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NASA NTRS1982

Tenth NASTRAN User's Colloquium

The development of the NASTRAN computer program, a general purpose finite element computer code for structural analysis, was discussed. The application and development of NASTRAN is presented in the following topics: improvements and enhancements; developments of pre and postprocessors; interactive review system; the use of harmonic expansions in magnetic field problems; improving a dynamic model with test data using Linwood; solution of axisymmetric fluid structure interaction problems; large displacements and stability analysis of nonlinear propeller structures; prediction of bead area contact load at the tire wheel interface; elastic plastic analysis of an overloaded breech ring; finite element solution of torsion and other 2-D Poisson equations; new capability for elastic aircraft airloads; usage of substructuring analysis in the get away special program; solving symmetric structures with nonsymmetric loads; evaluation and reduction of errors induced by Guyan transformation.

Source record↗

DOE OSTI2022

Drift kinetic theory of the NTM magnetic islands in a finite beta general geometry tokamak plasma

In (Imada et al 2019 Nucl. Fusion 59 046016 and references therein) a new 4D drift kinetic nonlinear theory, valid in the limit of a low beta, small inverse aspect ratio, circular cross section, toroidal geometry, to describe the plasma response to the neoclassical tearing mode (NTM) magnetic perturbation is derived. In (Dudkovskaia et al 2021 Plasma Phys. Control. Fusion 63 054001) this theory is reduced in a low collisionality limit, which allows a dimensionality reduction to a 3D problem to efficiently resolve the collisional dissipation layer in the vicinity of the trapped-passing boundary. (Dudkovskaia et al 2021 Plasma Phys. Control. Fusion 63 054001) adopts an improved model for the magnetic drift frequency, which reduces the threshold magnetic island half-width from $8.73\rho_{b i}$, where $\rho_{b i}$ is the trapped ion banana orbit width, to $1.46 \rho_{b i}$, making it in closer agreement with experimental observations for the large aspect ratio tokamak equilibrium. In the present paper, the theory is extended to a high beta, arbitrary tokamak geometry to capture the plasma shaping effects on the NTM threshold physics with the focus on the non-zero triangularity discharges that are known to have a strong impact on the plasma MHD stability. First, it is found that the higher triangularity plasma is more prone to NTMs which is in agreement with the 2/1 tearing mode onset relative frequency measurements in DIII-D. Second, the NTM threshold dependence on the tokamak inverse aspect ratio obtained in (Dudkovskaia et al 2021 Plasma Phys. Control. Fusion 63 054001) is refined and extended to a finite aspect ratio limit. Third, the NTM threshold dependence on poloidal beta is obtained and benchmarked against the EAST threshold island width measurements.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

Robust Learning with Implicit Residual Networks

In this effort, we propose a new deep architecture utilizing residual blocks inspired by implicit discretization schemes. As opposed to the standard feed-forward networks, the outputs of the proposed implicit residual blocks are defined as the fixed points of the appropriately chosen nonlinear transformations. We show that this choice leads to the improved stability of both forward and backward propagations, has a favorable impact on the generalization power, and allows for control the robustness of the network with only a few hyperparameters. In addition, the proposed reformulation of ResNet does not introduce new parameters and can potentially lead to a reduction in the number of required layers due to improved forward stability. Finally, we derive the memory-efficient training algorithm, propose a stochastic regularization technique, and provide numerical results in support of our findings.

