Search NASA⌕ Search

SEARCH · Search NASA

Results for “ORTHOGONAL FUNCTION”

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 397 records · Page 22
All sourcesNASA NTRSDOE OSTI
NASA NTRS2016

Calipso Observations of the Dependence of Homo- and Heterogeneous Ice Nucleation in Cirrus Clouds on Latitude, Season and Surface Condition

There are two fundamental mechanisms through which cirrus clouds form; homo- and heterogeneous ice nucleation (henceforth hom and het). The relative contribution of each mechanism to ice crystal production often determines the microphysical and radiative properties of a cirrus cloud. A new satellite remote sensing method is described in this study to estimate cirrus cloud ice particle number concentration and the relative contribution of hom and het to cirrus cloud formation as a function of altitude, latitude, season and surface type (e.g. land vs. ocean). This method uses co-located observations from the Infrared Imaging Radiometer (IIR) and from the CALIOP (Cloud and Aerosol Lidar with Orthogonal Polarization) lidar aboard the CALIPSO (Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation) polar orbiting satellite, employing IIR channels at 10.6 μm and 12.05 μm. The method is applied here to single-layered clouds of visible optical depth between about 0.3 and 3. Two years of Version 3 data have been analyzed for the years 2008 and 2013, with each season characterized in terms of 532 nm cirrus cloud centroid altitude and temperature, the cirrus cloud ice particle number concentration, effective diameter, layer-average ice water content and visible optical depth. Using a conservative criterion for hom cirrus, on average, the sampled cirrus clouds formed through hom occur about 43% of the time in the Arctic and 50% of the time in the Antarctic, and during winter at mid-latitudes in the Northern Hemisphere, hom cirrus occur 37% of the time. Elsewhere (and during other seasons in the Northern Hemisphere mid-latitudes), this hom cirrus fraction is lower. Processes that could potentially explain these observations are discussed, as well as the potential relevancy of these results to ice nucleation studies, climate modeling and jet-stream dynamics.

Mitchell, David L.↗
NASA NTRS1981

The three-dimensional boundary layer on a rotating helical blade

The laminar boundary layer on a twisted helical blade is considered. The blade geometry is the same as that proposed by Horlock and Wordsworth (1965). However, the blade is twisted about the leading edge in the manner described by Miyake and Fujita (1974). The flow may be considered to be the analog, in a rotating reference frame, of the flat-plate boundary layer in a stationary frame. It is shown that a coordinate system which is orthogonal in the blade surface may be developed. With the appropriate scaling of the dependent variables a solution for the boundary layer flow is readily obtained. The systems of ordinary differential equations for the stream function of the primary flow and the cross-flow are solved numerically.

Morris, P. J.↗
NASA NTRS1990

Mode I delamination of a three-dimensional fabric composite

Finite-element analysis was conducted on a double-cantilever-beam (DCB) specimen of carbon-epoxy (T300/3501-6) orthogonal interlocked fabric composites. The mode I strain-energy release rate G(I) was evaluated to investigate the influence of through-the-thickness (z-axis) fibers on crack driving force as a function of crack length. The analysis showed good agreement with experimental results for both compliance and G(I). The presence of z-axis fibers sharply reduced G(I) in comparison to the traditional two-dimensional laminated material. A parametric study revealed that increasing the z-axis fiber stiffness reduces G(I). Progressive debonding of the z-axis reinforcement was also modeled. G(I) increased as the fiber debonded but was significantly less than in the two-dimensional laminated material in all cases.

Byun, Joon-Hyung↗
NASA NTRS1990

Ground states of partially connected binary neural networks

Neural networks defined by outer products of vectors over (-1, 0, 1) are considered. Patterns over (-1, 0, 1) define by their outer products partially connected neural networks consisting of internally strongly connected, externally weakly connected subnetworks. Subpatterns over (-1, 1) define subnetworks, and their combinations that agree in the common bits define permissible words. It is shown that the permissible words are locally stable states of the network, provided that each of the subnetworks stores mutually orthogonal subwords, or, at most, two subwords. It is also shown that when each of the subnetworks stores two mutually orthogonal binary subwords at most, the permissible words, defined as the combinations of the subwords (one corresponding to each subnetwork), that agree in their common bits are the unique ground states of the associated energy function.

