SEARCH · Search NASA

Results for “Tensor”

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 289 records · Page 16

All sources NASA NTRS DOE OSTI

NASA NTRS1994

Modeling the two-point correlation of the vector stream function

A new model for the two-point vector stream function correlation has been developed using tensor invariant arguments and evaluated by the comparison of model predictions with DNS data for incompressible homogeneous turbulent shear flow. This two-point vector stream function model correlation can then be used to calculate the two-point velocity correlation function and other quantities useful in turbulence modeling. The model assumes that the two-point vector stream function correlation can be written in terms of the separation vector and a new tensor function that depends only on the magnitude of the separation vector. The model has a single free model coefficient, which has been chosen by comparison with the DNS data. The relative error of the model predictions of the two-point vector stream function correlation is only a few percent for a broad range of the model coefficient. Predictions of the derivatives of this correlation, which are of interest in turbulence modeling, may not be this accurate.

Oberlack, M.↗

NASA NTRS1994

Signatures of bulge triaxiality from kinematics in Baade's window

We study a sample of 62 Baade's Window, (l,b) = (1, -4)deg, K giants that have published proper motions, radial velocity, and metallicity. Using R(sub 0) = 8 kpc, we construct the velocity ellipsoids, namely the 3x3 velocity dispersion tensors, for the metal rich stars ((Fe/H) greater than or equal to 0) and metal poor stars ((Fe/H) less than or equal to -0.2). After diagonalizing the tensor, we find a vertex deviation characteristic of a nonaxisymmetric system. Eigenvalues for the two velocity ellipsoids (sigma(sub 1), sigma(sub 2), sigma(sub 3)) are (126, 89, 65) +/- 13 km/s for the metal rich sample and (154, 77, 83) +/- 25 km/s for the metal poor sample with their long axes pointing to two nearly perpendicular directions (l(sub v), b(sub v)) = (-65 +/- 9 deg, +14 +/- 9 deg) and (l(sub v), b(sub v)) = (25 +/- 14 deg, -11 +/- 14 deg), respectively. The vertex deviations of the velocity ellipsoids cannot be consistently explained by any oblate model. We are able to reject the hypothesis that the metal poor and metal rich populations are drawn from the same distribution at better than the 97% confidence level. We populate orbits in a realistic bar potential with a Gaussian velocity distribution, allowing us to simulate and interpret observations. We conclude that the data are consistent with a triaxial bulge pointing towards (l,b) with l less than 0 deg and b = 0 deg as suggested by earlier work on gas dynamics and the observed light distribution. We also predict that low latitude (absolute value of b less than or equal to 4 deg) bulge fields should show the vertex deviation more strongly and would therefore be the best locations for future proper motion studies. In the classification scheme of Athanassoula et al. (1983) the metal rich stars appear to occupy the B-family orbits which rotate in the prograde sense in the rest frame and have boxy shapes that are aligned with and supporting the bar. The metal poor stars in the sample lag behind the metal rich bulge and appear to occupy R-family orbits which rotate in the retrograde sense in the rest frame. They have nearly round loop shapes and are aligned perpendicularly to the bar, hence limit the triaxiality of the bar potential. The correlations between the metallicity and the orbit families can develop if the bulge forms dissipatively on a sufficiently long time scale. However, it is difficult to explain such correlations if most stars in the inner Galaxy form during the violent relaxation phase.

Zhao, Hongsheng↗

NASA NTRS1996

Element Library for Three-Dimensional Stress Analysis by the Integrated Force Method