Reshniak, Viktor↗

DOE OSTI2022

Optimal Operation of PV Sources in DC Grids for Improving Technical, Economical, and Environmental Conditions by Using Vortex Search Algorithm and a Matrix Hourly Power Flow

This document presents a master–slave methodology for solving the problem of optimal operation of photovoltaic (PV) distributed generators (DGs) in direct current (DC) networks. This problem was modeled using a nonlinear programming model (NLP) that considers the minimization of three different objective functions in a daily operation of the system. The first one corresponds to the minimization of the total operational cost of the system, including the energy purchasing cost to the conventional generators and maintenance costs of the PV sources; the second objective function corresponds to the reduction of the energy losses associated with the transport of energy in the network, and the third objective function is related to the minimization of the total emissions of CO2 by the conventional generators installed on the DC grid. The minimization of these objective functions is achieved by using a master–slave optimization approach through the application of the Vortex Search algorithm combined with a matrix hourly power flow. To evaluate the effectiveness and robustness of the proposed approach, two test scenarios were used, which correspond to a grid-connected and a standalone network located in two different regions of Colombia. The grid-connected system emulates the behavior of the solar resource and power demand of the city of Medellín-Antioquia, and the standalone network corresponds to an adaptation of the generation and demand curves for the municipality of Capurganá-Choco. A numerical comparison was performed with four optimization methodologies reported in the literature: particle swarm optimization, multiverse optimizer, crow search algorithm, and salp swarm algorithm. The results obtained demonstrate that the proposed optimization approach achieved excellent solutions in terms of response quality, repeatability, and processing times.

14 SOLAR ENERGY↗

NASA NTRS1977

A solution to the Navier-Stokes equations based upon the Newton Kantorovich method

An implicit finite difference scheme based on the Newton-Kantorovich technique was developed for the numerical solution of the nonsteady, incompressible, two-dimensional Navier-Stokes equations in conservation-law form. The algorithm was second-order-time accurate, noniterative with regard to the nonlinear terms in the vorticity transport equation except at the earliest few time steps, and spatially factored. Numerical results were obtained with the technique for a circular cylinder at Reynolds number 15. Results indicate that the technique is in excellent agreement with other numerical techniques for all geometries and Reynolds numbers investigated, and indicates a potential for significant reduction in computation time over current iterative techniques.

Davis, J. E.↗

NASA NTRS1978

Analytical and numerical investigation of structural response of compliant wall materials, part 1

Surface motion of compliant walls in drag reduction experiments was analyzed. Critical comparison was made between the dynamic motion of the structure and the postulated mechanism of drag reduction. The spectrum of surface motion indicated that membranes over deep cavities respond at low frequencies and large wavelengths. The membrane over a deep cavity is therefore found not to yield the desired response predicted by the postulated mechanism. The membrane over a thin air gap is found to act as a wavelength chopper, and analysis of the nonlinear response of that compliant surface indicated its possible suitability for compliant wall experiments. Periodic structures are found to lock in the desired wavelengths of motion, and it was shown that at least in Kramer's initial experiments they produced high frequency surface motions. Laminated structures are found to be very ineffective as compliant models, except when there is no bonding between the membrane and the backing. Computer programs developed for these analyses are documented.

Balasubramanian, R.↗

NASA NTRS1990

METCAN simulation of candidate metal matrix composites for high temperature applications

The METCAN (Metal Matrix Composite Analyzer) computer code is used to simulate the nonlinear behavior of select metal matrix composites in order to assess their potential for high temperature structural applications. Material properties for seven composites are generated at a fiber volume ratio of 0.33 for two bonding conditions (a perfect bond and a weak interphase case) at various temperatures. A comparison of the two bonding conditions studied shows a general reduction in value of all properties (except CTE) for the weak interphase case from the perfect bond case. However, in the weak interphase case, the residual stresses that develop are considerably less than those that form in the perfect bond case. Results of the computational simulation indicate that among the metal matrix composites examined, SiC/NiAl is the best candidate for high temperature applications at the given fiber volume ratio.