Baram, Yoram↗
NASA NTRS2001

Comparison of Angle of Attack Measurements for Wind Tunnel Testing

Two optical systems capable of measuring model attitude and deformation were compared to inertial devices employed to acquire wind tunnel model angle of attack measurements during the sting mounted full span 30% geometric scale flexible configuration of the Northrop Grumman Unmanned Combat Air Vehicle (UCAV) installed in the NASA Langley Transonic Dynamics Tunnel (TDT). The overall purpose of the test at TDT was to evaluate smart materials and structures adaptive wing technology. The optical techniques that were compared to inertial devices employed to measure angle of attack for this test were: (1) an Optotrak (registered) system, an optical system consisting of two sensors, each containing a pair of orthogonally oriented linear arrays to compute spatial positions of a set of active markers; and (2) Video Model Deformation (VMD) system, providing a single view of passive targets using a constrained photogrammetric solution whose primary function was to measure wing and control surface deformations. The Optotrak system was installed for this test for the first time at TDT in order to assess the usefulness of the system for future static and dynamic deformation measurements.

Jones, Thomas, W.↗
DOE OSTI2025

A Class of Sparse Johnson–Lindenstrauss Transforms and Analysis of their Extreme Singular Values

The Johnson–Lindenstrauss (JL) lemma is a powerful tool for dimensionality reduction in modern algorithm design. The lemma states that any set of high-dimensional points in a Euclidean space can be projected into lower dimensions while approximately preserving pairwise Euclidean distances. Random matrices satisfying this lemma are called JL transforms (JLTs). Inspired by existing $s$-hashing JLTs with exactly $s$ nonzero elements on each column, the present work introduces an ensemble of sparse matrices encompassing so-called $s$-hashing-like matrices whose expected number of nonzero elements on each column is $s$. The independence of the sub-Gaussian entries of these matrices and the knowledge of their exact distribution play an important role in their analyses. Using properties of independent sub-Gaussian random variables, these matrices are demonstrated to be JLTs, and their smallest nontrivial singular values and largest singular values are estimated nonasymptotically using a technique from geometric functional analysis. As the dimensions of the matrix grow to infinity, these singular values are proved to converge almost surely to fixed quantities (by using the universal Bai–Yin law) and in distribution to the Gaussian orthogonal ensemble Tracy–Widom law after proper rescalings. Understanding the behaviors of extreme singular values is important in general because they are often used to define a measure of stability of matrix algorithms. For example, JLTs were recently used in derivative-free optimization algorithmic frameworks to select random subspaces in which are constructed random models or poll directions to achieve scalability, and hence estimating their smallest singular value in particular helps determine the dimension of these subspaces.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1991

Analysis of structural response data using discrete modal filters

The application of reciprocal modal vectors to the analysis of structural response data is described. Reciprocal modal vectors are constructed using an existing experimental modal model and an existing frequency response matrix of a structure, and can be assembled into a matrix that effectively transforms the data from the physical space to a modal space within a particular frequency range. In other words, the weighting matrix necessary for modal vector orthogonality (typically the mass matrix) is contained within the reciprocal model matrix. The underlying goal of this work is mostly directed toward observing the modal state responses in the presence of unknown, possibly closed loop forcing functions, thus having an impact on both operating data analysis techniques and independent modal space control techniques. This study investigates the behavior of reciprocol modal vectors as modal filters with respect to certain calculation parameters and their performance with perturbed system frequency response data.