The Integrated Force Method, a recently developed method for analyzing structures, is extended in this paper to three-dimensional structural analysis. First, a general formulation is developed to generate the stress interpolation matrix in terms of complete polynomials of the required order. The formulation is based on definitions of the stress tensor components in term of stress functions. The stress functions are written as complete polynomials and substituted into expressions for stress components. Then elimination of the dependent coefficients leaves the stress components expressed as complete polynomials whose coefficients are defined as generalized independent forces. Such derived components of the stress tensor identically satisfy homogenous Navier equations of equilibrium. The resulting element matrices are invariant with respect to coordinate transformation and are free of spurious zero-energy modes. The formulation provides a rational way to calculate the exact number of independent forces necessary to arrive at an approximation of the required order for complete polynomials. The influence of reducing the number of independent forces on the accuracy of the response is also analyzed. The stress fields derived are used to develop a comprehensive finite element library for three-dimensional structural analysis by the Integrated Force Method. Both tetrahedral- and hexahedral-shaped elements capable of modeling arbitrary geometric configurations are developed. A number of examples with known analytical solutions are solved by using the developments presented herein. The results are in good agreement with the analytical solutions. The responses obtained with the Integrated Force Method are also compared with those generated by the standard displacement method. In most cases, the performance of the Integrated Force Method is better overall.

Kaljevic, Igor↗

NASA NTRS1995

Turbulence modeling for non-equilibrium flow

The work performed during this year has involved further assessment and extension of the k-epsilon-v(exp 2) model, and initiation of work on scalar transport. The latter is introduced by the contribution of Y. Shabany to this volume. Flexible, computationally tractable models are needed for engineering CFD. As computational technology has progressed, the ability and need to use elaborate turbulence closure models has increased. The objective of our work is to explore and develop new analytical frameworks that might extend the applicability of the modeling techniques. In past years the development of a method for near-wall modeling was described. The method has been implemented into a CFD code and its viability has been demonstrated by various test cases. Further tests are reported herein. Non-equilibrium near-wall models are needed for some heat transfer applications. Scalar transport seems generally to be more sensitive to non-equilibrium effects than is momentum transport. For some applications turbulence anisotropy plays a role and an estimate of the full Reynolds stress tensor is needed. We have begun work on scalar transport per se, but in this brief I will only report on an extension of the k-epsilon-v(exp 2) model to predict the Reynolds stress tensor.

Durbin, P. A.↗

NASA NTRS1995

A new approach to the formulation of scalar flux closure

This report shows that if a stochastic differential equation (Langevin equation) for velocity fluctuation vector is known, it is possible to derive the equations for scalar flux transport. Durbin and Speziale (1994) showed that the second moment of this stochastic differential equation gives an equation for the evolution of Reynolds stress tensor. Similarly, the stochastic equation will give an equation for scalar flux. Therefore, a coupling between these two is present. The basis for the present work is that there should be Langevin equations that can produce acceptable models for both the Reynolds stress tensor and the scalar flux vector. Having found this basic Langevin equation, the amount of work needed to model the second order closure problems is reduced; using the well developed models for Reynolds stress equations, it will be possible to derive corresponding models for scalar flux equation.

Shabany, Y.↗

NASA NTRS1996

The numerical simulation of multistage turbomachinery flows

The effect of the unsteady flow field in a multistage compressor on the time-averaged performance was assessed. The energy transport by the unsteady deterministic flow field was taken into account. The magnitude of the body force resulting from the aerodynamic loading on a blade row was compared to the gradient of the stress tensor associated with the unsteady time-resolved flow field generated by the blade row. The magnitude of the work performed by these forces was compared to the divergence of the energy correlations produced by the unsteady time-resolved flow field. The stress tensor and the energy correlations are non-negligible in the end wall regions. The results suggest that the turbulence is the primary source of flow mixing in the midspan region.

Adamczyk, John J.↗

NASA NTRS1995

The Physics of Turbulence in the Boundary Layer

The geometry of the velocity field in a numerically simulated incompressible turbulent boundary layer over a flat plate at Re theta=670 has been studied using the invariants of the velocity gradient tensor. These invariants are computed at every grid point in the flow and used to form the discriminant. Of primary interest are those regions in the flow where the discriminant is positive; regions where, according to the characteristic equation, the eigenvalues of the velocity gradient tensor are complex. An observer moving with a frame of reference which is attached to a fluid particle lying within such a region would see a local flow pattern of the type stable-focus-stretching or unstable-focus-compressing. When the flow is visualized this way, continuous, connected, large-scale structures are revealed that extend from the point just below the buffer layer out to the beginning of the wake region. These structures are aligned with the mean shear close to the wall and arch in the cross-stream direction away from the wall. In some cases the structures observed are very similar to to the hairpin eddy vision of boundary layer structure proposed by Theodorsen. That the structure of the flow is revealed more effectively by the discriminant rather than by the vorticity is important and adds support to recent observations of the discriminant in a channel flow simulation. Of particular importance is the fact that the procedure does not require the use of an arbitrary threshold in the discriminant. Further analysis using computer flow visualization shows a high degree of spatial correlation between regions of positive discriminant, extreme negative pressure fluctuations and large instantaneous values of Reynolds shear stress.

