Search NASA⌕ Search

SEARCH · Search NASA

Results for “Dimensionality”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Experiments on near-wall structure of three-dimensional boundary layers

Investigations of three-dimensional turbulent boundary layers have shown basic differences between two- and three-dimensional flows. These differences can significantly impact the modeling of three-dimensional flows since many flow models are based on results from two-dimensional boundary layers. In many cases the shear stress vector direction has been shown to lag relative to the direction of the mean velocity gradient as the cross flow grows downstream. Coincidence of these vectors is necessary for a scalar eddy viscosity modeling assumption. A second effect is a reduction in magnitude of the shear stress and/or the shear stress to turbulence energy ratio, a(sub 1). This reduction has been observed in several experiments. Recent numerical simulations also indicate wall-layer structural differences between two- and three-dimensional boundary layers. The differences in structure between two- and three-dimensional boundary layers was also addressed in the experiment of Littell & Eaton. The experiment used two-point correlations to investigate the vortical structures in a three dimensional boundary layer on a spinning disk. It was found that each sign of longitudinal vortex is equally likely to exist, but one sign of vorticity is associated with a structure which is better at producing ejections. The goal of the current investigation is to study the structure of the inner layers. Among other questions, the differences between the effects deduced from the three-dimensional flow simulations and the effects seen in experiments can be examined. The research concentrates on the structure of the wall-layer through flow visualization and direct turbulence measurements down to y(+) = 5.

Flack, Karen A.↗
NASA NTRS1993

Feature extraction and classification algorithms for high dimensional data

Feature extraction and classification algorithms for high dimensional data are investigated. Developments with regard to sensors for Earth observation are moving in the direction of providing much higher dimensional multispectral imagery than is now possible. In analyzing such high dimensional data, processing time becomes an important factor. With large increases in dimensionality and the number of classes, processing time will increase significantly. To address this problem, a multistage classification scheme is proposed which reduces the processing time substantially by eliminating unlikely classes from further consideration at each stage. Several truncation criteria are developed and the relationship between thresholds and the error caused by the truncation is investigated. Next an approach to feature extraction for classification is proposed based directly on the decision boundaries. It is shown that all the features needed for classification can be extracted from decision boundaries. A characteristic of the proposed method arises by noting that only a portion of the decision boundary is effective in discriminating between classes, and the concept of the effective decision boundary is introduced. The proposed feature extraction algorithm has several desirable properties: it predicts the minimum number of features necessary to achieve the same classification accuracy as in the original space for a given pattern recognition problem; and it finds the necessary feature vectors. The proposed algorithm does not deteriorate under the circumstances of equal means or equal covariances as some previous algorithms do. In addition, the decision boundary feature extraction algorithm can be used both for parametric and non-parametric classifiers. Finally, some problems encountered in analyzing high dimensional data are studied and possible solutions are proposed. First, the increased importance of the second order statistics in analyzing high dimensional data is recognized. By investigating the characteristics of high dimensional data, the reason why the second order statistics must be taken into account in high dimensional data is suggested. Recognizing the importance of the second order statistics, there is a need to represent the second order statistics. A method to visualize statistics using a color code is proposed. By representing statistics using color coding, one can easily extract and compare the first and the second statistics.

Lee, Chulhee↗
NASA NTRS2011

Optimal Padding for the Two-Dimensional Fast Fourier Transform

One-dimensional Fast Fourier Transform (FFT) operations work fastest on grids whose size is divisible by a power of two. Because of this, padding grids (that are not already sized to a power of two) so that their size is the next highest power of two can speed up operations. While this works well for one-dimensional grids, it does not work well for two-dimensional grids. For a two-dimensional grid, there are certain pad sizes that work better than others. Therefore, the need exists to generalize a strategy for determining optimal pad sizes. There are three steps in the FFT algorithm. The first is to perform a one-dimensional transform on each row in the grid. The second step is to transpose the resulting matrix. The third step is to perform a one-dimensional transform on each row in the resulting grid. Steps one and three both benefit from padding the row to the next highest power of two, but the second step needs a novel approach. An algorithm was developed that struck a balance between optimizing the grid pad size with prime factors that are small (which are optimal for one-dimensional operations), and with prime factors that are large (which are optimal for two-dimensional operations). This algorithm optimizes based on average run times, and is not fine-tuned for any specific application. It increases the amount of times that processor-requested data is found in the set-associative processor cache. Cache retrievals are 4-10 times faster than conventional memory retrievals. The tested implementation of the algorithm resulted in faster execution times on all platforms tested, but with varying sized grids. This is because various computer architectures process commands differently. The test grid was 512 512. Using a 540 540 grid on a Pentium V processor, the code ran 30 percent faster. On a PowerPC, a 256x256 grid worked best. A Core2Duo computer preferred either a 1040x1040 (15 percent faster) or a 1008x1008 (30 percent faster) grid. There are many industries that can benefit from this algorithm, including optics, image-processing, signal-processing, and engineering applications.