Freudinger, Lawrence C.↗
NASA NTRS2005

Analysis of Quantum Information Test-Bed by Parametric Down-Converted Photons Interference Measurement

Quantum optical experiments require all the components involved to be extremely stable relative to each other. The stability can be "measured" by using an interferometric experiment. A pair of coherent photons produced by parametric down-conversion could be chosen to be orthogonally polarized initially. By rotating the polarization of one of the wave packets, they can be recombined at a beam splitter such that interference will occur. Theoretically, the interference will create four terms in the wave function. Two terms with both photons going to the same detector, and two terms will have the photons each going to different detectors. However, the latter will cancel each other out, thus no photons will arrive at the two detectors simultaneously under ideal conditions. The stability Of the test-bed can then be inferred by the dependence of coincidence count on the rotation angle.

To, Wing H.↗
NASA NTRS2000

Capacity of Pulse-Position Modulation (PPM) on Gaussian and Webb Channels

This article computes the capacity of various idealized soft-decision channels modeling an optical channel using an avalanche photodiode detector (APD) and pulse-position modulation (PPM). The capacity of this optical channel depends in a complicated way on the physical parameters of the APD and the constraints imposed by the PPM orthogonal signaling set. This article attempts to identify and separate the effects of several fundamental parameters on the capacity of the APD-detected optical PPM channel. First, an overall signal-to-noise ratio (SNR) parameter is de ned such that the capacity as a function of a bit-normalized version of this SNR drops precipitously toward zero at quasi-brick-wall limits on bit SNR that are numerically the same as the well-understood brick-wall limits for the standard additive white Gaussian noise (AWGN) channel. A second parameter is used to quantify the effects on capacity of one unique facet of the optical PPM channel (as compared with the standard AWGN channel) that causes the noise variance to be higher in signal slots than in nonsignal slots. This nonuniform noise variance yields interesting capacity effects even when the channel model is AWGN. A third parameter is used to measure the effects on capacity of the difference between an AWGN model and a non-Gaussian model proposed by Webb (see reference in [2]) for approximating the statistics of the APD-detected optical channel. Finally, a fourth parameter is used to quantify the blending of a Webb model with a pure AWGN model to account for thermal noise. Numerical results show that the capacity of M-ary orthogonal signaling on the Webb channel exhibits the same brick-wall Shannon limit, (M ln 2)=(M 1), as on the AWGN channel ( 1:59 dB for large M). Results also compare the capacity obtained by hard- and soft-output channels and indicate that soft-output channels o er a 3-dB advantage.

Dolinar, S.↗
DOE OSTI2026

Electrochemically Initiated Depolymerization of Poly(Methyl Methacrylate)

Efficient depolymerization of polymers with all-carbon backbones under mild conditions would be valuable in chemically recycling commodity plastics. Poly(methyl methacrylate) (PMMA) is a commodity thermoplastic that is currently depolymerized under temperatures in excess of 400 °C. Herein, we lower the temperatures needed to achieve depolymerization of PMMA by performing radical generation and depropagation with orthogonal stimuli. This first demonstration of electrochemically initiated PMMA depolymerization relies on reduction of phthalimide esters that, upon subsequent decarboxylation, generate polymer-centered radicals. These radicals then spontaneously unzip the polymer back to its monomeric constituents at temperatures as low as 105 °C. We studied the mechanism and efficiency of this transformation as a function of phthalimide ester placement, incorporation density, and polymer molecular weight. We found that chain-end activation is effective for modest molecular weights but suffers diminished efficiency at higher degrees of polymerization. In contrast, pendent-group activation is more effective for depolymerizing higher molecular weight species. Integrating higher molar amounts of phthalimide ester pendants leads to more effective depolymerization, with >95% depolymerization in copolymers with 5 mol% phthalimide ester incorporation. We leveraged this understanding to create a custom electro-distillation apparatus that allowed us to simultaneously electrochemically depolymerize PMMA and directly distill methyl methacrylate in >22% yield, which could ultimately be repolymerized. These findings establish electrochemistry as a versatile and orthogonal stimulus for vinyl polymer depolymerization and provide a foundation for closed-loop electrochemical recycling of widely used plastics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1981

GRID3O: Computer program for fast generation of multilevel, three-dimensional boundary-conforming O-type computational grids