Lee, Ho-Jun↗

NASA NTRS2004

Two-Photon Fluorescence Microscopy Developed for Microgravity Fluid Physics

Recent research efforts within the Microgravity Fluid Physics Branch of the NASA Glenn Research Center have necessitated the development of a microscope capable of high-resolution, three-dimensional imaging of intracellular structure and tissue morphology. Standard optical microscopy works well for thin samples, but it does not allow the imaging of thick samples because of severe degradation caused by out-of-focus object structure. Confocal microscopy, which is a laser-based scanning microscopy, provides improved three-dimensional imaging and true optical sectioning by excluding the out-of-focus light. However, in confocal microscopy, out-of-focus object structure is still illuminated by the incoming beam, which can lead to substantial photo-bleaching. In addition, confocal microscopy is plagued by limited penetration depth, signal loss due to the presence of a confocal pinhole, and the possibility of live-cell damage. Two-photon microscopy is a novel form of laser-based scanning microscopy that allows three-dimensional imaging without many of the problems inherent in confocal microscopy. Unlike one-photon microscopy, it utilizes the nonlinear absorption of two near-infrared photons. However, the efficiency of two-photon absorption is much lower than that of one-photon absorption because of the nonlinear (i.e., quadratic) electric field dependence, so an ultrafast pulsed laser source must typically be employed. On the other hand, this stringent energy density requirement effectively localizes fluorophore excitation to the focal volume. Consequently, two-photon microscopy provides optical sectioning and confocal performance without the need for a signal-limiting pinhole. In addition, there is a reduction in photo-damage because of the longer excitation wavelength, a reduction in background fluorescence, and a 4 increase in penetration depth over confocal methods because of the reduction in Rayleigh scattering.

Fischer, David G.↗

NASA NTRS1992

Experimental characterization of nonlinear, rate-dependent behavior in advanced polymer matrix composites

In order to support materials selection for the next-generation supersonic civilian-passenger transport aircraft, a study has been undertaken to evaluate the material stress/strain relationships needed to describe advanced polymer matrix composites under conditions of high load and elevated temperature. As part of this effort, this paper describes the materials testing which was performed to investigate the viscoplastic behavior of graphite/thermoplastic and graphite/bismaleimide composites. Test procedures, results and data-reduction schemes which were developed for generating material constants for tension and compression loading, over a range of useful temperatures, are explained.

Gates, Thomas S.↗

NASA NTRS2002

Spectral Re-Growth Reduction for CCSDS 8-D 8-PSK TCM

This report presents a study on the CCSDS recommended 8-dimensional 8 PSK Trellis Coded Modulation (TCM) scheme. The important steps of the CCSDS scheme include: conversion of serial data into parallel form, differential encoding, convolutional encoding, constellation mapping, and filtering the 8-PSK symbols using the square root raised cosine (SRRC) pulses. The last step, namely the filtering of the 8 PSK symbols using SRRC pulses, significantly affects the bandwidth of the signal. If a nonlinear power amplifier is used, the SRRC filtered signal creates spectral regrowth. The purpose of this report is to investigate a technique, called the smooth phase interpolated keying (SPIK), that can provide an alternative to SRRC filtering so that good spectral as well as power efficiencies can be obtained with the CCSDS encoder. The results of this study show that the CCSDS encoder does not affect the spectral shape of the SRRC filtered signal or the SPIK signal. When a nonlinear traveling wave tube amplifier (TWTA) is used, the spectral performance of the SRRC signal degrades significantly while the spectral performance of SPIK remains unaffected. The degrading effect of a nonlinear solid state power amplifier (SSPA) on SRRC is found to be less than that due to a nonlinear TWTA. However, in both cases, the spectral performance of the SRRC modulated signal is worse than that of the SPIK signal. The bit error rate (BER) performance of the SRRC signal in a linear amplifier environment is about 2.5 dB better than that of the SPIK signal when both the receivers use algorithms of similar complexity. In a nonlinear TWTA environment, the SRRC signal requires accurate phase tracking since the TWTA introduces additional phase distortion. This problem does not arise with SPIK signal due to its constant envelope property. When a nonlinear amplifier is used, the SRRC method loses nearly 1 dB in the bit error rate performance. The SPIK signal does not lose any performance. Thus the performance gap between SRRC and SPIK reduces. The BER performance of SPIK can be improved even further by using a more optimal receiver. A similar optimal receiver for SRRC is quite complex since the amplifier distorts the pulse shape. However, this requires further investigation and is not covered in this report.

