of triad interactions (e.g. internal waves). The helical decomposition and the instability assumption offer detailed information about the homogeneous statistical dynamics of the Navier-Stokes equations. The objective was to explore the validity of the instability assumption and to study the contributions of the various types of helical interactions to the energy cascade and the subgrid-scale eddy-viscosity. This was done in the context of spectral closures of the Direct Interaction or Quasi-Normal type.

Waleffe, Fabian A.↗
NASA NTRS1993

PDF approach for turbulent scalar field: Some recent developments

The probability density function (PDF) method has been proven a very useful approach in turbulence research. It has been particularly effective in simulating turbulent reacting flows and in studying some detailed statistical properties generated by a turbulent field There are, however, some important questions that have yet to be answered in PDF studies. Our efforts in the past year have been focused on two areas. First, a simple mixing model suitable for Monte Carlo simulations has been developed based on the mapping closure. Secondly, the mechanism of turbulent transport has been analyzed in order to understand the recently observed abnormal PDF's of turbulent temperature fields generated by linear heat sources.

Gao, Feng↗
NASA NTRS1993

The evolution equation for the flame surface density in turbulent premixed combustion

The mean reaction rate in flamelet models for turbulent premixed combustion depends on two basic quantities: a mean chemical rate, called the flamelet speed, and the flame surface density. Our previous work had been primarily focused on the problem of the structure and topology of turbulent premixed flames, and it was then determined that the flamelet speed, when space-averaged, is only weakly sensitive to the turbulent flow field. Consequently, the flame surface density is the key quantity that conveys most of the effects of the turbulence on the rate of energy release. In flamelet models, this quantity is obtained via a modeled transport equation called the Sigma-equation. Past theoretical work has produced a rigorous approach that leads to an exact but unclosed formulation for the turbulent Sigma-equation. In the exact Sigma-equation, it appears that the dynamical properties of the flame surface density are determined by a single parameter, namely the turbulent flame stretch. Unfortunately, the turbulent flame stretch as well as the flame surface density is not available from experiments, and, in the absence of experimental data, little is known on the validity of the closure assumptions used in current flamelet models. Direct Numerical Simulation (DNS) is the alternative approach to get basic information on these fundamental quantities. In the present work, three-dimensional DNS of premixed flames in isotropic turbulent flow is used to estimate the different terms appearing in the Sigma-equation. A new methodology is proposed to provide the source and sink terms for the flame surface density, resolved both temporally and spatially throughout the turbulent flame brush. Using this methodology, our objective is to extract the turbulent flame stretch from the DNS data base and then perform extensive comparisons with flamelet models. Thanks to the detailed information produced by the DNS-based analysis, it is expected that this type of comparison will not only underscore the shortcomings of current models, but also suggest ways to improve them.

Trouve, Arnaud↗
NASA NTRS1993

Why does preferential diffusion strongly affect premixed turbulent combustion?

Combustion of premixed reactants in a turbulent flow is a classical but unresolved problem. The key problem is to explain the following data: the maximal turbulent and laminar burning velocities u(sub t) and u(sub L) occur at different equivalence ratios Phi. It is known that the equivalence ratio varies along a curved flame if molecular diffusivity D(sub fuel) does not equal D(sub oxygen). However, the mean flame radius of curvature is much larger than the laminar flame thickness delta-L. Therefore, significant influence of preferential diffusion should occur only if the flame propagation speed varies with flame curvature. This conclusion agrees with Zel'dovich's long-standing idea about the important role of leading points of a flame. The main objective of this paper is to prove Zel'dovich's hypothesis. An equation for the mean flame surface area density (MFSAD) is employed for this purpose. The second objective of this paper is to suggest a different approach to the derivation of the equation for MFSAD. It is based on the pdf equation for the reaction progress variable C and the relation between the pdf and MFSAD. This treatment suggests an entirely different closure assumption.