Dean, Bruce H.↗
NASA NTRS1985

New Directions in Asymptotically Stable Finite-dimensional Adaptive Control of Linear Distributed Parameter Systems

Distributed Parameter Systems (DPS), such as systems described by partial differential equations, require infinite-dimensional state space descriptions to correctly model their dynamical behavior. However, any adaptive control algorithm must be finite-dimensional in order to be implemented via on-line digital computers. Finite-dimensional adaptive control of linear DPS requires stability analysis of nonlinear, time-varying, infinite-dimensional systems. The structure of nonadaptive finite-dimensional control of linear DPS is summarized as it relates to the existence of limiting systems for adaptive control. Two candidate schemes for finite-dimensional adaptive control of DPS are described and critical issues in infinite-dimensional stability analysis are discussed, in particular, the invariance principle, center manifold theory, and relationships between input-output and internal stability.

Balas, M. J.↗
NASA NTRS1990

Extension of a three-dimensional viscous wing flow analysis user's manual: VISTA 3-D code

Three-dimensional unsteady viscous effects can significantly influence the performance of fixed and rotary wing aircraft. These effects are important in both flows about helicopter rotors in forward flight and flows about three-dimensional (swept and tapered) supercritical wings. A computational procedure for calculating such flow field was developed. The procedure is based upon an alternating direction technique employing the Linearized Block Implicit method for solving three-dimensional viscous flow problems. In order to demonstrate the viability of this method, two- and three-dimensional problems are computed. These include the flow over a two-dimensional NACA 0012 airfoil under steady and oscillating conditions, and the steady, skewed, three-dimensional flow on a flat plate. Although actual three-dimensional flows over wings were not obtained, the ground work was laid for considering such flows. In this report a description of the computer code is given.

Weinberg, Bernard C.↗
NASA NTRS1990

Verification of three-dimensional laser Doppler velocimeter measurements

An experimental comparison method is proposed for the verification of mean flow and turbulence measurements obtained with a three-dimensional laser Doppler velocimeter system. Such measurements can include large errors caused by problems unique to three-dimensional systems. Direct comparisons of laser and hot cross-wire measurements obtained in two-dimensional flows, as is the common practice, will not bear out all the errors associated with three-dimensional laser systems. It is proposed here that the errors may be adequately quantified by making the direct comparisons in a weakly three-dimensional turbulent shear flow. The weak three-dimensional flow ensures high accuracy of the cross-wire data while still generating sufficiently strong secondary mean flow and Reynolds shear stress so that all the laser measurements may be fully verified. This type of shear flow is easily generated by introducing a weak streamwise vortex into a nominally two-dimensional turbulent shear layer.

Mehta, R. D.↗
NASA NTRS1991

An exploratory study of a three-dimensional shock wave turbulent boundary layer interaction in a corner

Three-dimensional shock wave turbulent boundary layer interactions in a corner have been studied at M about 3. The first phase, detailed mean wall static pressure distributions, has shown the interaction of a two-dimensional flow on one wall with the three-dimensional flow generated by a fin. Major three-dimensional effects on both flows were observed, extending from the interaction of the initial region of the three-dimensional flow and the corner. A large part of the resulting corner flow has little resemblance to either the two-dimensional or three-dimensional interacting flows.

Bogdonoff, S. M.↗
NASA NTRS1990

Three-dimensional mode resonances in boundary layers, jets and wakes

The paper emphasizes understanding and promoting mechanisms, such as resonance mechanisms, governing the first growth of three-dimensionality in experiments on instability and transition to turbulence. It is noted that in past experiments, only two-dimensional modes were directlly forced leaving three-dimensional disturbance content undefined, both in amplitude and wave numbers. An approach offering to seed three-dimensional oblique modes along with two-dimensional modes is discussed. The technique introduces controlled three-dimensional (oblique) time-periodic waves through a spanwise phase shift between neighbor elements; a two-dimensional disturbance is added simultaneously.