A fast algorithm was developed for accurately generating boundary-conforming, three-dimensional, consecutively refined computational grids applicable to arbitrary wing-body and axial turbomachinery geometries. The method is based on using an analytic function to generate two-dimensional grids on a number of coaxial axisymmetric surfaces positioned between the centerbody and the outer radial boundary. These grids are of the O-type and are characterized by quasi-orthogonality, geometric periodicity, and an adequate resolution throughout the flow field. Because the built-in nonorthogonal coordinate stretching and shearing cause the grid lines leaving the blade or wing trailing edge to end at downstream infinity, the numerical treatment of the three-dimensional trailing vortex sheets is simplified.

Dulikravich, D. S.↗
NASA NTRS1982

GRID3C: Computer program for generation of C type multilevel, three dimensional and boundary conforming periodic grids

A fast computer program, GRID3C, was developed for accurately generating periodic, boundary conforming, three dimensional, consecutively refined computational grids applicable to realistic axial turbomachinery geometries. The method is based on using two functions to generate two dimensional grids on a number of coaxial axisymmetric surfaces positioned between the centerbody and the outer radial boundary. These boundary fitted grids are of the C type and are characterized by quasi-orthogonality and geometric periodicity. The built in nonorthogonal coordinate stretchings and shearings cause the grid clustering in the regions of interest. The stretching parameters are part of the input to GRID3C. In its present version GRID3C can generate and store a maximum of four consecutively refined three dimensional grids. The output grid coordinates can be calculated either in the Cartesian or in the cylindrical coordinate system.

Dulikravich, D. S.↗
NASA NTRS1984

SSME thrust chamber simulation using Navier-Stokes equations

The capability of the PHOENICS fluid dynamics code in predicting two-dimensional, compressible, and reacting flow in the combustion chamber and nozzle of the space shuttle main engine (SSME) was evaluated. A non-orthogonal body fitted coordinate system was used to represent the nozzle geometry. The Navier-Stokes equations were solved for the entire nozzle with a turbulence model. The wall boundary conditions were calculated based on the wall functions which account for pressure gradients. Results of the demonstration test case reveal all expected features of the transonic nozzle flows. Of particular interest are the locations of normal and barrel shocks, and regions of highest temperature gradients. Calculated performance (global) parameters such as thrust chamber flow rate, thrust, and specific impulse are also in good agreement with available data.

Przekwas, A. J.↗
NASA NTRS1990

Elliptic grid generation with orthogonality and spacing control on an arbitrary number of boundaries

A procedure for the generation of two and quasi-three-dimensional grids with control of orthogonality and spacing with respect to any and/or all boundaries of the domain is described. The elliptic grid generation equations of Thompson are solved implicitly. Control of the grid behavior is achieved through the introduction of forcing functions terms in the manner of Steger and Sorenson or in a modification of the method of Hilgenstock. The forcing function terms are constructed on the boundaries and propagated into the domain using transfinite Lagrangian bivariate interpolation. An anisotropic transfinite stencil is introduced and is shown to produce excellent grid behavior particularly in the vicinity of corner singularities. Emphasis is placed on the generation of viscous grids and the method is shown to be suited for use in the generation of grids for internal as well as external flow geometries. A FORTRAN program named PISCES has been written to implement the algorithm. Examples of grids for internal and external flows are given that highlight the characteristics and behavior of the algorithm.

White, J. A.↗
NASA NTRSDate not supplied

Dynamic Analysis of Reynolds Number Effects on Trailing Edge Transonic Vortex Shedding and Its Impact on Turbine Blade Aerodynamic Performance