Borah, Deva K.↗

NASA NTRS2020

Cloud-top pressure retrieval with DSCOVR EPIC oxygen A- and B-band observations

An analytic transfer inverse model for Earth Polychromatic Imaging Camera (EPIC) observations is proposed to retrieve the cloud-top pressure (CTP) with the consideration of in-cloud photon penetration. In this model, an analytic equation was developed to represent the reflection at the top of the atmosphere from above cloud, in cloud, and below cloud. The coefficients of this analytic equation can be derived from a series of EPIC simulations under different atmospheric conditions using a nonlinear regression algorithm. With estimated cloud pressure thickness, the CTP can be retrieved from EPIC observation data by solving the analytic equation. To simulate the EPIC measurements, a program package using the double-k approach was developed. Compared to line-by-line calculation, this approach can calculate high-accuracy results with a 100-fold computation time reduction. During the retrieval processes, two kinds of retrieval results, i.e., baseline CTP and retrieved CTP, are provided. The baseline CTP is derived without considering in-cloud photon penetration, and the retrieved CTP is derived by solving the analytic equation, taking into consideration in-cloud and below-cloud interactions. The retrieved CTPs for the oxygen A and B bands are smaller than their related baseline CTP. At the same time, both baseline CTP and retrieved CTP at the oxygen B band are larger than those at the oxygen A band. Compared to the difference in baseline CTP between the B band and A band, the difference in retrieved CTP between these two bands is generally reduced. Out of around 10 000 cases, in retrieved CTP between the A and B bands we found an average bias of 93 mb with a standard deviation of 81 mb. The cloud layer top pressure from Cloud–Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) measurements is used for validation. Under single-layer cloud situations, the retrieved CTPs for the oxygen A band agree well with the CTPs from CALIPSO, the mean difference of which within 5 mb in the case study. Under multiple-layer cloud situations, the CTPs derived from EPIC measurements may be larger than the CTPs of high-level thin clouds due to the effect of photon penetration.

DSCOVR↗

NASA NTRS1991

Effects of varying subatmospheric pressure on stationary plasma arc welds

An experimental study was performed examining the variation of penetration, fluid behavior, heat-affected zone and arc in plasma arc welding (PAW) with respect to subatmospheric ambient pressure. The results reveal nonlinear variation of keyhole size, time of penetration, and size of the heat-affected zone with pressure. In a restricted range of pressure, dynamic components of fluid flow directed out of the molten pool appear and have a profound effect on keyhole formation. The generated plasma arc is observed to decrease in intensity with decreasing pressure, resulting in a reduction of penetration at lower pressures.

Chin, J. J.↗

DOE OSTI2020

Implicit fast sweeping method for hyperbolic systems of conservation laws

Implicit time-accurate methods are often used to integrate stiff problems where explicit schemes impose severe time step restrictions. This paper presents an efficient numerical framework based on the Fast Sweeping Method (FSM) for solving linear and nonlinear hyperbolic systems of conservation laws. The solution at each discrete location is computed by sweeping the numerical domain in several predetermined directions that follow the causality of the characteristic families. The use of a fractional step strategy eliminates the need for a solution selection criterion while one-sided stencils limit the number of sweeps to at most 2 d for d space dimensions. This work focuses on the first-order implicit upwind method since it constitutes the building block for high-order conservative schemes. For problems where the degree of stiffness evolves over time, implicit-explicit hybridization can be accomplished with the same algorithm by simply switching the stencil at each time level. As opposed to traditional implicit solvers, the sweeping method does not require a local time linearization of the fluxes thereby preserving the nonlinear stability properties of the original implicit scheme. It also avoids the large computational and memory requirements associated with solving large block-diagonal systems of equations. Here, a series of one- and two-dimensional test cases are presented for the inviscid Burgers' equation and the reactive Euler equations. The results indicate that the implicit FSM can allow a major reduction in the number of time steps even in the presence of discontinuous solution profiles.