Kuznetsov, Vadim R.↗
NASA NTRS1993

Development of a recursion RNG-based turbulence model

Reynolds stress closure models based on the recursion renormalization group theory are developed for the prediction of turbulent separated flows. The proposed model uses a finite wavenumber truncation scheme to account for the spectral distribution of energy. In particular, the model incorporates effects of both local and nonlocal interactions. The nonlocal interactions are shown to yield a contribution identical to that from the epsilon-renormalization group (RNG), while the local interactions introduce higher order dispersive effects. A formal analysis of the model is presented and its ability to accurately predict separated flows is analyzed from a combined theoretical and computational stand point. Turbulent flow past a backward facing step is chosen as a test case and the results obtained based on detailed computations demonstrate that the proposed recursion -RNG model with finite cut-off wavenumber can yield very good predictions for the backstep problem.

Zhou, YE↗
NASA NTRS1993

A long-term space astrophysics research program: The evolution of the quasar continuum

The research program supported by this grant now has great momentum. Numerous papers are in progress, and a strong multi-wavelength observing program is rapidly accumulating data on samples of high redshift quasars across the spectrum. ROSAT spectra of quasars continue to yield surprises. Of four z = 3 quasars with X-ray spectra, three show strong absorption. This contrasts strongly with the situation for luminous AGN at low redshifts where fewer than 1 in 20 show X-ray absorption. A new site for this absorption is probably needed, either around the quasar (e.g. in a cluster cooling flow) or along the line of sight (e.g. in a Damped Lyman-alpha system). The unabsorbed quasar allows limits on the physical conditions in a damped Lyman-alpha cloud to be calculated, and will allow a X-ray Gunn-Peterson test to be applied that will limit the fraction of the closure mass in an intergalactic medium. The X-ray spectral indices of these z = 3 quasars show no change from those of similar objects at low z, suggesting that 'short-lifetime' models apply. Eight other z = 3-4 quasars have been detected and their energy distributions from X-rays to Infrared (using new infrared spectrographs) have been compiled. These are now being compared with the low z continua from the 'Atlas of Quasar Energy Distributions' to search for evolutionary changes. The discovery of a likely warm absorber in 3C351 made recognition of another example simple. Also, modeling of the conditions in the absorber in 3C351 using the OVI absorption line from HST and the high ionization emission lines, suggests that the broad line region is indeed the origin of the warm absorber in this quasar, and by extension, others. Warm absorbers can now be used as a new diagnostic of this region. The X-ray spectrum of a 'Red Quasar', 3C212, has a cut-off spectrum, which could be fitted by an absorbed power-law, or more remarkably, by an unabsorbed black body. Using our quasi-simultaneous optical data and photoionization modeling we are able to rule out this latter possibility. The long-sought key to understanding red quasars has now been found. (Reddening was earlier ruled out because no 2175A absorption feature was seen. This is now seen to have been misleading.)

Elvis, M.↗
NASA NTRS1992

The evolution equation for the flame surface density in turbulent premixed combustion

One central ingredient in flamelet models for turbulent premixed combustion is the flame surface density. This quantity conveys most of the effects of the turbulence on the rate of energy release and is obtained via a modeled transport equation, called the Sigma-equation. Past theoretical work has produced a rigorous approach that leads to an exact, but unclosed, formulation for the turbulent Sigma-equation. In this exact Sigma-equation, it appears that the dynamical properties of the flame surface density are determined by a single parameter, namely the turbulent flame stretch. Unfortunately, the flame surface density and the turbulent flame stretch are not available from experiments and, in the absence of experimental data, little is known on the validity of the closure assumptions used in current flamelet models. Direct Numerical Simulation (DNS) is the obvious, complementary approach to get basic information on these fundamental quantities. Three-dimensional DNS of premixed flames in isotropic turbulent flow is used to estimate the different terms appearing in the Sigma-equation. A new methodology is proposed to provide the source and sink terms for the flame surface density, resolved both temporally and spatially throughout the turbulent flame brush. Using this methodology, the effects of the Lewis number on the rate of production of flame surface area are described in great detail and meaningful comparisons with flamelet models can be performed. The analysis reveals in particular the tendency of the models to overpredict flame surface dissipation as well as their inability to reproduce variations due to thermo-diffusive phenomena. Thanks to the detailed information produced by a DNS-based analysis, this type of comparison not only underscores the shortcomings of current models but also suggests ways to improve them.