Kline, Stephen↗

NASA NTRS1995

Natural Strain

The purpose of this paper is to present a consistent and thorough development of the strain and strain-rate measures affiliated with Hencky. Natural measures for strain and strain-rate, as I refer to them, are first expressed in terms of of the fundamental body-metric tensors of Lodge. These strain and strain-rate measures are mixed tensor fields. They are mapped from the body to space in both the Eulerian and Lagrangian configurations, and then transformed from general to Cartesian fields. There they are compared with the various strain and strain-rate measures found in the literature. A simple Cartesian description for Hencky strain-rate in the Lagrangian state is obtained.

Freed, Alan D.↗

NASA NTRS1996

[Two-phase Interfaces in Weak External Fields]

Our aim has been that of understanding from first principles the behavior of two-phase interfaces in the absence of gravitational constraints. This is fundamental to our ability to deal with the fluid structures that abound in the real biological, chemical, and physical world. A substantial effort was mounted to determine how familiar hydrodynamic concepts have to be modified and interpreted to make them appropriate to the multi-level structure alluded to above. This was primarily in the context of the microscopic symmetric pressure tensor, which was, for the first time, expressed in the invaluable density functional format, and the used to follow the predictions of popular microscopic models of the energetics of interfacial systems. In the course of these investigations, the previous murky relation between pressure tensor and thermodynamics was completely clarified. The process of extending thermodynamic information to interfacial dynamics was initiated along two paths. One was from the viewpoint of an inertialess lattice gas, resulting in the surprising conclusion that at this level, all transport is governed by precisely the thermodynamic free energy, albeit with a non-trivial effective particle mobility. The other aimed at understanding the fashion in which slow macroscopic motions, accounted for by a time-varying microscopic energy, generate effective hydrodynamic parameters. By examining a solvable model system, it was found that all current procedures for doing so are deficient, and suitable alleviation suggested. The major effect of this project was to set the stage for the analysis of the substantial dynamical regimes in which extensive equilibrium information provides the dominant background. This produces a smooth junction to the models of Araki and Munakata, Giacomin and Lebowitz, and Oxtoby. It is also crucial to our understanding of the complex interfacial equilibrium configurations required for intermediate stages of two-phase separation, for which the "phase-field" techniques we have been developing are uniquely effective. And it puts us within striking range of the physical experiments that can provide incisive tests of the theoretical framework.

Percus, J. K.↗

NASA NTRS1999

Integrated Computational System for Aerodynamic Steering and Visualization

In February of 1994, an effort from the Fluid Dynamics and Information Sciences Divisions at NASA Ames Research Center with McDonnel Douglas Aerospace Company and Stanford University was initiated to develop, demonstrate, validate and disseminate automated software for numerical aerodynamic simulation. The goal of the initiative was to develop a tri-discipline approach encompassing CFD, Intelligent Systems, and Automated Flow Feature Recognition to improve the utility of CFD in the design cycle. This approach would then be represented through an intelligent computational system which could accept an engineer's definition of a problem and construct an optimal and reliable CFD solution. Stanford University's role focused on developing technologies that advance visualization capabilities for analysis of CFD data, extract specific flow features useful for the design process, and compare CFD data with experimental data. During the years 1995-1997, Stanford University focused on developing techniques in the area of tensor visualization and flow feature extraction. Software libraries were created enabling feature extraction and exploration of tensor fields. As a proof of concept, a prototype system called the Integrated Computational System (ICS) was developed to demonstrate CFD design cycle. The current research effort focuses on finding a quantitative comparison of general vector fields based on topological features. Since the method relies on topological information, grid matching and vector alignment is not needed in the comparison. This is often a problem with many data comparison techniques. In addition, since only topology based information is stored and compared for each field, there is a significant compression of information that enables large databases to be quickly searched. This report will (1) briefly review the technologies developed during 1995-1997 (2) describe current technologies in the area of comparison techniques, (4) describe the theory of our new method researched during the grant year (5) summarize a few of the results and finally (6) discuss work within the last 6 months that are direct extensions from the grant.