74 ATOMIC AND MOLECULAR PHYSICS↗

NASA NTRS1977

Analytical and numerical investigation of structural response of compliant wall materials

Surface motion of compliant walls in drag reduction experiments was analyzed. The spectrum of surface motion indicates that membranes over deep cavities respond at low frequencies and large wavelengths. The membrane over a deep cavity is therefore found not to yield the desired reponse predicted by the postulated mechanism. The membrane over a thin air gap is found to act as a wavelength chopper, and analysis of the nonlinear response of the compliant surface indicates its possible suitability for compliant wall experiments. Periodic structures are found to lock in the desired wavelengths of motion. Laminated structures are found to be very ineffective as compliant models, except when there is no bonding between the membrane and the backing. Computer programs developed for these analyses are documented.

Goglia, G. L.↗

NASA NTRS1979

Applying integrals of motion to the numerical solution of differential equations

A method is developed for using the integrals of systems of nonlinear, ordinary differential equations in a numerical integration process to control the local errors in these integrals and reduce the global errors of the solution. The method is general and can be applied to either scaler or vector integrals. A number of example problems, with accompanying numerical results, are used to verify the analysis and support the conjecture of global error reduction.

Jezewski, D. J.↗

NASA NTRS1980

Applying integrals of motion to the numerical solution of differential equations

A method is developed for using the integrals of systems of nonlinear, ordinary, differential equations in a numerical integration process to control the local errors in these integrals and reduce the global errors of the solution. The method is general and can be applied to either scalar or vector integrals. A number of example problems, with accompanying numerical results, are used to verify the analysis and support the conjecture of global error reduction.

Vezewski, D. J.↗

NASA NTRS1993

Simulations of ion cyclotron anisotropy instabilities in the terrestrial magnetosheath

Enhanced transverse magnetic fluctuations observed below the proton cyclotron frequency in the terrestrial magnetosheath have been identified as due to the proton cyclotron and helium cyclotron instabilities driven by the T-perpendicular greater than T-parallel condition of the sheath ions. One-dimensional hybrid computer simulations are used here to examine the nonlinear properties of these two growing modes at relatively weak fluctuation energies and for wave vectors parallel to the background magnetic field. Second-order theory predicts fluctuating magnetic field energies at saturation of the proton cyclotron anisotropy instability in semiquantitative agreement with the simulation results. Introduction of the helium component enhances the wave-particle exchange rate for proton anisotropy reduction by that instability, thereby reducing the saturation energy of that mode. The simulations demonstrate that wave-particle interactions by the proton cyclotron and helium cyclotron instabilities lead to the anticorrelation observed by Anderson and Fuselier (1993).

Gary, S. P.↗

NASA NTRS1990

Parametric analysis of swept-wing geometry with sheared wing tips

A computational parameter study is presented of potential reductions in induced drag and increases in lateral-directional stability due to sheared wing tips attached to an untwisted wing of moderate sweep and aspect ratio. Sheared tips are swept and tapered wing-tip devices mounted in the plane of the wing. The induced-drag results are obtained using an inviscid, incompressible surface-panel method that models the nonlinear effects due to the deflected and rolled-up wake behind the lifting surface. The induced-drag results with planar sheared tips are compared to straight-tapered tip extensions and nonplanar winglet geometries. The lateral-directional static-stability characteristics of the wing with sheared tips are estimated using a quasi-vortex-lattice method. For certain combinations of sheared-tip sweep and taper, both the induced efficiency of the wing and the relevant static-stability derivatives are predicted to increase compared to the wing with a straight-tapered tip modification.

Fremaux, C. M.↗