Trouve, A.↗
NASA NTRS1993

I-Xe structure of ILAFEGH 009 and shallowater: Evidence for early formation and rapid cooling of impact-derived enstatite meteorites

Enstatite meteorites have proven to be ideal samples for past studies of the I-Xe system. This work focuses on two enstatite meteorites that were formed by impact processes. Ilafegh 009 is a clast-free impact melt rock from the EL chondrite parent body. The Shallowater aubrite likely formed when a fully molten planetesimal collided with a solid planetesimal, mixing fragments of the solid planetesimal into the enstatite mantle of the molten planetesimal. A complex three-stage cooling history resulted from this mixing and later break-up and reassembly of the parent body. The present study indicates that the I-Xe structure of these two meteorites resulted from in situ decay of live I-129 and that both experienced xenon closure of the iodine host phase at approximately the same time. I-Xe cooling rates are consistent with the cooling rates derived from mineralogic and petrologic studies of these objects. The similarities in ages suggest that the region of the nebula in which enstatite parent bodies formed must have experienced an intense early bombardment.

Kehm, K.↗
NASA NTRS1993

Navier-Stokes calculations on multi-element airfoils using a chimera-based solver

A study of Navier-Stokes calculations of flows about multielement airfoils using a chimera grid approach is presented. The chimera approach utilizes structured, overlapped grids which allow great flexibility of grid arrangement and simplifies grid generation. Calculations are made for two-, three-, and four-element airfoils, and modeling of the effect of gap distance between elements is demonstrated for a two element case. Solutions are obtained using the thin-layer form of the Reynolds averaged Navier-Stokes equations with turbulence closure provided by the Baldwin-Lomax algebraic model or the Baldwin-Barth one equation model. The Baldwin-Barth turbulence model is shown to provide better agreement with experimental data and to dramatically improve convergence rates for some cases. Recently developed, improved farfield boundary conditions are incorporated into the solver for greater efficiency. Computed results show good comparison with experimental data which include aerodynamic forces, surface pressures, and boundary layer velocity profiles.

Jasper, Donald W.↗
NASA NTRS1993

Convex set and linear mixing model

A major goal of optical remote sensing is to determine surface compositions of the earth and other planetary objects. For assessment of composition, single pixels in multi-spectral images usually record a mixture of the signals from various materials within the corresponding surface area. In this report, we introduce a closed and bounded convex set as a mathematical model for linear mixing. This model has a clear geometric implication because the closed and bounded convex set is a natural generalization of a triangle in n-space. The endmembers are extreme points of the convex set. Every point in the convex closure of the endmembers is a linear mixture of those endmembers, which is exactly how linear mixing is defined. With this model, some general criteria for selecting endmembers could be described. This model can lead to a better understanding of linear mixing models.

Xu, P.↗
NASA NTRS1993

Model-based automatic generation of grasping regions

The problem of automatically generating stable regions for a robotic end effector on a target object, given a model of the end effector and the object is discussed. In order to generate grasping regions, an initial valid grasp transformation from the end effector to the object is obtained based on form closure requirements, and appropriate rotational and translational symmetries are associated with that transformation in order to construct a valid, continuous grasping region. The main result of this algorithm is a list of specific, valid grasp transformations of the end effector to the target object, and the appropriate combinations of translational and rotational symmetries associated with each specific transformation in order to produce a continuous grasp region.

Bloss, David A.↗