Corke, Thomas C.↗
NASA NTRS1991

The three-dimensional evolution of a plane mixing layer. Part 1: The Kelvin-Helmholtz roll-up

The Kelvin Helmholtz roll up of three dimensional, temporally evolving, plane mixing layers were simulated numerically. All simulations were begun from a few low wavenumber disturbances, usually derived from linear stability theory, in addition to the mean velocity profile. The spanwise disturbance wavelength was taken to be less than or equal to the streamwise wavelength associated with the Kelvin Helmholtz roll up. A standard set of clean structures develop in most of the simulations. The spanwise vorticity rolls up into a corrugated spanwise roller, with vortex stretching creating strong spanwise vorticity in a cup shaped region at the vends of the roller. Predominantly streamwise rib vortices develop in the braid region between the rollers. For sufficiently strong initial three dimensional disturbances, these ribs collapse into compact axisymmetric vortices. The rib vortex lines connect to neighboring ribs and are kinked in the opposite direction of the roller vortex lines. Because of this, these two sets of vortex lines remain distinct. For certain initial conditions, persistent ribs do not develop. In such cases the development of significant three dimensionality is delayed. When the initial three dimensional disturbance energy is about equal to, or less than, the two dimensional fundamental disturbance energy, the evolution of the three dimensional disturbance is nearly linear (with respect to the mean and the two dimensional disturbances), at least until the first Kelvin Helmholtz roll up is completed.

Rogers, Michael M.↗
NASA NTRS1992

Progress in multi-dimensional upwind differencing

Multi-dimensional upwind-differencing schemes for the Euler equations are reviewed. On the basis of the first-order upwind scheme for a one-dimensional convection equation, the two approaches to upwind differencing are discussed: the fluctuation approach and the finite-volume approach. The usual extension of the finite-volume method to the multi-dimensional Euler equations is not entirely satisfactory, because the direction of wave propagation is always assumed to be normal to the cell faces. This leads to smearing of shock and shear waves when these are not grid-aligned. Multi-directional methods, in which upwind-biased fluxes are computed in a frame aligned with a dominant wave, overcome this problem, but at the expense of robustness. The same is true for the schemes incorporating a multi-dimensional wave model not based on multi-dimensional data but on an 'educated guess' of what they could be. The fluctuation approach offers the best possibilities for the development of genuinely multi-dimensional upwind schemes. Three building blocks are needed for such schemes: a wave model, a way to achieve conservation, and a compact convection scheme. Recent advances in each of these components are discussed; putting them all together is the present focus of a worldwide research effort. Some numerical results are presented, illustrating the potential of the new multi-dimensional schemes.

Vanleer, Bram↗
NASA NTRS1994

A note on two-dimensional asymptotic magnetotail equilibria

In order to understand, on the fluid level, the structure, the time evolution, and the stability of current sheets, such as the magnetotail plasma sheet in Earth's magnetosphere, one has to consider magnetic field configurations that are in magnetohydrodynamic (MHD) force equilibrium. Any reasonable MHD current sheet model has to be two-dimensional, at least in an asymptotic sense (B(sub z)/B (sub x)) = epsilon much less than 1. The necessary two-dimensionality is described by a rather arbitrary function f(x). We utilize the free function f(x) to construct two-dimensional magnetotail equilibria are 'equivalent' to current sheets in empirical three-dimensional models. We obtain a class of asymptotic magnetotail equilibria ordered with respect to the magnetic disturbance index Kp. For low Kp values the two-dimensional MHD equilibria reflect some of the realistic, observation-based, aspects of three-dimensional models. For high Kp values the three-dimensional models do not fit the asymptotic MHD equlibria, which is indicative of their inconsistency with the assumed pressure function. This, in turn, implies that high magnetic activity levels of the real magnetosphere might be ruled by thermodynamic conditions different from local thermodynamic equilibrium.