Hesselink, Lambertus↗

NASA NTRS1999

Co-Seismic Mass Dislocation and Its Effect on Earth's Rotation and Gravity

Mantle processes often involve large-scale mass transport, ranging from mantle convection, tectonic motions, glacial isostatic adjustment, to tides, atmospheric and oceanic loadings, volcanism and seismicity. On very short time scale of less than an hour, co-seismic event, apart from the "shaking" that is the earthquake, leaves behind permanent (step-function-like) dislocations in the crust and mantle. This redistribution of mass changes the Earth's inertia tensor (and hence Earth's rotation in both length-of-day and polar motion), and the gravity field (in terms of spherical harmonic Stokes coefficients). The question is whether these effects are large enough to be of any significance. In this paper we report updated calculation results. The calculation uses the normal mode summation scheme, applied to 15,814 major earthquakes that occurred during 1976-1998, according to source mechanism solutions given by the Harvard Central Moment Tensor catalog. Compared to the truly large ones earlier in the century, the earthquakes we study are individually all too small to have left any discernible signature in geodetic records of Earth rotation or global gravity field. However, their collective effects continue to exhibit an extremely strong statistical tendencies. For example, earthquakes conspire to decrease J(sub 2) and J(sub 22) while shortening LOD, resulting in a rounder and more compact Earth. Strong tendency is also seen in the earthquakes trying to "nudge" the Earth rotation pole towards about 140 degree E, roughly opposite to the observed polar drift direction. The geophysical significance and implications will be further studied.

Chao, Benjamin F.↗

NASA NTRS2000

Coseismic Excitation of the Earth's Polar Motion

Apart from the "shaking" near the epicenter that is the earthquake, a seismic event creates a permanent field of dislocation in the entire Earth. This redistribution of mass changes (slightly) the Earth's inertia tensor; and the Earth's rotation will change in accordance with the conservation of angular momentum. Similar to this seismic excitation of Earth rotation variations, the same mass redistribution causes (slight) changes in the Earth's gravitational field expressible in terms of changes in the Stokes coefficients of its harmonic expansion. In this paper, we give a historical background of the subject and discuss the related physics; we then compute the geodynamic effects caused by earthquakes based on normal-mode summation scheme. The effects are computed using the centroid moment tensor (CMT) solutions for 15,814 major earthquakes from Jan., 1977, through Feb., 1999, as provided in the Harvard CMT catalog. The computational results further strengthens these findings and conclusions: (i) the strong tendency for earthquakes to make the Earth rounder and more compact (however slightly) continues; (ii) so does the trend in the seismic "nudging" of the rotation pole toward the general direction of approx. 140 E, roughly opposite to that of the observed polar drift, but two orders of magnitude smaller in drift speed.

Chao, B. F.↗

NASA NTRS1999

Scale-Similar Models for Large-Eddy Simulations

Scale-similar models employ multiple filtering operations to identify the smallest resolved scales, which have been shown to be the most active in the interaction with the unresolved subgrid scales. They do not assume that the principal axes of the strain-rate tensor are aligned with those of the subgrid-scale stress (SGS) tensor, and allow the explicit calculation of the SGS energy. They can provide backscatter in a numerically stable and physically realistic manner, and predict SGS stresses in regions that are well correlated with the locations where large Reynolds stress occurs. In this paper, eddy viscosity and mixed models, which include an eddy-viscosity part as well as a scale-similar contribution, are applied to the simulation of two flows, a high Reynolds number plane channel flow, and a three-dimensional, nonequilibrium flow. The results show that simulations without models or with the Smagorinsky model are unable to predict nonequilibrium effects. Dynamic models provide an improvement of the results: the adjustment of the coefficient results in more accurate prediction of the perturbation from equilibrium. The Lagrangian-ensemble approach [Meneveau et al., J. Fluid Mech. 319, 353 (1996)] is found to be very beneficial. Models that included a scale-similar term and a dissipative one, as well as the Lagrangian ensemble averaging, gave results in the best agreement with the direct simulation and experimental data.