Time-resolved, high-speed self-aligned focusing schlieren images were acquired in the NASA Glenn Research Center Transonic Turbine Blade Cascade facility to help understand the aerodynamic behavior of high-pressure, thick trailing edge turbine blades. The trailing edge thickness of 9% of axial chord tested represents simulated ceramic matrix composite fabrication constraints, which was verified previously to possess a high-loss flow regime at high inlet turbulence conditions over a narrow range of Reynolds numbers and at a fixed design exit Mach number of 0.74. Our high-speed images, which were acquired at 10 distinct Reynolds numbers, show a significant increase in energy from flow oscillations due to transonic vortex shedding at Reynolds numbers corresponding to the high loss conditions. For those conditions, strong acoustic waves turn into shock waves. Spectral Proper Orthogonal Decomposition of the high-speed images shows acoustic waves from trailing edge vortex shedding at all conditions, with increased spectral energy at the high-loss conditions and slightly increasing frequency (about 6%) as a function of Reynolds number. Analysis of potential feedback timing is performed using velocity fields from a previous LES simulation, considering different feedback mechanisms. Most noteworthy is the acoustic/shock-boundary layer interaction mechanism on the suction surface at the blade geometric throat, which likely plays an important role in realistic curved blade passages.

Trailing Edge↗
NASA NTRS1976

Optimal control of spin-stabilized spacecraft with telescoping appendages

The control of a spin-stabilized spacecraft consisting of a rigid central hub and one or two movable offset telescoping booms (with end masses) is considered. The equations of rotational motion are linearized about either of two desired final states. A control law for the boom end mass position is sought such that a quadratic cost functional involving the weighted components of angular velocity plus the control is minimized when the final time is unspecified and involves the solution of the matrix Riccati algebraic equation. For three axis control more than one offset boom (orthogonal to each other) is required. For two-axis control with a single boom offset from a symmetrical hub, an analytic solution is obtained; when this system is used for nutation decay the time constant is one order of magnitude smaller than previously achieved using nonoptimal control logic. For the general case results are obtained numerically.

Bainum, P. M.↗
NASA NTRS1992

Wall functions for the kappa-epsilon turbulence model in generalized nonorthogonal curvilinear coordinates

A k-epsilon turbulence model suitable for compressible flow, including the new wall function formulation, has been incorporated into an existing compressible Reynolds-averaged Navier-Stokes code, F3D. The low Reynolds number k-epsilon model of Chien (1982) was added for comparison with the present method. A number of features were added to the F3D code including improved far-field boundary conditions and viscous terms in the streamwise direction. A series of computations of increasing complexity was run to test the effectiveness of the new formulation. Flow over a flat plate was computed by using both orthogonal and nonorthogonal grids, and the friction coefficients and velocity profiles compared with a semi-empirical equation. Flow over a body of revolution at zero angle of attack was then computed to test the method's ability to handle flow over a curved surface. Friction coefficients and velocity profiles were compared to test data. All models gave good results on a relatively fine grid, but only the wall function formulation was effective with coarser grids. Finally, in order to demonstrate the method's ability to handle complex flow fields, separated flow over a prolate spheroid at angle of attack was computed, and results were compared to test data. The results were also compared to a k-epsilon model by Kim and Patel (1991), in which one equation model patched in at the wall was employed. Both models gave reasonable solutions, but improvement is required for accurate prediction of friction coefficients in the separated regions.

Sondak, D. L.↗
NASA NTRS1991

Stability of a non-orthogonal stagnation flow to three dimensional disturbances

A similarity solution for a low Mach number nonorthogonal flow impinging on a hot or cold plate is presented. For the constant density case, it is known that the stagnation point shifts in the direction of the incoming flow and that this shift increases as the angle of attack decreases. When the effects of density variations are included, a critical plate temperature exists; above this temperature the stagnation point shifts away from the incoming stream as the angle is decreased. This flow field is believed to have application to the reattachment zone of certain separated flows or to a lifting body at a high angle of attack. Finally, the stability of this nonorthogonal flow to self similar, 3-D disturbances is examined. Stability properties of the flow are given as a function of the parameters of this study; ratio of the plate temperature to that of the outer potential flow and angle of attack. In particular, it is shown that the angle of attack can be scaled out by a suitable definition of an equivalent wavenumber and temporal growth rate, and the stability problem for the nonorthogonal case is identical to the stability problem for the orthogonal case.

Lasseigne, D. G.↗