Voigt, Gerd-Hannes↗
NASA NTRS1995

Working toward a three-dimensional fatigue closure model for surface cracks

The first reliable elastic fracture mechanics solutions for a surface crack in a plate were obtained by Newman and Raju. The authors, both from the Mechanics of Materials Branch at NASA-Langley, used a highly detailed finite element solution requiring substantial computational resources. Computers have since become more powerful and available; however, many important related problems remain computationally expensive. The problem of three-dimensional fatigue crack growth taking into account plasticity-induced crack closure is one such problem. It is the goal of this research to provide an efficient method to account for three-dimensional crack closure in fatigue. Newman developed a two-dimensional plasticity-induced crack closure model for center cracked specimens. This model requires iterations to determine both the contact solution at each growth step and the extent of the plastic zone at the crack tip. A three-dimensional version of this model would require obtaining these nonlinear variables all along the crack front. This model must be efficient so that repeated calculations can be performed during crack growth simulations. The highly versatile line spring model (LSM) with contact, fatigue, and plasticity will form the basis of the closure model. There are several required additions to past work to address the three-dimensional crack closure problem. Initially, these additions will include (1) an improved LSM to more accurately obtain the crack opening displacement, stress intensity factors, and elastic T-stress near the ends of the surface crack; (2) a method to determine the extent of the plastic zone all along the crack front; (3) a method to determine the contact zone given a perfectly plastic layer of material on the crack surfaces; (4) a method to determine the magnitude of the compressive contact stress; and (5) a way to implement the degree of constraint along the curved crack front. During the summer ASEE program an enhanced LSM was developed. A method similar to that of 'strip synthesis' first introduced by Fujimoto was used. Briefly, the crack opening displacements of 'slices' of the surface crack in a direction parallel to the plate surface are considered in addition to the standard LSM approach that makes use of springs obtained from slices perpendicular to the plate surface. This enhancement is necessary so that an accurate three-dimensional representation of quantities such as contact zone size, plastic zone size, stress intensity factors, T-stress, and crack opening displacement can be determined. By combining results of previous investigations with the LSM, the problem of three-dimensional crack closure will be addressed. In addition to a closure model, the enhanced LSM can be used for many other problems including interacting surface cracks and fatigue crack growth of a through crack with a curved crack front.

Joseph, Paul F.↗
NASA NTRS2000

Object Based Numerical Zooming Between the NPSS Version 1 and a 1-Dimensional Meanline High Pressure Compressor Design Analysis Code

Within NASA's High Performance Computing and Communication (HPCC) program, NASA Glenn Research Center is developing an environment for the analysis/design of propulsion systems for aircraft and space vehicles called the Numerical Propulsion System Simulation (NPSS). The NPSS focuses on the integration of multiple disciplines such as aerodynamics, structures, and heat transfer, along with the concept of numerical zooming between 0- Dimensional to 1-, 2-, and 3-dimensional component engine codes. The vision for NPSS is to create a "numerical test cell" enabling full engine simulations overnight on cost-effective computing platforms. Current "state-of-the-art" engine simulations are 0-dimensional in that there is there is no axial, radial or circumferential resolution within a given component (e.g. a compressor or turbine has no internal station designations). In these 0-dimensional cycle simulations the individual component performance characteristics typically come from a table look-up (map) with adjustments for off-design effects such as variable geometry, Reynolds effects, and clearances. Zooming one or more of the engine components to a higher order, physics-based analysis means a higher order code is executed and the results from this analysis are used to adjust the 0-dimensional component performance characteristics within the system simulation. By drawing on the results from more predictive, physics based higher order analysis codes, "cycle" simulations are refined to closely model and predict the complex physical processes inherent to engines. As part of the overall development of the NPSS, NASA and industry began the process of defining and implementing an object class structure that enables Numerical Zooming between the NPSS Version I (0-dimension) and higher order 1-, 2- and 3-dimensional analysis codes. The NPSS Version I preserves the historical cycle engineering practices but also extends these classical practices into the area of numerical zooming for use within a companies' design system. What follows here is a description of successfully zooming I-dimensional (row-by-row) high pressure compressor results back to a NPSS engine 0-dimension simulation and a discussion of the results illustrated using an advanced data visualization tool. This type of high fidelity system-level analysis, made possible by the zooming capability of the NPSS, will greatly improve the fidelity of the engine system simulation and enable the engine system to be "pre-validated" prior to commitment to engine hardware.