Sarghini, F.↗

NASA NTRS2002

Co-Seismic Mass Dislocation and its Effect on Earth's Rotation and Gravity

Mantle processes often involve large-scale mass transport, ranging from mantle convection, tectonic motions, glacial isostatic adjustment, to tides, atmospheric and oceanic loadings, volcanism and seismicity. On very short time scale of less than an hour, co-seismic event, apart from the shaking that is the earthquake, leaves behind permanent (step-function-like) dislocations in the crust and mantle. This redistribution of mass changes the Earth's inertia tensor (and hence Earth's rotation in both length-of-day and polar motion), and the gravity field (in terms of spherical harmonic Stokes coefficients). The question is whether these effects are large enough to be of any significance. In this paper we report updated calculation results based on Chao & Gross (1987). The calculation uses the normal mode summation scheme, applied to nearly twenty thousand major earthquakes that occurred during 1976-2002, according to source mechanism solutions given by the Harvard Central Moment Tensor catalog. Compared to the truly large ones earlier in the century, the earthquakes we study are individually all too small to have left any discernible signature in geodetic records of Earth rotation or global gravity field. However, their collective effects continue to exhibit an extremely strong statistical tendencies. For example, earthquakes conspire to decrease J2 and J22 while shortening LOD, resulting in a rounder and more compact Earth. Strong tendency is also seen in the earthquakes trying to nudge the Earth rotation pole towards approximately 140 degrees E, roughly opposite to the observed polar drift direction. The geophysical significance and implications will be further studied.

Chao, B. F.↗

NASA NTRS2003

Macroscopic Models of Radiative Transfer as Applied to Computation of the Radiation Field in the Solar Atmosphere

In this paper a new three dimensional half-moment model for radiative transfer is presented for a gray medium. It describes the evolution of the zeroth and first directional half moments of the radiative intensity. The closure is provided, similarly to Dubroca and Klar, by the maximum entropy concept. This work generalizes that model to three dimensions. The model presented here (the derivation being done in Ripoll and Wray, called the M(sup 1/2)(sub 1) model, is a hyperbolic system consisting of a total of eight equations in three dimensions, four equations for each direction. Each half model has the classical form of a macroscopic moment model in which the pressure tensor is constructed from the well-known Eddington tensor with a particular Eddington factor. Moreover, different source and border terms occur. The latter introduce couplings between the macroscopic and microscopic quantities and between the + and - streams, through the intensity in the plane perpendicular to the flux. The main theoretical application of the half moment model, treated in this paper, is its reduction to a full moment model, called M(sup +)(sub 1), for the particular but important case of a hot, opaque source radiating in a cold transparent (or semi-transparent) medium for very specific applications, such as stellar interiors or atmospheres, or combustion problems. The structure of the paper is as follows. In section 2, the model M(sup 1/2)(sub 1) is presented. In section 3, for the particular case of a hot, opaque source radiating into a cold medium, the half moment model is reduced to the M(sup +)(sub 1) model. In section 4, we first solve a simple and academic problem to validate the models, followed by a simplified solar atmosphere.

Ripoll, J.-F.↗

NASA NTRS2004

Parameter Estimation in Atmospheric Data Sets

In this study the structure tensor technique is used to estimate dynamical parameters in atmospheric data sets. The structure tensor is a common tool for estimating motion in image sequences. This technique can be extended to estimate other dynamical parameters such as diffusion constants or exponential decay rates. A general mathematical framework was developed for the direct estimation of the physical parameters that govern the underlying processes from image sequences. This estimation technique can be adapted to the specific physical problem under investigation, so it can be used in a variety of applications in trace gas, aerosol, and cloud remote sensing. As a test scenario this technique will be applied to modeled dust data. In this case vertically integrated dust concentrations were used to derive wind information. Those results can be compared to the wind vector fields which served as input to the model. Based on this analysis, a method to compute atmospheric data parameter fields will be presented. .