Follen, G.↗
NASA NTRS2010

Two-Dimensional Synthetic-Aperture Radiometer

A two-dimensional synthetic-aperture radiometer, now undergoing development, serves as a test bed for demonstrating the potential of aperture synthesis for remote sensing of the Earth, particularly for measuring spatial distributions of soil moisture and ocean-surface salinity. The goal is to use the technology for remote sensing aboard a spacecraft in orbit, but the basic principles of design and operation are applicable to remote sensing from aboard an aircraft, and the prototype of the system under development is designed for operation aboard an aircraft. In aperture synthesis, one utilizes several small antennas in combination with a signal processing in order to obtain resolution that otherwise would require the use of an antenna with a larger aperture (and, hence, potentially more difficult to deploy in space). The principle upon which this system is based is similar to that of Earth-rotation aperture synthesis employed in radio astronomy. In this technology the coherent products (correlations) of signals from pairs of antennas are obtained at different antenna-pair spacings (baselines). The correlation for each baseline yields a sample point in a Fourier transform of the brightness-temperature map of the scene. An image of the scene itself is then reconstructed by inverting the sampled transform. The predecessor of the present two-dimensional synthetic-aperture radiometer is a one-dimensional one, named the Electrically Scanned Thinned Array Radiometer (ESTAR). Operating in the L band, the ESTAR employs aperture synthesis in the cross-track dimension only, while using a conventional antenna for resolution in the along-track dimension. The two-dimensional instrument also operates in the L band to be precise, at a frequency of 1.413 GHz in the frequency band restricted for passive use (no transmission) only. The L band was chosen because (1) the L band represents the long-wavelength end of the remote- sensing spectrum, where the problem of achieving adequate spatial resolution is most critical and (2) imaging airborne instruments that operate in this wavelength range and have adequate spatial resolution are difficult to build and will be needed in future experiments to validate approaches for remote sensing of soil moisture and ocean salinity. The two-dimensional instrument includes a rectangular array of patch antennas arranged in the form of a cross. The ESTAR uses analog correlation for one dimension, whereas the two-dimensional instrument uses digital correlation. In two dimensions, many more correlation pairs are needed and low-power digital correlators suitable for application in spaceborne remote sensing will help enable this technology. The two-dimensional instrument is dual-polarized and, with modification, capable of operating in a polarimetric mode. A flight test of the instrument took place in June 2003 and it participated in soil moisture experiments during the summers of 2003 and 2004.

LeVine, David M.↗
NASA NTRS2014

Integrated Aeromechanics with Three-Dimensional Solid-Multibody Structures

A full three-dimensional finite element-multibody structural dynamic solver is coupled to a three-dimensional Reynolds-averaged Navier-Stokes solver for the prediction of integrated aeromechanical stresses and strains on a rotor blade in forward flight. The objective is to lay the foundations of all major pieces of an integrated three-dimensional rotor dynamic analysis - from model construction to aeromechanical solution to stress/strain calculation. The primary focus is on the aeromechanical solution. Two types of three-dimensional CFD/CSD interfaces are constructed for this purpose with an emphasis on resolving errors from geometry mis-match so that initial-stage approximate structural geometries can also be effectively analyzed. A three-dimensional structural model is constructed as an approximation to a UH-60A-like fully articulated rotor. The aerodynamic model is identical to the UH-60A rotor. For preliminary validation measurements from a UH-60A high speed flight is used where CFD coupling is essential to capture the advancing side tip transonic effects. The key conclusion is that an integrated aeromechanical analysis is indeed possible with three-dimensional structural dynamics but requires a careful description of its geometry and discretization of its parts.

Three-Dimensional↗
NASA NTRS1976

Classification improvement by optimal dimensionality reduction when training sets are of small size

A computer simulation was performed to test the conjecture that, when the sizes of the training sets are small, classification in a subspace of the original data space may give rise to a smaller probability of error than the classification in the data space itself; this is because the gain in the accuracy of estimation of the likelihood functions used in classification in the lower dimensional space (subspace) offsets the loss of information associated with dimensionality reduction (feature extraction). A number of pseudo-random training and data vectors were generated from two four-dimensional Gaussian classes. A special algorithm was used to create an optimal one-dimensional feature space on which to project the data. When the sizes of the training sets are small, classification of the data in the optimal one-dimensional space is found to yield lower error rates than the one in the original four-dimensional space.

Starks, S. A.↗
NASA NTRS1978

Three-dimensional effects on pure tone fan noise due to inflow distortion

Two dimensional, quasi three dimensional and three dimensional theories for the prediction of pure tone fan noise due to the interaction of inflow distortion with a subsonic annular blade row were studied with the aid of an unsteady three dimensional lifting surface theory. The effects of compact and noncompact source distributions on pure tone fan noise in an annular cascade were investigated. Numerical results show that the strip theory and quasi three-dimensional theory are reasonably adequate for fan noise prediction. The quasi three-dimensional method is more accurate for acoustic power and model structure prediction with an acoustic power estimation error of about plus or minus 2db.

Kobayashi, H.↗
NASA NTRS1979

Higher dimensional Hadamard matrices

The paper defines higher dimensional Hadamard matrices and enumerates on some of the simplest three-, four-, and five-dimensional cases and procedures for generating them. Special emphasis is given to proper matrices that have a dimensional hierarchy of orthogonalities. It is determined that this property lends itself primarily to the application of higher dimensional Hadamard matrices to error-correcting codes. A list of derived statements for n-dimensional Hadamard matrices are given, as well as a definition of Hadamard matrix families, such as minimal, Petrie polygon, antipodal (n-2)-dimensional sections, and double proximity shells.

Schlichta, P. J.↗