Wenig, Mark↗

NASA NTRS1990

A new continuum model for suspensions of gyrotactic micro-organisms

A new continuum model is formulated for dilute suspensions of swimming micro-organisms with asymmetric mass distributions. Account is taken of randomness in a cell's swimming direction, p, by postulating that the probability density function for p satisfies a Fokker-Planck equation analogous to that obtained for colloid suspensions in the presence of rotational Brownian motion. The deterministic torques on a cell, viscous and gravitational, are balanced by diffusion, represented by an isotropic rotary diffusivity Dr, which is unknown a priori, but presumably reflects stochastic influences on the cell's internal workings. When the Fokker-Planck equation is solved, macroscopic quantities such as the average cell velocity Vc, the particle diffusivity tensor D and the effective stress tensor sigma can be computed; Vc and D are required in the cell conservation equation, and sigma in the momentum equation. The Fokker-Planck equation contains two dimensionless parameters, lambda and epsilon; lambda is the ratio of the rotary diffusion time Dr-1 to the torque relaxation time B (balancing gravitational and viscous torques), while epsilon is a scale for the local vorticity or strain rate made dimensionless with B. In this paper we solve the Fokker-Planck equation exactly for epsilon = 0 (lambda arbitrary) and also obtain the first-order solution for small epsilon. Using experimental data on Vc and D obtained with the swimming alga, Chlamydomonas nivalis, in the absence of bulk flow, the epsilon = 0 results can be used to estimate the value of lambda for that species (lambda approximately 2.2; Dr approximately 0.13 s-1). The continuum model for small epsilon is then used to reanalyse the instability of a uniform suspension, previously investigated by Pedley, Hill & Kessler (1988). The only qualitatively different result is that there no longer seem to be circumstances in which disturbances with a non-zero vertical wavenumber are more unstable than purely horizontal disturbances. On the way, it is demonstrated that the only significant contribution to sigma, other than the basic Newtonian stress, is that derived from the stresslets associated with the cells' intrinsic swimming motions.

NASA Discipline Number 28-20↗

NASA NTRS2004

Co-Seismic Mass Displacement and its Effect on Earth's Rotation and Gravity

Mantle processes often involve large-scale mass transport, ranging from mantle convection, tectonic motions, glacial isostatic adjustment, to tides, atmospheric and oceanic loadings, volcanism and seismicity. On very short time scale of less than an hour, co-seismic event, apart from the "shaking" that is the earthquake, leaves behind permanent (step-function-like) displacements in the crust and mantle. This redistribution of mass changes the Earth's inertia tensor (and hence Earth's rotation in both length-of-day and polar motion), and the gravity field. The question is whether these effects are large enough to be of any significance. In this paper we report updated calculation results based on Chao & Gross. The calculation uses the normal mode summation scheme, applied to over twenty thousand major earthquakes that occurred during 1976-2002, according to source mechanism solutions given by the Harvard Centroid Moment Tensor catalog. Compared to the truly large ones earlier in the century, the earthquakes we study are individually all too small to have left any discernible signature in geodetic records of Earth rotation or global gravity field. However, their collective effects continue to exhibit an extremely strong statistical tendencies, conspiring to decrease J2 and J22 while shortening LOD, resulting in a rounder and more compact Earth. Strong tendency is also seen in the earthquakes trying to "nudge" the Earth rotation pole towards approx. 140 deg.E, roughly opposite to the observed polar drift direction. Currently, the Gravity Recovery And Climate Experiment (GRACE) is measuring the time-variable gravity to high degree and order with unprecedented accuracy. Our results show that great earthquakes such as the 1960 Chilean or 1964 Alaskan events cause gravitational field changes that are large enough to be detected by GRACE.

Chao, B. F.↗